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in this paper we give a proof ( of a generalization to the context of _ o - minimal structures _ on the real field , or to _ analytic ( nash ) geometric categories _ ) of the following intersection formula : [ thm : int1 ] let @xmath0 be an m - dimensional real analytic manifold and @xmath1 a subanalytic @xmath2-function . consider on @xmath0 a bounded subanalytically constructible complex @xmath3 of sheaves of vector spaces ( over a base - field @xmath4 ) , with finite dimensional stalks @xmath5 ( @xmath6 ) . suppose that the intersection of @xmath7 and the support @xmath8 of the characteristic cycle of @xmath3 is contained in a compact subanalytic subset @xmath9 , with @xmath10 . then one has @xmath11\cap [ cc({\cal f})]\ ; \bigr ) \:.\ ] ] here we use the following notations : 1 . @xmath12 is the usual _ euler characteristic _ ( note that @xmath13 has finite dimensional cohomology , since @xmath14 , with @xmath15 the natural projection , is a compact subanalytic subset ) . 2 . @xmath16 \in h^{m}_{|cc({\cal f})|}(t^{*}m,\pi^{-1}or_{m})$ ] is the _ characteristic cycle _ of @xmath3 ( as in @xcite , and see the next section ) , with @xmath17 the _ orientation sheaf _ on @xmath0 . @xmath18\in h^{m}_{\sigma_{f}}(t^{*}m , or_{t^{*}m / m})$ ] corresponds to @xmath19 ( as in ( * ? ? ? 9.3.5 ) , with @xmath20\;$ ] ) . 4 . the _ intersection number _ @xmath21 is defined by @xmath22 here we use @xmath23 , and the above cup - product is the composition of the usual cup - product with support and the natural maps @xmath24 this intersection formula is an important and useful generalization of ( * ? ? ? * thm.9.1 , p.207 ) and ( * ? ? ? * thm.9.5.6 , p.386 ) . note that we only assume , that the intersection of @xmath25 and the _ support _ @xmath8 of the characteristic cycle of @xmath3 is contained in a compact subanalytic set , and this is the reason why our formula is a result about _ lagrangian cycles_. the results of loc.sit . are formulated under suitable assumptions on the _ micro - support _ of @xmath3 , which is in general much bigger than @xmath8 . the characteristic cycle @xmath26 of @xmath3 depends only on the _ constructible function _ @xmath27 ( compare with ( * ? ? ? * thm.9.7.11 ) and ( * ? ? ? * subsec.5.0.3 ) ) . therefore our results can also be stated in terms of the associated constructible function @xmath28 . in this context , one can only use the support of the characteristic cycle @xmath29 as an invariant of the constructible function @xmath28 ( the micro - support @xmath30 depends on the sheaf complex @xmath3 , and _ not _ ( ! ) only on the corresponding constructible function ) . our proof of theorem [ thm : int1 ] is a modification of the proof of ( * ? ? ? * thm.9.5.6 ) . we use the result of @xcite ( due in the subanalytic context to bierstone , milman and pawlucki ) , that @xmath31 is the zero - set of a non - negative subanalytic @xmath2-function @xmath32 . then there exists a relatively compact open neighborhood @xmath33 of @xmath34 in @xmath0 , and a @xmath35 such that @xmath36 is proper ( since @xmath37 is compact ) . after restriction to @xmath33 we can assume @xmath38 . then @xmath39 calculates for @xmath40 ( i.e. for @xmath41 and @xmath42 sufficiently small , with @xmath42 small compared to @xmath41 ) the euler characteristic of the relative cohomology of a `` tube '' @xmath43 modulo the _ left milnor fiber _ @xmath44 ( compare @xcite ) . in terms of the constructible function @xmath28 , this euler characteristic can also be rewritten as ( compare @xcite and @xcite ) : @xmath45 here we use for a _ compact _ subanalytic subset @xmath46 the notation @xmath47 the _ unique _ @xmath48-linear map on the group @xmath49 of @xmath48-valued subanalytically constructible functions with _ compact _ support such that @xmath50 for @xmath51 a compact subanalytic subset . + for the special case @xmath52 we get @xmath53 so that theorem [ thm : int1 ] implies the following generalization of the classical _ poincar - hopf index formula _ , which corresponds to the case @xmath54 for a @xmath0 a compact manifold ( with @xmath55 the zero - section of @xmath56 ) : [ cor : globalindex ] consider a constructible complex @xmath3 as in theorem [ thm : int1 ] and denote by @xmath28 the corresponding constructible function @xmath57 . assume @xmath3 or @xmath28 has a compact support . then @xmath58\cap [ cc({\cal f})]\ ; \bigr ) \quad \text{or } \quad \int_{m}\ , \alpha \,d\chi = \sharp\bigl(\ ; [ t^{*}_{m}m]\cap [ cc(\alpha)]\ ; \bigr ) \:.\ ] ] this global index formula goes back to dubson ( * ? ? ? * thm.2 , p.115 ) in the complex , and to kashiwara ( * ? ? ? * thm.8.1 , p.205 ) in the real context . other presentations can be found in ( * ? ? ? * thm.1.5 , p.832 ) , ( * ? ? ? * thm.9.1 , p.382 ) , ( * ? ? ? * cor.9.5.2 , p.384 ) and ( * ? ? ? * eq.(5.30 ) , p.298 ) . + another important special case of our intersection formula ( [ eq : int1 ] ) is the case @xmath59 given by a point @xmath60 , with @xmath61 and @xmath62 . in this case we can use for @xmath32 the usual distance function ( in suitable coordinates @xmath63 ) . then we get ( cf . * thm.9.5.6 , p.386 ) ) : @xmath64\cap [ cc({\cal f})]\ ; \bigr)\ ] ] and @xmath65\cap [ cc(\alpha)]\ ; \bigr ) \:,\ ] ] with @xmath66 the corresponding _ local intersection number _ and @xmath67 the _ local left milnor fiber _ of @xmath68 in @xmath69 . we get in particular : @xmath70 in another paper , we will use the formula ( [ eq : int3 ] ) ( together with a specialization result for lagrangian cycles ) for a proof of the non - characteristic pullback formula ( * ? ? ? * prop.9.4.3 , p.378 ) under the _ weaker _ assumption , that the map is only non - characteristic with respect to the _ support _ @xmath8 of the characteristic cycle of @xmath3 . as a further example , let us consider ( locally ) the case @xmath71 a ( real analytic ) distance function to the point @xmath69 , i.e. @xmath72 with @xmath73 . by the _ curve selection lemma _ there exists an open neighborhood @xmath33 of @xmath69 in @xmath0 , with @xmath74 this will be explained later on in terms of stratification theory ( and compare with ( * ? ? ? * prop.8.3.12 , p.332 ) ) . so if we work on the manifold @xmath33 , then we can apply ( [ eq : int2 ] ) and ( [ eq : int2cf ] ) with @xmath75 : [ cor : localindex ] @xmath76\cap [ cc({\cal f})]\ ; \bigr ) \quad \text{and } \quad \alpha(x ) = \sharp_{dr_{x}}\bigl(\ ; [ dr(u)]\cap [ cc(\alpha)]\ ; \bigr ) \:.\ ] ] so ( [ eq : localindex ] ) describes an inversion formula for reconstructing the constructible function @xmath28 out of the lagrangian cycles @xmath16 $ ] and @xmath77 $ ] ( compare ( * ? ? ? * thm.2 , p.115 ) , ( * ? ? ? * thm.8.3 , p.205 ) , ( * ? ? ? * eq.(9.5.8 ) , p.386 ) and ( * ? ? ? * eq.(5.30 ) , p.298 ) ) . + theorem [ thm : int1 ] also gives a purely _ real _ proof of the corresponding intersection formula in complex geometry : [ cor : int2 ] let @xmath0 be an m - dimensional complex analytic manifold and @xmath78 a holomorphic function . consider on @xmath0 a bounded complex analytically constructible complex @xmath3 of sheaves of vector spaces , with finite dimensional stalks @xmath5 ( @xmath6 ) . suppose that the intersection of @xmath79 and the support @xmath8 of the characteristic cycle of @xmath3 is contained in a compact analytic subset @xmath9 , with @xmath80 . then one has @xmath81\;{\cal f})\bigr ) = \sharp\bigl(\ ; [ dh(m)]\cap [ cc({\cal f})]\ ; \bigr ) \:.\ ] ] here we use the notation @xmath56 for the _ holomorphic _ cotangent bundle , and @xmath82 is the _ vanishing cycle functor _ of deligne . the holomorphic section @xmath83 of @xmath56 corresponds under the natural isomorphism @xmath84 to the section @xmath85 of @xmath86 , with @xmath86 the _ real _ cotangent bundle of the underlying real manifold @xmath87 . if we use the induced _ complex orientation _ of @xmath86 , then the class @xmath88\in h^{2m}_{\sigma_{f}}(t^{*}m , or_{t^{*}(m^{r})/m^{r}})\simeq h^{2m}_{\sigma_{h}}(t^{*}m,{\mbox{$\mathbb{z}$}})\ ] ] for @xmath89 corresponds under poincar duality to the _ fundamental class _ in borel - moore homology of the complex manifold @xmath90 . + then the corollary follows from theorem [ thm : int1 ] and the isomorphism ( cf . * lem.1.3.2 , p.70 ) and ( * ? ? ? * cor.1.1.1 , p.32 ) ) : @xmath91\;{\cal f } ) \simeq r\gamma(k , r\gamma_{\{re(h)\geq 0\}}{\cal f})\:.\ ] ] or in terms of the constructible function @xmath28 : @xmath92 and @xmath93\;{\cal f})\bigr ) = \int_{k}\ , \alpha \,d\chi - \int_{m_{h}}\ , \alpha \,d\chi \:,\ ] ] with @xmath94 the _ milnor fiber _ of the holomorphic function @xmath95 . + this holomorphic intersection formula for the vanishing cycle functor is due to dubson ( * ? ? ? * thm.1 , p.183 ) , ginsburg ( * ? ? ? * prop.7.7.1 , p.378 ) , l ( * ? ? ? * thm.4.1.2 , p.242 ) and sabbah ( * ? ? ? * thm.4.5 , p.174 ) . for a discussion of the history of this holomorphic intersection formula we recommend the paper @xcite . but most of these references are in the language of ( regular ) _ holonomic d - modules _ , or _ perverse sheaves _ ( with respect to middle perversity ) . so the assumption on the intersection for a holomorphically constructible complex of sheaves corresponds to an assumption on the micro - support ( ( * ? ? ? * thm.11.3.3 , p.455 ) ) . only the result of sabbah ( * ? ? ? * thm.4.5 , rem.4.6 , p.174 ) is in terms of the underlying ( complex analytic ) lagrangian cycle , which corresponds therefore to an assumption on the intersection of @xmath90 and the support of the corresponding characteristic cycle ! similarly , only this reference @xcite , and in the real subanalytic context also ( * ? ? ? * thm.9.1 , p.207 ) consider the case of an intersection in a _ subset @xmath96 . + the other references deal only with the case @xmath59 given by a point @xmath60 . in this special case we get back a formula conjectured by deligne ( with @xmath61 and @xmath62 ) : @xmath97\;{\cal f})_{x}\bigr ) = \sharp_{dh_{x}}\bigl(\ ; [ dh(m)]\cap [ cc({\cal f})]\ ; \bigr)\ ] ] and @xmath98\cap [ cc(\alpha)]\ ; \bigr ) \:,\ ] ] with @xmath99 the _ local milnor fiber _ of @xmath95 in @xmath69 . we get in particular : @xmath100\;{\cal f})_{x}\bigr ) = 0\:.\ ] ] we used this formula in our paper @xcite for a short proof of a formula of brasselet , l and seade for the _ euler obstruction _ ( ( * ? ? ? * thm.3.1 ) ) . + as another application of the formula ( [ eq : vcyc ] ) let us consider the following example : @xmath101 , with @xmath102 a _ closed _ complex analytic submanifold . consider a holomorphic function germ @xmath103 such that @xmath104 has in @xmath105 a _ complex morse critical point_. then we get @xmath106 $ ] , with the orientation convention of @xcite . if we denote by @xmath107_{c}\in h^{2m}_{t^{*}_{n}m}(t^{*}m,{\mbox{$\mathbb{z}$}})\ ] ] the class , which corrresponds under poincar duality to the fundamental class of the complex manifold @xmath108 , then we get of course @xmath109\cap [ t^{*}_{n}m]_{c}\ ; \bigr)\;= 1\:.\ ] ] but @xmath110 has in @xmath69 a _ real morse critical point _ of index @xmath111 . we therefore get by ( * ? ? ? * eq.(9.5.18 ) , p.388 ) for @xmath89 : @xmath112\cap [ cc(k_{n})]\ ; \bigr)\;= ( -1)^{n}\:.\ ] ] and this implies @xmath107_{c } = ( -1)^{n}\cdot [ t^{*}_{n}m ] \in h^{2m}_{t^{*}_{n}m}(t^{*}m,{\mbox{$\mathbb{z}$}})\:.\ ] ] so one has to be very careful about _ orientation conventions _ and the definition of _ characteristic cycles _ that one uses . here we follow the notations and conventions of @xcite . note that there are many approaches to this subject , often using quite different techniques and conventions . we recall in the next section a detailed comparison , which is worked out in ( * ? ? ? * subsec.5.0.3 ) . + let us only recall , that the theory of characteristic cycles has its origin in the theory of _ holonomic d - modules _ and the _ local index formula _ of kashiwara ( * ? ? ? * thm . on p.804 ) ( compare ( * ? ? ? * thm.6.3.1 , p.127 ) , ( * ? ? ? * thm.2 , p.574 ) and ( * ? ? ? * thm.11.7 , p.393 ) ) . this corresponds to corollary [ cor : localindex ] for @xmath113 the _ solution complex _ of a holonomic @xmath114-module @xmath115 . later on , the theory of characteristic cycles was extended to constructible functions and sheaves in the context of real geometry . first in the _ subanalytic _ context by kashiwara @xcite , and independently also by fu @xcite . a simple approach in the _ semialgebraic _ context is sketched in @xcite , and the extension to _ o - minimal structures _ and _ analytic geometric categories _ has been worked out in @xcite . all these approaches in real geometry are based on a suitable _ morse theory _ , e.g. the _ micro - local sheaf theory _ of kashiwara - schapira @xcite , or the _ stratified morse theory _ of goresky - macpherson @xcite . + for a detailed comparison and translation of these two different theories in the framework of _ morse theory for constructible sheaves _ , including a _ geometric _ introduction to characteristic cycles of constructible functions and sheaves , we refer to our book @xcite . this language will be used in the proof of theorem [ thm : int1 ] . moreover , we use the following important result about the behaviour of the _ support _ @xmath8 of the characteristic cycle of @xmath3 under a suitable intersection : [ thm : int2 ] let @xmath0 be a real analytic manifold and @xmath116 a subanalytic @xmath2-function . consider on @xmath0 a bounded subanalytically constructible complex @xmath3 of sheaves of vector spaces , with finite dimensional stalks @xmath5 ( @xmath6 ) . assume @xmath3 is constructible with respect to a subanalytic whitney b - regular stratification ( i.e. the cohomology sheaves of @xmath3 are locally constant on the subanalytic strata @xmath117 ) such that the set of nondegenerate covectors ( with respect to this stratification ) is dense in all fibers of the projection @xmath118 ( for all strata @xmath117 ) . let @xmath41 be a regular value of @xmath32 such that @xmath119 is _ transversal _ to all strata @xmath117 . then one has for the open inclusion @xmath120 the following estimate for the support @xmath121 of the characteristic cycle of @xmath122 : @xmath123 the assumption on our stratification is for example satisfied for a subanalytic _ @xmath124-stratification _ in the sense of ( * ? ? ? * def.8.3.19 , p.334 ) ( see ( * ? ? ? * cor.8.3.24 , p.336 ) ) . this _ @xmath124-condition _ is by @xcite equivalent to the _ w - condition _ of verdier , and such a _ w - regular _ stratification can always be used in the context of `` geometric categories '' as in the last section of this paper ( cf . but it is not known ( at least to the author ) , if the _ w - condition _ implies the assumption on our stratification ( used in the theorem ) in this more general context . kashiwara - schapira used in their proof of ( * ? ? ? * thm.9.5.6 , p.386 ) a similar result in terms of the _ micro - support _ of the corresponding constructible complex of sheaves ( cf . * prop.8.4.1 , p.338 ) and ( * ? ? ? * prop.5.4.8.(a ) , p.233 ) ) . we will give a proof based on our results on _ morse theory for constructible sheaves _ @xcite , especially on an explicit result about suitable `` stratified spaces with boundary '' ( * ? ? ? * thm.5.0.2 , p.286 ) . this approach works also , if one uses the supports of the corresponding characteristic cycles . it implies a similar estimate for @xmath125 ( with @xmath126 ) , from which we deduce ( [ eq : est * ] ) by _ duality_.

we prove a generalization to the context of real geometry of an intersection formula for the vanishing cycle functor , which in the complex context is due to dubson , l , ginsburg and sabbah ( after a conjecture of deligne ) . it is also a generalization of similar results of kashiwara - schapira , where these authors work with a suitable assumption about the micro - support of the corresponding constructible complex of sheaves . we only use a similar assumption about the support of the corresponding characteristic cycle so that our result can be formulated in the language of constructible functions and lagrangian cycles .

we prove a generalization to the context of real geometry of an intersection formula for the vanishing cycle functor , which in the complex context is due to dubson , l , ginsburg and sabbah ( after a conjecture of deligne ) . it is also a generalization of similar results of kashiwara - schapira , where these authors work with a suitable assumption about the micro - support of the corresponding constructible complex of sheaves . we only use a similar assumption about the support of the corresponding characteristic cycle so that our result can be formulated in the language of constructible functions and lagrangian cycles .

1503.01282

i

optimal systolic inequalities were studied since the mid - twentieth century after c. loewner proved in an unpublished work the following result , _ cf . _ @xcite . every riemannian two - torus @xmath0 satisfies @xmath1 with equality if and only if @xmath0 is a flat hexagonal torus . recall that the _ systole _ of a nonsimply connected riemannian surface @xmath2 , denoted by @xmath3 , represents the length of the shortest noncontractible loop of @xmath2 . this inequality leads us to introduce the _ systolic area _ of @xmath2 defined as @xmath4 where @xmath5 runs over all the riemannian metrics on @xmath2 ( hence the subscript @xmath6 for riemannian ) . thus , @xmath7 . following this direction , p. pu @xcite showed that @xmath8 , where the infimum is attained exactly by the riemannian metrics with constant ( positive ) curvature on the projective plane @xmath9 . in the eighties , c. bavard @xcite proved that @xmath10 , where the infimum on the klein bottle @xmath11 is not attained by a smooth riemannian metric . see also @xcite , @xcite and @xcite for other proofs and variations on this inequality . these are the only nonsimply connected closed surfaces with a known systolic area . the existence of extremal metrics in higher dimension is wide open . the original proofs of the optimal riemannian systolic inequalities on @xmath0 , @xmath9 and @xmath11 rely on the conformal representation theorem ( a consequence of the uniformization theorem on riemann surfaces ) and proceed as follows . by the uniformization theorem , every riemannian metric @xmath5 on a closed surface is conformally equivalent to a riemannian metric @xmath12 of constant curvature . taking the average of @xmath5 over the isometry group of @xmath12 gives rise to a new metric @xmath13 with the same area as @xmath5 . by the cauchy - schwarz inequality , the systole of @xmath13 is at most the systole of @xmath5 . thus , the new metric @xmath13 has a lower ratio @xmath14 than the original metric @xmath5 . now , if the isometry group of @xmath12 is transitive , which is the case for @xmath0 and @xmath9 , the metric @xmath13 has constant curvature . hence the result for the projective plane . then , it is not difficult to find the extremal metric among flat torus . the case of the klein bottle requires an extra argument since the isometry group of @xmath12 is not transitive , _ cf . _ section [ sec : klein ] . + indeed , let @xmath15 be a riemannian surface . then by the uniformization theorem , @xmath5 is conformally equivalent to a riemannian metric @xmath12 of constant curvature on @xmath2 , _ i.e. _ , there exists a function @xmath16 such that @xmath17 . we deduce by the cauchy - schwarz inequality that @xmath18 where @xmath19 is the integration of @xmath20 over the isometry group of @xmath21 . now , if the latter is transitive ( this is the case of @xmath0 and @xmath9 ) , we conclude that @xmath19 is constant and we can easily then deduce the extremal riemannian metrics on @xmath2 . in this article , we consider finsler systolic inequalities . loosely speaking , a finsler metric @xmath22 is defined as a riemannian metric except that its restriction to a tangent plane is no longer a euclidean norm but a minkowski norm , _ cf . _ section [ preliminaries ] . from a dynamical point of view , the function @xmath23 can be considered as a lagrangian which induces a lagrangian flow on the tangent bundle @xmath24 of @xmath2 . thus , finsler manifolds can be considered as degree @xmath25 homogeneous lagrangian systems . the trajectories of the lagrangian correspond to the geodesics of the finsler metric . there exist several definitions of volume for finsler manifolds which coincide in the riemannian case . we will consider the holmes - thompson volume @xmath26 , _ cf . _ section [ preliminaries ] . as previously , we can define the systolic area @xmath27 , with the subscript @xmath22 for finsler , by taking the infimum in over all finsler metrics on @xmath2 . contrary to the riemannian case , there is no uniformization theorem for finsler surfaces . as a result , the classical riemannian tools to prove optimal systolic inequalities on surfaces , which are based on the conformal length method described above , do not carry over to the finsler case . new methods are thus required to deal with finsler metrics . the first optimal finsler systolic inequality has been obtained by s. ivanov @xcite who extended pu s systolic inequality to finsler projective planes . [ iv02 ] let @xmath9 be a finsler projective plane . then @xmath28 furthermore , equality holds if all the geodesics are closed of the same length . in particular , the systolic area of the projective plane is the same in the riemannian and finsler settings , that is , @xmath29 note that theorem [ iv02 ] provides an alternate proof of pu s inequality in the riemannian case which does not rely on the uniformization theorem . using a different method based on @xcite and @xcite , a finsler version of loewner s inequality has been obtained by the first author @xcite . [ sa10 ] let @xmath0 be a finsler two - torus . then @xmath30 equality holds if @xmath0 is homothetic to the quotient of @xmath31 , endowed with a parallelogram norm @xmath32 , by a lattice whose unit disk of @xmath32 is a fundamental domain . observe that @xmath33 contrary to the riemannian case . an optimal finsler systolic inequality holds for non - reversible finsler metrics on @xmath0 , _ cf . _ @xcite . note also that there is no systolic inequality for non - reversible finsler two - tori if one considers the busemann volume instead of the holmes - thompson volume , _ cf . _ @xcite . no systolic inequality holds for manifolds with boundary either . however , p. pu @xcite and c. blatter @xcite obtained optimal riemannian systolic inequalities in each conformal class of the mobius band and described the extremal metrics , _ cf . _ section [ sec : candidates ] . later , these inequalities were used by c. bavard @xcite and t. sakai @xcite in their proofs of the systolic inequality on the klein bottle in the riemannian case . the proof of the optimal conformal riemannian systolic inequalities on the mobius band relies on the uniformization theorem and the conformal length method ( as in the original proofs of the riemannian systolic inequalities on @xmath0 , @xmath9 and @xmath11 ) . among manifolds with boundary , one can not expect to get a positive systolic constant . we only know that in the riemannian case , the mobius band @xmath34 does have an extremal metric in each conformal class , _ cf . _ @xcite . pu @xcite and c. blatter @xcite obtained conformal systolic inequalities on @xmath34 , _ cf . _ section [ sec : candidates ] . these inequalities were used later by c. bavard @xcite and t. sakai @xcite in their proofs of the systolic inequality on the klein bottle in the riemannian case . as in the original proofs of the riemannian systolic inequalities on @xmath0 , @xmath9 and @xmath11 , the uniformization theorem was also essential in the proof of the conformal systolic inequalities on @xmath34 . in this article , we first prove a finsler generalization of the optimal systolic inequality on @xmath0 extending loewner s inequality , _ cf . _ @xcite , and derive further optimal geometric inequalities on finsler cylinders , _ cf . _ section [ sec : torus ] . these results allow us to establish an optimal inequality on every finsler mobius band @xmath34 relating its systole @xmath35 , its height @xmath36 and its ( holmes - thompson ) volume @xmath37 at least when @xmath34 is wide enough , _ cf . _ section [ sec : wide ] . here , the height @xmath36 represents the minimal length of arcs with endpoints on the boundary @xmath38 , which are not homotopic to an arc in @xmath38 , _ cf . _ definition [ heightdefinition ] . more precisely , we prove the following . [ finslermobius ] let @xmath34 be a finsler mobius band . let @xmath39 . then @xmath40 \\ \frac{1}{\pi}\frac{\lambda+1}{\lambda } & \text{otherwise}. \end{cases}\ ] ] moreover , the above inequalities are optimal for every value of @xmath41 . we describe extremal and almost extremal metric families in details in section [ sec : candidates ] , example [ ex : extremal - wide ] and example [ ex : extremal - narrow ] . + the optimal finsler systolic inequality on the klein bottle is still unknown . however , based on the inequality on finsler mobius bands , we obtain a partial result for finsler klein bottles with nontrivial symmetries . we refer to definition [ def : sym ] for a description of the symmetries considered in the statement of the following theorem . [ finslerkleinbottle ] let @xmath42 be a finsler klein bottle with a soul , soul - switching or rotational symmetry . then @xmath43 moreover , the inequality is optimal . we also present some extremal metric family in example [ ex : extremal2 ] . + finally , we present as a conjecture that the inequality should hold for every finsler klein bottle with or without symmetries . that is , @xmath44 should be equal to @xmath45 ( as @xmath46 and @xmath47 ) .

we prove optimal systolic inequalities on finsler mobius bands relating the systole and the height of the mobius band to its holmes - thompson volume . we also establish an optimal systolic inequality for finsler klein bottles of revolution , which we conjecture to hold true for arbitrary finsler metrics .

we prove optimal systolic inequalities on finsler mobius bands relating the systole and the height of the mobius band to its holmes - thompson volume . we also establish an optimal systolic inequality for finsler klein bottles of revolution , which we conjecture to hold true for arbitrary finsler metrics . extremal metric families both on the mobius band and the klein bottle are also presented .

1009.3027

c

the issue of planetary tidal evolution has a long and illustrious history , with many applications to our own solar system ( e.g. peale 1999 ) . the importance of tides was realised immediately upon the discovery of the first extrasolar planets ( e.g. rasio et al . 1996 ; marcy et al . 1997 ) because of the extremely short periods of the first planets discovered using radial velocities . the interest in tidal effects has been unwavering ever since , especially since the advent of transit surveys , which strongly favour the detection of short period planets . as such , our results have relevance to many other studies ( and vice versa ) . however , before we can compare and contrast our results with those of others , we need to provide a translation between the traditional manner of parameterising the dissipation using ` @xmath0 ' , and our intentionally different approach . as a large fraction of the literature on this subject is phrased in terms of a particular value of the tidal dissipation parameter @xmath5 , it is of interest to see how our model compares . if we compare of our expression with an equivalent expression cast in terms of @xmath5 , such as jackson et al ( 2008 ) , we obtain an expression @xmath91 where @xmath7 is the orbital angular frequency . putting our best - fit numerical values into this yields @xmath92 note that this is no longer a constant , but has a dependence on both semi - major axis and planetary radius ( although not planetary mass ) . the radius dependence is quite strong and this is , in part , the reason for the strong effect of tidal dissipation . in general , @xmath5 will drop as the planet approaches the star and dissipation will increase . an equivalent analysis for the dissipation in the star yields an expression for the @xmath0 of the star , @xmath93 figure [ qq ] shows the resulting values of @xmath94 and @xmath95 for the close planet sample . we see that a large fraction of the close jupiter systems are characterised by present day values @xmath96 , although the closest systems ( a few are labelled in the plot ) show values a little smaller . the range of values of @xmath95 shows somewhat greater variation , presumably because the strong dependence on @xmath97 means that @xmath95 can vary by an order of magnitude with a 60% change in radius . the functional form of equations ( [ qp ] ) and ( [ qs ] ) can be easily understood by analogy with the simple harmonic oscillator description of the equilibrium tide model ( greenberg 2009 ) . many authors have estimated @xmath5 values for individual systems based on various observational constraints and model requirements ( e.g. matsumura , takeda & rasio 2008 ; miller et al . 2009 ; ibgui et al . these are often significantly different than the corresponding values above , suggesting that efforts like this one to enforce consistency within the basis of a single physical model will be increasingly necessary as the observed sample grows . one of the traditional cornerstones of estimating tidal dissipation in giant planets is to draw a comparison with the constraints on the dissipation in jupiter , inferred by assuming that the resonant configuration of the gallilean satellites is driven by tidal dissipation in jupiter ( goldreich & soter 1966 ) . to cast our results in an appropriate form for this comparison , we must re - arrange terms in the formalism of [ model ] , moving jupiter to the role of ` star ' , and io to the role of planet . furthermore , the forcing frequency ( @xmath98 ) of this system comes from the rotation of jupiter , not the orbit of io , so that we need adopt the limit of @xmath99 . once again , in this limit , we infer @xmath100 for a rotation period of 10 hours and @xmath101 . this is only slightly higher than the usually quoted range of @xmath102@xmath103 . of course , it is also possible that the laplace resonance of the satellites is primordial ( peale & lee 2002 ) , in which case there are no constraints on @xmath104 from the io system . this value is somewhat larger than the @xmath105 inferred by lainey et al . ( 2009 ) from a long - term astrometric monitoring program , suggesting that a stronger frequency dependance may be required at higher forcing frequencies and the observation of lainey could be explained if @xmath3 scales quadratically , as in the goldreich - nicholson formalism assuming the conversion is from 3 days to 10 hours . ] . one of the principal motivations for our study was the recent flurry of interest in whether tidal dissipation can contribute to the inflated radii observed for some planets . several authors have attempted to account for the enhanced radii of certain planets by invoking the dissipation due to tides to heat the planet internally . jackson et al . ( 2008a , b ) have run the evolution of various systems backwards and claim that , for reasonable choices of @xmath0 , one could explain the tidally inflated radii of some planets as the result of residual heat left over from recent circularisation . however , they do not treat the evolution of the planetary radius self - consistently , an important omission , as the strength of tides can be strongly influenced by the radius . to do this correctly required forward modelling , and calculations of this type have been recently performed ( miller et al . 2009 ; igbui et al . miller et al . find that tidal inflation may explain some systems , but not all . igbui , spiegel & burrows ( 2009 ) find consistent solutions for systems such as wasp-4b and wasp-12b with values of @xmath106 and @xmath107 , ( which amounts to @xmath108 for these two systems ) . one concern about such studies is that it is not clear how the choices of @xmath0 should be related between different systems . one of the motivations for this current study was to see what a consistent formalism might yield . another concern is that the tidal evolution equations in the above papers were truncated at second order in the eccentricity , even when the eccentricity was large . this approach has been ( rightly ) criticised recently by leconte et al . ( 2010 ) , who use a set of equations derived from the model of hut ( 1981 ) . this study is the closest extant one to ours , both in spirit and execution ( since the ekh model is also ultimately derived from the same model as that of hut ) . with our final calibration , tidal inflation is not a likely cause of planetary inflation . figure [ twopanel ] shows the evolution for two prominent inflated planet systems , wasp-12 and wasp-4 . in each case , the initial parameters were chosen such that the forward evolution with the parameterised model would yield the correct semi - major axis and eccentricity at the estimated age of the system . in both cases ( and all others we investigated ) the damping of the eccentricity does cause inflation of the planet , but happens on short times ( @xmath109 years ) , so that the planetary cooling reduces the radius to more traditional values by the time the planet reaches it s current semi - major axis . discrepancies are even larger for more distant inflated systems ( like tres-4 ) , which experience little tidal evolution in this model . the only way tidal inflation could explain these radii is if the planetary orbit was circularised only within the last @xmath110 years , requiring a late injection of the planet orbit . in this we are in complete agreement with leconte et al , who find a similar disagreement with previous studies , and ascribe it to the fact that the truncation of the tidal equations to quadratic order weakens the strength of the tide , allowing the planet to dissipate energy at later times , and increasing the amount of tidal inflation . this is ultimately why we can not reproduce the evolutionary history of igbui et al . ( 2010 ) in figure [ tr ] , no matter what parameterisation we adopt . given the similar philosophy , it is of interest to compare the values of @xmath5 assumed in leconte et al . with our calibrations . the leconte model assumes a constant time lag , which ekh showed is an equivalent assumption to that of a bulk dissipation constant such as we use here . as a result , their @xmath5 values have the same frequency dependence as ours , and they have normalised them by assuming different values at a period of 1 day . we can use equation ( [ qs ] ) to normalise our model in a similar fashion . for our calibration , @xmath111 and @xmath112 at 1 day periods ( with some scatter resulting from the radius dependence in our model ) . thus , our planetary dissipation is comparable to the upper range assumed by leconte et al , although our stellar dissipation is an order of magnitude weaker than the range they studied . for completeness , we should note that our inability to find a reasonable tidal inflation model is confined to the simple case of single planet tidal evolution . some studies ( e.g. bodenheimer et al . 2001 ; mardling 2007 ; batygin , bodenheimer & laughlin 2009 ; ibgui et al . 2010 ) invoke a third body to perturb the eccentricity and maintain some level of tidal inflation . figure [ floor ] shows the evolution of the wasp-12b system in our tidal model with the addition of an eccentricity floor for the planet . as the stellar tide starts to drag in the orbit , the continued dissipation in the planet does indeed inflate the radius , and could potentially explain wasp-12b if @xmath37 . this is consistent with the initial claims for the system ( hebb et al . 2009 ; lopez - morales et al . 2009 ) , but is not consistent with more recent measurements ( campo et al . 2010 ; husnoo et al . 2010 ) . in conclusion , we find that it is difficult to explain the inflated planetary radii within the context of an equilibrium tide model parameterised to match the overall properties of the exoplanet distribution , especially if one uses a tidal evolution model that treats large eccentricity systems self - consistently . searches for planets around more massive stars ( @xmath113 ) report a higher frequency of planets , but a conspicuous lack of close - in planets ( johnson et al . 2007 ; lovis & mayor 2007 ; sato et al . 2008 ; niedzielski et al . 2009 ) . however , the recent report of a likely transitting planet in a 1.2 day orbit around the 1.5@xmath48 star hd15082 ( collier cameron et al . 2010 ) suggests that the existence of such planets is possible at least during the main sequence stage . the fact that the radial velocity searches are performed around subgiants ( so that the atmospheres are slowly rotating and more amenable to radial velocity measurement ) means that one can speculate whether the close - in planets have been swallowed as the result of the evolution of the central star . johnson et al . ( 2007 ) discount this possibility because the stellar radii do not approach the semi - major axes of the hot jupiters until much later stages . however , we have seen that the stellar tidal coupling can cause a planet to spiral inwards . can this process , with our stellar dissipation calibration , explain the paucity of hot jupiters around a - type subgiants ( e.g. sato et al . figure [ swallow ] suggests that tidal effects will contribute , at least partially , to the removal of close - in planets . we can determine the degree to which tides can drag in planets , as a function of stellar radius , by integrating the tidal evolution in concert with a model for the stellar evolution , and noting at which point a planet from a given initial orbit is swallowed . figure [ swallow ] has been calculated by performing this calculation for a series of @xmath69 planets , using the evolutionary histories for metal - rich stars of mass 1.5@xmath48 and 2.5@xmath48 , using the padova models ( girardi et al . we show the results as a function of stellar radius , as a proxy for age . also shown ( dotted line ) is the criterion indicating the orbital period at the surface of the star . this is the line used by johnson et al . , and it indeed reaches orbital periods of several days only after the star has evolved significantly . the criterion derived from tidal evolution is somewhat stricter , suggesting that orbital periods out as far as 8 days are denuded by the time the star reaches the subgiant stage , and periods out to @xmath114 days are removed by the time the star reaches a radius of @xmath115 . thus , any true hot jupiters are removed rapidly , although it remains to be seen whether the remaining gap between 8 and 200 days is real or simply the result of low statistics . after submission of this paper , johnson et al . ( 2010 ) announced the discovery of hd102956b , a planet in a 6.5 day orbit around an a subgiant . this system supports the latter answer , and lies on the edge of the tidal survival boundary , as shown in figure [ swallow ] . the above calculations have assumed that the host stars are spinning slowly , consistent with what is observed for the majority of systems . if the star was spinning sufficiently rapidly , the tidal transfer of angular momentum from stellar spin to planetary orbit could potentially drive the planet outwards ( e.g. dobbs - dixon , lin & mardling 2004 ) . it has been noted that many of the massive planet hosts discussed in [ massive ] are rotating more rapidly than the average for the sample as a whole , so we have investigated the effects of stellar spin on our calibration . in each case we investigated a range of initial stellar spins and repeated the calculation with our original and final values of stellar dissipation . no appreciable change in the period - eccentricity relation was found . as an illustration , consider the case of the hat - p-2 system that was used to finalise the calibration in [ final ] . this is also the only one of the systems in which the stellar spin is actually faster than the orbital spin , which would reverse the sign of the tide . we repeated our tidal evolution calculations for the same distributions in period and eccentricity , but now also sampling uniformly an initial stellar spin period distribution from 1 to 100 days . one might wonder whether the sign reversal of the stellar - spin dependant term would yield a consistent fit with our original , larger , stellar dissipation rate from [ synth ] . figure [ eom ] shows that this is not the case . in this case we plot final stellar spin against eccentricity , for all periods @xmath116 days . we see that it is not possible to match both stellar spin and planetary eccentricity for tidally evolved systems using the stronger dissipation . ultimately , matching the parameters of the hat - p-2 system required weakening the stellar tide , irrespective of the stellar spin contribution . even if the spin of the star is not dynamically important , it is possible that conservation of angular momentum would spin the star up , if it drags a planet inwards through tidal coupling . it has been suggested ( pont 2009 ) that several observed host stars are rotating anomalously rapidly , and that this may indicate a non - negligible influence of tides on the host star itself . within the context of our model calibration , none of the proposed systems ( hd189733 , corot-2b , hat - p-2b and xo-3b ) exhibits a sufficiently strong coupling to spin the stars up to significant levels . the more recently discovered system , wasp-18b , offers perhaps the best chance of observing stellar spin - up , as it is a massive planet in a very short period orbit ( hellier et al . 2009 ) . however , even this system , within the context of stellar solid - body rotation , fails , by an order of magnitude , to spin the star up to the observed rotation period of 5.6 days ( assuming a system lifetime of 1.5 gyr ) . thus , we do not expect the dynamics of the previous sections to be significantly affected by stellar rotation . it is possible , however , that the observed rotation period represents the spin - up of the surface convection zone only . wasp-18b is an f - star and thus it is quite possible that the inspiral spun - up the surface convection zone while leaving the interior less rapidly rotating . the best system for observing outward migration driven by stellar spin is wasp-33b ( collier cameron et al . the estimated stellar rotation period is 0.81 days , and the orbital period is 1.2 days . this is sufficiently close that the tidal coupling is strong enough to be important even with the calibration of [ final ] . figure [ wasp33 ] shows the expected orbital evolution of the system , assuming the surface rotation represents the bulk solid body rotation of the star . we see that the planet is eventually driven out to orbital periods @xmath117 2 days . the effect gets rapidly weaker with distance , and planets with orbital periods @xmath283 days experience little change . we have calibrated the planetary and stellar dissipation using a single bulk constant , within the context of the equilibrium tide model . it is clearly of some interest to understand how the final value compares to more detailed models for the true microphysical dissipation . the simplest microphysical model is dissipation of the equilibrium tide due to the turbulence in the convection zone . in appendix [ internal ] we use the formalism of eggleton et al to relate the bulk @xmath20 and @xmath21 to the internal dissipative processes , using our models for planetary and stellar structure . for the planets , we find that the amount of dissipation required by our calibration is several orders of magnitude lower than that obtained if one adopts a simple local turbulent viscosity based on convective velocities and scale heights . this is encouraging , because the largest eddy overturn times are of the order of years , and so it is not clear how strong a coupling is likely to occur to forcing periods on the order of days . indeed , there are several proposed prescriptions regarding how inefficient such a coupling is . zahn ( 1989 ) proposes that the strength of the turbulent viscosity is reduced by a linear factor in the period , while goldreich & nicholson ( 1977 ) propose a quadratic scaling . our calculations in appendix [ internal ] favour a value intermediate between these prescriptions . this is perhaps not surprising in the light of recent studies by penev , barranco & sasselov ( 2009 ) , who have performed simulations of forced anelastic convection . they find rates of dissipation that scale similar to the zahn prescription when the forcing period is not too different from the eddy overturn times , but faster losses of efficiency as the forcing frequency becomes significantly faster . they suggest that the ultimate root of this behaviour is that the turbulence deviates from the kolmogorov form used to derive the above scalings . while our results clearly can not shed any further light at this level of detail , it is encouraging that the order of magnitude values are within range of what one might naturally expect . our estimate of the stellar dissipation is not as sensitive to the various scalings , as the eddy overturn periods are of order days in this case , and thus should couple well to the observed properties . the effective calibration is a factor @xmath49 lower than what we infer from the simple model estimate , so that it is consistent with a slightly inefficient dissipation of the nominal equilibrium tide . the fact that this equilibrium tide value is broadly consistent with our calibration based on planets but not based on stars finds broad support in studies such as those of ogilvie & lin ( 2007 ) . the essential difference is that planet host stars do not have spins synchronised to the orbital period , while stars in close , equal - mass binaries do . in the latter case , ogilvie & lin show that the equivalence of forcing period and rotation period allows for the excitation of inertial modes ( an example of the ` dynamical tide ' ) , which can substantially enhance the rate of tidal dissipation . similar modes are not excited by planets because the host stars rotate much slower than the orbital period . excitation of modes in the radiative core ( goodman & dickson 1998 ; witte & savonije 2002 ; ogilvie & lin 2007 ; barker & ogilvie 2010 ) may also contribute an enhanced dissipation the case of planets , but the extent to which they do depends on the uncertain non - linear dissipation of waves that propagate to the center ( in the limit of low dissipation , the excitations result in global modes with specific resonant frequencies , which do not generate a broad - band tidal response ) .

the model is valid to high order in eccentricity and parameterised by two constants of bulk dissipation one for dissipation in the planet and one for dissipation in the host star . the paucity of short period planets around evolved a stars is explained as the result of enhanced tidal inspiral resulting from the increase in stellar radius with evolution .

we provide an ` effective theory ' of tidal dissipation in extrasolar planet systems by empirically calibrating a model for the equilibrium tide . the model is valid to high order in eccentricity and parameterised by two constants of bulk dissipation one for dissipation in the planet and one for dissipation in the host star . we are able to consistently describe the distribution of extrasolar planetary systems in terms of period , eccentricity and mass ( with a lower limit of a saturn mass ) with this simple model . our model is consistent with the survival of short - period exoplanet systems , but not with the circularisation period of equal mass stellar binaries , suggesting that the latter systems experience a higher level of dissipation than exoplanet host stars . our model is also not consistent with the explanation of inflated planetary radii as resulting from tidal dissipation . the paucity of short period planets around evolved a stars is explained as the result of enhanced tidal inspiral resulting from the increase in stellar radius with evolution .

0907.1374

i

`` soft '' physics is manifest in various places in different guises . the interest in soft interactions at _ very high _ energies is stimulated , theoretically , by the fact that the observed hadronic cross sections are growing with energy and , experimentally , by the advent of the lhc . at the lhc energy we have to allow for unitarity effects , which are necessary to provide the consistency of the strong interaction . in fact , when we face a cross section which grows as a power of the energy , there are two possible ways to restore unitarity . first , we may introduce a new particle ( sufficiently heavy to have not been observed yet ) which cancels the growth of the cross section at energies larger than the mass of the particle ( for example , higgs boson , super - partners , etc . ) . after this , we deal with a _ weak _ interaction , where the main contribution comes from one , or a few , simple diagrams . more complicated feynman graphs just describe corrections to the lowest - order amplitude . another possibility is to consider a _ strong _ interaction . here , from the beginning , we start with a hermitian lagrangian , which should already account for unitarity . when the born amplitude ( or an amplitude obtained via the summation of some group of diagrams ) becomes too large and the interaction becomes strong , then new more complicated diagrams must enter the game . it is the contribution due to these new graphs which tames the growth of cross section such that the final result satisfies unitarity . in the case of qcd , where the bfkl amplitude ( @xmath3 ) grows as a non - integer power ( @xmath4 ) of energy , @xmath5 , we expect to observe the second scenario by introducing a new particle . ] . therefore it is important to observe , and to study , the role of more complicated diagrams ( arising from multiple interactions ) at lhc energies , and to trace how the theory restores the unitarity of the _ strong _ interaction . that is , from a theoretical viewpoint , it is of great interest to observe experimentally how unitarity tames the growth of high - energy hadronic amplitudes , leading to saturation both in the transverse momenta @xmath6 and in the impact parameter @xmath7 distributions of the produced particles . in other words , unitarity replaces the growth of the amplitude by the growth of configuration space occupied by the particles , both in @xmath7 and in @xmath6 . here , we do not present new results but attempt to recall , using modern language , the ideas and understanding of high - energy soft interactions which originated some 40 or more years ago . the discussion may be divided into three main topics : ( i ) elastic scattering and the total cross section , ( ii ) the cross sections of processes with gaps in rapidity ( including high - mass diffractive dissociation ) , and , ( iii ) the saturation of particle densities in transverse momenta @xmath6 . soft high - energy @xmath8 interactions are clearly important at the lhc . moreover , they can complicate our ability to observe new physics . for example , topic ( iii ) is relevant to the search for new physics , since particles with a rather large @xmath6 from the underlying inclusive event will affect the jet searching algorithm , as is already the case for jets at hera and the tevatron . on the other hand , the evaluation of the cross section for an exclusive process , such as @xmath9 , requires knowledge of the gap survival probability @xmath10 , which is the subject of topic ( ii ) , see , for example , @xcite . here , we focus on the qualitative features of high energy soft interactions . these features are quite general . with the advent of the lhc , it is timely to gather them together and to emphasize the underlying physics .

unitarity tames the power growth of the elastic proton - proton scattering amplitude with energy , and leads to the migration of the secondary particles produced in high - energy proton - proton collisions to larger transverse momenta . ippp/09/24 + dcpt/09/48 + + * soft physics at the lhc * + m.g .

we recall the main features of the regge approach used to understand soft interactions at lhc and higher energies . unitarity tames the power growth of the elastic proton - proton scattering amplitude with energy , and leads to the migration of the secondary particles produced in high - energy proton - proton collisions to larger transverse momenta . we discuss , in qualitative terms , the role of processes containing large rapidity gaps ( lrg ) , and the probability that the gaps survive population by secondaries produced in additional soft interactions . we explain how the regge diagram corresponding to a lrg event simultaneously describes events with different ( single , double , etc . ) particle density in the same rapidity interval . we show that the role of these , enhanced , multi - pomeron diagrams can be studied by measuring multiplicity fluctuations and long - range rapidity correlations between secondaries produced at the tevatron and the lhc . finally , we make a list of the characteristic features of the multi - pomeron description of soft interactions that may be observed at the high energies accessible at the tevatron and the lhc . ippp/09/24 + dcpt/09/48 + + * soft physics at the lhc * + m.g . ryskin , a.d . martin , v.a . khoze and a.g . shuvaev + institute for particle physics phenomenology , university of durham , durham , dh1 3le + petersburg nuclear physics institute , gatchina , st . petersburg , 188300 , russia

0907.1374

c

we should discuss how the saturation of particle densities can be consistent with confinement . the growth of the transverse momenta @xmath6 tames the increase of the interaction radius with energy . one possibility is that the simultaneous action of confinement and the growth of @xmath6 will finally lead to the saturation of the interaction radius ; that is to the saturation of the elastic slope , @xmath226 as @xmath227 . however the idea , discussed at the end of section [ sec : tot ] , that when the interaction radius becomes large confinement leads to the formation of colourless clusters , allows an alternative possibility . in a large , but finite , interval of rapidity the evolution is driven by the gluon ladder . in this case the impact parameter is almost frozen ; that is , the variation of the interaction radius @xmath228 is small . the system then emits a pion ( or another meson ) and this ` colourless cluster ' provides a noticeable increase of the impact parameter @xmath7 . following this , we again have gluons in some interval of evolution , and so on , as shown in fig . [ fig : m](a ) . the hard qcd interactions will be responsible for the growth of @xmath6 , while the part of the evolution described in terms of colourless mesons will be responsible for the increase in the interaction radius , that is of @xmath46 , due to the diffusion in * b * plane see fig . [ fig : m](b ) . in such a ` mixed ' picture we expect lower @xmath6 in peripheral collisions ( since the available rapidity interval was used to enlarge the value of @xmath7 ) and maximal @xmath6 in central collisions . [ t ] it may be informative to study multiparticle production at the lhc for individual events , as well as in terms of inclusive cross sections . at the high lhc energy the multiplicity of secondaries is large . thus it might be possible to observe the fluctuation of particle densities in individual events like those shown in fig . [ fig : b ] , or the effects arising from a mixture of intervals of evolution via colourless meson and coloured gluon exchanges , like those shown in fig . [ fig : m ] . in the latter case , the rapidity correlation length ( measured via @xmath185 of ( [ eq : r2 ] ) ) should be rather small for peripheral collisions since the main part of the available rapidity interval was used for meson exchange ( to enlarge @xmath7 ) and so only small intervals are left for gluon exchange where we expect a large probability to have several ` cut ' pomerons . it is appropriate to say a few final words about models of high - energy soft interactions . we emphasize that the aim of experiment is not to reject or to confirm one or another model by saying that the data prefer monte carlo version x or y. rather , the objective should be to isolate , and to study , the main qualitative features of the interaction . what , therefore , are the requirements of a realistic model of high - energy soft interactions ? to describe all the qualitative features discussed in this paper , it is clear that a realistic model should * contain , not only the eikonal but also the enhanced multi - pomeron contributions ; * include , not just the triple - pomeron vertex , but more complicated multi - pomeron vertices ( otherwise we will get an asymptotically decreasing cross section ) ; * allow for ` diffusion ' of the partons both in impact parameter , @xmath7 , and in transverse momenta , or , more precisely , @xmath87 space . a recent attempt at building such a multi - pomeron model , tuned to describe all the available data for high - energy soft interactions , is presented in @xcite . for convenience , we call this the kmr model . [ t ] cross sections , and the cross sections of dissociation to a fixed @xmath229 state ( c ) ; ( d ) the parton multiplicity ( solid lines ) and the number of ` colour tubes ' ( dashed ) produced by pomeron components of different size . the figure is taken from the kmr model of @xcite.,height=680 ] finally , can the characteristic features of the multi - pomeron description of soft interactions be observed at the high tevatron and lhc energies ? we list some below . * the multi - pomeron absorptive effects tame the power growth of the @xmath8 total cross section leading to values smaller than predicted before . for example , the kmr model prefers a value close to the lower of the two tevatron measurements , and a value of about 90 mb at the lhc energy of @xmath230 14 tev , see fig . [ fig : kmr](a ) . at 100 tev the prediction of 108 mb is at the lower limit of cosmic ray expectations . * simultaneously , these absorptive effects shrink the elastic differential cross section peak as the energy increases through the lhc range more than the expectations arising from a naive effective pomeron - pole of a donnachie - landshoff type of parametrization @xcite . * the cross section for proton dissociation into high - mass systems should grow with energy and be comparable to the elastic scattering cross section . the reason is that although , for each fixed rapidity interval , the probability of high - mass dissociation is relatively small , the overall effect is enhanced by the large phase space that is available in rapidity at high collider energies . the predicted values of @xmath69 and @xmath70 for the kmr multi - pomeron model are shown in figs . [ fig : kmr](b , c ) for energies in the tevatron lhc energy range . * the main growth in multiplicity , as we go from tevatron to lhc energies , is due to the small size ( ` qcd ' ) pomeron component , which produces particles with typically @xmath231 gev . there is essentially no growth in multiplicity at small @xmath232 . this simply confirms the trend that has been observed through the cern - isr to tevatron energy range , see the data points in fig . [ fig : inclmult ] . + [ h ] + ranges correspond to the large- , intermediate- and small - size components of the pomeron , see also fig . [ fig : kmr](d),height=566 ] + in other words , starting with the same pomeron intercept ( @xmath117 of section [ sec : pqcd ] ) the contribution of the large - size component _ after the absorptive correction _ becomes practically flat in energy ( @xmath233 ) , while the small - size contribution , which is much less affected by the absorption , continues to grow with energy ( @xmath234 ) . such behaviour is consistent with the experiment ( see fig . [ fig : inclmult ] ) where the density of low @xmath232 secondaries is practically saturated while probability to produce a hadron with a large ( say , more than 5 gev ) transverse momentum grows with the initial energy . * multi - pomeron exchange diagrams have a characteristic pattern of ` enhanced ' multiplicities of secondary particles , as well as large rapidity gaps , governed by the agk cutting rules . these lead to long - range rapidity correlations , for example , which may be observed at the lhc via @xmath185 of ( [ eq : r2 ] ) . * the observed rate of large rapidity gap ( lrg ) events in various processes at the lhc will be particularly informative . the survival probability of a lrg may be calculated in terms of a multi - pomeron exchange model of soft interactions . it is necessary to calculate the survival to both _ eikonal _ soft rescattering ( between the colliding protons ) , and _ enhanced _ rescattering ( involving soft interactions with intermediate partons with different @xmath6 ) . to calculate the latter we need to include the @xmath6 dependence of pomeron exchange , see @xcite this was the third requirement listed for a realistic model . * a topical example of a lrg process is the _ exclusive _ production of a heavy mass system @xmath56 , that is @xmath235 where the @xmath236 signs denote lrgs . this process , with @xmath237higgs , is a novel and promising way to study the higgs sector at the lhc , which gives a strong motivation for the addition of forward proton detectors to enhance the discovery and physics potential of the atlas and cms detectors at the lhc @xcite . already , at the tevatron , the cdf collaboration have observed exclusive processes with @xmath238 , dijet and @xmath239 with rates consistent with the estimates of the lrg survival probabilities predicted by the multi - pomeron model of soft interactions , see @xcite and references therein . more data on exclusive processes , from both the tevatron and , especially , the lhc , will be illuminating .

we recall the main features of the regge approach used to understand soft interactions at lhc and higher energies . finally , we make a list of the characteristic features of the multi - pomeron description of soft interactions that may be observed at the high energies accessible at the tevatron and the lhc . shuvaev + institute for particle physics phenomenology , university of durham , durham , dh1 3le + petersburg nuclear physics institute , gatchina , st .

we recall the main features of the regge approach used to understand soft interactions at lhc and higher energies . unitarity tames the power growth of the elastic proton - proton scattering amplitude with energy , and leads to the migration of the secondary particles produced in high - energy proton - proton collisions to larger transverse momenta . we discuss , in qualitative terms , the role of processes containing large rapidity gaps ( lrg ) , and the probability that the gaps survive population by secondaries produced in additional soft interactions . we explain how the regge diagram corresponding to a lrg event simultaneously describes events with different ( single , double , etc . ) particle density in the same rapidity interval . we show that the role of these , enhanced , multi - pomeron diagrams can be studied by measuring multiplicity fluctuations and long - range rapidity correlations between secondaries produced at the tevatron and the lhc . finally , we make a list of the characteristic features of the multi - pomeron description of soft interactions that may be observed at the high energies accessible at the tevatron and the lhc . ippp/09/24 + dcpt/09/48 + + * soft physics at the lhc * + m.g . ryskin , a.d . martin , v.a . khoze and a.g . shuvaev + institute for particle physics phenomenology , university of durham , durham , dh1 3le + petersburg nuclear physics institute , gatchina , st . petersburg , 188300 , russia

1208.0181

i

the role of spin - fluctuations in superconducting materials has been a subject of sustained interest for the last 50 years . in 1960s doniach @xcite and berk and schrieffer @xcite made the important observation that itinerant ferromagnetic spin - fluctuations tend to suppress superconductivity in elemental s - wave superconductors . they pointed out that the absence of superconductivity in heavy transition elements such as palladium and platinum is due to the itinerant ferromagnetic spin - fluctuations resulting from the large @xmath6-electron density of states near the fermi level . the same formalism was used to suggest that the superconducting transition temperature t@xmath7 of elements such as nb and v was limited by spin - fluctuations @xcite . hence it was conjectured that when these metals were properly engineered in the form of alloys , the t@xmath7 could increase significantly as was observed in nb@xmath8sn , and v@xmath8si , etc . , later on , the effects of localized spin - fluctuations on the properties of dilute superconducting alloys were studied by zukermann @xcite . he showed that the superconducting transition shifted to temperatures lower than those expected from the band structure calculations performed without considering the spin - fluctuations @xcite . on the other hand , many families of superconductors have been identified during last 30 years , where spin - fluctuations actually play an important role in the superconductivity itself . these include various exotic low temperature superconductors such as y@xmath9co@xmath10 @xcite , cecoin@xmath11 @xcite , ube@xmath12 @xcite , sr@xmath13ruo@xmath14 @xcite , fese @xcite , and mo@xmath8sb@xmath10 @xcite etc . this concept of spin - fluctuation influenced superconductivity , however , came into much prominence in connection with the high temperature superconductors @xcite . this has now become a subject of even more attention with the discovery of a newer class of fe based high temperature superconductors @xcite . most recently it has been reported that the longitudinal ferromagnetic spin - fluctuations induce superconductivity in ucoge @xcite . it is well known that any addition of a magnetic impurity in non - transition element based s - wave superconductor suppresses the superconductivity due to the pair breaking . it is also reported in literature that even the addition of the non magnetic transition elements also suppresses the t@xmath15 @xcite due to the formation of localized states . however , it has been observed that the t@xmath7 of a dirty limit superconductor is not effected significantly by disorder @xcite , in fact a very high level of disorder is required to change the t@xmath7 @xcite . surprisingly an enhancement in t@xmath15 is observed in spite of increased disorder when certain transition elements are alloyed , even though these elements either have t@xmath7 s lower than the host material , or are non superconducting @xcite . the present ti - v alloys are the examples of one such system @xcite . in recent times , it has been recognized that ti - v alloys with their good mechanical , thermal and superconducting properties @xcite can be promising candidates for application as superconducting magnets in the environment of heavy neutron irradiation as in a fusion reactor @xcite . in addition , higher value of lower - critical field h@xmath16(0 ) of ti - v alloys at 2 k @xcite as compared to the commercial polycrystalline nb samples @xcite makes them potential candidates for superconducting rf cavity applications . thus a complete understanding of the normal and superconducting states in these ti - v alloys can lead to the possibility of enhancing their superconducting properties ( e.g. , increasing the experimental superconducting transition temperature t@xmath7 , the lower critical field h@xmath16(0 ) and the upper critical field h@xmath17(0 ) to the theoretical limits ) and enhancing other functional properties like critical current density by suitable engineering techniques . however , several features of ti - v alloys are not understood yet , of which we list below the two significant anomalies . there is an increase in t@xmath7 when ti content is increased from zero to 40 at . % in v @xcite . the significant enhancement in debye temperature @xmath18 or the electron phonon coupling is not expected in ti - v alloys as ti and v are adjacent atoms . the density of states decreases as ti content is increased in v @xcite . hence , the increase in t@xmath7 in ti - v alloys does not follow the mcmillan formula . there is a large region in h - t phase diagram where superconducting fluctuations are observed well above t@xmath7 and well above h@xmath17 @xcite . hake and coworkers @xcite have shown that superconducting fluctuations well above t@xmath7 and well above h@xmath17 are intrinsic property of certain class of transition element binary alloys such as ti - v , ti - mo and ti - ru systems . they have also observed that these fluctuations are not dependent on the sample preparation , surface polishing , size and shape of the sample and on the current density . several models such as the occurrence of reversible @xmath19 phase in the @xmath20 matrix @xcite , weak localization @xcite , kondo ( s - d ) interaction @xcite and associated localized spin fluctuation @xcite have been considered for explaining the observed physical properties in ti - v alloys . the increase in magnetic susceptibility with temperature was attributed mainly to the occurrence of reversible @xmath19 phase in the @xmath20 matrix @xcite . according to this model , the metastable hexagonal closed pack ( hcp ) @xmath19 phase appears inside the body centered cubic ( bcc ) @xmath20 phase when the temperature is decreased below 300 k. however , this model does not explain the large difference between the experimental value of superconducting transition temperature t@xmath7 and that estimated theoretically @xcite . prekul et al @xcite on the other hand invoked the idea of the localized spin fluctuations to understand the normal state properties of ti - v alloys . however , this model could not explain the superconductivity fluctuations observed well above t@xmath7 and well above h@xmath17 @xcite . in this direction we present a detailed study of the superconducting and normal state properties of a ti@xmath0v@xmath1 alloy investigated through the measurements of temperature dependence of electrical resistivity , dc magnetic susceptibility and heat capacity in the presence of zero and externally applied magnetic fields . the observed temperature dependence of the normal state properties is explained within the realm of itinerant spin - fluctuation model .

the temperature dependence of the normal state dc magnetic susceptibility in this tiv alloy shows tlnt behavior . such temperature dependence of dc magnetic susceptibility , resistivity and heat capacity are indications of the presence of spin - fluctuations in the system . _ keywords _ : alloy superconductor , spin fluctuations , electrical conductivity , magnetization , heat capacity

we report experimental studies of the temperature and magnetic field dependence of resistivity and dc magnetic susceptibility and the temperature dependence of zero field heat capacity in a tiv alloy . the temperature dependence of the normal state dc magnetic susceptibility in this tiv alloy shows tlnt behavior . the temperature dependence of resistivity follows a t behaviour in the range 20 - 50 k. on the other hand , a term lnt is needed in the expression containing the electronic and lattice heat capacities to explain the temperature dependence of heat capacity at temperatures where dependence of resistivity is observed . such temperature dependence of dc magnetic susceptibility , resistivity and heat capacity are indications of the presence of spin - fluctuations in the system . further experimental evidence for the spin fluctuations is obtained in the form of a negative value of t term in the temperature dependence of resistivity . the influence of spin - fluctuations on the superconducting properties of tiv is discussed in detail . we show from our analysis of resistivity and the susceptibility in normal and superconducting states that the spin fluctuations present in tiv alloy are itinerant in nature . there is some evidence of the existence of preformed cooper - pairs in the temperature range well above the superconducting transition temperature . our study indicates that the interesting correlations between spin - fluctuations and superconductivity may actually be quite widespread amongst the superconducting materials , and not necessarily be confined only to certain classes of exotic compounds . _ keywords _ : alloy superconductor , spin fluctuations , electrical conductivity , magnetization , heat capacity

1208.0181

r

the ti - v alloys form in @xmath20 phase for ti composition exceeding 20 at . the space group corresponding to @xmath20 phase is body centered cubic ( bcc ) im@xmath22 m with ti or v occupying 2a site randomly . figure 1 shows the xrd pattern of ti@xmath0v@xmath1 alloy along with the fitted curve obtained using rietveld refinement . all the peaks observed in xrd pattern are correspond to the @xmath20 phase in the ti@xmath0v@xmath1 alloy . the rietveld analysis ( red solid line ) shows that the sample is formed in bcc structure with lattice parameters 0.31879(2 ) nm , which is in agreement with the literature @xcite . figure 2 presents the superconducting properties of ti@xmath0v@xmath1 . figure 2a shows the temperature dependence of magnetization measured using vsm in the temperature range 2 - 7.2 k in an applied field of 10 mt . the measurements were performed in the zero field cooled ( zfc ) , field cooled cooling ( fcc ) and field cooled warming ( fcw ) modes . in the zfc mode , the sample is first cooled from a temperature well above 10 k to 2 k in zero field and then the measurements are performed while warming up the sample in presence of 10 mt . in the fcc mode , the magnetic field ( 10 mt ) is applied at a temperature well above 10 k , and the measurement is done while cooling the sample down to 2 k. after reaching 2 k , the measurement is continued while warming up the sample in the same field and this last protocol is called fcw . the superconducting transition temperature t@xmath7 is the temperature at which the m(t ) starts to drop towards the negative value when temperature is decreased . the t@xmath7 thus estimated at 10 mt is about 7.15 k , which is in agreement with the literature @xcite . the t@xmath7 of ti@xmath0v@xmath1 is higher than that for elemental vanadium ( 5.4 k @xcite ) or titanium ( 0.9 k @xcite ) . the meissner fraction is estimated as m@xmath23(2 k)/m@xmath24(2k ) is about 7 x 10@xmath25 at 10 mt which indicates the strong flux pinning . figure 2b shows the magnetization as a function of magnetic field measured using vsm at various constant temperatures below superconducting transition temperature 7.15 k. the measurements were performed as a function of magnetic field after cooling the sample from well above the 10 k to the desired temperature in zero magnetic field . there is a considerable hysteresis at low fields in all the isothermal m - h curves . for field greater than a characteristic field h@xmath26 magnetization becomes reversible . the upper inset ( i ) of the fig . 2b shows the m v / s h data near h@xmath17 and the lower inset ( ii ) shows the low field m v / s h data at selected temperatures which are used to estimate the h@xmath16 from the magnetization data . we plot in figure 2c the temperature dependence of resistivity below 15 k at various constant magnetic fields up to 5 t. in zero magnetic field , the resistivity decreases as temperature is lowered below 15 k and drops to zero at t@xmath7 = 7.06 k with a transition width of 0.085 k. the inset in fig . 2c shows the effect of magnetic field ( up to 5 t ) on the superconducting transition temperature ; an application of 5 t suppresses the t@xmath7 to 5.66 k. we have observed a rounding - off behavior in the temperature dependence of resistivity just above the t@xmath7 . figure 2d shows the temperature dependence of heat capacity plotted as c / t as a function of t@xmath2 in selected magnetic fields . the application of magnetic field shifts the heat capacity peak to lower temperature . the superconducting transition temperature t@xmath27 is obtained as that temperature at which a deviation is observed from the normal state linearity in c / t v / s t@xmath2 plot . in zero magnetic field , t@xmath27 is estimated to be about 7.17 k. at 8 t magnetic field , the superconducting transition is observed at 4.8 k.there is no difference in normal state heat capacity between the zero field data to that in magnetic fields . the sommerfeld coefficient of electronic heat capacity @xmath28 and the debye temperature @xmath18 are obtained to be about 9.46(2 ) x 10@xmath29 j/ mol k@xmath2 and 258.5(2 ) k respectively by fitting a straight line to the normal state heat capacity data in figure 2d . the jump in heat capacity @xmath30c/@xmath28t@xmath7 across the t@xmath7 in the zero magnetic field is estimated at the onset of the transition t@xmath27 as well as at the middle of the transition t@xmath31 = 6.63 k. the @xmath30c/@xmath28t@xmath27 is about 2.65 whereas @xmath30c/@xmath28t@xmath31 is about 2.22 indicating that ti@xmath0v@xmath1 is a bulk and a strong coupling superconductor . the value of t@xmath27 is in agreement with the t@xmath7 estimated using resistivity and magnetization measurements . the upper critical field h@xmath17 at various temperatures were estimated from such isothermal m - h curves is shown in fig . the magnetic field at which a distinct deviation takes place from the magnetic field dependence of the normal state magnetization is taken as the h@xmath17 . a straight line is fitted to the m v / s h data for the normal state m just above the superconducting state . the h@xmath17 is taken as that point at which the difference between the experimental data and the fitted line exceeds the standard deviation of the fitting . this procedure has been effectively used to estimate the h@xmath17 in superconductors such as borocarbides @xcite and skutterudite @xcite where enhanced paramagnetism is observed in the normal state . the error in the estimation of h@xmath17 is found to be less than 2 % . the temperature dependence of h@xmath17 is analyzed on the basis of formalism by orlando et al @xcite ( red solid line ) which will be discussed in detail later . the h@xmath17(t = 0 ) is estimated to be about 13.68 t. the lower critical field h@xmath16 ( fig . is estimated as that field where the slope of the linear fit to the low field data ( inset ( ii ) to fig . 2b . ) deviates about 2 % from the value of 1 . the magnetization data at low fields are corrected for demagnetization effects before estimating the h@xmath16 . the t@xmath7 estimated from the experimental h@xmath16(t ) is about 7.1 k. the temperature dependence of h@xmath16 follows a t@xmath2 dependence . the experimental data deviates from the t@xmath2 fit near t@xmath15 . the h@xmath16(0 ) is estimated by the t@xmath2 fit to be about 24.38(1 ) mt . the rounding - off behavior of electrical resistivity shown in fig . 2c . is an indication of fluctuation conductivity above the t@xmath7 ( 7.06 k ) . in order to verify this , we have studied this region through the estimation of excess conductivity @xmath32 = @xmath33 in zero magnetic field ( fig . 4a . ) and the magneto resistance @xmath34 = ( @xmath35(h ) - @xmath35(0 ) ) x 100 / @xmath35(0 ) as a function of magnetic field at temperatures above the t@xmath7 ( fig . 4b . ) . figure 4a shows the log - log plot of @xmath32 as a function of ( t - t@xmath7)/t@xmath7 in the temperature range 7.15 - 15 k. the excess conductivity may be explained in terms of the additional conductivity that results from the formation of cooper pair pockets well above t@xmath7 ; these cooper pairs are yet to be in the condensed state . the @xmath36 stands for the normal state conductivity , which is generally estimated by extrapolating the temperature dependence of resistivity from a temperature well above 3 times of t@xmath7 to the region where the fluctuation conductivity is observed @xcite . the @xmath37 is the experimentally observed conductivity , and the transition temperature t@xmath7 = 7.06 k is taken as the temperature at which the temperature - derivative of resistivity shows a maximum . according to theory of aslamazov and larkin ( al ) @xcite , the excess conductivity @xmath38 is expressed as @xmath39 where , @xmath40=(t - t@xmath7)/t@xmath7 is the reduced temperature , @xmath41 is a constant ( temperature independent ) , @xmath42=2-@xmath43/2 is the critical exponent , and @xmath43 is the dimensionality of the superconducting fluctuations . for a three dimensional superconductor , @xmath44 and @xmath42= 0.5 , where @xmath45(0 ) is the coherence length at zero temperature @xcite . the straight line fit near t@xmath7 to the data in fig.4a . , shows that @xmath42= 0.5 indicating 3@xmath43 character of the superconducting fluctuations in ti@xmath0v@xmath1 . however , the temperature range over which this fluctuation is observed is limited to 7.25 to 8.03 k. the upturn in @xmath32 below 7.25 k is due to the broadening of the superconducting transition @xcite . the maki - thompson ( mt ) @xcite effect can also contribute to the fluctuation conductivity where electron -electron interactions are strong . however , the @xmath45(0 ) estimated from the temperature independent amplitude of the al contribution to fluctuation conductivity is about 4.49 nm which is in agreement with the @xmath45(0 ) estimated from h@xmath17(0 ) . this indicates that the mt contribution to fluctuation conductivity is not dominant in ti@xmath0v@xmath1 . apart from this , mt contribution is dominant only in the clean limit @xcite whereas ti@xmath0v@xmath1 is in the dirty limit . it may be noted here that the al model is valid only in limited range of temperature close to t@xmath7 . the figure 4b shows @xmath34 as a function of magnetic field at temperatures above the t@xmath7 . at 7.5 k and 5 t , the @xmath34 is about 0.45 % . the @xmath34 at 5 t decreases as the temperature increases . hence , from fig . 4b , it appears that the magneto - resistance in ti@xmath0v@xmath1 exists up to 3t@xmath7 , where as fig . 4a . , shows that fluctuation conductivity exists up to at least 2t@xmath7 . such positive magneto - resistance below 3t@xmath7 , which is linear in magnetic field , was interpreted by hake to be due to the breaking of these pre - formed cooper pairs which formed well above t@xmath7 but were not condensed yet to give rise to superconductivity @xcite . in this latter argument , the temperature and magnetic field dependence of resistivity in the temperature range t@xmath7=7.15 k to 14.3 k in ti@xmath0v@xmath1 is due to the excess conductivity or the fluctuation conductivity resulting from cooper pair fluctuations well above t@xmath7 . then the effect of the magnetic field is to break the cooper pairs and drive the sample to its normal state . lue et al have shown experimentally that the magnetic field required to drive a system into normal state is more than the h@xmath17(0 ) @xcite for temperature even above t@xmath7 . the observed large positive magnetoresistance above t@xmath7 can not be accounted by the al fluctuation conductivity in presence of magnetic field for a 3d superconductor in the dirty limit is given by @xcite . in case of niobium as well as alloy and compound superconductors such as nb@xmath8sn , it is reported that the disorder generated by the high flux neutron irradiation does not decrease the t@xmath7 significantly @xcite . as pointed out earlier @xcite , the moderate disorder does not influence the transition temperature in dirty limit superconductors . very high disorders are required to drive the t@xmath7 to lower temperatures which are accompanied by a transition from superconducting state to insulating state at t@xmath7 @xcite . since , our system is a metallic and when vanadium is alloyed with the titanium , the t@xmath7 of the alloy increases , the origin of the observed fluctuation conductivity in ti@xmath0v@xmath1 may not be due to the disorder present in the alloy . however , in our alloy , the coherence length is about twice the unit cell . hence it is necessary to consider the effect of disorder on the superconducting properties . the transition from fluctuation conductivity region to condensate region ( @xmath35 = 0 ) in resistivity for ti@xmath0v@xmath1 takes place over a temperature width @xmath46 = 0.085 k centered on t@xmath7 = 7.06 k. this transition temperature width @xmath46 is very large when compared to the @xmath46 of nb and v which is about 0.001 - 0.01 k @xcite . the @xmath46 is estimated by extrapolating the derivative of temperature dependence of resistivity to zero from both side of t@xmath7 . within the landau theory of phase transitions @xcite , the transition broadening due to disorder is given by @xmath47 = ( dt@xmath7/dx ) ( @xmath30x@xmath2)@xmath48 where , ( @xmath30x@xmath2)@xmath48 is the root mean square ( rms ) fluctuation in the composition . for a a@xmath49b@xmath50 binary alloy , the average number of a and b atoms are @xmath51n and n@xmath52 respectively , where n = v@xmath7/@xmath53 is the number of atoms in the characteristic volume v@xmath7=(4/3)@xmath54(0)@xmath55 and @xmath53 is the mean atomic volume . if the alloy is taken to be ideally random , then the rms deviation in the number of b atom @xmath56(n@xmath52)@xmath48 and the rms deviation in the compositional variable , ( @xmath30x@xmath2)@xmath57 @xmath58 . for ti@xmath0v@xmath1 , @xmath59 1.108 x 10@xmath60 m@xmath55 , and v@xmath7 @xmath56 4.78 x 10@xmath61 m@xmath55 which leads to n @xmath56 3.93 x 10@xmath62 . the dt@xmath7/dx for ti - v alloys is about 0.05 k / at . , for v rich samples @xcite . then the @xmath30t@xmath7 due to disorder is about 16 mk which is distinctly small as compared to that observed experimentally . the transition broadening due to the fluctuation of atomic density @xcite is also observed to be negligibly small . hence , we believe that the disorder is not the origin for the observed physical properties viz . , \1 . the increase in t@xmath7 when ti content is increased from zero to 40 at . % in v. \2 . the presence of fluctuation conductivity and superconducting origin of magneto resistance above t@xmath7 . in order to understand the origin of these superconducting properties , we have performed a detailed study on the normal state properties of the ti@xmath0v@xmath1 alloy , which is presented below . figure 5(a ) shows the temperature dependence of dc susceptibility @xmath63 of ti@xmath0v@xmath1 alloy in the temperature range of 10 - 300 k measured using squid magnetometer in an applied magnetic field of 1 t. the data is corrected for background signal . the dc susceptibility is defined as the ratio of measured magnetization ( m ) and applied magnetic field ( h ) . as the temperature decreases below 300 k , the @xmath63(t ) decreases down to about 30 k before showing an upturn at still lower temperature . the isothermal field dependence of magnetization at 10 k measured with background correction using squid magnetometer up to 7 t is shown in fig . 5(b ) . the isothermal field dependence of magnetization at various temperatures t = 10 , 20 , 30 , 50 , 100 , 150 , 200 , 250 and 300 k is also measured up to 8 t using vibrating sample magnetometer . for the sake of clarity , we have provided such isothermal m v / s h curves at 10 , 30 and 300 k in fig . these curves does not show any indications of saturation even at 8 t. these curves rule out any predominant contribution from ferromagnetic impurities . since , the difference between m v / s h curves at various temperatures is not clearly seen in fig . 5(b ) , we have plotted the difference m(h , t ) - m(h , 300 k ) in the inset to fig . 5(b ) which clearly demonstrate the effect of temperature on the magnetic susceptibility . the susceptibility estimated as the high field slope of the isothermal m v / s h data at various temperatures normalized to that at 30 k is shown in the inset to the figure 5(a ) . for comparison we have also plotted the temperature dependence of @xmath63(t ) at 1 t ( measured with squid magnetometer ) normalized to that at 30 k. the increase in the dc susceptibility with temperature has been observed earlier in various 4d and 5d transition metals and rare earth and actinide based paramagnetic intermetallic compounds ( ref . @xcite and ref . @xcite and the references therein ) and mo@xmath8sb@xmath10 @xcite . the temperature dependence of susceptibility of such paramagnetic metals is observed to follow @xcite @xmath64 here t@xmath65 is a characteristic temperature which is related to the peak position t@xmath66 in temperature dependence of susceptibility as t@xmath66 = t@xmath65/@xmath67 with @xmath68 as natural logarithmic base , @xmath69 is a temperature independent constant . the solid red line in fig . 5(a ) show the fit using above equation ( 2 ) to the experimental @xmath63(t ) of the ti@xmath0v@xmath1 alloy along with a curie - weiss term for the low temperature upturn . this low temperature feature appears to be due to paramagnetic impurities ( such as other transition metal elements , oxygen , nitrogen and the oxides and nitrides of vanadium as well ) as in the case of vanadium @xcite . the values of the fitting parameters are as follows : @xmath63(0 ) = 4.92 x 10@xmath21 wba@xmath70m@xmath70 , @xmath69 = 3.88 x 10@xmath71 wba@xmath70m@xmath70k@xmath72 , t@xmath65 = 512 k. the errors in the parameters estimated are less than 10 % . figure 6 presents the resistivity of the ti@xmath0v@xmath1 alloy in the temperature range 5 - 300 k in zero magnetic field . at 300 k the electrical resistivity is about 105.5 @xmath73 m . the electrical resistivity decreases linearly down to 90 k. the decrease in resistivity is sharper when the temperature is lowered below t@xmath65 = 90 k. the residual resistivity @xmath74 is about 99 x 10@xmath75 @xmath73 m . the resistivity goes to zero below 7 k as the system becomes a superconductor . the inset to the fig . 6 shows the resistivity of ti@xmath0v@xmath1 plotted as a function of t@xmath2 . the resistivity in the temperature range 20 - 50 k is observed to be linear in t@xmath2 and can be expressed as @xmath35 ( x 10@xmath75 @xmath73 m ) = 98.98 + 5.05 x 10@xmath25 t@xmath2 . the error in the coefficients of linear fit is less than 0.1 % . however , the plot of ( @xmath35-@xmath74)/t@xmath2 as a function of t@xmath55 which shows a negative slope ( inset ( b ) ) indicating coefficient of t@xmath5 term in resistivity is negative @xcite . the estimated mean free path @xmath76 of the conduction electrons is estimated in the framework of free electron model as @xmath77 , where @xmath78 is the radius of sphere whose volume is equal to the volume per conduction electron , a@xmath79 is he bohr atomic radius and @xmath80 is the residual resistivity expressed in @xmath81-cm @xcite . in ti@xmath0v@xmath1 alloy , the mean free path estimated to be about 0.3 x 10@xmath82 m which is of the order of unit cell . in case of large residual resistivity values such as 99 x 10@xmath75 @xmath73 m , the estimation of the mean free path is not true as matthiessens rule is not valid @xcite . in such cases , the superconducting property can be used to estimate the mean free path @xcite . in the dirty limit superconductor , the coherence length is limited by the mean free path and hence @xmath83 . then the mean free path in this alloy is expected to be about 4.5 x 10@xmath82 m. according to mooij , short mean free path resulting from various scattering mechanism such as @xmath84 interaction , disorder , magnetic interaction etc . , is the reason for the small temperature variation of resistivity @xcite . the figure 7 shows the temperature dependence of the heat capacity c for ti@xmath0v@xmath1 in the temperature range 20 - 220 k. the fitted line represents the expression @xmath28 t + d(t/@xmath18 ) , where @xmath28 is the sommerfeld coefficient of electronic specific heat and d(t/@xmath18 ) is the debye specific heat for lattice . a good fitting to the experimental heat capacity curve is obtained only in the high temperature region ( 150 - 220 k ) . the value of @xmath28 and @xmath18 obtained as the fitting parameters are about 8.06(1 ) x 10@xmath29 j / mol k@xmath2 and 322.5(4 ) k respectively . the fitted @xmath28 t + d(t/@xmath18 ) curve deviates from the experimental curve below 105 k ( inset to the fig . 7 . ) . the figure 8 shows the c / t plotted as a function of t@xmath2 in the temperature range 7 - 45 k. a nonlinearity is observed in c / t with respect to t@xmath2 . such nonlinearity as well as the deviation from @xmath28 t + d(t/@xmath18 ) might originate from a finite temperature dependence of the debye temperature @xmath18 in a bcc structure @xcite . normally , the @xmath18 increases with decrease in temperature below 30 k , especially in case of bcc systems the values at low temperature increases more than that at room temperature @xcite . the variation of @xmath18 for elemental bcc vanadium in the temperature range 4.2 k to 300 k estimated by measuring elastic constants is about 403.8 k to 392.1 k which is about 3 % @xcite . in ti@xmath0v@xmath1 alloy we have observed that @xmath18 estimated from the low temperature fit is about 258 k which is quite low when compared to that estimated at high temperatures . hence , we believe that the origin of the difference between the experimentally observed heat capacity and the heat capacity estimated using @xmath28 t + d(t/@xmath18 ) is not due to the temperature variation of the @xmath18 . however , we have done the thermal expansion measurement to estimate the debye temperature @xcite as function of temperature @xcite . we have observed that the variation in @xmath18 with temperature in the range 30 - 300 k is about 7.5 % . hence , the deviation observed in heat capacity of ti@xmath0v@xmath1 from @xmath28 t + d(t/@xmath18 ) below 100 k is not due to variation in @xmath18 with temperature . the difference may also arise from the acoustic phonons which show peak structures in the phonon dispersion curves . these modes act as a einstein oscillators and hence , we have checked for contributions from einstein modes obtained from the phonon dispersion curve reported in literature for vanadium @xcite . we have observed that for any value of einstein temperature @xmath85 , the value of @xmath18 diverges during fitting . hence , it appears that the contribution to the heat capacity due to the einstein modes is negligible for the present system . by comparing our results with the literature we found that @xmath86 is observed to follow a temperature dependence such as dt@xmath55ln(t ) @xcite this is verified by the presence of linearity in @xmath87 as a function of lnt ( inset a to fig 8 . ) . whenever , t@xmath2 dependence in resistivity is observed , generally the kadowaki - woods relation is checked for its validity . the inset ( b ) to the figure 8 shows the kadowaki woods plot for ti@xmath0v@xmath1 along with several other spin fluctuations and heavy fermion systems . surprisingly , the kadowaki - woods relation is observed to be valid in our system . kadowaki and woods have empirically shown that the coefficient @xmath41 of t@xmath2 term in resistivity scales with the square of the coefficient @xmath28 of electronic specific heat for heavy fermions and spin - fluctuation systems @xcite . the proportionality constant ( kadowaki - woods ratio , a/@xmath88 ) is found to be about 1 x 10@xmath89-cm ( mol k / mj)@xmath2 @xcite . the coefficient a of the t@xmath2 term in resistivity for the present ti@xmath0v@xmath1 is estimated to be about 5.00(1 ) x 10@xmath90-cm /k2 ( inset to fig . 6 . ) . the ratio ( a/@xmath88 ) for ti@xmath0v@xmath1 is about 0.60(5 ) x 10@xmath91 @xmath81-cm ( mol k / mj)@xmath2 which is close to the proportionality constant obtained by kadowaki - woods. we summarize below the important observations made in the present set of experimental results on the normal state of ti@xmath0v@xmath1 alloy . the temperature dependence of dc susceptibility shows the characteristic `` temperature induced magnetic moment '' and follows @xmath63(t ) = @xmath63(0 ) -bt@xmath2 ln(t / t@xmath65 ) . the magnetization is linear in h. \3 . resistivity shows a t@xmath2 dependence at low temperatures . the coefficient of t@xmath5 term in resistivity is negative . there is an enhancement of sommerfeld coefficient of electronic specific heat @xmath28 . the excess heat capacity ( @xmath30 c = c - @xmath28 t - d(t/@xmath18 ) ) follows a dt@xmath55ln(t ) temperature dependence . kadowaki - woods relation is valid in this system . all these features together have been observed only in pauli enhanced paramagnets such as rco@xmath13(r = y , sc , lu , etc . , ) @xcite , etc . , where the physical properties have been explained in terms of the existence of itinerant spin fluctuations . we argue that itinerant spin fluctuations may be present in the ti@xmath0v@xmath1 alloys as well . we now present a model based on the existence of itinerant spin fluctuations in the ti@xmath0v@xmath1 alloy and show that the observed superconducting properties of the alloy can be explained in this picture . in our understanding , the characteristic temperature t@xmath65 = 90 k observed in resistivity is the spin fluctuation temperature t@xmath92 @xcite . it has been shown by frings and franse that the t@xmath92 may be identified as the temperature at which the second derivative of the susceptibility with respect to temperature is zero @xcite . in the present ti@xmath0v@xmath1 alloy , the second derivative of susceptibility goes to zero at t@xmath93 120 k. the t@xmath92 estimated from the straight line fit to data @xmath87 v / s lnt is about 53 k. however , t@xmath92 estimated by resistivity , dc susceptibility and heat capacity are in the same order of magnitude . variation of t@xmath92 among various experiments to about 2t@xmath92 is not uncommon , and is often found in literature @xcite . the presence of spin fluctuations in a material can be characterized through the stoner enhancement factor @xcite . the stoner enhancement factor s is defined as @xmath63(0)/@xmath94 where @xmath63(0 ) is the experimentally observed susceptibility and @xmath94 is the susceptibility due to density of states @xcite . the @xmath94 ( dimensionless ) is given as ( 3/2)@xmath95 = 3@xmath96 where @xmath97 is the permittivity of the free space , @xmath98 is the bohr magneton , @xmath99 is the free electron density , @xmath100 is the fermi energy , and @xmath101 is the boltzmann constant @xcite . the value of s for strong spin fluctuating systems like pd or pt is about 6 @xcite where as the value of s for superconducting nb or v is about 2 @xcite . the value of @xmath94 for ti@xmath0v@xmath1 is about 1.57 x 10@xmath25 . then for ti@xmath0v@xmath1 the value of s = 2.5 , where experimentally observed @xmath63(0 ) = 3.92 x 10@xmath25 ( dimensionless ) . this value of s is similar to that of v and nb and is much less than that of metals like pt and pd @xcite . this is also similar to the value of s for mo@xmath8sb@xmath10 system @xcite . the sommerfeld coefficient of electronic heat capacity @xmath28 enhances due to the presence of spin fluctuations as @xmath28 = @xmath102 where @xmath103 is the sommerfeld coefficient of electronic heat capacity without spin fluctuations . our results suggest that the spin fluctuations are absent temperatures more than about 100 k. our fit to the heat capacity at temperatures above 100 k provided a value of @xmath28 to be about @xmath104 = 8.06 x 10@xmath29 j / molk@xmath2 whereas the low temperature fit provided a value of @xmath28 to be about @xmath1059.46 x 10@xmath29 j / molk@xmath2 . then the value of @xmath106 can be estimated as @xmath107 which turns out to be about 0.17 . the two major effects of the itinerant spin fluctuations on the superconducting properties in the ti@xmath0v@xmath1 alloy are : ( i ) the enhancement of superconducting transition temperature in ti@xmath0v@xmath1 with respect to vanadium , and ( ii ) the origin of the fluctuation conductivity above t@xmath7 and above h@xmath17 . these effects are discussed below : \(i ) the enhancement of superconducting transition temperature in ti@xmath0v@xmath1 with respect to vanadium : the itinerant spin - fluctuations are reported to be responsible for the absence of superconductivity in heavy transition elements such as palladium and platinum @xcite . the same formalism was used to suggest that the superconducting transition temperature t@xmath7 of elements such as nb and v is limited by spin - fluctuations @xcite . the spin fluctuation coupling constant @xmath106 in v is estimated to be about 0.34 @xcite . then , when non magnetic ti is alloyed with vanadium , there is a reduction in spin fluctuation , hence , t@xmath7 increases in spite of decrease in the free electron density . at very high content of ti , the t@xmath7 again starts decreasing when the effect of loss of free electron density wins over the effect of reduction of spin fluctuations . the value of 2 - 3 times t@xmath7 falls in the range of the superconducting transition temperatures of ti - v alloys calculated by estimating the electron - phonon coupling constant @xmath108 from band structure calculation ( which is about 12 - 20 k ) @xcite . hence , we can estimate the @xmath106 for ti@xmath0v@xmath1 by considering the suppression of t@xmath7 from the theoretical limit ( in absence of spin fluctuations ) of about 14.3 k to the experimentally observed value of 7.15 k ( in presence of spin fluctuations ) as described below . daams et al have shown that the properties of superconductors with spin fluctuations can be scaled to that of a superconductor without spin fluctuation by introducing the renormalized parameters @xmath109 and @xmath110 @xcite . in this formalism , the superconducting transition temperature is given by the modified mcmillan formula @xcite as @xmath111 where @xmath112(1+@xmath113 and @xmath114 . here , @xmath115 is the coulomb coupling constant and @xmath106 is the electron - spin fluctuation coupling constant . using this formalism , the @xmath108 and @xmath106 for ti@xmath0v@xmath1 are estimated to be about 0.85 and 0.081 respectively . the value of @xmath106 estimated in this way is in agreement with that estimated from the enhancement of @xmath28 at low temperatures . the value of @xmath115 is taken to be 0.1 @xcite . the other parameters @xmath109 and @xmath110 were estimated to be 0.79 and 0.17 respectively . these values are used to analyze temperature dependence of h@xmath17 on the basis of formalism by orlando et al @xcite . the solid line in the fig . 3b . , shows the temperature dependence of h@xmath17 estimated in this manner @xcite . the spin - orbit interaction parameter @xmath116 is estimated to be about 0.3 . \(ii ) the origin of the fluctuation conductivity above t@xmath7 and above h@xmath17 : when vanadium is diluted with the titanium without changing the bcc structure , the spin fluctuations become inhomogeneous in space due to the spatial disorder in vanadium sublattice . in such a case electron spin - fluctuation coupling constant @xmath106 is expected to vary in space over the sample volume . this is similar to the disordered kondo lattice with spatial distribution of kondo temperatures t@xmath117 s @xcite leading to inhomogeneous short range conduction electron polarization which in turn results in the itinerant spin fluctuations . since , the mobility of the conduction electrons are large , the life time of these spin fluctuations decreases leading to the small spin fluctuation coupling constant @xmath106 of about 0.081 in the ti@xmath0v@xmath1 alloy . our conjecture about the itinerant nature of the spin fluctuations is also supported by the fact that there is no significant magnetic field dependence of physical properties above 20 k , where the signature of the existence of spin fluctuations are observed in the ti@xmath0v@xmath1 alloy @xcite . since the itinerant spin fluctuations are weakly dependent on the magnetic field , the @xmath118 dependence of the ( negative ) magneto - resistance is absent in ti@xmath0v@xmath1 .

the temperature dependence of resistivity follows a t behaviour in the range 20 - 50 k. on the other hand , a term lnt is needed in the expression containing the electronic and lattice heat capacities to explain the temperature dependence of heat capacity at temperatures where dependence of resistivity is observed . further experimental evidence for the spin fluctuations is obtained in the form of a negative value of t term in the temperature dependence of resistivity . the influence of spin - fluctuations on the superconducting properties of tiv is discussed in detail .

we report experimental studies of the temperature and magnetic field dependence of resistivity and dc magnetic susceptibility and the temperature dependence of zero field heat capacity in a tiv alloy . the temperature dependence of the normal state dc magnetic susceptibility in this tiv alloy shows tlnt behavior . the temperature dependence of resistivity follows a t behaviour in the range 20 - 50 k. on the other hand , a term lnt is needed in the expression containing the electronic and lattice heat capacities to explain the temperature dependence of heat capacity at temperatures where dependence of resistivity is observed . such temperature dependence of dc magnetic susceptibility , resistivity and heat capacity are indications of the presence of spin - fluctuations in the system . further experimental evidence for the spin fluctuations is obtained in the form of a negative value of t term in the temperature dependence of resistivity . the influence of spin - fluctuations on the superconducting properties of tiv is discussed in detail . we show from our analysis of resistivity and the susceptibility in normal and superconducting states that the spin fluctuations present in tiv alloy are itinerant in nature . there is some evidence of the existence of preformed cooper - pairs in the temperature range well above the superconducting transition temperature . our study indicates that the interesting correlations between spin - fluctuations and superconductivity may actually be quite widespread amongst the superconducting materials , and not necessarily be confined only to certain classes of exotic compounds . _ keywords _ : alloy superconductor , spin fluctuations , electrical conductivity , magnetization , heat capacity

1208.0181

i

the temperature and magnetic field dependent dc magnetic susceptibility and electrical resistivity and the zero field heat capacity of ti@xmath0v@xmath1 have been analyzed in a quantitative manner . these results provide some experimental evidences of the presence of spin - fluctuations in this alloy system . the kadowaki - woods scaling is shown to be valid for the ti@xmath0v@xmath1 alloy . we have argued that the spin fluctuations present in ti@xmath0v@xmath1 alloy are itinerant in nature . the onset of superconductivity is suppressed in ti@xmath0v@xmath1 from its expected theoretical limit due to the presence of such spin - fluctuations while the distribution of @xmath106 induces the superconducting fluctuation above t@xmath7 . there are some indications based on the present study of the existence of preformed cooper - pairs in the temperature range well above the superconducting transition temperature . the present study suggests that the interesting correlations between spin - fluctuations and superconductivity may not necessarily be the properties of only certain classes of exotic compounds . relatively simple alloy systems like ti@xmath0v@xmath1 shows such interesting correlations . a complete understanding of the normal state and superconducting properties of this technologically important alloy system ti - v would help in tuning its properties for suitable technological applications .

we report experimental studies of the temperature and magnetic field dependence of resistivity and dc magnetic susceptibility and the temperature dependence of zero field heat capacity in a tiv alloy . we show from our analysis of resistivity and the susceptibility in normal and superconducting states that the spin fluctuations present in tiv alloy are itinerant in nature . there is some evidence of the existence of preformed cooper - pairs in the temperature range well above the superconducting transition temperature . our study indicates that the interesting correlations between spin - fluctuations and superconductivity may actually be quite widespread amongst the superconducting materials , and not necessarily be confined only to certain classes of exotic compounds .

we report experimental studies of the temperature and magnetic field dependence of resistivity and dc magnetic susceptibility and the temperature dependence of zero field heat capacity in a tiv alloy . the temperature dependence of the normal state dc magnetic susceptibility in this tiv alloy shows tlnt behavior . the temperature dependence of resistivity follows a t behaviour in the range 20 - 50 k. on the other hand , a term lnt is needed in the expression containing the electronic and lattice heat capacities to explain the temperature dependence of heat capacity at temperatures where dependence of resistivity is observed . such temperature dependence of dc magnetic susceptibility , resistivity and heat capacity are indications of the presence of spin - fluctuations in the system . further experimental evidence for the spin fluctuations is obtained in the form of a negative value of t term in the temperature dependence of resistivity . the influence of spin - fluctuations on the superconducting properties of tiv is discussed in detail . we show from our analysis of resistivity and the susceptibility in normal and superconducting states that the spin fluctuations present in tiv alloy are itinerant in nature . there is some evidence of the existence of preformed cooper - pairs in the temperature range well above the superconducting transition temperature . our study indicates that the interesting correlations between spin - fluctuations and superconductivity may actually be quite widespread amongst the superconducting materials , and not necessarily be confined only to certain classes of exotic compounds . _ keywords _ : alloy superconductor , spin fluctuations , electrical conductivity , magnetization , heat capacity

0906.4885

c

one of the most important questions concerning coronal lines in agn is the excitation mechanism that drives their emission . here we discuss whether photoionization or shock ionization can account for the locations and strengths of the coronal line emission in ngc 1068 . a summary is provided at the end of this section . @xcite carried out a number of illustrative photoionization simulations in an effort to identify the optimal conditions and locations in which the coronal lines form around agn . assuming ultraviolet radiation from the central engine as the only excitation mechanism and plane - parallel , constant density slabs of gas , they determined the distances from the ionizing source in which the lines are emitted as a function of density . they provide line equivalent widths in the density - distance plane , indicating where the bulk of the emission occurs for each line , and allowing rough comparisons between observed and predicted emission line flux ratios . the [ alvi ] , [ ar vi ] and [ siix ] lines observed here are included in their calculations . their figures assume an ionizing ultraviolet continuum similar to that of a typical seyfert galaxy with @xmath38 ergs@xmath4 , but distances scale as @xmath39 . @xcite and @xcite estimate ionizing luminosities 12 orders of magnitude higher in ngc 1068 . in the discussion below we assume an ionizing luminosity of 10@xmath40 ergs@xmath4 , which implies locations and dimensions of the emission regions are five times larger than those shown by @xcite , if all other parameters remain constant . the model then predicts that the distance and density for peak [ siix ] line emission cover 1.5100 pc and 10@xmath4110@xmath42 @xmath29 , respectively ( with the largest distances corresponding to the lowest densities ) . the observed distance of 20 pc ( 0.3 ) from the nucleus to the peak line emission corresponds to @xmath43@xmath110@xmath44 @xmath29 ) . if the actual peak is closer to the agn than observed but obscured by dust , then higher density gas would be required . for the [ alvi ] and [ arvi ] lines the adjusted @xcite models predict distances to the peak of roughly 15400 pc for the same density range . although the spatial distribution of the [ arvi ] line flux is less precise than the other lines , it appears to be similar to that of the other two lines , with a peak at the same location . clearly the observation that the offset from the agn to the peaks of these lines of with widely varying excitations are the same is incompatible with an ionized medium of uniform density , unless the extinction is highly non - uniform across the nucleus . the current observations can be roughly reconciled with a slab of density several times 10@xmath44 @xmath29 if there is increasing extinction of the coronal line emission closer to agn , of sufficient strength to mask the true peak of the [ siix ] line emission . if the coronal line emission region is symmetrically distributed to the north and south of the agn , the extinction would need increase further to the south of the agn in order to block the line emission there from view . evidence for higher extinction to the south is in fact widespread ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) . a rough lower limit to the additional extinction required to the south based on the assumption of a symmetric distribution of coronal line emission is two magnitudes at 3.93 @xmath0 m , which corresponds to approximately 70 visual magnitudes . if the highly non - uniform extinction postulated above is not present , only a density distribution of ionized gas strongly peaked 20 pc north of the agn could result in photoionization producing the observed maximum line emission from all of these ions at the same location . the calculations of @xcite also indicate that for these ions the regions of significant coronal line emission can extend to much larger distances ( @xmath1100 pc ) if gas densities decrease gradually with distance from the agn . the near agreement of our estimates of the total flux from the [ siix ] and [ arvi ] lines with measurements made by others in much larger apertures , imply that the ionized gas density must drop steeply at distance greater than @xmath150 pc from the agn . evidence supporting shock ionization in the narrow line regions of agns abounds @xcite . in the case of ngc 1068 , @xcite found that 1.5 north of the nucleus [ fe vii ] is enhanced at the location of the radio jet . they interpreted this as evidence of interaction between the jet and the surrounding medium . the radio jet proceeds outward from the nucleus for an angular distance of several arc - seconds , first nearly due north and then at position angle 35 degrees @xcite . more recently , @xcite and @xcite have studied the influence of the radio jet on the kinematics of [ o iii ] @xmath454959,5007 . they observed an increase in the radial velocity roughly proportional to distance from the nucleus followed by a linear decrease beyond @xmath1100 pc ( 1.4 ) and concluded that the magnitudes of these changes were so large that the neither can the jet be the sole driving force nor can gravity be the sole decelerating mechanism ( frictional forces must be significant ) . however , in the case of that line the deceleration occurs well outside of the region where we observe the higher excitation 35 @xmath0 m coronal lines . the line emission reported here originates in ionized regions much closer to the nucleus than those observed by @xcite and @xcite . nevertheless , evidence for shock excitation of the coronal lines is also readily apparent when one compares the 5 ghz image in fig . 1 of @xcite with our data . assuming , as they and @xcite have inferred , that source s1 is coincident with the agn , and hence with the infrared continuum peak , the peaks of [ siix ] and [ alvi ] line emission at 0.3 north are coincident with the bright radio knot c , where the jet bends to the northeast . this is highly suggestive of an interaction between the jet and gas in the nlr . also suggestive of an interaction at this location is a bright knot of h@xmath46 2.12 @xmath0 m line emission found by @xcite connecting two streamers of line emission , one of which they interpret as feeding the innermost few parsecs . the velocity profiles of the of [ siix ] line along the spatial direction , shown in figure [ fig : velocity ] , also appear to support a jet - nlr interaction . at 0.2@xmath47 north , a prominent blue shoulder is evident in the line profile . that structure also appears to be present 0.4 north , but it weakens significantly at 0.6 . the shoulder at 0.20.4 could be associated with ionized gas accelerated toward us by the interaction of the jet with the ambient gas near knot c. the line profile variations are somewhat reminiscent of the behavior of the [ fevii ] @xmath366087 line reported by @xcite , but the latter is at a much larger distance north of the agn and , also unlike the infrared lines , far from where that line has its peak intensity . if shocks are the dominant excitation mechanism for these coronal lines at radio knot c , then it seems likely that some of the remaining [ siix ] and [ alvi ] line flux outside of that knot originates in other localized regions and is associated with other radio knots . the knot labeled `` ne '' in fig . 1 of @xcite , located 0.4@xmath47 to the ne of knot `` c '' and not included in our slit , is a possible candidate for some of this missing line flux . however , judging from the large extent over which [ sivii ] was observed by @xcite , we do not think that shocks totally dominate over photoionization , and expect that some contribution of the latter is present , perhaps even at radio knot c. the infrared coronal line emission peaks 20 pc to the north of the agn for ions of a wide range of excitation , and extends to 50 pc in the highly excited [ siix ] line and presumably at least as far in the other lines . to the south there is no clear detection of any of the 35 @xmath0 m lines . increased extinction to the south can account for the north - south asymmetry , regardless of the line excitation mechanism . however , photoionization by the agn producing peaks at equal northern distances from the agn for such a large range of excitations requires a highly asymmetric gas distribution and/or a highly asymmetric distribution of obscuring dust to the north . this explanation appears contrived . evidence for collisional excitation of these lines is more compelling ; it consists of the spatial coincidence between radio knot c ( where the jet changes direction ) , a prominent knot of h@xmath46 line emission , and the emission peaks of all of the 35 @xmath0 m coronal lines . the presence at the same location of a localized prominent high velocity blue - shifted shoulder on the [ siix ] line provides further support . higher angular resolution studies of the coronal line emission would allow a more detailed comparison with the morphology of the radio emission . in his subsection we discuss that portion of the interstellar medium producing the hydrocarbon and silicate absorption features at 3.4 @xmath0 m and 9.7 @xmath0 m , but little or no absorption by gaseous co at 4.55.0 @xmath0 m . our discussion makes use of the silicate absorption feature as reported by @xcite ; its similar behavior across the nucleus as the 3.4 @xmath0 m feature provides a strong clue as to the nature of the interstellar medium . the subsection on co examines a number of possible explanations for its absence , and results in a similar conclusion regarding the ism . a summary is provided at the end of this section . it is important to note that in the direction along the ( ns ) slit the continuum source was partially resolved at ukirt and therefore we are assured that it has a characteristic dimension of a few tens of parsecs . thus the bulk of the material producing the 3.4 @xmath0 m absorption feature and not producing co absorption lies 10 pc or more from the central engine . dust and gas in the central few parsecs can only be a minor contributor to the present spectrum and our arguments as to the nature of the interstellar medium therefore apply to the more extended region and not to the core " or the innermost region of the torus observed via interferometry . the spectral profile of the 3.4 @xmath0 m feature is well characterized in the current data . overall the profile is smooth , showing only the two principal sub - features seen in galactic sources , those at 3.420 @xmath0 m and 3.485 @xmath0 m . the profile in ngc 1068 contains no evidence of a distinct 3.385 @xmath0 m sub - feature , which is sometimes present in galactic sources and sometimes blended with the 3.420 @xmath0 m feature @xcite . the data also reveal that the depth of the 3.4 @xmath0 m feature has a similar north - south variation across the nucleus as the 9.7 @xmath0 m silicate absorption ( fig . [ fig : chsil ] ) . both features are at maximum depth on and just to the south of the nucleus . the similarity is also quantitative ; the fractional increase in the depth of each feature at its maximum compared to the depth at adjacent locations is @xmath140 percent . _ this indicates that the carriers of the features are significantly mixed . _ the compactness and nuclear location of the region of enhanced 3.4 @xmath0 m and silicate extinction suggests that the extra absorption to the south occurs quite close to the nucleus . in the silicate feature the weaker off - nuclear absorption extends over 2 to the north and south . because the 3 @xmath0 m continuum source is much more compact , the depth of the 3.4 @xmath0 m feature could not be measured more than 0.4 distant from the nucleus . the lower level and more extended silicate feature largely arises in a circumnuclear region of much larger dimensions than the torus - like structures seen with mid - ir interferometry . it may be associated with material in the disk of the host galaxy , which crosses the line of sight south of the nucleus . the distinction between these two regions is not necessarily sharp @xcite . the ratio of the optical depths of the 3.4 @xmath0 m and silicate features at the infrared continuum peak of ngc 1068 is 0.19 @xmath15 0.02 . in the galaxy the silicate feature is found in both diffuse and dense interstellar clouds , whereas the hydrocarbon feature is found only in diffuse clouds . in diffuse clouds far from the galactic center the ratio of optical depths of the two features can be derived from their optical depths relative to @xmath48 , @xmath48/@xmath49 @xmath50 18.5 @xcite and @xmath48/@xmath51 @xmath50 250 @xcite , yielding @xmath52@xmath53@xmath49 = 0.07 @xmath15 0.01 , a value roughly forty percent of that measured in ngc 1068 . toward the galactic center , where @xmath48 @xmath50 30 mag ) , the value of @xmath52/@xmath49 averaged over sources observed by both @xcite and @xcite is 0.064 @xmath15 0.017 , the same as the above value to within the uncertainties . the ratio _ in just the diffuse gas on the galactic center sightline _ may be estimated as follows . @xcite find @xmath48/@xmath52 = 156 @xmath1516 and @xcite find @xmath49 = 3.6 @xmath15 0.3 . however , one - third of the visual extinction to the galactic center is believed to occur in dense clouds , located mostly in intervening spiral arms @xcite . following @xcite , for values of @xmath48@xmath2212 mag the ratio of visual extinction to silicate optical depth is the same in dense clouds as in diffuse clouds , and thus we associate those 10 mag of dense cloud visual extinction with a silicate optical depth of 0.54 . this gives @xmath52/@xmath49 @xmath50 0.23/3.06 = 0.075 for galactic center diffuse clouds , again far less than the ratio toward the nucleus of ngc 1068 . even if half of the silicate optical depth toward the galactic center arises in the dense clouds in the galactic disk , the above ratio would only be 0.15 , less than the value in ngc 1068 . clearly then , the 3.4 @xmath0 m absorption in ngc 1068 is unusually strong relative to the silicate absorption . this can not be explained away by placing the 3.4 @xmath0 m absorber in a more remote location than the silicate feature , because even in galactic diffuse clouds the optical depth of 0.08 observed in ngc 1068 , corresponds to a silicate optical depth @xmath541 , significantly larger than is observed . the high ratio could be the result of the silicate absorption being significantly filled in , as might arise if thermal emission close to the agn were absorbed in the cooler outer portions of the source . because such filling in would be much less for the 3.4 @xmath0 m feature , the similar variation in optical depths of the features across the nucleus tends to argue that this is not the entire explanation , however . as suggested by @xcite , the high ratio could be explained , at least in part , by the typical continuum surface at 3.4 @xmath0 m lying interior to the typical surface at 9.7 @xmath0 m such that the added pathlength , unobservable at 9.7 @xmath0 m , contains a significant fraction of the observed column density of the 3.4 @xmath0 m absorber . the result also could be a consequence of either unusual elemental abundances or the chemistry of the dust in the vicinity of the agn . the co fundamental band has been searched for previously without success in ngc 1068 at spectral resolutions ranging from 20 km s@xmath4 to 250 km s@xmath4 @xcite . the current data , obtained at 150 km s@xmath4 resolution , significantly tightens the limit on absorption by co in the warm and presumably rapidly moving gas just outside of the 35 @xmath0 m continuum - emitting dust , whose fwhm along the ionization cones is @xmath120 pc . in its lack of detectable co in this band ngc 1068 is similar to the five other type 2 seyferts studied by @xcite , although the limits on co absorption in those galaxies are considerably less strict . we consider three possible explanations for the lack of strong co absorption lines toward the agn in ngc 1068 : ( 1 ) the molecules are distributed among many rotational states ; ( 2 ) the molecules reside in a clumpy obscuring medium ; and ( 3 ) there is a paucity of dense cloud " molecular gas in front of the agn . to explain the non - detection of transitions of co , oh and h@xmath46co lines from low rotational levels towards the highly obscured nucleus of cygnus a at radio wavelengths , it has been pointed out that at the temperatures of the nuclear clouds the lowest rotational levels may contain only a small fraction of the molecules @xcite . for example , in lte at 300 k roughly twenty rotational levels of co have populations within a factor of ten of that of the most populated level , whereas at 25 k only the six lowest levels are so highly populated . it also has been suggested by these authors that under some circumstances a strong and compact nuclear radio source could redistribute the rotational level populations in the surrounding gas , further weakening the strengths of lines from the low rotational levels . @xcite find this explanation unlikely , however , because the 19% of their sources in which high - excitation oh lines are detected also show absorption from the ground state transition . in the case of ngc 1068 , whose 35 @xmath0 m continuum - emitting dust , and presumably the gas associated with this dust , are at temperatures of several hundred kelvins , the lte fractional populations in the low lying levels normally observed at radio and millimeter wavelengths would be much less than in galactic dense clouds . this can not be the explanation for the non - detection of the co fundamental band lines , however , as the @xmath13 band spectrum in fig . [ fig : spectrum ] encompasses lines with a wide range of lower state energies ( corresponding to @xmath26 = 130 in the case of the p branch ) . the second possibility is that , although there is a large amount of molecular material along the line of sight to the nuclear continuum source , it is concentrated into clumps that cover only a small fraction of the source . each individual clump produces deep co lines but as most of the continuum source is unobscured , the net effect is much weaker co absorption . such small cloud volume filling factors have been invoked in order to explain the mid - infrared observational properties of seyfert 1 and seyfert 2 galaxies in the unified model ( in particular the lack of silicate emission in the former and the broad spectral range of the far - infrared continuum ; * ? ? ? small filling factors for toroids surrounding agns are also predicted by the hydrodynamic simulations of @xcite . if the detectability of co absorption is related to the cloud filling factor , then for similar total extinction co should be detected in objects with smooth obscuration ( i.e. , covering the entire nuclear continuum source ) , but not in those with clumpy obscuration . @xcite propose that clumpy and smooth obscuration in agn can be separated on the basis of the strength of the 10 and 18 @xmath0 m silicate features . strong co absorption , in gas that is warm and presumably close to the nuclear source , has been detected in several agn - hosting ultraluminous infrared galaxies ( ulirgs ) @xcite , whose silicate features would classify their dust distribution as smooth , whereas in the single seyfert 2 ulirg whose spectrum would classify it as clumpy , only a weak co band has been tentatively detected @xcite . this may suggest that the strength of the molecular absorption in agn is indeed governed by the clumpiness of the obscuring medium , but a stringent test of this hypothesis will require a larger sample of objects spanning a wide range of dust geometries . nevertheless , the presence in ngc 1068 of the 3.4 @xmath0 m feature , whose spatial behavior suggests that much of it arises in the same gas as much of the silicate feature , close to the agn , raises immediate complications with the clumpy model . that model has the dust and gas local to the agn residing in dense clouds with a small filling factor , so that the silicate absorption , which is strong in each clump , is both diluted and filled in by emission @xcite . the co absorption lines would also be diluted by this arrangement , apparently to undetectability in the case of ngc 1068 . however , the absence of the 3.4 @xmath0 m band in galactic dense molecular clouds suggests that in ngc 1068 the carrier of that band would not reside in such clumps , and thus that a second , more diffuse medium is needed for it ( ignoring , for the moment the evidence that the carriers of the two dust features are mixed ) . the diffuse material could , for example , be a low - density interclump medium . however , the 3.4 @xmath0 m band in galactic diffuse clouds is invariably accompanied by a silicate absorption feature . as pointed out earlier , the previously estimated value of @xmath52/@xmath49 in the diffuse interstellar medium toward the galactic center , when applied to ngc 1068 , implies that most or all of silicate absorption in ngc 1068 must arise in that material carrying the 3.4 @xmath0 m band . the by now almost inevitable solution to these problems is the third explanation : at 313 @xmath0 m essentially all of the absorbing material in the line of sight has the chemical characteristics of galactic diffuse clouds . in this explanation clumpy absorbing material is not needed to account for the lack of detectable co , because in diffuse clouds co is mostly dissociated , comprising only one percent of the carbon . diffuse clouds do have large molecular components , with h@xmath5 accounting for typically half of the hydrogen ; thus h@xmath5 should be available to provide the line emission observed by @xcite . the dust grains in diffuse clouds are comprised of a refractory component responsible for the 3.4 @xmath0 m feature and a silicate component . gas densities in galactic diffuse clouds are 101000 @xmath29 . densities in the inner few tens of parsecs of ngc 1068 might be greater than this . however , at distances of only a few tens of parsecs from a luminous agn it may well be possible that somewhat denser gas also has the above characteristics . as discussed earlier , in the galaxy fairly tight relationships have been found between the visual extinction in the diffuse ism and the depth of the 3.4 @xmath0 m feature @xcite for sightlines to the galactic center and to local diffuse clouds . here we employ the former relationship , @xmath48/@xmath52 = 150 . using it we estimate a typical visual extinction of 12 mag to the 3.4 @xmath0 m continuum - emitting region , implying for a normal gas - to - dust ratio that @xmath55(h ) = 2.3 @xmath6 10@xmath7 @xmath8 . then , assuming that , as in galactic diffuse clouds , one percent of the carbon is in co , and also ( conservatively ) that the typical continuum surface at 3.4 @xmath0 m and 4.7 @xmath0 m are at the same depth , @xmath55(co ) = 6 @xmath6 10@xmath56 @xmath8 , which is consistent with the upper limit of @xmath57 10@xmath28 @xmath8 set by these observations . the above column density of hydrogen is much less than the column density that attenuates our view of the central engine , @xmath55(h ) @xmath14 10@xmath58 @xmath8 @xcite , but much of that gas must be interior to the dust that is emitting the observed 35 @xmath0 m continuum . we have found that the 3.4 @xmath0 m hydrocarbon and 9.7 @xmath0 m silicate bands have spatial variations that are similar across the central 0.2 @xmath6 0.8 arcsecond of ngc 1068 and that only a small fraction of interstellar carbon in this region can be in the form of co. the first finding indicates that the carriers of the 3.4 @xmath0 m and 9.7 @xmath0 m bands are largely mixed and that significant fractions of each are located in material very close to the nucleus . in the galaxy both features are present in diffuse interstellar clouds , but the 3.4 @xmath0 m band is _ only _ observed there . the fraction of co in diffuse clouds is small and our observed upper limit in ngc 1068 is consistent with such a location . measurable co absorption would be present if even a modest fraction of the silicate absorption arose in fully molecular material . the straightforward conclusion is that _ the 3 - 13 @xmath0 m absorption spectrum of ngc 1068 is produced in material chemically similar to the galactic diffuse interstellar medium . _ we reiterate the significance of the lack of detection of co and its incompatibility with models employing clumps of _ dense molecular _ material , even if such material near an agn is capable of producing the 3.4 @xmath0 m feature . if the filling factor of such fully molecular clumps were low enough to dilute " the co band to non - detection , as observed , similar dilutions would occur for the silicate and 3.4 @xmath0 m absorptions , contradicting the observations . the adaptive optics measurements of @xcite show that nuclear thermal infrared continuum arises in part from numerous clumps covering a few tens of parsecs . if the source of the 3 - 13 @xmath0 m continuum is dominated by such clumps , then absorbing material could either be located on surfaces of the clumps or be more continuously distributed in front of them . however , if a significant portion of the continuum is emitted by an extended component , the present observations constrain the degree of clumpiness in the absorbing material . in that case a low , e.g. @xmath220.1 , filling factor for the absorbing clumps probably would be inconsistent with the observed strength of the 3.4 @xmath0 m feature , as it would imply , e.g. , @xmath59(3.4 @xmath0 m ) @xmath14 0.8 in the clumps . the maximum observed optical depth of the feature is 0.5 , in the deeply buried ulirg iras 08572 + 3915 @xcite .

four coronal lines of widely different excitations were detected ; the intensity of each peaks near radio knot c , approximately 0.3 north of the infrared continuum peak , where the radio jet changes direction . a new and tighter limit is set on the column density of co. although clumpy models of the dust screen might explain the shallowness of the silicate feature , the presence of the 3.4 m feature and the absence of co are strongly reminiscent of galactic diffuse cloud environments and a consistent explanation for them and the observed silicate feature is found if all three phenomena occur in such an environment , existing as close as 10 pc to the central engine .

we report moderate resolution 3 - 5 m spectroscopy of the nucleus of ngc 1068 obtained at 0.3 ( 20 pc ) resolution with the spectrograph slit aligned approximately along the ionization cones of the agn . the deconvolved fwhm of the nuclear continuum source in this direction is 0.3 . four coronal lines of widely different excitations were detected ; the intensity of each peaks near radio knot c , approximately 0.3 north of the infrared continuum peak , where the radio jet changes direction . together with the broadened line profiles observed near that location , this suggests that shock - ionization is the dominant excitation mechanism of the coronal lines . the depth of the 3.4 m hydrocarbon absorption is maximum at and just south of the continuum peak , similar to the 10 m silicate absorption . that and the similar and rapid variations of the optical depths of both features across the nucleus suggest that substantial portions of both arise in a dusty environment just in front of the continuum source(s ) . a new and tighter limit is set on the column density of co. although clumpy models of the dust screen might explain the shallowness of the silicate feature , the presence of the 3.4 m feature and the absence of co are strongly reminiscent of galactic diffuse cloud environments and a consistent explanation for them and the observed silicate feature is found if all three phenomena occur in such an environment , existing as close as 10 pc to the central engine .

astro-ph9907378

c

our hst _ wide field and planetary camera 2 _ and _ near infrared and multi object spectrograph _ observations of centaurus a ( ngc 5128 ) have provided several new insights about the active galactic nucleus . detection of unresolved emission in both visible light and near - ir suggests that two different emission mechanisms are required : a non - thermal component which represents an extrapolation of the x - ray power law , reddened by @xmath0 ( consistent with mid - ir and x - ray estimates ) , and a thermal component probably caused by emission from hot dust within 2pc of the nucleus . these results are in agreement with previous suggestions that centaurus a harbors a misaligned bl lac nucleus . we have shown that only variability on time scales shorter than @xmath116 months can unambiguously prove the existence of a non - thermal component in the near - ir . we have detected the 20pc - scale nuclear disk in the @xmath1$}}\lambda 1.64\mu$]m line which shows a morphology similar to that observed in with an / ratio typical of low ionization seyfert galaxies and liners . we do not see evidence for optical emission from , or star formation associated with , the radio / x ray jet . we do detect a blue linear structure , aligned with jet and extending from the nucleus to knot a , which we interpret as a region of relatively low reddening . this feature may represent a channel in which gas and dust have been swept away by the jet , consistent with simple energetic arguments . the data allow us to derive a map of dust extinction , e(b - v ) , in a 20@xmath320 circumnuclear region and reveal a several arcsecond long dust feature near but below the nucleus , oriented in a direction transverse to the large dust lane . this structure may be related to the bar observed with iso and scuba , as reported by mirabel et al . ( @xcite ) . we find rows of pa@xmath2 emission knots along the top and bottom edges of the bar , which we interpret as star formation regions , possibly caused by shocks driven into the gas . the inferred star formation rates are moderately high ( @xmath151m@xmath5 yr@xmath6 ) . if we hypothesize , with mirabel , that the bar represents a mechanism for transferring gas in to the center of the galaxy , then the large dust lane across the galaxy , the bar , the knots , and the inner pa@xmath2 disk previously reported in paper ii , all represent aspects of the feeding of the agn . gas and dust are supplied by a recent galaxy merger ; a several arcminute - scale bar allows the dissipation of angular momentum and infall of gas toward the center of the galaxy ; subsequent shocks trigger star formation ; and the gas eventually accretes onto the agn via the 20pc disk . reconstructing the radial light profile of the galaxy to within 01 of the nucleus by combining v , h and k measurements , corrected for reddening , shows that centaurus a has a core profile , according to the classification of faber et al . ( @xcite ) . using the models of van der marel ( @xcite ) , we estimate a black hole mass of @xmath8m@xmath5 , consistent with ground based kinematical measurements ( israel @xcite ) . this is consistent with the presence of a strong agn , as suggested by the large radio lobes , the jet , and the strong x - ray emission . it further suggests that the ionized gas disk seen in pa@xmath2 ( paper ii ) would have relatively high rotational velocities , of order 800 km / sec . planned high spatial resolution near - ir spectroscopy should be able to accurately determine the mass of the super - massive black hole in this nearest agn . a.m. acknowledge the partial support of the italian space agency ( asi ) through the grant ars98116/22 and of the italian ministry for university and research ( murst ) under grant cofin98 - 02 - 32 . a.m. and a.c . acknowledge support from the stsci visitor program . acknowledge support through go grants o0570/go-7267 and o0568/go-6578 from space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 526555 . we thank nino panagia , tino oliva , marco salvati , roberto maiolino and lucia pozzetti for helpful discussions which greatly improved this paper . we also thank felix mirabel and dave saunders for useful discussions and pre - publication access to the iso data . alonso - herrero a. , rieke m.j . , rieke g.h . , ruiz m. , 1997 apj , 482 , 747 athanassoula e. , 1992a mnras , 259 , 328 athanassoula e. , 1992b mnras , 259 , 345 axon d.j . , marconi a. , capetti a. , macchetto f.d . , schreier e.j . , robinson a. , 1998 , apj , 496 , l75 baade w. , minkowski r. , 1954 apj , 119 , 215 bahcall j.n . , kirhakos s. , saxe d.h . , schneider d.p . , 1997 apj , 479 , 642 bailey j. , sparks w.b . , hough j.h . , axon d.j . , 1986 nature , 32 , 150 balick b. , heckman t.m . , 1982 ara&a , 20 , 431 barnes j.e . , hernquist l. , 1992 ara&a , 30 , 705 barvainis r. , 1987 apj , 320 , 537 binney j. , tremaine s. , 1987 , `` galactic dynamics '' , princeton university press biretta j.a , et al . , 1996 , _ wfpc2 instrument handbook _ , version 4.0 ( baltimore : stsci ) bolton j.g . , stanley g.j . , slee o.b . , 1949 nature , 164 , 101 bowyer c.s . , lampton m. , mack j. , 1971 , apj , 161 , l1 burns j.o . , feigelson e.d . , schreier e.j . , 1983 apj , 273 , 128 bushouse h. , skinner c.j . , mackenty j.w . , 1997 , _ nicmos instrument sci . _ 97 - 28 ( baltimore : stsci ) capetti a. , axon d.j . , macchetto f.d . , 1997 apj , 487 , 560 cardelli j.a . , clayton g.c . , mathis j.s . , 1989 apj , 345 , 245 carollo c.m . , et al . , 1997 , apj , 481 , 710 clarke d.a . , burns j.o . , feigelson e.d . , 1986 apj , 300 , l41 clarke d.a . , burns j.o . , norman m.l . , 1992 apj , 395 , 444 de robertis m.m . , yee h.k.c . , hayhoe k. , 1998 apj , 496 , 93 dopita m.a . , et al . , 1997 , apj , 490 , 202 draine b.t . , lee h.m . , 1984 apj , 285 , 89 dufour r.j . , van den bergh s. , harvel c.a . , et al . , 1979 aj , 84 , 284 faber s.m . , tremaine s. , ajhar e.a . , et al . , 1997 aj , 114 , 1771 feigelson e.d . , schreier e.j . , delvaille j.p . , et al . , 1981 apj , 251 , 31 granato g.l . , danese l. , franceschini a. , 1997 apj , 486 , 147 gonzales delgado r.m . , leitherer c. , heckman t.m . , cervino m. , 1997 , apj , 483 , 705 gonzales delgado r.m . , heckman t.m . , leitherer c. , et al . , 1998 , apj , 505 , 174 graham j.a . , 1979 apj , 232 , 60 grindlay j.e . , schnopper h. , schreier e.j . , gursky h. , parsignault d.r . , 1975 , apj , 201 , l133 heckman t.m . , smith e.p . , baum s.a . , et al . , 1986 apj , 311 , 526 heckman t.m . , gonzales delgado r.m . , leitherer c. , et al . , 1997 , apj , 482 , 114 hernquist l. , mihos j.c . , 1995 apj , 448 , 41 hui x. , ford h.c . , ciardullo r. , jacoby g.h . , 1993 apj , 414 , 463 hunt l.k . , malkan m.a . , salvati m. , et al . , 1997 apjs , 108 , 229 israel f.p . , 1998 a&a rev . , 8 , 237 jones d.l . , tingay s.j . , murphy d.w . , et al . , 1996 apj , 466 , l63 kellogg e. , gursky h. , leong c. , schreier e. , tananbaum h. , giacconi r. , 1971 , apj , 165 , l49 lauer t.r . , ajhar e.a . , byun y .- i . , et al . , 1995 aj , 110 , 2622 leitherer c. , heckman t.m . , 1995 apjs , 96 , 9 lpine j.r.d . , braz m.a . , epchtein n. , 1984 a&a , 131 , 72 mackenty j.w . , et al . , 1997 , _ nicmos instrument handbook _ , version 2.0 ( baltimore : stsci ) magorrian j. , et al . , 1998 , aj , 115 , 2285 maiolino r. , ruiz m. , rieke g.h . , keller l.d . , 1995 apj , 446 , 561 maiolino r. , alonso - herrero a. , anders s. , et al . , 1999 apj , submitted malin d.f . , quinn p.j . , graham j.a . , 1983 apj , 272 , l5 mihos j.c . , hernquist l. , 1994 apj , 425 , l13 mihos j.c . , hernquist l. , 1996 apj , 464 , 641 mirabel i.f . , laurent o. , sanders d.b . , et al . , 1999 a&a , 341 , 667 moorwood a.f.m . , oliva e. , 1988 a&a , 203 , 278 morganti r. , robinson a. , fosbury r.a.e . , di serego alighieri s. , tadhunter c.n . , malin d.f . , 1991 mnras , 249 , 91 oliva e. , origlia l. , maiolino r. , moorwood a.f.m . , 1999 a&a , submitted packham c. , hough j.h . , young s. , et al . , 1996 mnras , 278 , 406 quillen a.c . , de zeeuw p.t . , phinney e.s . , phillips t.g . , 1992 apj , 391 , 121 quillen a.c . , graham j.r . , frogel j.a . , 1993 apj , 412 , 550 rieke g.h . , lebofsky m.j . , 1981 apj , 250 , 87 rodriguez - espinoza j.m . , rudy r.j . , jones b. , 1986 , apj , 309 , 76 rothschild r.e . , band d.l . , blanco p.r . , et al . , 1999 apj , 510 , 651 sanders d.b . , phinney e.s . , neugebauer g. , et al . , 1989 apj , 347 , 29 schreier e.j . , feigelson e. , delvaille j. , et al . , 1979 apj , 234 , l39 schreier e.j . , burns j.o . , feigelson e.d . , 1981 apj , 251 , 523 schreier e.j . , capetti a. , macchetto f. , sparks w.b . , ford h.j . , 1996 apj , 459 , 535 ( paper i ) schreier e.j . , marconi a. , axon d.j . , caon n. , macchetto d. , capetti a. , hough j.h . , young s. , packham c. , 1998 , apj , 499 , l143 ( paper ii ) simpson c. , meadows v. , 1998 apj , 505 , l99 steinle h. , bennett k. , bloemen h. , et al . , 1998 a&a , 330 , 97 toomre a. , toomre j. , 1972 apj , 178 , 623 turner p.c . , forrest w.j . , pipher j.l . , shure m.a . , 1992 apj , 393 , 648 van der marel r.p . , 1999 aj , 117 , 744 voit , m. , et al . , 1997 , _ hst data handbook - vol . i _ , version 3.0 ( baltimore : stsci ) walker i.r . , mihos j.c . , hernquist l. , 1996 apj , 460 , 121 weil m.l . , hernquist l. , 1993 apj , 405 , 142 whitmore b. , 1995 , in _ calibrating hst : post servicing mission _ , a. koratkar and c. leitherer ( eds . ) , baltimore stsci , p.269 wills b.j . , in `` quasars and cosmology '' , a.s.p . conference series ( 1999 ) , eds . g.ferland , j.baldwin ( san francisco : asp ) , in press ( astro - ph/9905093 )

we detect the active nucleus in the near ir ( k and h ) and , for the first time , in the optical ( i and v ) , deriving the spectral energy distribution of the nucleus from the radio to x - rays . the optical and part of the near - ir emission can be explained by the extrapolation of the x - ray power law reddened by , a value consistent with other independent estimates . the 20pc - scale nuclear disk discovered by schreier et al . ( ) is detected in the$}}\lambda 1.64\mu$]m line and presents a morphology similar to that observed in with a / ratio typical of low ionization seyfert galaxies and liners . nicmos 3 pa observations in a 50 circumnuclear region suggest enhanced star formation (m yr ) at the edges of the putative bar seen with iso , perhaps due to shocks driven into the gas . the light profile , reconstructed from v , h and k observations , shows that centaurus a has a core profile with a resolved break at and suggests a black hole mass ofm . a linear blue structure aligned with the radio / x ray jet may indicate a channel of relatively low reddening in which dust has been swept away by the jet .

we report new hst _ wfpc2 _ and _ nicmos _ observations of the center of the nearest radio galaxy centaurus a ( ngc 5128 ) and discuss their implications for our understanding of the active nucleus and jet . we detect the active nucleus in the near ir ( k and h ) and , for the first time , in the optical ( i and v ) , deriving the spectral energy distribution of the nucleus from the radio to x - rays . the optical and part of the near - ir emission can be explained by the extrapolation of the x - ray power law reddened by , a value consistent with other independent estimates . the 20pc - scale nuclear disk discovered by schreier et al . ( ) is detected in the$}}\lambda 1.64\mu$]m line and presents a morphology similar to that observed in with a / ratio typical of low ionization seyfert galaxies and liners . nicmos 3 pa observations in a 50 circumnuclear region suggest enhanced star formation (m yr ) at the edges of the putative bar seen with iso , perhaps due to shocks driven into the gas . the light profile , reconstructed from v , h and k observations , shows that centaurus a has a core profile with a resolved break at and suggests a black hole mass ofm . a linear blue structure aligned with the radio / x ray jet may indicate a channel of relatively low reddening in which dust has been swept away by the jet . 0.5 cm

astro-ph0112299

i

according to the unification paradigm for seyfert galaxies , seyfert 1s , which show broad optical emission lines , and 2s , which do not , are intrinsically the same objects , but the nuclei of the latter class are obscured by dust along our line of sight in dusty molecular tori @xcite . it is widely accepted that the ultimate energy source of seyfert _ nuclei _ ( although not of their extended host galaxies ) is the release of gravitational energy caused by mass accretion onto a central supermassive blackhole ( so - called agn activity ) . however , it has recently been argued that strong signatures of starbursts are detected in the nuclear uv optical spectra of seyfert 2 galaxies ( heckman et al . 1997 ; gonzalez delgado et al . 1998 ; storchi - bergmann et al . 2000 ; gonzalez delgado , heckman & leitherer 2001 ) , and that the intrinsic extinction - corrected luminosities of compact nuclear starbursts ( hereafter ` compact ' is used to mean a size scale of less than a few 100 pc ) could be comparable to the luminosities of the agn @xcite . in contrast , @xcite investigated the co indices in the near - infrared @xmath1-band spectra of seyfert 2 nuclei , and found no evidence for the presence of strong compact nuclear starbursts . although these authors observed different samples of seyfert 2 galaxies , it is nevertheless striking that they draw such contradictory conclusions on the energetic role of compact nuclear starbursts in seyfert 2 nuclei . according to @xcite , compact nuclear starbursts are natural byproducts of agns dusty molecular tori . in this case , since direct uv optical emission from the agn is highly attenuated in seyfert 2 nuclei , the less strongly obscured compact nuclear starburst emission will inevitably make a relatively strong contribution to the observed uv optical fluxes in these objects . thus , the detection of signatures of compact nuclear starbursts in the observed uv optical spectra of seyfert 2 nuclei @xcite would not be surprising . however , to obtain a deeper understanding of the nature of seyfert 2 nuclei , it is certainly more important to quantify the energetic importance of compact nuclear starbursts than simply to investigate their presence . @xcite estimated the magnitudes of compact nuclear starbursts , based on their extinction - corrected uv data , for four uv - bright seyfert 2 galaxies , while for many other seyfert 2 galaxies that have been studied optically , no quantitative discussions of the absolute magnitudes of compact nuclear starbursts have been made @xcite . even the uv - based quantitative discussion could contain large uncertainties , because of the susceptibility of uv emission to dust extinction ; the extinction correction factor for uv data may vary drastically depending on the assumed amount of dust and its spatial distribution , and has often been claimed to be quantitatively uncertain in particular applications @xcite . the uncertainties in the dust extinction correction are much less in the near - infrared @xmath1-band data taken by ivanov et al . however , the spectral signatures of starbursts are weak , so that careful subtraction of old stellar and agn emission is required to estimate the magnitudes of compact nuclear starbursts @xcite . at 34 @xmath0 m , we possess powerful diagnostic tools to distinguish between starburst and agn activity , to detect weak starbursts , and to estimate the magnitudes of compact nuclear starbursts in seyfert 2 galaxies with fewer quantitative uncertainties . as shown by imanishi & dudley ( 2000 , their figure 1 ) , * if a seyfert 2 nucleus is powered by starbursts , strong polycyclic aromatic hydrocarbon ( pah ) emission will be detected at 3.3 @xmath0 m regardless of dust extinction . * if it is powered by obscured agn activity , a carbonaceous dust absorption feature will be detected at 3.4 @xmath0 m . * if it is powered by weakly obscured agn activity , the 34 @xmath0 m spectrum will be nearly featureless . * if it is a composite of starburst and agn activity , the absolute luminosity and the equivalent width of the 3.3 @xmath0 m pah emission feature will be smaller than in starburst galaxies , so that these values can be used to quantitatively estimate the energetic importance of starburst activity . since the 3.3 @xmath0 m pah emission is intrinsically strong @xcite , even the signatures of weak starbursts are detectable ; even if only @xmath210 % of the observed nuclear 34 @xmath0 m flux originates in starbursts , the 3.3 @xmath0 m pah emission peak is @xmath220 % higher than the continuum level , and thus is clearly recognizable in normal s / n @xmath2 1520 spectra . additionally , the effects of dust extinction are smaller at 34 @xmath0 m than at shorter wavelengths , which makes the uncertainties in the dust extinction correction factor much smaller . this advantage is demonstrated quantitatively below . suppose that the dust extinction in starbursts is found to be a@xmath3 = 24 mag , with an uncertainty of a factor of 2 in a@xmath3 . since the dust extinction in the uv ( @xmath22000 ) is @xmath22.5 @xmath4 a@xmath3 @xcite , the corresponding dust extinction correction factor in the uv is 10010000 , differing by a factor of 100 depending on the adopted a@xmath3 . the difference becomes even larger if we go to shorter - wavelength parts of the uv region or if the actual dust extinction is larger . in contrast , since the dust extinction at 34 @xmath0 m is @xmath20.05 @xmath4 a@xmath3 @xcite , the extinction correction factor at 34 @xmath0 m in the case of a@xmath3 = 24 mag is 1.11.2 . thus , the extinction correction is negligible at 34 @xmath0 m , and the uncertainty in the correction factor is only at the 10% level . the high detectability of weak starbursts and the small uncertainties in dust extinction correction at 34 @xmath0 m combine to make 34 @xmath0 m observations a very powerful tool to quantitatively address the issue of the energetics of compact nuclear starbursts in seyfert 2 nuclei . this paper reports the results of 34 @xmath0 m spectroscopy of seyfert 2 nuclei and their implications for the energetics of these objects . throughout the paper , @xmath5 @xmath6 75 km s@xmath7 mpc@xmath7 , @xmath8 = 0.3 , and @xmath9 = 0.7 are adopted .

the 3.3 m polycyclic aromatic hydrocarbon ( pah ) emission is used to estimate the magnitudes of compact nuclear starbursts ( on scales less than a few 100 pc ) and to resolve the controversy over their energetic importance in seyfert 2 nuclei . for three selected seyfert 2 nuclei that have been well studied in the uv ,

we report on 34 m slit spectroscopy of 13 seyfert 2 nuclei . the 3.3 m polycyclic aromatic hydrocarbon ( pah ) emission is used to estimate the magnitudes of compact nuclear starbursts ( on scales less than a few 100 pc ) and to resolve the controversy over their energetic importance in seyfert 2 nuclei . for three selected seyfert 2 nuclei that have been well studied in the uv , the magnitudes of the compact nuclear starbursts estimated from the 3.3 m pah emission ( with no extinction correction ) are in satisfactory quantitative agreement with those based on the uv after extinction correction . this agreement indicates that the flux attenuation of compact nuclear starburst emission due to dust extinction is insignificant at 34 m , and thus allows us to use the observed 3.3 m pah luminosity to estimate the magnitudes of the compact nuclear starbursts in seyfert 2 nuclei . based directly on our 34 m slit spectra , the following two main conclusions are drawn : ( 1 ) except in one case , the observed nuclear 34 m emission is dominated by agn and not by starbursts , and ( 2 ) compact nuclear starbursts are detected in 6 out of 13 seyfert 2 nuclei , but can not dominate the energetics of the galactic infrared dust emission in the majority of the observed seyfert 2 galaxies . for several sources for which infrared space observatory spectra taken with larger apertures and/or soft x - ray data are available , these data are combined with our 34 m slit spectra , and it is suggested that ( 3 ) extended ( kpc scale ) star - formation activity is energetically more important than compact nuclear starbursts , and contributes significantly to the infrared luminosities of seyfert 2 galaxies , although the agn is still an important contributor to the luminosities , and ( 4 ) the bulk of the energetically significant extended star - formation activity is of starburst type rather than quiescent normal disk star - formation ; the extended starbursts are responsible for the superwind - driven soft x - ray emission from seyfert 2 galaxies . finally , a correlation between the luminosities of agns and compact nuclear starbursts is implied ; more powerful agns tend to be related to more powerful compact nuclear starbursts .

astro-ph0112299

c

the fraction of the observed nuclear 34 @xmath0 m fluxes in our slit spectra that originates in starbursts can be estimated from the rest - frame equivalent widths of the 3.3 @xmath0 m pah emission feature ( ew@xmath20 ) . the ew@xmath20 value decreases as the agn contribution increases ( @xmath17 1 ) . the equivalent widths for starburst - dominated galaxies are @xmath2120 nm @xcite . in table [ tbl-4 ] , only mrk 266sw shows an ew@xmath20 value similar to those of starburst galaxies ; we can conclude from this that only the observed nuclear 34 @xmath0 m flux of mrk 266sw is dominated by starbursts . mrk 78 , mrk 273 , mrk 477 , ngc 3227 , and ngc 5135 all show detectable , moderately strong 3.3 @xmath0 m pah emission features , but their ew@xmath20 values are a factor 39 smaller than those of starburst galaxies . for these five sources , starbursts contribute some fraction , but less than half , of the observed nuclear 34 @xmath0 m fluxes , and the bulk of the observed 34 @xmath0 m fluxes originate in agn activity . for the remaining seven seyfert 2 nuclei ( ic 3639 , mrk 34 , mrk 463 , mrk 686 , ngc 1068 , ngc 5033 , and ngc 5929 ) , the ew@xmath20 is more than a factor of 7 smaller than that expected for starburst - dominated galaxies , indicating that the predominant fraction ( larger than 80% ) of their 34 @xmath0 m emission comes from agn activity . _ our first conclusion is that , except in the case of mrk 266sw , the observed compact nuclear 34 @xmath0 m emission is dominated by the agn and not by starbursts_. this result has implications for infrared studies of agns . @xmath13- ( 3.5 @xmath0 m ) and @xmath21-band ( 4.8 @xmath0 m ) emission from agns is usually dominated by compact emission , and photometric data at these bands are used to discuss dust obscuration toward agns , on the assumption that this compact emission comes predominantly from the agn and not from compact nuclear starbursts @xcite . our results provide supporting evidence for this assumption . the 3.4 @xmath0 m carbonaceous dust absorption feature is detected in mrk 463 and ngc 1068 . the observed 3.4 @xmath0 m absorption optical depths are @xmath22(observed ) @xmath6 0.042@xmath230.005 and 0.12@xmath230.01 for mrk 463 and ngc 1068 , respectively . in agns , the 34 @xmath0 m continuum emission is dominated by dust in thermal equilibrium with a temperature of 8001000k , close to the dust sublimation temperature , located at the innermost part of the dusty torus @xcite . the dust extinction toward the 34 @xmath0 m continuum emitting region is thus almost the same as that toward the agn itself . assuming a galactic dust model ( @xmath22/a@xmath3 @xmath6 0.0040.007 ; pendleton et al . 1994 ) , the dust extinction toward the agns is estimated to be 611 and 1730 mag for mrk 463 and ngc 1068 , respectively . mrk 463 shows a broad emission component in its near - infrared hydrogen recombination lines @xcite so that dust obscuration toward the agn has been suggested to be relatively modest in this object . our result is consistent with this suggestion . for the remaining 11 seyfert 2 nuclei , no detectable 3.4 @xmath0 m absorption feature is found . the 3.4 @xmath0 m absorption feature may be suppressed if the bulk of the dust grains in the obscuring material is covered with an ice mantle @xcite . however , no strong 3.08 @xmath0 m ice absorption feature is found in their 34 @xmath0 m spectra . the dust absorption feature is smeared out if less obscured starburst emission contributes significantly to the observed nuclear 34 @xmath0 m flux @xcite . the six sources with detectable pah emission ( mrk 78 , mrk 266sw , mrk 273 , mrk 477 , ngc 3227 , and ngc 5135 ) could be this case . for the five pah - undetected seyfert 2 nuclei ( ic 3639 , mrk 34 , mrk 686 , ngc 5033 , and ngc 5929 ) , the 3.4 @xmath0 m absorption feature could remain undetectable if dust obscuration toward these agns is weak ( @xmath17 1 ) . the r - value , defined as @xmath24 is a good measure for dust extinction toward agns ( murayama , mouri , & taniguchi 2000 ) . it becomes smaller with higher dust extinction toward agns , and the boundary value between seyfert 1 and 2 nuclei is estimated to be r = @xmath250.6 @xcite . based on the 3.5 @xmath0 m ( table [ tbl-3 ] ) and _ iras _ 25 @xmath0 m ( table [ tbl-1 ] ) fluxes , the r - values for ic 3639 , mrk 34 , mrk 686 , ngc 5033 , and ngc 5929 , are estimated to be @xmath251.2 , @xmath250.8 , @xmath250.3 , @xmath250.6 , and @xmath251.2 , respectively . the r - values of mrk 686 and ngc 5033 are in the range of seyfert 1 nuclei , and thus weak dust obscuration is indicated , explaining the non - detection of the 3.4 @xmath0 m absorption . however , ic 3639 , mrk 34 , and ngc 5929 show small r - values . the non - detection could be caused by the effects of time variability or contamination from extended star - formation to the observed 25 @xmath0 m flux taken with large apertures @xcite . the bulk of the uv optical emission from the agns in seyfert 2 galaxies and starbursts @xcite is absorbed by dust and re - emitted as dust thermal emission in the infrared . infrared ( 81000 @xmath0 m ) luminosities are thus used to estimate the magnitudes of agn and starburst activity throughout this paper . infrared ( 81000 @xmath0 m ) luminosities are obviously better for evaluating these kinds of activity than far - infrared ( 40500 @xmath0 m ) luminosities because not all activity shows dust emission peaking in the far - infrared . in starburst - dominated galaxies , the 3.3 @xmath0 m pah to far - infrared ( 40500 @xmath0 m ) luminosity ratios ( l@xmath20/l@xmath26 ) are @xmath21 @xmath4 10@xmath27 @xcite . the 3.3 @xmath0 m pah to infrared ( 81000 @xmath0 m ) luminosity ratio ( l@xmath28/l@xmath29 ) is tentatively assumed to be also 1 @xmath4 10@xmath27 for the compact nuclear starbursts in seyfert 2 nuclei . the scatter of the pah - to - infrared luminosity ratio is likely to be a factor of 23 toward both higher and lower values around a typical value @xcite . for ic 3639 , mrk 477 , and ngc 5135 , @xcite explicitly estimated the extinction - corrected luminosities of compact nuclear starbursts , based on their uv data . the respective luminosities are 1.1 @xmath4 10@xmath30 , 1.4 @xmath4 10@xmath31 , and 4.2 @xmath4 10@xmath30 ergs s@xmath7 . the infrared luminosities of the compact nuclear starbursts estimated from the observed ( extinction - uncorrected ) 3.3 @xmath0 m pah emission , based on the assumption of l@xmath20/l@xmath29 @xmath2 1 @xmath4 10@xmath27 , are @xmath321.2 @xmath4 10@xmath30 , 1.5 @xmath4 10@xmath31 , and 5.8 @xmath4 10@xmath30 ergs s@xmath7 , respectively , for ic 3639 , mrk 477 , and ngc 5135 . it is noteworthy that the compact nuclear starburst luminosities estimated from uv data after extinction correction and from the 3.3 @xmath0 m pah emission with _ no _ extinction correction are in satisfactory agreement for all three sources . this agreement indicates that ( 1 ) discussions of the magnitudes of compact nuclear starbursts based on uv data after extinction correction are quantitatively reliable , ( 2 ) the extinction correction factor is not significant at 34 @xmath0 m , and ( 3 ) the assumption of l@xmath20/l@xmath29 @xmath2 1 @xmath4 10@xmath27 is reasonable . we have been concerned by the possibility that , if compact nuclear starbursts close to the central agns are directly exposed to x - ray emission from agns , pah emission from the compact nuclear starbursts might be suppressed due to the destruction of pahs @xcite . however , the agreement suggests that this is not the case . if the bulk of the compact nuclear starbursts in seyfert 2 nuclei occur at the outer reaches of the dusty tori around agns @xcite , pahs are shielded from the energetic radiation from the agns and thus are not destroyed , explaining the strong pah emission from compact nuclear starbursts in seyfert 2 nuclei . based on these findings , the magnitudes of compact nuclear starbursts can be estimated from the observed 3.3 @xmath0 m pah emission luminosities with some confidence . if compact nuclear starbursts energetically dominated the whole galactic infrared dust emission luminosities of seyfert 2 galaxies , the observed l@xmath20/l@xmath29 ratios measured from our slit spectra should be similar to those of starburst galaxies ( @xmath21 @xmath4 10@xmath27 ) . as shown in table [ tbl-4 ] , however , none of the observed seyfert 2 galaxies show such a large value of l@xmath20/l@xmath29 . the differences are by a factor of 3 ( mrk 477 ) to larger than 10 , and in most cases much larger than a factor of 23 , the possible flux loss in our slit spectra and the intrinsic scatter of the l@xmath20/l@xmath33 ratios for starbursts . therefore , _ our second conclusion is that compact nuclear starbursts can not be the dominant energy source of the whole galactic infrared dust emission luminosities in the majority of the observed seyfert 2 galaxies_. for the remaining ten seyfert 2 galaxies other than ic 3639 , mrk 477 , and ngc 5135 , our quantitative estimates of the magnitudes of the compact nuclear starbursts are compared with qualitative arguments based on the optical and @xmath1-band data @xcite . @xcite found signatures of compact nuclear starbursts ( young stars ) in the optical spectrum of mrk 273 . for mrk 273 , 3.3 @xmath0 m pah emission is detected ; ew@xmath20 and l@xmath20/l@xmath29 are a factor of @xmath23 and @xmath210 smaller , respectively , than those of starburst galaxies . the l@xmath20/l@xmath29 ratio indicates that the compact nuclear starbursts explain @xmath21/10 of the total galactic infrared luminosity . thus , compact nuclear starbursts are certainly present , supporting the optical results . for mrk 78 and ngc 1068 , @xcite found no signatures of compact nuclear starbursts , and detected only intermediate age stars in their optical spectra . for ngc 1068 , only stringent upper limits are found for the ew@xmath20 and l@xmath20/l@xmath29 , both of which are more than an order of magnitude smaller than those of starburst galaxies . for mrk 78 , however , 3.3 @xmath0 m pah emission is marginally detected . for mrk 463 , @xcite claimed that compact nuclear starbursts might be present , subject to further confirmation . no detectable 3.3 @xmath0 m pah emission is found . the upper limits for both ew@xmath20 and l@xmath20/l@xmath29 are more than an order of magnitude smaller than starburst galaxies . compact nuclear starbursts in mrk 463 are energetically insignificant , if they exist at all . for mrk 34 , @xcite found no signs of compact nuclear starbursts in the optical spectrum , with only old population stars being detected . no 3.3 @xmath0 m pah emission is detected either , supporting the conclusions based on the optical data . both @xcite and @xcite studied ngc 5929 and found no evidence for strong compact nuclear starbursts . no clear 3.3 @xmath0 m pah emission is detected . the remaining sources , mrk 266sw , mrk 686 , ngc 3227 , and ngc 5033 , were studied only by @xcite . they found that no strong compact nuclear starbursts are required in terms of the co indices after correction for agn emission . no 3.3 @xmath0 m pah emission is detected in mrk 686 and ngc 5033 , supporting their argument . however , in mrk 266sw , the nuclear 34 @xmath0 m emission must be dominated by starbursts , although these detected compact nuclear starbursts can explain only @xmath210% of the total galactic infrared luminosity . 3.3 @xmath0 m pah emission was also clearly detected in ngc 3227 , and compact nuclear starbursts can explain @xmath220% of the whole galactic infrared luminosity . in mrk 266sw and ngc 3227 , compact nuclear starbursts are certainly present , and they explain a non - negligible fraction of the total galactic infrared luminosities . the signatures of compact nuclear starbursts may have been missed during the complicated procedures required to find their weak signatures in the @xmath1-band @xcite . since the observed nuclear 34 @xmath0 m emission is dominated by agn activity ( @xmath17 5.1 ) , it would be expected that agn activity also contributes much more than compact nuclear starbursts to the net galactic infrared ( 81000 @xmath0 m ) luminosities of seyfert 2 galaxies . however , the agn - driven infrared luminosities of these objects are difficult to estimate because they are highly dependent on the spatial distribution of dust in the dusty torus , which is poorly constrained observationally . thus , we estimate the energetic importance of extended star - formation in the host galaxies , which is the remaining probable power source of seyfert 2 galaxies other than compact nuclear starbursts and agns , by using the pah emission . pah emission can be produced both with starbursts and normal quiescent star - formation in a similar way @xcite . to investigate the magnitude of extended ( kpc scale ) star - formation activity , _ infrared space observatory ( iso ) _ spectra taken with large apertures are useful . @xcite summarized the _ iso _ results ; they found that ( 1 ) the 7.7 @xmath0 m pah to far - infrared luminosity ratios in seyfert galaxies are similar to those of starburst galaxies , and that ( 2 ) the bulk of the pah emission is spatially extended . therefore , they argued that the bulk of the far - infrared emission from seyfert galaxies originates in extended star - formation activity . of the 13 seyfert 2 galaxies , @xcite have presented _ iso _ 2.511 @xmath0 m spectra taken with 24 @xmath4 24 arcsec@xmath34 apertures , and quote pah fluxes for four sources ( mrk 266 , ngc 3227 , ngc 5033 , and ngc 5929 ) . for these sources , the energetic importance of extended star - formation activity can be investigated by comparing the measured pah fluxes in our slit spectra with those in the _ iso _ spectra . the effects of dust extinction are similar at 38 @xmath0 m @xcite . the 7.7 @xmath0 m pah emission is the strongest pah emission feature . however , its flux estimates in the _ iso _ spectra may be highly uncertain @xcite , due to the presence of strong , spectrally broad 9.7 @xmath0 m silicate dust absorption feature and insufficient wavelength coverage longward of these emission and absorption features , which make a continuum determination difficult @xcite . quantitatively reliable flux estimates of the 3.3 @xmath0 m pah emission in the _ iso _ spectra are also difficult due to the scatter in the data points at 34 @xmath0 m ( clavel et al . 2000 , their figure 8) . consequently , the 6.2 @xmath0 m pah emission , which is isolated and moderately strong , is most suitable to investigate the extended star - formation activity based on the _ iso _ spectra @xcite . the 6.2 @xmath0 m pah to infrared luminosity ratios ( l@xmath35/l@xmath29 ) for starbursts are estimated to be @xmath2 6 @xmath4 10@xmath27 , with a scatter of a factor of 23 toward both higher and lower values @xcite , where it is assumed that l@xmath29 @xmath2 l@xmath26 for starbursts . the respective l@xmath35/l@xmath29 ratios are 4 @xmath4 10@xmath27 , 4 @xmath4 10@xmath27 , 3 @xmath4 10 @xmath27 , and 1 @xmath4 10@xmath27 , for mrk 266 , ngc 3227 , ngc 5033 , and ngc 5929 @xcite , roughly half of ( mrk 266 , ngc 3227 , and ngc 5033 ) or more than six times smaller than ( ngc 5929 ) the typical value for systems dominated by starbursts . since the observed l@xmath20/l@xmath29 ratios indicate that the compact nuclear starbursts energetically fall short of the total infrared luminosities by a factor of larger than 6 for these four sources ( table [ tbl-4 ] ) , it can be said that extended star - formation ( but not compact nuclear starbursts ) contributes significantly to the infrared luminosities of these seyfert 2 galaxies . this statement was made by @xcite for seyfert galaxies as a whole based on the 7.7 @xmath0 m pah emission . based on the 6.2 @xmath0 m pah emission , here , it has been confirmed that this is true also for the four individual seyfert 2 galaxies , and probably for seyfert 2 galaxies as a whole . the individual l@xmath35/l@xmath29 ratios for mrk 266 , ngc 3227 , and ngc 5033 are within the scattered range of the ratios for starbursts . however , the overall trend of lower values implies that agn activity also makes an important contribution to the infrared luminosities of seyfert 2 galaxies . while both starbursts and quiescent disk star - formation in normal galaxies can produce pah emission ( @xmath17 5.5 ) , strong soft x - ray emission driven by superwind is observed only if the star - formation rate per unit area exceeds a certain threshold ( 10@xmath7 m@xmath36 yr@xmath7 kpc@xmath37 ; heckman 2000 ) . starbursts surpass this threshold , while quiescent normal disk star - formation does not @xcite . these different characteristics can be used to understand the properties of energetically significant extended star - formation activity . of the 13 seyfert 2 galaxies , @xcite have estimated superwind - driven soft x - ray luminosities for eight sources ( ic 3639 , mrk 78 , mrk 266 , mrk 273 , mrk 463 , mrk 477 , ngc 1068 , and ngc 5135 ) , and found that , as a whole , their soft x - ray to far - infrared luminosity ratios are as high as those of starburst galaxies . therefore , starburst activity is a significant contributor to the far - infrared emission and also to the infrared dust emission . since compact nuclear starbursts detected in our slit spectra were found to be energetically insignificant ( @xmath17 5.3 ) , the energetically significant starbursts must be extended . _ our third conclusion is that the bulk of the energetically significant extended ( kpc scale ) star - formation activity is of starburst - type and not quiescent normal disk star - formation . it is the extended ( kpc scale ) starbursts , rather than the compact ( less than a few 100 pc ) nuclear starbursts , that are responsible for the superwind - driven soft x - ray emission . _ if starbursts are inevitable phenomena in seyfert 2 galaxies , their extended starburst activity is energetically more important than their compact nuclear starbursts . this is actually the case for the four seyfert 2 galaxies studied in detail in the uv @xcite and for the famous , well - studied seyfert 2 galaxy ngc 1068 @xcite . we test the hypothesis that more powerful agns might be related to more powerful compact nuclear starbursts @xcite . figure [ fig2 ] compares the 12 @xmath0 m luminosity with the 3.3 @xmath0 m pah emission luminosity . the total galactic 12 @xmath0 m luminosity is regarded as a measure of agn power @xcite . the 3.3 @xmath0 m pah luminosities , measured with our slit spectroscopy , reflect the magnitudes of compact nuclear starbursts . the picture of @xcite would be supported if we were to find a positive correlation between 12 @xmath0 m luminosity and 3.3 @xmath0 m pah emission luminosity . in fig . [ fig2 ] , this trend appears to be present , although the scatter is moderately large . we apply the generalized kendall s rank correlation statistic @xcite to the data points in fig . [ fig2 ] , and estimate the probability that a correlation is not present to be 0.11 , by using the software available at the web page : http://www.astro.psu.edu / statcodes/. thus , provided that the 12 @xmath0 m luminosity is a good measure of agn power , _ it is found that the luminosities of agns and compact nuclear starbursts in seyfert 2 galaxies are correlated , and more powerful agns tend to contain more powerful compact nuclear starbursts . _

the magnitudes of the compact nuclear starbursts estimated from the 3.3 m pah emission ( with no extinction correction ) are in satisfactory quantitative agreement with those based on the uv after extinction correction . based directly on our 34 m slit spectra , the following two main conclusions are drawn : ( 1 ) except in one case , the observed nuclear 34 m emission is dominated by agn and not by starbursts , and ( 2 ) compact nuclear starbursts are detected in 6 out of 13 seyfert 2 nuclei , but can not dominate the energetics of the galactic infrared dust emission in the majority of the observed seyfert 2 galaxies . for several sources for which infrared space observatory spectra taken with larger apertures and/or soft x - ray data are available , these data are combined with our 34 m slit spectra , and it is suggested that ( 3 ) extended ( kpc scale ) star - formation activity is energetically more important than compact nuclear starbursts , and contributes significantly to the infrared luminosities of seyfert 2 galaxies , although the agn is still an important contributor to the luminosities , and ( 4 ) the bulk of the energetically significant extended star - formation activity is of starburst type rather than quiescent normal disk star - formation ; the extended starbursts are responsible for the superwind - driven soft x - ray emission from seyfert 2 galaxies . finally , a correlation between the luminosities of agns and compact nuclear starbursts is implied ; more powerful agns tend to be related to more powerful compact nuclear starbursts .

we report on 34 m slit spectroscopy of 13 seyfert 2 nuclei . the 3.3 m polycyclic aromatic hydrocarbon ( pah ) emission is used to estimate the magnitudes of compact nuclear starbursts ( on scales less than a few 100 pc ) and to resolve the controversy over their energetic importance in seyfert 2 nuclei . for three selected seyfert 2 nuclei that have been well studied in the uv , the magnitudes of the compact nuclear starbursts estimated from the 3.3 m pah emission ( with no extinction correction ) are in satisfactory quantitative agreement with those based on the uv after extinction correction . this agreement indicates that the flux attenuation of compact nuclear starburst emission due to dust extinction is insignificant at 34 m , and thus allows us to use the observed 3.3 m pah luminosity to estimate the magnitudes of the compact nuclear starbursts in seyfert 2 nuclei . based directly on our 34 m slit spectra , the following two main conclusions are drawn : ( 1 ) except in one case , the observed nuclear 34 m emission is dominated by agn and not by starbursts , and ( 2 ) compact nuclear starbursts are detected in 6 out of 13 seyfert 2 nuclei , but can not dominate the energetics of the galactic infrared dust emission in the majority of the observed seyfert 2 galaxies . for several sources for which infrared space observatory spectra taken with larger apertures and/or soft x - ray data are available , these data are combined with our 34 m slit spectra , and it is suggested that ( 3 ) extended ( kpc scale ) star - formation activity is energetically more important than compact nuclear starbursts , and contributes significantly to the infrared luminosities of seyfert 2 galaxies , although the agn is still an important contributor to the luminosities , and ( 4 ) the bulk of the energetically significant extended star - formation activity is of starburst type rather than quiescent normal disk star - formation ; the extended starbursts are responsible for the superwind - driven soft x - ray emission from seyfert 2 galaxies . finally , a correlation between the luminosities of agns and compact nuclear starbursts is implied ; more powerful agns tend to be related to more powerful compact nuclear starbursts .

astro-ph0112299

i

we performed 34 @xmath0 m spectroscopy of 13 seyfert 2 nuclei that were previously studied in the uv , optical , and near - infrared @xmath1-band . making use of the 3.3 @xmath0 m pah emission feature detected in our slit spectra , the following results were obtained . 1 . our pah - based , extinction - uncorrected estimates of the luminosities of compact ( less than a few 100 pc ) nuclear starbursts were found to agree well with those based on extinction - corrected uv data in three selected seyfert 2 galaxies ( ic 3639 , mrk 477 , and ngc 5135 ) . this agreement indicates that compact nuclear starburst emission is not significantly attenuated due to dust extinction at 34 @xmath0 m , so that the observed 3.3 @xmath0 m pah emission luminosity is a powerful diagnostic of the magnitudes of compact nuclear starbursts . 2 . for the remaining ten seyfert 2 galaxies , our pah - based diagnostic results were compared with qualitative arguments based on the optical and @xmath1-band spectra . for mrk 273 , signs of compact nuclear starbursts were found , supporting the qualitative optically based argument . for mrk 463 , possible compact nuclear starbursts implied from the optical data were not confirmed at 34 @xmath0 m . for mrk 78 and ngc 1068 , both of which show signatures of only intermediate age stars in the optical , 3.3 @xmath0 m pah emission was marginally detected in mrk 78 . optical and/or @xmath1-band spectra show no evidence for compact nuclear starbursts in mrk 34 , mrk 266sw , mrk 686 , ngc 3227 , ngc 5033 , and ngc 5929 . at 34 @xmath0 m , signatures of compact nuclear starbursts were found in mrk 266sw and ngc 3227 . quantitative estimates of the magnitudes of nuclear starbursts were made based on the observed 3.3 @xmath0 m pah emission luminosities for the 13 seyfert 2 galaxies , and found that ( 1 ) nuclear 34 @xmath0 m emission is dominated by agn activity rather than by starburst activity in all seyfert 2 galaxies but one ( mrk 266sw ) , and ( 2 ) compact nuclear starbursts can explain only a small fraction ( @xmath321/101/3 ) of the infrared dust emission luminosities . the 3.4 @xmath0 m carbonaceous dust absorption feature is detected only in the two seyfert 2 nuclei , mrk 463 and ngc 1068 . when our observations were combined with large - aperture _ iso _ spectra for the four sources ( mrk 266 , ngc 3227 , ngc 5033 , and ngc 5929 ) , it was confirmed that extended ( kpc scale ) star - formation activity is energetically more important than compact nuclear starbursts , and contributes significantly to the infrared dust emission luminosities of seyfert 2 galaxies . however , the agns are likely to be still important contributors to the luminosities . 6 . making use of soft x - ray data for the eight sources ( ic 3639 , mrk 78 , mrk 266 , mrk 273 , mrk 463 , mrk 477 , ngc 1068 , and ngc 5135 ) , it was suggested that the energetically significant extended star - formation activity is of starburst - type and not quiescent normal disk star - formation . these extended starbursts are responsible for the superwind - driven soft x - ray emission from seyfert 2 galaxies . we find evidence supporting the scenario in which more powerful agns are related to more powerful compact nuclear starbursts , provided that 12 @xmath0 m luminosity is a good measure of agn power . we thank s. k. leggett , j. davies , t. wold , and t. carroll for their support during the ukirt observing runs , and j. rayner and b. golisch for their support before and during the irtf observing run . we are grateful to drs . k. aoki , t. nakajima , and y. p. wang for their useful comments on this manuscript , and dr . t. t. takeuchi for invaluable discussions about statistical tests . the anonymous referee and the scientific editor , dr . s. willner , gave invaluable comments , which improved this paper significantly . spectra of mrk 273 and mrk 463 were obtained while mi was at the university of hawaii . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . alonso - 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bergmann , t. , raimann , d. , bica , e. l. d. , & fraquelli , h. a. 2000 , apj , 544 , 747 surace , j. a. , & sanders , d. b. 1999 , apj , 512 , 162 surace , j. a. , sanders , d. b. , & evans , a. s. 2000 , apj , 529 , 170 tokunaga , a. t. , sellgren , k. , smith , r. g. , nagata , t. , sakata , a. , & nakada , y. 1991 , apj , 380 , 452 tokunaga , a. t. 2000 , in allen s astrophysical quantities , ed . a. n. cox ( 4th ed : aip press : springer ) , chapter 7 , p.143 veilleux , s. , goodrich , r. w. , & hill , g. j. 1997 , apj , 477 , 631 voit , g. m. 1992 , mnras , 258 , 841 zhou , s. , wynn - williams , c. g. , & sanders , d. b. 1993 , apj , 409 , 149 lcrrrrccc ic 3639 & 0.011 & 0.64 & 2.26 & 7.52 & 10.7 & 44.25 & 44.33 & g + mrk 34 & 0.051 & 0.07 & 0.46 & 0.81 & 0.80 & 44.59 & 44.78 & g + mrk 78 & 0.037 & 0.13 & 0.56 & 1.11 & 1.13 & 44.44 & 44.63 & g + mrk 266 & 0.028 & 0.23 & 0.98 & 7.34 & 11.1 & 45.07 & 45.03 & i + mrk 273 & 0.038 & 0.24 & 2.28 & 21.7 & 21.4 & 45.75 & 45.69 & g + mrk 463 & 0.051 & 0.51 & 1.58 & 2.18 & 1.92 & 45.00 & 45.34 & g + mrk 477 & 0.038 & 0.13 & 0.51 & 1.31 & 1.85 & 44.58 & 44.70 & g + mrk 686 & 0.014 & @xmath320.11 & 0.13 & 0.57 & 1.79 & 43.49 & 43.4343.56 & i + ngc 1068 & 0.004 & 39.70 & 85.04 & 176.2 & 224.0 & 44.72 & 44.96 & g + ngc 3227 & 0.004 & 0.67 & 1.76 & 7.83 & 17.6 & 43.46 & 43.49 & i + ngc 5033 & 0.003 & 0.95 & 1.15 & 13.8 & 43.9 & 43.54 & 43.48 & i + ngc 5135 & 0.014 & 0.64 & 2.40 & 16.9 & 28.6 & 44.84 & 44.81 & g + ngc 5929 & 0.008 & 0.43 & 1.62 & 9.14 & 13.7 & 44.06 & 44.06 & g , i + llccccc ic 3639 & 2001 apr 8 & 1920 & hr 5212 & 4.8 & f7v & 6240 + mrk 34 & 2001 apr 9 & 2520 & hr 4112 & 3.4 & f8v & 6200 + mrk 78 & 2001 apr 9 & 1728 & hr 3028 & 4.8 & f6v & 6400 + mrk 266sw & 2001 apr 9 & 2160 & hr 4767 & 4.8 & f8v g0v & 6000 + mrk 273 & 2000 feb 20 & 2560 & hr 4761 & 4.8 & f68v & 6200 + mrk 463 & 2000 jun 13 & 800 & hr 5243 & 4.9 & f6v & 6400 + mrk 477 & 2001 apr 9 & 2592 & hr 5581 & 4.3 & f7v & 6240 + mrk 686 & 2001 apr 9 & 2400 & hr 5423 & 4.7 & g5v & 5700 + ngc 1068 & 1995 nov 15 & 640 & hr 8781 & 2.6 & b9v & 10700 + ngc 3227 & 2001 apr 8 & 1050 & hr 3650 & 4.6 & g9v & 5400 + ngc 5033 & 2001 apr 8 & 2280 & hr 5423 & 4.7 & g5v & 5700 + ngc 5135 & 2001 apr 8 & 2160 & hr 5212 & 4.8 & f7v & 6240 + ngc 5929 & 2001 apr 9 & 2064 & hr 5581 & 4.3 & f7v & 6240 + lccc ic 3639 & 10.2 ( 1@xmath112 @xmath4 5@xmath38 ) & 10.4 ( 6@xmath38 ) & g + mrk 34 & 11.3 ( 1@xmath112 @xmath4 4@xmath38 ) & 11.1 ( 8@xmath115 ) & r + mrk 78 & 11.0 ( 1@xmath112 @xmath4 5@xmath38 ) & 11.0 ( 5@xmath119 ) & r + mrk 266sw & 12.1 ( 1@xmath112 @xmath4 5@xmath38 ) & 11.5 ( 8@xmath116 ) & i + mrk 273 & 10.5 ( 1@xmath112 @xmath4 10@xmath38 ) & 10.5 ( 5@xmath38 ) & z + mrk 463 & 8.2 ( 1@xmath112 @xmath4 7@xmath38 ) & 8.2 ( 4@xmath38 ) & m + mrk 477 & 11.1 ( 1@xmath112 @xmath4 4@xmath38 ) & 11.8 ( 6@xmath38 ) & l + mrk 686 & 11.0 ( 1@xmath112 @xmath4 5@xmath38 ) & 11.2 ( 5@xmath114 ) & i + ngc 1068 & 4.8 ( 3@xmath118 @xmath4 3@xmath118 ) & 4.8 ( 3@xmath38 ) & ma + ngc 3227 & 9.5 ( 1@xmath112 @xmath4 4@xmath38 ) & 9.0 ( 8@xmath116 ) & i + ngc 5033 & 10.7 ( 1@xmath112 @xmath4 5@xmath38 ) & 9.5 ( 8@xmath116 ) & i + ngc 5135 & 10.1 ( 1@xmath112 @xmath4 6@xmath38 ) & 9.7 ( 6@xmath38 ) & g + ngc 5929 & 11.6 ( 1@xmath112 @xmath4 5@xmath38 ) & 10.8 ( 5@xmath114 ) & i + lcccc ic 3639 & @xmath324.9 & @xmath3211.3 & @xmath325.2 @xmath4 10@xmath37 & @xmath328.5 @xmath4 10@xmath37 + mrk 34 & @xmath320.33 & @xmath3217.5 & @xmath322.9 @xmath4 10@xmath37 & @xmath321.6 @xmath4 10@xmath37 + mrk 78 & 3.9@xmath231.0 & 108@xmath2327 & 2.5 @xmath4 10@xmath7 & 1.5@xmath230.4 @xmath4 10@xmath7 + mrk 266sw & 8.5@xmath230.5 & 133@xmath237 & 1.2 @xmath4 10@xmath7 & 8.7@xmath230.5 @xmath4 10@xmath7 + mrk 273 & 14.5@xmath230.7 & 422@xmath2319 & 8.7 @xmath4 10@xmath37 & 3.5@xmath230.2 @xmath4 10@xmath7 + mrk 463 & @xmath323.0 & @xmath32159 & @xmath327.4 @xmath4 10@xmath37 & @xmath328.1 @xmath4 10@xmath27 + mrk 477 & 5.1@xmath230.7 & 151@xmath2321 & 3.0 @xmath4 10@xmath7 & 2.2@xmath230.3 @xmath4 10@xmath7 + mrk 686 & @xmath323.3 & @xmath3212 & @xmath324.6 @xmath4 10@xmath7 & @xmath321.2 @xmath4 10@xmath7 + ngc 1068 & @xmath3286.7 & @xmath3226.7 & @xmath322.9 @xmath4 10@xmath37 & @xmath321.2 @xmath4 10@xmath37 + ngc 3227 & 16.6@xmath231.3 & 5.1@xmath230.4 & 1.7 @xmath4 10@xmath7 & 1.4@xmath230.1 @xmath4 10@xmath7 + ngc 5033 & @xmath320 & @xmath320 & @xmath320 & @xmath320 + ngc 5135 & 15.3@xmath232.8 & 58@xmath2311 & 9.1 @xmath4 10@xmath37 & 2.4@xmath230.4 @xmath4 10@xmath7 + ngc 5929 & @xmath322.5 & @xmath323.0 & @xmath322.7 @xmath4 10@xmath37 & @xmath321.4 @xmath4 10@xmath7 +

we report on 34 m slit spectroscopy of 13 seyfert 2 nuclei . this agreement indicates that the flux attenuation of compact nuclear starburst emission due to dust extinction is insignificant at 34 m , and thus allows us to use the observed 3.3 m pah luminosity to estimate the magnitudes of the compact nuclear starbursts in seyfert 2 nuclei .

we report on 34 m slit spectroscopy of 13 seyfert 2 nuclei . the 3.3 m polycyclic aromatic hydrocarbon ( pah ) emission is used to estimate the magnitudes of compact nuclear starbursts ( on scales less than a few 100 pc ) and to resolve the controversy over their energetic importance in seyfert 2 nuclei . for three selected seyfert 2 nuclei that have been well studied in the uv , the magnitudes of the compact nuclear starbursts estimated from the 3.3 m pah emission ( with no extinction correction ) are in satisfactory quantitative agreement with those based on the uv after extinction correction . this agreement indicates that the flux attenuation of compact nuclear starburst emission due to dust extinction is insignificant at 34 m , and thus allows us to use the observed 3.3 m pah luminosity to estimate the magnitudes of the compact nuclear starbursts in seyfert 2 nuclei . based directly on our 34 m slit spectra , the following two main conclusions are drawn : ( 1 ) except in one case , the observed nuclear 34 m emission is dominated by agn and not by starbursts , and ( 2 ) compact nuclear starbursts are detected in 6 out of 13 seyfert 2 nuclei , but can not dominate the energetics of the galactic infrared dust emission in the majority of the observed seyfert 2 galaxies . for several sources for which infrared space observatory spectra taken with larger apertures and/or soft x - ray data are available , these data are combined with our 34 m slit spectra , and it is suggested that ( 3 ) extended ( kpc scale ) star - formation activity is energetically more important than compact nuclear starbursts , and contributes significantly to the infrared luminosities of seyfert 2 galaxies , although the agn is still an important contributor to the luminosities , and ( 4 ) the bulk of the energetically significant extended star - formation activity is of starburst type rather than quiescent normal disk star - formation ; the extended starbursts are responsible for the superwind - driven soft x - ray emission from seyfert 2 galaxies . finally , a correlation between the luminosities of agns and compact nuclear starbursts is implied ; more powerful agns tend to be related to more powerful compact nuclear starbursts .

astro-ph0307235

c

as a first step in the investigation of our results we compare them with some qualitative correlations between glitch variables studied by lyne et al . ( 2000 ) in a sample of 48 radio pulsar glitches . it is usually assumed that glitches are a manifestation of the angular momentum exchange between the bulk of a neutron star s moment of inertia and some superfluid component , loosely coupled to it , that slows down at discrete steps . let the spin up rate associated with glitches be @xmath86 , where the summation is over all glitches observed during the time @xmath33 . lyne et al.(2000 ) found a good correlation between the long term spin down rate of radio pulsars and @xmath87 . their best fit linear relation is : @xmath88 in the framework discussed above , conservation of total angular momentum and eq . ( [ lyne ] ) imply that a fraction @xmath89 of the moment of inertia of the star is on average contributed by the superfluid that is slowed down at glitches ( see sec . [ vortexcreep ] ) . in the case of the two glitches observed in rxs j170849.0400910 @xmath90 s@xmath91 , which is strikingly close to the value ( 2.7 @xmath92 ) predicted by formula ( [ lyne ] ) . we stress however that this result still needs a confirmation , being based on only two events . further , the polynomial fit to the recovery from glitch n.1 is consistent with the trend observed in radio pulsars for rotators with decreasing @xmath43 to have smaller exponential recovery fractions ( q ) and increasingly important long term linear recoveries . based on such observed trend a recovery fraction q @xmath93 would be expected for rxs j170849.0400910 ( se fig.6 of lyne et al . a short time transient of this magnitude can not be excluded given the sparse temporal monitoring of this source . on the other hand , the trend is contradicted by the exponential fit to the recovery from glitch n.2 . this is dominated by an exponential component ( q @xmath35 1 ) . recovery fractions greater than 10% have been found only in the fastest and youngest ( the crab pulsar ) and in the slowest and oldest ( psr b0525 + 21 ) radio pulsars in the sample of lyne et al . axps do likely spin down under different conditions with respect to common radio pulsars and may have higher temperatures than radio pulsars of the same spin down age . both effects may be relevant in determining the properties of their recovery from glitches . we notice that two other suggestions made by lyne et al.(2000 ) do not fit with what is observed in rxs j170849.0400910 ; the tendency for stars with a lower rotational frequency to experience , if any , glitches of smaller amplitude and , second , the tendency for stars with a higher dipole field to show more frequent but smaller glitches , at a given characteristic age . indeed , the average @xmath94 of the two observed glitches amounts to @xmath35 2 @xmath95 , very close to the value of the vela pulsar ( @xmath96 as derived from tab . 3 of lyne et al . 2000 ) . thus , though the average amplitude of the glitches in 1rxs j170849.0400910 and the interglitch time are consistent with those found in radio pulsars of comparable spin down age ( particularly with those of the vela pulsar ) , looking more closely at the results one finds peculiarities difficult to account for . first , the average glitch ampitude and the short interglitch time are unexpected , since slow rotators do on average experience glitches of smaller amplitude and less frequently . this result may rule out a clear dependence on the rotation period and suggest that the main role could be played by the age of the neutron star . indeed , contrary to radio pulsars with comparable rotational frequency , axps are slow but relatively young rotators . second , a fractional increase of @xmath43 as high as @xmath35 30% , and with a relatively long recovery timescale ( tens to hundreds days ) has never been observed in glitching radio pulsars . the only other source with such an anomalous behaviour is 1e 2259 + 586 , in which the glitch recently detected produced a change of @xmath35 100% in the spin first derivative , recovered over @xmath9760 d ( kaspi et al . the fact that both glitching axps , and only them , have displayed such changes of @xmath43 after a glitch hints to an axp mechanism triggering more extreme events than in radio pulsars , but a larger sample of glitches and of sources is needed to check this possibility . finally , one may explain the high fractional change of @xmath43 if the recovery in glitch n.2 is modeled as an exponential . even in this case , however , a problem is presented by the very smooth and linear recovery seen after glitch n.1 ; the star appears to have undergone an important change in its dynamical response over the short time interval elapsed between the two glitches . a way out may be assuming that the two events have been triggered by two different mechanisms , a possibility that will be discussed along with others in the following sections . it is generally assumed that neutron rich nuclei in the inner crust of a neutron star act as pinning centers for the vortices created by the superfluid in response to the rotation of the star ( andersson & itoh 1975 ) . the superfluid can follow the crust s spin down by outward migration of vortices , which is impeded by the pinning energy barrier . in vortex creep model ( alpar et al . 1984 , 1989 , 1993 ) the rotational lag ( @xmath98 ) that develops between the crust ( spinning at @xmath99 ) and the superfluid ( spinning at @xmath100 ) causes a magnus force to arise , so that vortices overcoming the pinning energy barrier through thermal activation are driven outwards by this force , establishing a continuous vortex current through which the superfluid spins down . in doing so , it exerts an internal spin up torque on the crust opposed to the magnetic braking . eventually a steady state is reached in the relaxation time @xmath101 , when both the crust and the superfluid spin down at the same rate ( @xmath102 ) with a steady state lag @xmath103 , subject to the external torque n@xmath104 . in steady state , the equation of motion is simply : @xmath105 a glitch results from an instability of the steady state . inhomogeneities of the pinning force throughout the crust determine a non uniform distribution of vortices : local values of @xmath100 will be enhanced by accumulation of vortices until a critical lag @xmath106 is reached , beyond which an avalanche unpinning of vortices occurs and angular momentum is transfered to the crust . relaxation to the new steady state will determine the post glitch recovery . the value of @xmath106 determines whether the pinning is strong or weak . at the high density of the deep crust a change in the nature of pinning is thought to occurr , bringing it to a superweak regime , even though this conclusion is not testable in terrestrial materials . the conservation of total angular momentum during the glitch gives ( alpar et . 1993 , alpar 2000 ) : @xmath107 where @xmath108 is the moment of inertia of the pinned superfluid , @xmath109 is its change in rotational frequency and the right hand side refers to the crust plus all matter components coupled to it on very short timescales : these include the bulk of the core material ( alpar , langer and sauls 1984 ) which makes up most of the moment of inertia of the star . two different situations may occur in the crustal superfluid : in type a ( accumulation ) regions unpinning takes place , vortices move outwards and repin in another type a region . for a uniform density of unpinned vortices @xmath110 ( @xmath111 in general ) . b regions exist between accumulation zones and are vortex depleted regions . thus they are decoupled from the crust and spin down only at glitches , when a net outward flux of vortices crosses them . thus they contribute to @xmath112 at the glitch but not to changes in @xmath113 . the relaxation time @xmath101 depends on whether the response of the superfluid to the initial perturbation of the lag , @xmath114 , is linear or non linear . the corresponding expressions are ( alpar et al.1989 ) : @xmath115 @xmath116 in the linear and non linear regime , respectively . the former situation will occur when @xmath117 , the latter when the steady state is close to the condition for unpinning , @xmath118 . the system will always be in the regime with the shortest time , so a transition value for @xmath119 can be found by equating the two ( alpar et al . 1993 ) . for rxs j170849.0400910 it obtains @xmath120 . if the ratio is below this limit the superfluid responds linearly , while non linearity corresponds to a value higher than critical . the non steady state equivalent of eq.([slowdown ] ) in the linear and non linear regime are , respectively ( alpar et al . 1989 ) : @xmath121 and @xmath122\mbox{exp } ( -t / \tau_{nl})}\ ] ] where @xmath123 is an offset time indicating how long , after the decoupling , the region of interest will start recoupling through creep . in the linear regime an exponential recovery is expected while nonlinear regions have a more complex response . with @xmath124=(1/2 ) and @xmath125 , @xmath113 will recover linearly in time due to the progressive recoupling of type a regions . glitch n.1 has been previously interpreted in terms of a non linear response . if most of the superfluid had been involved in vortex motion ( then @xmath126 ) , a fraction 1.72@xmath127 of the whole moment of inertia of the star needs to be contributed by the pinned superfluid . the expected time to the next glitch is then @xmath128 days ( a smaller value ensues if allowance for a significant @xmath129 is made ) , remarkably close to the measured interval of 550 days . for the recovery to be linear in time it is required that @xmath130 , implying @xmath131 even for the largest values of the ratio ( @xmath132 ) . from eq.([deltaomega ] ) and the glitch amplitude in tab.[glitch1 ] one gets @xmath133 . the condition ( alpar et al . 1989 ) @xmath134 for the non linear regime thus gives the lower bound @xmath135 . a non linear regime obtains only for a very low value of @xmath106 , requiring superweak pinning throughout most of the crust . this is surprising since superweak pinning should characterize the innermost and densest layers of the crust . the change in @xmath43 measured in glitch n.2 can not arise from a non linear response . the fractional change in @xmath43 in this regime is always less than the ratio @xmath136 ( eq.[nonlin ] ) , thus an unplausibly high moment of inertia of the superfluid would be implied . only the linear response ( and consequently an exponential recovery ) of a region where unpinning did take place ( @xmath137 ) can account for such a high fractional change . if the two glitches were due to the same mechanism , the recovery from glitch n.1 should be modeled as an exponential as well or one should invoke a change in the response regime of the superfluid . in the case of two exponential recoveries , the different timescales hint to the association of the two glitches with different regions of the superfluid . in particular , they must reflect the different values of @xmath106 or @xmath138 . the value of @xmath139 is very sensitive to the ratio ( @xmath132 ) ( eq.[taulin ] ) , so that a difference of a factor @xmath140 can arise from a small difference in that ratio . since both recoveries are fit with only one of the two exponential components , these must have unpinned alternately . stated differently , the possibility of local unpinning should be introduced in the model . the shorter recovery timescale of glitch n.2 would require a smaller @xmath106 or a lower @xmath119 , corresponding to a region of weaker pinning , given the same response regime . in particular , the smaller value of @xmath106 would imply a correspondingly larger fraction of superfluid to have unpinned , in order to produce the larger glitch n.2 . glitch n.1 may have originated in the outer layers of the crust , where @xmath106 is likely higher , leaving the more weakly pinned , inner superfluid unperturbed ( apart from the very small @xmath141 ) . the roles of the two components should be interchanged to explain glitch n.2 . anyway , in vortex creep model unpinning is a widespread rather than local mechanism ( pines 1999 , jones 2002 ) , so this would be an ad hoc assumption . if one modeled the recovery from glitch n.1 as a linear decay , a change in the response regime of at least some parts of the superfluid must have occurred over the @xmath35 500 days of interglitch time . this may happen if after glitch n.1 , where the response was non linear , a significant release of heat acted to decrease the ratio @xmath132 , bringing the latter below the transition value . however , such a heat release would require some new mechanism not included in vortex creep model ( _ e.g. _ a starquake , see sec . [ starquake ] ) . furthermore , as already discussed in sec . [ nuovidati ] , the period evolution after glitch n.2 is unusual . after the initial recovery of the spin up , the spin frequency becomes lower than expected from the extrapolation of the pre glitch solution . in the exponential fit this effect is due to the unrecovered increase in the long term spin down rate . link , epstein and baym ( 1992 ) have shown that in vortex creep model , where no explicit temporal dependence of the net ( external+internal ) torque acting on the crust is included , the post glitch spin frequency must always remain higher than the extrapolation of the pre glitch value , approaching it in the long run . [ aprilglitch ] argues against an interpretation of glitch n.2 in terms of vortex creep model , unless allowing for a change in the torque , either external or internal , induced by the glitch . in summary , one needs a contrived interpretation in order to account for the different amplitudes and recoveries of the two observed glitches within the framework of vortex creep model . in fact one should assume the two glitches to be produced by different mechanisms , thus attributing the different recoveries to the response of the star to different kinds of perturbation . one of the basic assumptions of crustal superfluid models is that the core neutron superfluid be strictly coupled to the protons ( the star s crust , core superconducting protons and degenerate electrons ) on the timescales of post glitch recoveries . the coupling is provided by scattering of the electrons following the crust spin off magnetic flux tubes that thread neutron vortex cores as a result of the entrainment induced circulation of superconducting protons around them ( alpar , langer and sauls 1984 , prix et al . it has been suggested ( andersson and comer 2001 , andersson et al . 2002 , sedrakian & sedrakian 1995 ) that the above assumption may be questionable , as the coupling time @xmath142 between neutron vortices and protons depends on the uncertain parameter @xmath143 , the ( drag to lift ) ratio between the drag force due to entrainment and the magnus force , both acting on neutron vortex lines in the decelerating core . from the above expression , @xmath144 is found to be smallest for @xmath145 , while in both cases of weak ( @xmath146 ) and strong ( @xmath147 ) coupling , @xmath144 can increase significantly . andersson et al . ( 2002 ) studied a two superfluid instability that may take place in the core of neutron stars if a rotational lag between the superfluid neutrons and the protons can develop , due to a long coupling time . the instability triggers a sudden rearrangement of the neutron vortex distribution in an outer core shell , leading to a glitch . in this model a simple formula is given to estimate the interglitch time @xmath48 in rxs j170849.0400910 . the instability takes place when the rotational lag ( @xmath18 ) between the two components is large enough to overcome the coupling due to the drag force ( @xmath148 ) . thus : @xmath149 where @xmath106 has an analogous meaning as it has in vortex creep model while @xmath150 is the spin down age of the star . assuming @xmath151 as a typical value of the lag for unpinning ( andersson et al . 2002 and references therein ) , no glitch would be expected within @xmath35 30 years after glitch n.1 . thus , for this model to apply to rxs j170849.0400910 , a very low value of @xmath152 would be required . whether such a low value still allows the lag to effectively develop is an open question . an attractive feature is that , if 30 yrs did represent the characteristic recurrence time for the core instability in 1rxs j170849.0400910 , this model would allow a natural interpretation of the different properties of the two observed glitches , since these could not be due to the same mechanism . in particular , if glitch n.2 was due to this instability , a substantial fraction of the core superfluid could have decoupled , thus explaining the large increase of @xmath43 as a significant reduction in the moment of inertia acted on by the braking torque . the different responses and recovery timescales of the two glitches would be at least qualitatively accounted for , since in glitch n.2 they would reflect mainly the dynamical relaxation of the core rather than crustal superfluid . thus two different glitch mechanisms could be at work in the same source . future timing observations will help testing this interesting possibility , as more glitches are expected . since it may take more than a decade for a new event similar to glitch n.2 to occur , the lack of such events in the next years may indeed provide an indirect hint to the viability of this picture . it has been recently shown ( wang et al . 2000 ) that most glitch models are difficult to reconcile with observations of a growing number of glitches . all models requiring a catastrophic ( _ i.e. _ widespread ) unpinning of crustal superfluid require simple correlations between the amplitudes and recovery timescales of glitches in a single source as well as an approximately constant q value , which is found not to be the case , in general . this is the same difficulty met in sec . [ vortexcreep ] for the two glitches of 1rxs j170849.0400910 . we suggested the possibility that these events were due to a local , rather than global , release of angular momentum . this is the same conclusion of wang et al.(2000 ) based on a sample of 30 glitches . an entirely different explanation with respect to those discussed previously has been proposed for at least the large glitches of radio pulsars : these may be associated to starquakes and subsequent movements of cracked platelets ( ruderman 1991 , ruderman , zhu and chen 1998 , epstein and link 2000 ) . several cracking mechanisms have been proposed for radio pulsars ; quakes have been ascribed to the stress acted on the crust by the interaction in the core between superfluid neutrons and magnetic flux tubes threading the crust ( ruderman , zhu and chen 1998 ) . alternatively , the growing strain in the crust of a spinning down neutron star may fracture it due to the resulting shear stress ( franco , link and epstein 2000 ) . whatever the trigger , the movement of a sector of the crust with its frozen in magnetic flux can cause an increase of the angle @xmath124 between the rotation and magnetic axis and a subsequent increase of the braking torque exerted on the star . the most important feature of this scenario is its local nature ; only the moving sector and its surroundings are affected leaving the rest of the star mainly unperturbed ( jones 2002 ) . further , following a starquake , a permanent increase of @xmath43 could result as a consequence of the net increase in the braking torque . a residual torque increase has indeed been observed after several glitches in the crab pulsar which may result from permanent changes in the magnetic torque ( link , epstein and baym 1992 , link & epstein 1997 ) . our exponential fit to the recovery from glitch n.2 provides evidence for an increase in the spin down rate , though greater than those observed in the crab pulsar . whether this increase is recovered over a timescale longer than 1 yr or not is a crucial question to be answered only with future observations . in vortex creep model this change would be attributed to some of the pinning layers responding non linearly to the glitch and recoverying over a time @xmath153 . if vortices did unpin in these layers a linear recovery of @xmath43 is expected , while if they did not unpin @xmath154 and a step like ( alpar et al . 1984 ) recovery of @xmath43 would occur , after a waiting time @xmath155 . on the other hand , finding no significant recovery of @xmath78 in future observations would be in agreement with the expectations from plate tectonics . in the model by ruderman , zhu and chen ( 1998 ) glitch activity is expected to cease at rotational periods p@xmath67 0.7 s because of the decreasing pull of core neutron vortices on flux tubes . thus an intrinsically different mechanism would be required to cause starquakes in slow rotators such as axps . in the case of shear stress induced fractures , the high spin down of axps may well produce starquakes . alhough it has been proved to be impossible on energetic grounds to account for the frequent glitches ( every @xmath35 2 yrs ) of the vela pulsar through this mechanism ( sauls 1988 and references therein ) , we stress that a vela like glitch in an axp ( @xmath156 ) will involve some 4 orders of magnitude less energy ( @xmath157 ) . thus the energetic argument may still leave room for spin down induced glitches in axps . however axps in the magnetar model are candidates for starquakes triggered by a peculiar mechanism ( thompson and duncan 1996 ) . the super strong magnetic field diffusing through the core can induce stresses in the crustal lattice strong enough to crack it . a range of length scales for magnetically driven fractures is expected ; continuous small scale fracturing is produced by the diffusion of the field through the crust while larger scales , comparable to the thickness of the crust , are likely involved by sudden rearrangements of the field distribution . when the crust yields , the sudden shaking of magnetic footpoints excites magnetospheric alfvn waves ; in particular , burst like enhancements of the x ray emission are expected in association with larger scale fractures . this mechanism has been proposed to explain the repeat bursts of soft gamma repeaters ( thompson @xmath158 duncan 1993 ) and may be relevant also to axps . indeed , the simultaneous occurrence of a major x ray outburst and a large glitch in the axp 1e2259 + 86 ( kaspi et al . 2003 ) has provided a strong hint in favour of this interpretation . on the other hand , observations of burst activity in sgrs have revealed no clear correlation with glitch like changes in the rotational parameters of the sources ( woods et al . 2002 , 2003 ) , making the interpretation of such effects still controversial . though the mechanism for cracking the crust may be different in axps and radio pulsars , the post starquake evolution is likely to be similar , if determined mainly by the dynamical coupling of the superfluid components to crustal matter . jones ( 2002 ) has investigated the post glitch evolution of a neutron star following a starquake , taking into account the responses of both superfluids in the crust and the core . in that picture several physical parameters determine the mutual interaction between the superfluid components and the magnetic field and the interaction of crustal vortex lines with crustal nuclei . the location at which the fracture occurs is a key element , determining the relative importance of such parameters . a variety of glitch amplitudes , recovery fractions and timescales is expected not only in different sources but also in a single one , as fractures with different dimensions and at different depths would occurr . as a general remark , the complexity of the model and its dependence on poorly known parameters make predictions , if any , and quantitative observational tests very difficult . on the other hand , its complex nature makes it more suited than other models to the description of a variety of different glitches . in particular , the two glitches of rxs j170849.0400910 do require a complex picture if not ad hoc assumptions even within other models . in the starquake scenario the two glitches would be explained assuming that the cracking and platelet movement did happen at two different locations within the crust . the unrecovered increase in the spin down rate ( @xmath159 1% ) of glitch n.2 could then be attributed to a permanent change in the braking torque . this would require a change in the inclination angle between the magnetic and rotation axes @xmath160 , actually a large value compared to expected ones ( @xmath161 , ruderman , zhu and chen 1998 ) . finally , a change in the magnetic field orientation would be expected to produce some changes in the shape of the pulse profile ( franco , link and epstein 2000 ) , such as those we may have found here , particularly after glitch n.2 .

no bursts were detected in any lightcurve , but our search was limited in sensitivity with respect to short ( t 60 ms ) bursts . observed glitch properties are compared to those of radio pulsar glitches ; current models are discussed in light of our results . starquake based models appear to be prefered on qualitative grounds . thus the two events may as well arise from two different mechanisms .

we report on a timing analysis of archival observations of the anomalous x ray pulsar 1rxs j170849.0400910 made with the rxte proportional counter array . we detect a new large glitch ( ) which occurred between 2001 march 27 and 2001 may 6 , with an associated large increase in the spin down rate ( 0.3 ) . the short time ( 1.5 yrs ) elapsed from the previously detected glitch and the large amplitude of the new spin up place this source among the most frequent glitchers , with large average glitch amplitudes , similar to those of the vela pulsar . the source shows different recoveries after the glitches : in the first one it is well described by a long term linear trend similar to those seen in vela like glitches ; in the second case the recovery is considerably faster and is better described by an exponential plus a fractional change in the long term spin down rate of the order of 1% . no recovery of the latter is detected but additional observations are necessary to confirm this result . we find minor but significant changes in the average pulse profile after both glitches . no bursts were detected in any lightcurve , but our search was limited in sensitivity with respect to short ( t 60 ms ) bursts . observed glitch properties are compared to those of radio pulsar glitches ; current models are discussed in light of our results . it appears that glitches may represent yet another peculiarity of axps . starquake based models appear to be prefered on qualitative grounds . alternative models can be applied to individual glitches but fail in explaining both . thus the two events may as well arise from two different mechanisms .

0904.4725

i

the fine structure constant today , @xmath9 , is usually thought of as a fundamental , unchanging , constant of nature , but recently both experimental and theoretical papers have challenged this assumption , ( e.g. , see the review by garcia - berro , isern , and kubyshin ( 2007 ) ) . motivated especially by the possible experimental detection ( see below ) of a change in @xmath0 , we applied for and took four nights of keck data , half of it through the keck iodine cell , on qso phl957 . our goal was to get an extremely well - calibrated , high signal / noise absorption spectrum on a distant damped ly@xmath0 ( dla ) system ( @xmath1 ) in order to measure the value of the fine structure constant more than 10 billion years ago and compare it to the value today . the basic method to determine @xmath10 , is to measure differences in redshifts between different atomic transitions of elements in the same physical system , and use the fact that for small changes in @xmath0 the energy level of a given atomic transition can be approximated as @xmath11 where @xmath12 is the frequency of the transition on earth , @xmath13 is the frequency in the high redshift cloud , and the @xmath14-values measure the dependence of @xmath13 on @xmath0 and have been calculated for many common transitions . ( see for example , murphy et al . 2001a , dzuba , et al . 2002 , and porsev , et al . 2007 for more detailed discussion and table [ tab : lineinfo ] for the values of @xmath14 for various transitions . ) the values of @xmath14 depend upon the electron orbital configurations of the initial and final quantum states , and therefore different transitions have different values of @xmath14 . if all transitions had the same @xmath14 , then all wavelength shifts would be the same and one could absorb any change in @xmath0 into the determination of the redshift of the physical system . however , since different transitions have different values of @xmath14 , the relative transition wavelengths will differ from what they are in the lab if @xmath15 . for example , murphy , et al . ( 2001a ; 2001b ; 2003 ; 2004 ) , used a many - multiplet method on keck hires data of 143 absorption systems in the redshift range @xmath16 to find a significant reduction of @xmath0 in the past , @xmath17 , while chand , et al . ( 2004 ) and srianand et al ( 2004 ) , used the same method for a subset of transitions on vlt / uves data on 23 absorbers to find @xmath18 . this latter analysis was criticized by murphy , et al . ( 2008 ) who reanalyzed the chand et al . data to get @xmath19 , consistent with their previous result . in the meantime other groups returned results , for example , levshakov , et al . ( 2006 ) used the vlt / uves spectrograph to study fe ii lines in one system at @xmath20 and found a null result , @xmath21 , and in another system at @xmath22 to find @xmath23 ( levshakov , et al . murphy , et al . ( 2006 ) have also criticized these results , claiming that the data do not allow limits as strong as those reported . subsequently , the levshakov , et al ( 2006 ) results were weakened to @xmath24 for the @xmath20 system and @xmath25 for the @xmath22 system ( molaro , et al . 2008 ) , still a null result inconsistent with the detections . given the above inconsistent results , we were particularly interested in the fe ii @xmath261608 and fe ii @xmath261611 transitions since these have @xmath14 values that are both large and more importantly of opposite sign . thus , if @xmath0 was different in the past , the relative positions of these two lines should be significantly shifted from their laboratory values . for our dla at @xmath1 , a relative shift between fe ii @xmath261608 and fe ii @xmath261611 of about @xmath27 m / s is expected if the murphy et al . value @xmath28 is correct . ( fe ii @xmath261608 shifts by @xmath29 m / s , while fe ii @xmath261611 shifts by @xmath30 m / s in the rest frame . ) thus our goal was to centroid these lines to better than 50 m / s , so as to determine @xmath8 in a single ion in a single absorption system . our method , which is close to that used by levshakov , et al 2006 , contrasts with that of murphy et al . ( 2001a ; 2001b ; 2003 ; 2004 ) and chand et al . ( 2004 ) where the signal / noise was not high enough to detect the @xmath8 signal in any single pair of lines ; they did a statistical averaging over many transitions in many absorption systems , and thus might be subject to systematic errors in selection , calibration , or averaging procedures . since we expected to have superbly well - calibrated spectra , and these two fe ii lines appear in the same echelle order we hoped we could give convincing evidence for or against a change in the fine structure constant . for our work , in addition to the fe ii lines , there are also several ni ii , si ii , al ii , and al iii lines that fall in the wavelength range covered by the iodine cell and that we can use . in what follows , besides the fe ii @xmath261608/@xmath261611 pair , various other sets of lines are used . potentially we could fit all 16 lines that have calculated @xmath14 values and that appear in our spectra : fe ii @xmath261608/@xmath261611/@xmath262344 , ni ii @xmath261709/@xmath261741/@xmath261751 , si ii @xmath261526/@xmath261808 , al iii @xmath261854/@xmath261862 , al ii @xmath261670 , cr ii @xmath26 2062/@xmath262056/@xmath262066 , and zn ii @xmath262026/@xmath262062 . if we restrict ourselves to lines that occur at wavelengths for which we have iodine spectra we would use only the 9 lines : fe ii @xmath261608/@xmath26 1611 , niii @xmath261709/@xmath261741/@xmath261751 , si ii @xmath261808 , al iii @xmath261854/@xmath261862 , and al ii @xmath261670 . if we worry that saturated lines ( those with minimum flux less than 10% ) may not be accurately fit we can restrict ourselves to the 7 lines that meet the above criteria and are unsaturated : feii @xmath261611 , niii @xmath261709/@xmath261741/@xmath261751 , siii @xmath261808 , and al iii @xmath261854/@xmath261862 . finally , we note that al iii has a systematically higher ionization potential than the other ions and is a sub - dominant ionization state of al . it thus could exist in a physically different location . thus , we most reliably consider the five calibratable , unsaturated , singly ionized transitions : feii @xmath261611 , niii @xmath261709/@xmath261741/@xmath261751 , and siii @xmath261808 .

lines in a damped ly system at . / s over a single night , and drifts of nearly 2000 m / s over several nights . these offsets correspond to an absolute redshift of uncertainty of about ( ) , with daily drifts of around ( ) , and multiday drifts of nearly ( ) . the causes of the wavelength offsets are not known , but since claimed shifts in the fine structure constant would result in velocity shifts of less than 100 m / s , this level of systematic uncertainty may make it difficult to use keck hires data to constrain the change in the fine structure constant . using our calibrated data , we applied both our own fitting software and standard fitting software to measure , but discovered that we could obtain results ranging from significant detection of either sign , to strong null limits , depending upon which sets of lines and which fitting method was used .

we report on an attempt to accurately wavelength calibrate four nights of data taken with the keck hires spectrograph on qso phl957 , for the purpose of determining whether the fine structure constant was different in the past . using new software and techniques , we measured the redshifts of various ni ii , fe ii , si ii , etc . lines in a damped ly system at . roughly half the data were taken through the keck iodine cell which contains thousands of well calibrated iodine lines . using these iodine exposures to calibrate the normal th - ar keck data pipeline output we found absolute wavelength offsets of 500 m / s to 1000 m / s with drifts of more than 500 m / s over a single night , and drifts of nearly 2000 m / s over several nights . these offsets correspond to an absolute redshift of uncertainty of about ( ) , with daily drifts of around ( ) , and multiday drifts of nearly ( ) . the causes of the wavelength offsets are not known , but since claimed shifts in the fine structure constant would result in velocity shifts of less than 100 m / s , this level of systematic uncertainty may make it difficult to use keck hires data to constrain the change in the fine structure constant . using our calibrated data , we applied both our own fitting software and standard fitting software to measure , but discovered that we could obtain results ranging from significant detection of either sign , to strong null limits , depending upon which sets of lines and which fitting method was used . we thus speculate that the discrepant results on reported in the literature may be due to random fluctuations coming from under - estimated systematic errors in wavelength calibration and fitting procedure . .2truein

0904.4725

c

we tried and failed to give a definitive answer to the question of whether the fine structure constant was different at early times in high redshift ly alpha systems . in order to investigate this problem in detail we used data taken through the keck iodine cell and wrote our fitting software from scratch . using the iodine cell for wavelength calibration we found a serious source of systematic error that did not allow calibration of the keck hires spectrograph to the precision needed . we also found degeneracies in the fitting procedures that added to the calibration systematic errors . due to all the systematic errors we were able to derive various results , running from very significant detections , to strong null limits . does this imply that a meaningful measurement of or limit on @xmath8 is impossible using keck hires ? it is not clear . perhaps more careful attention to voigt profile fitting , as advocated by m. murphy ( private communication 2008 ) will solve the fit degeneracy problem . perhaps a careful selection of absorbers would also help , or trying to focus on systems with a single component . perhaps the wavelength calibration errors we discovered can be corrected , or perhaps they will average away if a large sample of absorbers is considered . in this paper we raise these questions , but do not answer them . we also used a fisher matrix technique to investigate the minimum possible errors in @xmath8 that our spectra s signal / noise would allow . we found our fit results did not exceed these limits . for example , for the set of 9 lines used in most of our analyses , the minimum possible error on @xmath8 , as given in table [ tab : minsigdelalpha ] , is @xmath89 , a result consistent with our fit results . since the calculation of minimum possible errors is not difficult , we suggest that workers always calculate them and never report results with uncertainties smaller than the data theoretically can allow . while we have not yet looked carefully at data or analysis done by other workers in the field , we worry that some of the systematic errors and overestimation of precision we found here may also be present in other analyses . thus one possible explanation for the discrepant findings on @xmath8 discussed in the introduction , is that several workers in the field are overestimating the precision of their measurements and the discrepancies reported in the literature are due to random fluctuations occurring within the larger , under - reported , systematic errors . at this point it is not clear how to make further progress in this subject using keck hires , but other techniques such as frequency combs ( steinmetz , et al . 2008 ) may become available and be of use in resolving the question . in addition , proposed new instruments ( e.g. , codex for e - elt or espresso for the vlt ) are being designed for doppler measurement stability and will hopefully be be free of these problems . we thank david kirkman , bob carswell , marc rafelski , joel heinrich , john johnson , and michael j. simmonds for helpful discussions . we especially thank michael murphy for many insightful comments , suggestions and questions , including several that led to corrections of errors in early versions of this paper . finally , we thank nao suzuki for discussion of an early version of this paper where we discovered that he had already understood and published several of the points made here . k.g . and j.b.w . were supported in part by the doe under grant de - fg03 - 97er40546 . is partially supported by an nsf career grant ( ast-0548180 ) , and j.x.p . and a.m.w . are supported in part by nsf grant ( ast-07 - 09235 ) . the w. m. keck observatory is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w. m. keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . barlow , t. 2002 , makee keck observatory hires data reduction software ( pasadena : caltech ) , http://spider.ipac.caltech.edu/staff/tab/makee /index.html beaver , e.a . , et al . , 1972 , apj , 178 , 95 bouchy , f. , pepe , f. , and queloz , d. , 2001 , a&a , 374 , 733 butler , r.p . , et al . , 1996 , pasp , 108 , 500 carswell , r.f . , webb , j.k . , cooke , a.j . , irwin , m.j . , 2008 , vpfit version 9.5 web page , http://www.ast.cam.ac.uk/ rfc / vpfit.html chand , h. , srianand , r. , petitjean , p. , aracil , 2004 , a&a , 417 , 853 dzuba , v.a . & flambaum , v. v. , 2008 , astro - ph/0805.0461v2 dzuba , v.a . , flambaum , v. v. , kozlov , m. g. , and marchenko , m. , 2002 , phys . rev . a , 66 , 022501 garcia - berro , e. , isern , j. , & kubyshin , y.a . , 2007 , astron . , 14 , 113 kirkman , d. , et al . , 2003 , apj suppl , 149 , 1 levshakov , s.a . , et al . , 2007 , a&a , 466 , 1077 levshakov , s.a . , et al . , 2006 , a&a , 449 , 879 marcy , g. w. , 2008 , unpublished . marcy , g. w. , & butler , r.p . , 2008 , unpublished . molaro , p. , reimers , d. , agafonova , i.i . , & levshakov , s.a . , 2008 , j. st , 163 , 173 murphy , m. t. , et al . , 2001a , mnras , 327 , 1208 murphy , m. t. , webb , j. k. , flaumbaum , v. v. , churchill , c. w. , prochaska , j. x. , 2001b , mnras , 327 , 1236 murphy , m. t. , webb , j. k. , and flambaum , v. v. , 2003 , mnras , 345 , 609 murphy , m. t. , webb , j. k. , and flambaum , v. v. , 2006 , arxiv : astro - ph/0611080 murphy , m. t. , webb , j. k. , and flambaum , v. v. , 2008 , mnras , 384 , 1053 osterbrock , d. e. , et al . , 2000 , pasp , 112 , 733 porsev , s.g . , , 2007a , phys . a 76 , 052507 srianand , r. , chand , h. , petitjean , & p. , aracil , b. , 2004 , phys . , 92 , 121302 steinmetz , t. , et al . 2008 , science , 321 , 1335 . suzuki , n. , et al . 2003 , pasp , 115 , 1050 . wells , r.j . , 1999 , j.quant . transfer , 62 , 29 cccccccccc 1 nov 02 & 33 & out & 5:26 & 1800 & 3.75 & & & & + 1 nov 02 & 34 & out & 5:58 & 1800 & 3.76 & & & & + 1 nov 02 & 35 & in & 6:30 & 1800 & 3.79 & & & & + 1 nov 02 & 36 & in & 7:01 & 1800 & 3.76 & & & & + 1 nov 02 & 47 & out & 7:58 & 1800 & 3.61 & & & & + 1 nov 02 & 48 & out & 8:30 & 1800 & 3.68 & & & & + 1 nov 02 & 49 & in & 9:03 & 1800 & 3.68 & & & & + 1 nov 02 & 50 & in & 9:34 & 1800 & 3.78 & & & & + 1 nov 02 & 60 & out & 10:34 & 1800 & 3.71 & & & & + 1 nov 02 & 61 & out & 11:06 & 1800 & 3.75 & & & & + 1 nov 02 & 62 & in & 11:39 & 1800 & 3.71 & & & & + 3 oct 04 & 67/3 - 0 & out & 9:18 & 3600 & 4.26 & 66 & 09:15 & no & 0.042 + 3 oct 04 & 68/3 - 1 & in & 10:31 & 3600 & 4.21 & 66 & 09:15 & no & 0.097 + 3 oct 04 & 69/3 - 2 & in & 11:33 & 3600 & 4.07 & 66 & 09:15 & no & 0.236 + 3 oct 04 & 70/3 - 3 & out & 12:35 & 3600 & 4.00 & 66 & 09:15 & no & .0306 + 4 oct 04 & 1096/4 - 0 & out & 9:25 & 3600 & 3.00 & 1144 & 15:35 & yes & -0.153 + 4 oct 04 & 1098/4 - 1 & in & 10:56 & 3600 & 2.97 & 1144 & 16:35 & yes & -0.125 + 4 oct 04 & 1099/4 - 2 & in & 11:57 & 3600 & 3.01 & 1144 & 16:35 & yes & -0.167 + 4 oct 04 & 1100/4 - 3 & out & 12:58 & 3600 & 2.93 & 1144 & 16:35 & yes & -0.083 + 5 oct 04 & 2094/5 - 0 & in & 8:25 & 3600 & 2.87 & 2026 & 3:01 & yes & 0.125 + 5 oct 04 & 2095/5 - 1 & out & 9:27 & 3600 & 2.86 & 2107 & 15:46 & yes & 0.430 + 5 oct 04 & 2096/5 - 2 & out & 10:29 & 3600 & 2.91 & 2107 & 15:46 & yes & 0.375 + 5 oct 04 & 2097/5 - 3 & in & 11:30 & 3600 & 3.62 & 2107@xmath90 & 15:46 & yes & -0.333 + 5 oct 04 & 2098/5 - 4 & out & 12:32 & 2700 & 3.55 & 2107 & 15:46 & yes & -0.264 + cccccc fe ii @xmath261608.45 & 67 & @xmath91 & 25.0 & yes + fe ii @xmath261611.20 & 67 & @xmath92 & 153 & yes + al ii @xmath261670.79 & 65 & @xmath93 & 34.0 & yes + ni ii @xmath261709.60 & 63 & @xmath94 & 83.1 & yes + ni ii @xmath261741.55 & 62 & @xmath95 & 48.7 & yes + ni ii @xmath261751.92 & 62 & @xmath96 & 70.8 & yes + si ii @xmath261808.01 & 60 & @xmath97 & 36.4 & yes + al iii @xmath261854.72 & 58 & @xmath98 & 76.0 & yes + al iii @xmath261862.79 & 58 & @xmath99 & 125 & yes + si ii @xmath261526.71 & 71 & @xmath100 & 28.8 & no + zn ii @xmath262026.14 & 53 & @xmath101 & 129 & no + zn ii @xmath262062.66 & 52 & @xmath102 & 229 & no + cr ii @xmath262056.26 & 52 & @xmath103 & 89.9 & no + cr ii @xmath262062.24 & 52 & @xmath104 & 102 & no + cr ii @xmath262066.16 & 52 & @xmath105 & 143 & no + fe ii @xmath262344.21 & 46 & @xmath106 & 41.7 & no + all 16 lines ( 2002 and 2004 data ) & @xmath107 & @xmath108 & + all 16 lines & @xmath109 & @xmath110 & @xmath111 + 9 calibratable lines & @xmath112 & @xmath113 & @xmath89 + 7 calibratable , unsaturated lines & @xmath114 & @xmath115 & @xmath116 + fe ii @xmath261608/@xmath261611 pair & @xmath117 & @xmath118 & @xmath119 + ccrrc simple ( comp 1 ) & the ( 5 ) & @xmath120 & 1.09 & 0.35 + simple ( comp 1 ) & ( 5)+fe ii @xmath261608 & @xmath121 & 323 & @xmath122 + simple ( comp 1 ) & ( 5)+al iii @xmath261854/@xmath261862 & @xmath123 & 22 & @xmath124 + simple ( comp 1 ) & ( 5)+fe ii @xmath261608 + al iii @xmath261854/@xmath261862 & @xmath125 & 248 & @xmath126 + simple ( comp 1 ) & the ( 9 ) & @xmath127 & 264 & 0 + simple ( comp 2 ) & the ( 5 ) & @xmath128 & 0.66 & 0.57 + simple ( comp 2 ) & ( 5)+fe ii @xmath261608 & @xmath129 & 75 & @xmath130 + simple ( comp 2 ) & the ( 9 ) & @xmath131 & 92 & @xmath132 + simple ( comp 3 ) & ( 5)+fe ii @xmath261608 & @xmath133 & 3.8 & 0.004 + global joint fit & fe ii @xmath261608 and fe ii @xmath261611 pair & @xmath134 & 0.96 & - + global joint fit & the ( 5 ) & @xmath135 & 0.80 & - + global joint fit & ( 5 ) + fe ii @xmath261608 & @xmath136 & 0.92 & - + global joint fit & ( 5 ) + al iii @xmath261854/@xmath261862 & @xmath137 & 0.83 & - + global joint fit & the ( 9 ) & @xmath138 & 1.01 & - + vpfit global ( w / o iodine ) & ( 5 ) + fe ii @xmath261608 & @xmath139 & 3.1 & @xmath140 + vpfit global ( w / o iodine ) & all 16 & @xmath141 & 6.0 & @xmath142 +

we report on an attempt to accurately wavelength calibrate four nights of data taken with the keck hires spectrograph on qso phl957 , for the purpose of determining whether the fine structure constant was different in the past . using new software and techniques , we measured the redshifts of various ni ii , fe ii , si ii , etc . roughly half the data were taken through the keck iodine cell which contains thousands of well calibrated iodine lines . using these iodine exposures to calibrate the normal th - ar keck data pipeline output we found absolute wavelength offsets of 500 m / s to 1000 m / s with drifts of more than 500 m we thus speculate that the discrepant results on reported in the literature may be due to random fluctuations coming from under - estimated systematic errors in wavelength calibration and fitting procedure . .2truein

we report on an attempt to accurately wavelength calibrate four nights of data taken with the keck hires spectrograph on qso phl957 , for the purpose of determining whether the fine structure constant was different in the past . using new software and techniques , we measured the redshifts of various ni ii , fe ii , si ii , etc . lines in a damped ly system at . roughly half the data were taken through the keck iodine cell which contains thousands of well calibrated iodine lines . using these iodine exposures to calibrate the normal th - ar keck data pipeline output we found absolute wavelength offsets of 500 m / s to 1000 m / s with drifts of more than 500 m / s over a single night , and drifts of nearly 2000 m / s over several nights . these offsets correspond to an absolute redshift of uncertainty of about ( ) , with daily drifts of around ( ) , and multiday drifts of nearly ( ) . the causes of the wavelength offsets are not known , but since claimed shifts in the fine structure constant would result in velocity shifts of less than 100 m / s , this level of systematic uncertainty may make it difficult to use keck hires data to constrain the change in the fine structure constant . using our calibrated data , we applied both our own fitting software and standard fitting software to measure , but discovered that we could obtain results ranging from significant detection of either sign , to strong null limits , depending upon which sets of lines and which fitting method was used . we thus speculate that the discrepant results on reported in the literature may be due to random fluctuations coming from under - estimated systematic errors in wavelength calibration and fitting procedure . .2truein

1207.0616

i

the orion a and b clouds are the archetypes of local giant molecular clouds ( gmcs ) where interstellar gas condenses and stars are formed ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) . the clouds have been studied in various wavebands including millimeter observations of the transition lines between co rotational states , especially from @xmath8 to @xmath9 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , infrared emission ( e.g. , * ? ? ? * ) , attenuation of star light ( e.g. , * ? ? ? * ) , and near infrared extinction @xcite . the two clouds are prime targets for the large area telescope ( lat ) on - board the _ fermi gamma - ray space telescope _ ( _ fermi _ ) in the research of molecular clouds and cr interaction because they lie isolated from the galactic plane and no intense gamma - ray point source overlaps with the clouds @xcite . gamma rays from the orion - monoceros region were first detected by cos - b in the energy range between 100 mev and 5 gev @xcite . egret detected gamma rays in the range between 100 mev and @xmath3 gev @xcite . in these studies , the gamma - ray intensity distribution in a region including orion a , b and monoceros r2 was fitted with three independent contributions , one proportional to the atomic hydrogen ( ) column density , another proportional to the co line intensity ( ) to @xmath9 in @xmath10c@xmath11o . ] , and the last , a presumed isotropic distribution . under the assumptions that traces the column density , the cr spectrum does nt change in the region and spin temperature ( ) is constant , the ratio was determined , from the ratio of the gamma - ray intensities associated with the and co distributions , to be @xmath12 @xcite and @xmath13 @xcite . the ratio was not separately measured for the three clouds , orion a , b and monoceros r2 , due to the limited statistics and spatial resolution of the instruments . we note that @xcite determined on the diffuse galactic gamma rays observed by cos - b to be @xmath14 and @xcite , by comparing smoothed infrared intensity and distributions across the galaxy , determined it to be @xmath15 . since the publications on the egret data @xcite , much progress has been made in studies on orion a and b : new observational data became available ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ; study of the molecular clouds was renewed ( e.g. , * ? ? ? * ; * ? ? ? * ) ; a new modeling of the galactic diffuse gamma - ray emission was proposed incorporating large - scale cr propagation @xcite ; theoretical calculations of collisional co rotational - level excitation were revisited ( @xcite ; see also @xcite ) and the distance to the orion nebula in the orion a cloud was measured accurately @xcite . the _ fermi _ gamma - ray space telescope mission , launched on 2008 june 11 , has been surveying the sky with the large area telescope ( lat ) since 2008 august . its wide field of view , large effective area , improved spatial resolution , and broad energy coverage provide much higher sensitivity relative to its predecessor egret @xcite . studies based on egret observations have established that gamma rays from galactic molecular clouds are dominated by neutral pion decays ( which we refer to as the `` pionic gamma rays '' or `` pionic emission '' ) in the energy band between 0.2 gev and 10 gev @xcite . orion a and b are located far ( @xmath16 kpc ) from the galactic center . ] and displaced from the galactic plane by @xmath17 pc . the two clouds are only @xmath18 pc away from the solar system where spectra of cr species upto the sub - tev domain are predicted to be similar to those measured directly at the earth after correction for the solar modulation . we can now analyze orion a and b through the high - energy gamma rays detected by the _ lat in the light of the recent developments and study the relation between and mass column density ( or ) in various parts of the galaxy and obtain the total mass of the clouds ( ) typically between 100 and 2000 @xmath19 ( e.g. * ? ? ? the improved spatial resolution and higher gamma - ray statistics provided by the _ fermi_-lat allow us to determine the relation on angular scales of @xmath20 deg@xmath21 ( pixels ) , without being directly affected by the thermodynamical , chemical , or radiation environment inside the orion clouds , albeit within the limited angular resolution of the _ fermi _ lat and uncertainties due to any unresolved weak sources and cr flux variation . the results can be used conversely to study various environmental effects on in the translucent parts of clouds where most gas in orion a and b resides and where the factor has not been straightforward to derive ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? theoretical analyses have long suggested that depends on the environment and the - relation may be nonlinear ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? suggestions have also been made that depends on the relative abundances of co , , and ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the existence of gas not traced by and co at the interface between the two phases ( the `` dark gas '' ) has been discovered @xcite . the relation between the fraction of carbon in co and density in translucent and diffuse clouds has been updated based on observations and numerical simulations , for example , by @xcite . our results will be interpreted in the light of these recent works . the - relation will be characterized including the `` dark gas , '' and the measured mass column density will be related to the value at which the relation is predicted to become non - linear . in this paper we analyze diffuse gamma rays spatially associated with the molecular clouds orion a and b , extract their pionic gamma - ray components , obtain mass distributions , and compare them with those predicted for measured by @xcite and @xcite . in section [ sec_data ] we describe the gamma - ray event selection applied in this analysis . the analysis procedure is described in section [ sec_ana ] in 4 subsections : the spatial templates used to extract mass column density associated with multiple emission components are given in subsection [ subsec_spatial_templates ] ; energy - binned spatial fits on the templates are described in subsection [ subsec_spatial_fit ] ; the pionic emission is extracted from the spectra obtained in the spatial fits and is calculated thereon in subsection [ subsec_spec_ana ] ; and the total masses of orion a and b are estimated in subsection [ subsec_mass_ana ] . in section [ sec_dis ] , we assess systematic uncertainties in the analyses ; check the results with recent infrared excess emission maps by @xcite ; summarize the results ; and interpret them in the light of recent studies of the relation between the and co fraction in the translucent clouds . the paper is concluded in section [ sec_conclusion ] .

we present here such distributions for orion a and b , and correlate them with those of the velocity integrated co intensity ( ) at a pixel level . the -to - mass conversion factor , , is found to be for the high - longitude part of orion a ( ) , times higher than found for the rest of orion a and b. we interpret the apparent high in the high - longitude region of orion a in the light of recent works proposing a non - linear relation between and co densities in the diffuse molecular gas .

we report on the gamma - ray observations of giant molecular clouds orion a and b with the large area telescope ( lat ) on - board the _ fermi gamma - ray space telescope_. the gamma - ray emission in the energy band between mev and gev is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the galactic cosmic rays ( crs ) and interstellar gas . the gamma - ray production cross - section for the nuclear interaction is known to% precision which makes the lat a powerful tool to measure the gas mass column density distribution of molecular clouds for a known cr intensity . we present here such distributions for orion a and b , and correlate them with those of the velocity integrated co intensity ( ) at a pixel level . the correlation is found to be linear over a range of fold when divided in 3 regions , suggesting penetration of nuclear crs to most of the cloud volumes . the -to - mass conversion factor , , is found to be for the high - longitude part of orion a ( ) , times higher than found for the rest of orion a and b. we interpret the apparent high in the high - longitude region of orion a in the light of recent works proposing a non - linear relation between and co densities in the diffuse molecular gas . decreases faster than the column density in the region making the gas `` darker '' to .

1207.0616

c

we have reported on the first 21 months observations of orion a and b with the _ fermi gamma - ray space telescope _ in the energy band between @xmath176 mev and @xmath0 gev . we have measured the mass column density distribution within the clouds at the angular scale of the instrument psf using the @xmath141 production cross - section accurately calibrated at accelerators as well as using the gamma - ray emissivity of the local gas . we found with the pionic method that a linear relation holds between mass density and with @xmath177 @xmath178 , @xmath179 , @xmath180 @xmath181 with a systematic uncertainty of @xmath161 , @xmath162 , and @xmath163% ( relative in the 3 regions ) , and @xmath158 , @xmath159 , and @xmath160% ( absolute ) for orion a region i , region ii , and orion b , respectively . these values are consistent with the values determined with the more traditional / method ( @xmath182 @xmath183 , @xmath184 , @xmath185 @xmath181 ) within our overall systematic error . this implies that galactic crs are penetrating into most parts of the clouds . the analyses also included the `` dark gas '' @xcite not traced by co or . we found that the gamma - ray flux associated with the `` dark gas '' spatial template exceeds that associated with the template in orion a region i. the situation is reversed in region ii and in orion b. this is generally consistent with the fit finding a higher value for orion region i in the absence of the dark - gas template . we have interpreted the increase in and `` dark gas '' fraction in orion a region i in the light of recent studies of the relation between the and co fractions by @xcite . is expected to increase rapidly as the gas column density decreases to @xmath186 or less @xcite . the mass column density we have measured in region i corresponds to @xmath187 , close to the predicted threshold for onset of the non - linearity predicted between and . the mass column density drops further ( @xmath188 ) toward the high galactic longitude end of the orion a where the gas becomes `` dark '' to , consistent with the predicted non - linear relation . the _ fermi_-lat collaboration is continuing to reduce uncertainty in the irf , identify extended gamma - ray sources , and improve the modeling of the galactic - scale diffuse gamma - ray emission . we expect the systematic uncertainties quoted in subsection [ subsec_error_ana ] to be reduced significantly through these efforts . the systematic uncertainty in the cr spectra and the mass density also will be reduced when the data from new experiments and surveys become available . the present analyses can then be updated to a higher precision and the relation among and the gas mass density characterized further for various molecular clouds in the galaxy . the _ fermi _ lat collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the lat as well as scientific data analysis . these include the national aeronautics and space administration and the department of energy in the united states , the commissariat lenergie atomique and the centre national de la recherche scientifique / institut national de physique nuclaire et de physique des particules in france , the agenzia spaziale italiana and the istituto nazionale di fisica nucleare in italy , the ministry of education , culture , sports , science and technology ( mext ) , high energy accelerator research organization ( kek ) and japan aerospace exploration agency ( jaxa ) in japan , and the k. a. wallenberg foundation , the swedish research council and the swedish national space board in sweden . kalberla , p. m. w. , mcclure - griffiths , n. m. , pisano , d. j. and calabretta , m. r. , alyson ford , h. , lockman , f. j. , staveley - smith , l. , kerp , j. , winkel , b. , murphy , t. , & newton - mcgee , k. 2010 , , 521 , a17 ccccc @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath193 + @xmath194 & @xmath195 & @xmath196 & @xmath197 & @xmath198 + @xmath199 & @xmath200 & @xmath201 & @xmath202 & @xmath203 + @xmath204 & @xmath205 & @xmath206 & @xmath207 & @xmath208 + @xmath209 & @xmath210 & @xmath211 & @xmath212 & @xmath213 + @xmath214 & @xmath215 & @xmath216 & @xmath217 & @xmath218 + @xmath219 & @xmath220 & @xmath221 & @xmath222 & @xmath223 + @xmath224 & @xmath225 & @xmath226 & @xmath227 & @xmath228 + @xmath229 & @xmath230 & @xmath231 & @xmath232 & @xmath233 + @xmath234 & @xmath235 & @xmath236 & @xmath237 & @xmath238 + @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 + @xmath244 & @xmath245 & @xmath246 & @xmath247 & @xmath248 + @xmath249 & @xmath250 & @xmath251 & @xmath252 & @xmath253 + @xmath254 & @xmath255 & @xmath256 & @xmath257 & @xmath258 + @xmath259 & @xmath260 & @xmath261 & @xmath262 & @xmath263 [ abctable ] lllll + entire roi & @xmath264 & na & @xmath265 & na + + orion a region i & @xmath266 & @xmath153 & @xmath267 & @xmath158 + orion a region ii & @xmath268 & @xmath154 & @xmath269 & @xmath159 + orion b & @xmath270 & @xmath155 & @xmath271 & @xmath160 + elsewhere & @xmath269 & na@xmath272 & @xmath273 & na@xmath274 + + entire roi & @xmath275 & @xmath276%@xmath277 & @xmath278 & @xmath279@xmath277 + [ tablexco ] cccc @xmath189 & @xmath280 & @xmath281 & @xmath282 + @xmath194 & @xmath283 & @xmath284 & @xmath285 + @xmath199 & @xmath286 & @xmath287 & @xmath288 + @xmath204 & @xmath289 & @xmath290 & @xmath291 + @xmath209 & @xmath292 & @xmath293 & @xmath294 + @xmath214 & @xmath295 & @xmath296 & @xmath297 + @xmath219 & @xmath298 & @xmath299 & @xmath300 + @xmath224 & @xmath301 & @xmath302 & @xmath303 + @xmath229 & @xmath304 & @xmath305 & @xmath306 + @xmath234 & @xmath307 & @xmath308 & @xmath309 + @xmath239 & @xmath310 & @xmath311 & @xmath312 + @xmath244 & @xmath313 & @xmath314 & @xmath315 + @xmath249 & @xmath316 & @xmath317 & @xmath318 + @xmath254 & @xmath319 & @xmath320 & @xmath321 + @xmath259 & @xmath322 & @xmath323 & @xmath324 [ darkgas_table ]

we report on the gamma - ray observations of giant molecular clouds orion a and b with the large area telescope ( lat ) on - board the _ fermi gamma - ray space telescope_. the gamma - ray emission in the energy band between mev and gev is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the galactic cosmic rays ( crs ) and interstellar gas .

we report on the gamma - ray observations of giant molecular clouds orion a and b with the large area telescope ( lat ) on - board the _ fermi gamma - ray space telescope_. the gamma - ray emission in the energy band between mev and gev is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the galactic cosmic rays ( crs ) and interstellar gas . the gamma - ray production cross - section for the nuclear interaction is known to% precision which makes the lat a powerful tool to measure the gas mass column density distribution of molecular clouds for a known cr intensity . we present here such distributions for orion a and b , and correlate them with those of the velocity integrated co intensity ( ) at a pixel level . the correlation is found to be linear over a range of fold when divided in 3 regions , suggesting penetration of nuclear crs to most of the cloud volumes . the -to - mass conversion factor , , is found to be for the high - longitude part of orion a ( ) , times higher than found for the rest of orion a and b. we interpret the apparent high in the high - longitude region of orion a in the light of recent works proposing a non - linear relation between and co densities in the diffuse molecular gas . decreases faster than the column density in the region making the gas `` darker '' to .

astro-ph9910319

i

the gamma - ray burst ( grb ) of may 8 , 1997 was a watershed event in the study of these intriguing objects . there were two major advances resulting from afterglow observations of : ( 1 ) the first unambiguous evidence that some grbs are a cosmological population was obtained with the detection of red - shifted metal lines in absorption against the optical afterglow ( metzger et al . the resulting lower limit on the distance , combined with the measured gamma - ray fluence , established an approximate energy scale for these events . ( 2 ) the discovery of the first radio afterglow and the demonstration of relativistic expansion of the fireball ( frail et al . the latter was made possible by the observations of distinctive variations in the radio flux and attributed to interstellar scintillation ( goodman 1997 ) . it is worth noting that grbs now join quasars and galactic micro - quasars as sources for which superluminal motions have been inferred . the afterglow from grb 970508 was particularly bright and long - lived . indeed , to this date , this grb remains unusual in both these respects . consequently , astronomers carried out intensive observations of the afterglow across the electromagnetic spectrum . the principal motivation of the observations were to infer the fundamental parameters of the explosion : the total energy of the explosion ( @xmath7 ) , the distribution of the circumburst medium ( density , @xmath8 and possible radial dependence as would be the case if the explosion took place in a circumburst medium shaped by mass loss from the progenitor ) and the geometry of the afterglow ( sphere versus collimated flow or `` jets '' ) . of all the parameters listed above , @xmath7 is perhaps the most eagerly sought parameter . after all , in a manner similar to supernovae , it is @xmath7 which sets the scale for the entire grb phenomenon and thus it is a truly fundamental parameter of the explosion . with few exceptions ( katz & piran 1997 , brainerd 1998 ) most of the early estimates for @xmath7 ( waxman 1997 , wijers & galama 1999 , granot et al . 1999 ) lie within a factor of three of @xmath9 erg . although their precise methodologies differ , all of these determinations use information gleaned from the early afterglow observations . unfortunately , the lorentz factor is large during the early phase and due to relativistic beaming the observer sees only solid angle @xmath10 of the emitting surface . thus the inferred energy is necessarily the `` isotropic equivalent '' value . however , if fireballs are jet sources ( as appears to be the case ) , such `` isotropic equivalent '' estimates are upper limits and in some cases can be gross upper limits ( e.g. grb 990510 , harrison et al . 1999 ) radio observations are essentially immune from the geometry of the fireball and thus offer us the best method to infer @xmath7 since much of the radio afterglow is emitted at later epoch when @xmath11 is falling . indeed , over the duration of the radio emission , the emitting material typically becomes sub - relativistic . once the flow becomes sub - relativistic it will in due course also become spherical . thus observations of radio afterglows allow us the opportunity of inferring @xmath7 without the usual concerns of the geometry of the fireball . radio observations offer two additional advantages : ( 1 ) at x - ray and optical wavelengths , the afterglow emission rapidly enters the monotonic decaying regime within minutes to hours of the burst . unfortunately , at the current time , logistical difficulties prevent us from responding so rapidly to grb events . x - ray and optical afterglow observations are typically initiated hours after the burst . however , at radio wavelengths , the entire afterglow phenomenon is stretched in time . thus monitoring the radio afterglow observations allows us to see all the important transitions ( save the cooling transition ) which in turn provides key diagnostics to infer the fundamental parameters of the explosion . ( 2 ) radio observations offer us , via interstellar scintillations , the only way to measure the tiny angular size ( few microarcseconds ) of grb afterglows . the measured size in turn allows us to verify the dynamics of the explosion . in this paper , we present the complete radio light curves from the radio afterglow of beginning 3.5 hrs after the burst and ending 450 d later when the source was no longer detectable . this is the third and final paper of an ambitious monitoring program that we initiated following the discovery of radio afterglow from . in the first paper ( frail et al . 1997 ) we reported the discovery of the radio afterglow and the first 90 d of observations , and we interpreted the strong variations as being due to diffractive scintillation . in the second paper ( waxman , kulkarni & frail 1998 ; hereafter , wkf98 ) we compared these observations to theoretical models and showed that the size estimated from diffractive scintillation was in excellent accord with that expected from hydrodynamical models . in the same paper we noted that the observed flux at late times ( @xmath12 d ) was well below that predicted by a spherical model and suggested that this deviation was most likely explained by a jet - like geometry for the fireball rather than a sphere . we suggested that @xmath7 would be significantly lower than the @xmath9 erg isotropic equivalent estimate from the early afterglow observations and the isotropic equivalent @xmath3-ray energy release and further suggested that the fireball would undergo a transition from relativistic to sub - relativistic expansion at @xmath0 d. the organization of the paper is as follows . the observations are summarized in [ sec : observations ] . in [ sec : results ] we present the basic results in the form of light curves in three bands , 8.46 ghz , 4.86 ghz and 1.43 ghz . in [ sec : riss ] we note a transition of the variations in the light curve from the diffractive to the refractive regimes . in [ sec : spherical ] we compare the data to the expectations from the simple adiabatic fireball model . in [ sec : deviations ] we point out important deviations from model predictions and argue that the afterglow was not spherical but was a jet with an opening angle of about 30 degrees . finally , in [ sec : sub - relativistic ] we propose a detailed sub - relativistic model which provides a satisfactory explanation to the very late time observations . the transition to non - relativistic regime allows us to carry out proper calorimetry of the explosion ( [ sec : calorimetry ] ) .

we report on the results of an extensive monitoring campaign of the radio afterglow of grb 970508 , lasting 450 days after the burst . the spectral and temporal radio behavior indicate that the fireball has undergone a transition to sub - relativistic expansion at days . this allows us to perform `` calorimetry '' of the explosion . a natural consequence of this result , which can also account for deviations at days from the spherical relativistic fireball model predictions , is that the fireball was initially a wide - angle jet of opening angle . the inferred density rules out the possibility that the fireball expands into a strongly non - uniform medium , as would be expected , e.g. , in the case of a massive star progenitor . no . no . . lett . ,

we report on the results of an extensive monitoring campaign of the radio afterglow of grb 970508 , lasting 450 days after the burst . the spectral and temporal radio behavior indicate that the fireball has undergone a transition to sub - relativistic expansion at days . this allows us to perform `` calorimetry '' of the explosion . the derived total energy , erg is well below the erg inferred under the assumption of spherical symmetry from-ray and early afterglow observations . a natural consequence of this result , which can also account for deviations at days from the spherical relativistic fireball model predictions , is that the fireball was initially a wide - angle jet of opening angle . our analysis also allows to determine the energy fractions carried by electrons and magnetic field , and the density of ambient medium surrounding the fireball . we find that during the sub - relativistic expansion electrons and magnetic field are close to equipartition , and that the density of the ambient medium is . the inferred density rules out the possibility that the fireball expands into a strongly non - uniform medium , as would be expected , e.g. , in the case of a massive star progenitor . #1#2#3#1 , a&a , # 2 , # 3 . # 1#2#3#1 , a&as , # 2 , # 3 . # 1#2#3#1 , aj , # 2 , # 3 . # 1#2#3#1 , _ ap . j. _ , * # 2 * , # 3 . # 1#2#3#1 , _ ap . j. ( letters ) _ , * # 2 * , # 3 . # 1#2#3#1 , apjs , # 2 , # 3 . # 1#2#3#1 , ara&a , # 2 , # 3 . # 1#2#3#1 , baas , # 2 , # 3 . # 1#2#3#1 , icarus , # 2 , # 3 . # 1#2#1 , iau circ . no . # 2 # 1#2#1 , gcn circ . no . # 2 # 1#2#3#1 , _ m.n.r.a.s . _ , * # 2 * , # 3 . # 1#2#3#1 , _ nature _ , * # 2 * , # 3 . # 1#2#3#1 , pasj , # 2 , # 3 . # 1#2#3#1 , pasp , # 2 , # 3 . # 1#2#3#1 , qjras , # 2 , # 3 . # 1#2#3#1 , science , # 2 , # 3 . # 1#2#3#1 , soviet astr . , # 2 , # 3 . # 1#2#3#1 , soviet astr . lett . , # 2 , # 3 . # 1#2#3#4#1 , # 2 , # 3 , # 4 . # 1#1 .

astro-ph0203491

c

the observations obtained for sn 1999ee constitute the most complete spectral and temporal coverage ever achieved for a sn ia . its branch - normal character makes it an ideal reference for comparative studies of sne ia . before maximum light sn 1999ee displayed a normal spectrum with a strong si ii @xmath06355 absorption , thus showing that not all slow - declining sne are spectroscopically peculiar at these evolutionary phases . we conclude that the photometric properties of luminous sne ia can not be used to predict spectroscopic peculiarities . from a comparison of the ir spectra of sn 1999ee and other sne ia that encompass a wide range in decline rates we find that there is a remarkable homogeneity among the branch - normal sne ia during their first 60 days of evolution . although the slow - decliner luminous sn 2000cx showed a premaximum featureless ir spectrum similar to that of normal sne , the mg ii @xmath45 line was characterized by a high expansion velocity . the fast - decliner subluminous sn 1999by was noticeably different than the other sne at all epochs . this study reveals that the spectroscopic peculiarities displayed by sn 1991bg - like objects at optical wavelengths are also present in the ir . the fortunate occurrence of sn 1999ex within three weeks and in the same galaxy that hosted sn 1999ee permitted us to obtain optical and ir spectroscopy of a ib / c event . sn 1999ex was characterized for the lack of hydrogen lines , weak optical he i lines , and strong he i @xmath010830,20581 , thus providing an example of an intermediate case between pure ib and ic sne . we conclude therefore that sn 1999ex provides first clear evidence for a link between the ib and ic classes and that there is a continuous spectroscopic sequence ranging from the he deficient sne ic to the sne ib which are characterized by strong optical he i lines . m. h. is very grateful to las campanas and cerro caln observatories for allocating an office and providing generous operational support to the soirs program during 1999 - 2000 . m. h. and j. m. thank the eso , ctio , and las campanas visitor support staffs for their assistance in the course of our observing runs , and the director general of eso for allocating director s discretionary telescope time to this project . we are very grateful to a. filippenko , p. hflich , s. jha , d. leonard , w. li , p. meikle , r. rudy , and j. spyromilio , for making us available their spectra of sne 1984l , 1987 m , 1994d , 1994i , 1999by , 1998bu , and 2000cx . support for this work was provided by nasa through hubble fellowship grant hst - hf-01139.01-a awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . j.m . acknowledges support from fondecyt grant 1980172 . this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . this research has made use of the simbad database , operated at cds , strasbourg , france . axelrod , t. s. 1980 , ph . d. thesis , univ . california at santa cruz baron , e. , branch , d. , hauschildt , p. h. , filippenko , a. v. , & kirshner , r. p. 1999 , , 527 , 739 bowers , e. j. c. , meikle , w. p. s. , geballe , t. r. , walton , n. a. , pinto , p. a. , dhillon , v. s. , howell , s. b. , & harrop - allin , m. k. 1997 , , 290 , 663 branch , d. , fisher , a. , & nugent , p. 1993 , , 106 , 2383 clocchiatti , a. , wheeler , j. c. , brotherton , m. s. , cochran , a. l. , wills , d. , barker , e. s. , & turatto , m. 1996 , , 462 , 462 elias , j. h , frogel , j. a. , hackwell , j. a. , & persson , s. e. 1981 , , 251 , l13 elias , j. h , matthews , k. , neugebauer , g. , & persson , s. e. 1985 , , 296 , 379 filippenko , a. v. 1988 , , 96 , 1941 filippenko , a. v. , matheson , t. , & ho , l. c. 1993 , , 415 , l103 filippenko , a. v. , et al . 1995 , , 450 , l11 filippenko , a. v. 1997 , , 35 , 309 garnavich , p. m. , et al . 2001 , , submitted ( astro - ph/0105490 ) gray , r. o. , & corbally , c. j. 1994 , , 107 , 742 hamuy , m. , suntzeff , n. b. , heathcote , s. r. , walker , a. r. , gigoux , p. , & phillips , m. m. 1994 , , 106 , 566 hamuy , m. , et al . 1996 , , 112 , 2408 hamuy , m. , & phillips , m. m. 1999 , iauc 7310 hamuy , m. , et al . 2001 , , 558 , 615 hernndez , m. , et al . 2000 , , 319 , 223 hflich , p. , khokhlov , a. m. , & wheeler , j. c. 1995 , , 444 , 831 hflich , p. , gerardy , c. l. , fesen , r. a. , & sakai , s. 2002 , , in press ( astro - ph/0112126 ) jha , s. , et al . 1999 , , 125 , 73 krisciunas , k. , hastings , n. c. , loomis , k. , mcmillan , r. , rest , a. , riess , a. g. , & stubbs , c. 2000 , , 539 , 658 krisciunas , k. , et al . 2002 , in preparation leibundgut , b. , kirshner , r. p. , filippenko , a. v. , shields , j. , c. , foltz , c. b. , phillips , m. m. , & sonneborn , g. 1991 , , 371 , l23 li , w. , filippenko , a. v. , & riess , a. g. 2001a , , 546 , 719 li , w. , filippenko , a. v. , treffers , r. r. , riess , a. g. , hu , j. , & qiu , y. l. 2001b , , 546 , 734 li , w. , et al . 2001c , , 113 , 1178 lira , p. , et al . 1998 , , 115 , 234 maiolino , r. , rieke , g. h. , & rieke , m. j. 1996 , , 111 , 537 matheson , t. , filippenko , a. v. , li , w. , leonard , d. c. , & schields , j. c. 2001 , , 121 , 1648 maza , j. , & hamuy , m. , iauc 7272 meikle , w. p. s , et al . 1996 , , 281 , 263 millard , j. , et al . 1999 , , 527 , 746 moorwood , a. f. 1997 , in proc . spie , vol . 2871 , 1146 munari , u. , & zwitter , t. 1997 , , 318 , 269 phillips , m. m , wells , l. a. , suntzeff , n. b. , hamuy , m. , leibundgut , b. , kirshner , r. p. , & foltz , c. b. 1992 , , 103 , 1632 phillips , m. m , lira , p. , suntzeff , n. b. , schommer , r. a. , hamuy , m. , & maza , j. 1999 , , 118 , 1766 pinto , p. a. , & eastman , r. g. 2000 , , 530 , 757 qiu , y. , li . w. , qiao , q. , & hu , j. 1999 , , 117 , 736 rudy , r. j. , lynch , d. k. , mazuk , s. , venturini , c. c. , puetter , r. c. , & hflich , p. 2002 , , 565 , 413 schlegel , d. j. , finkbeiner , d. p. , & davis , m. 1998 , , 500 , 525 spyromilio , j. , pinto , p. a. , & eastman , r. g. 1994 , , 266 , l17 stritzinger , m. , et al . 2002 , in preparation van dyk , s. d. , hamuy , m. , & filippenko , a. v. 1996 , , 111 , 2017 wheeler , j. c. , & harkness , r. p. 1990 53 , 1467 wheeler , j. c. , hflich , p. , harkness , r. p. , & spyromilio , j. 1998 , , 496 , 908 woosley , s. e. , langer , n. , & weaver , t. a. 1995 , , 448 , 315 1999 oct 09 & 460.53 & paranal & vlt / antu & isaac & rockwell1k & & 5,4,3,2 & 0.98 - 2.50 & 2.9,3.6,4.7,7.1 & clear & hamuy , lidman + 1999 oct 09 & 460.56 & tololo & 4-m & r - c spec . & loral3kx1k & kpgl-2 & 1 & 0.33 - 0.87 & 1.9 & cirrus & maza + 1999 oct 11 & 462.52 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.33 - 1.01 & 2.7,3.5 & clear & hamuy , doublier + 1999 oct 16 & 467.56 & campanas & 2.5-m & wfccd & tek2048 & blue & & 0.36 - 0.92 & 3.0 & clouds ? & phillips + 1999 oct 18 & 469.49 & la silla & ntt & sofi & rockwell1k & red & & 1.50 - 2.53 & 10.2 & clear & doublier , maza + 1999 oct 18 & 469.60 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.33 - 1.00 & 2.7,3.5 & clear & maza + 1999 oct 19 & 470.50 & paranal & vlt / antu & isaac & rockwell1k & & 5,4,3,2 & 0.98 - 2.50 & 2.9,3.6,4.7,7.1 & clear & hamuy , cuby , petr + 1999 oct 20 & 471.56 & la silla & d1.5-m & dfosc & loral2kx2k & 3,5 & 1 & 0.33 - 0.98 & 2.3,3.1 & & pompei + 1999 oct 22 & 473.61 & la silla & ntt & sofi & rockwell1k & blue , red & & 0.95 - 2.47 & 7.0,10.2 & clear & hainaut , lefloch + 1999 oct 25 & 476.51 & la silla & d1.5-m & dfosc & loral2kx2k & 3,5 & 1 & 0.33 - 0.98 & 2.3,3.1 & clear & augusteyn + 1999 oct 26 & 477.48 & la silla & ntt & sofi & rockwell1k & blue , red & & 0.95 - 2.46 & 7.0,10.2 & & hainaut , vanzi + 1999 oct 27 & 478.52 & tololo & 1.5-m & r - c spec . & loral1.2kx0.8k & 58 & 2 & 0.37 - 0.50 & 1.1 & clear & olsen + 1999 oct 29 & 480.51 & la silla & d1.5-m & dfosc & loral2kx2k & 3,5 & 1 & 0.34 - 0.98 & 2.3,3.1 & & augusteyn + 1999 nov 02 & 484.49 & paranal & vlt / antu & isaac & rockwell1k & & 5,4,3,2 & 0.98 - 2.50 & 2.9,3.6,4.7,7.1 & clear & hamuy , lidman , petr + 1999 nov 03 & 485.62 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.33 - 1.01 & 2.7,3.5 & & maza + 1999 nov 06 & 488.52 & la silla & ntt & sofi & rockwell1k & blue & & 0.94 - 1.65 & 7.0 & clear & brillant + 1999 nov 06 & 488.53 & la silla & d1.5-m & dfosc & loral2kx2k & 3,5 & 1 & 0.34 - 0.98 & 2.3,3.1 & clear ? & augusteyn + 1999 nov 09 & 491.50 & la silla & ntt & sofi & rockwell1k & blue , red & & 0.95 - 2.51 & 7.0,10.2 & clear & hamuy , brillant + 1999 nov 09 & 491.62 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.34 - 1.00 & 2.7,3.5 & clear & hamuy , brillant + 1999 nov 14 & 496.56 & la silla & ntt & sofi & rockwell1k & blue , red & & 0.95 - 2.46 & 7.0,10.2 & clear & hamuy , doublier + 1999 nov 14 & 496.62 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.34 - 1.00 & 2.7,3.5 & clear & hamuy , doublier + 1999 nov 18 & 500.53 & paranal & vlt / antu & isaac & rockwell1k & & 5,4,3,2 & 0.98 - 2.50 & 2.9,3.6,4.7,7.1 & clear & serv . + 1999 nov 19 & 501.58 & la silla & ntt & emmi & tek1024 + 2048 & 5,13 & 1 & 0.34 - 1.00 & 2.7,3.5 & clear & hamuy , doublier + 1999 nov 28 & 510.52 & paranal & vlt / antu & isaac & rockwell1k & & 5,4,3,2 & 0.98 - 2.50 & 2.9,3.6,4.7,7.1 & clear & hamuy , lidman , chadid + 1999 nov 28 & 510.63 & la silla & d1.5-m & dfosc & loral2kx2k & 3,5 & 1 & 0.40 - 0.98 & 2.3,3.1 & & pinfield +

sn 1999ee displayed a normal spectrum with a strong si ii absorption , thus showing that not all slow - declining sne are spectroscopically peculiar at these evolutionary phases . a comparative study of the infrared spectra of sn 1999ee and other type ia supernovae shows that there is a remarkable homogeneity among the branch - normal sne ia during their first 60 days of evolution . sn 1999ex was characterized by the lack of hydrogen lines , weak optical he i lines , and strong he i,20581 , thus providing an example of an intermediate case between pure ib and ic supernovae . we conclude therefore that sn 1999ex provides first clear evidence for a link between the ib and ic classes and that there is a continuous spectroscopic sequence ranging from the he deficient sne ic to the sne ib which are characterized by strong optical he i lines .

we report optical and infrared spectroscopic observations of the type ia sn 1999ee and the type ib / c sn 1999ex , both of which were hosted by the galaxy ic 5179 . for sn 1999ee we obtained a continuous sequence with an unprecedented wavelength and temporal coverage beginning 9 days before maximum light and extending through day 42 . before maximum light sn 1999ee displayed a normal spectrum with a strong si ii absorption , thus showing that not all slow - declining sne are spectroscopically peculiar at these evolutionary phases . a comparative study of the infrared spectra of sn 1999ee and other type ia supernovae shows that there is a remarkable homogeneity among the branch - normal sne ia during their first 60 days of evolution . sn 1991bg - like objects , on the other hand , display spectroscopic peculiarities at ir wavelengths . sn 1999ex was characterized by the lack of hydrogen lines , weak optical he i lines , and strong he i,20581 , thus providing an example of an intermediate case between pure ib and ic supernovae . we conclude therefore that sn 1999ex provides first clear evidence for a link between the ib and ic classes and that there is a continuous spectroscopic sequence ranging from the he deficient sne ic to the sne ib which are characterized by strong optical he i lines .

0706.3424

i

we have presented deimos spectra for objects detected by _ galex _ in the mis survey with imaged counterparts in sdss ; a total exposure time of 30 min per slitmask was used . galex has proven to be a sensitive instrument for wide field galaxy surveys . we have shown that the _ galex _ medim imaging survey followed up with a 30 m integration with keck / deimos yields redshifts and line measurements for star forming galaxies to z@xmath4 0.7 , and has yielded 4 qso s 3 of which are previously un cataloged . the matched sample reaches approximately 3 magnitudes fainter in _ r _ than the sdss spectroscopic survey limits . the sample is not a homogenous sample , but is indicative of the types of galaxies forming stars out to z@xmath106 . we have derived physical parameters for these galaxies from the seds and compared this sample to a sample of 50,000 sdss galaxies with galex detections . we find that roughly one - third of the galaxies are starforming late type disk galaxies , four are qsos at @xmath3 , and the remaining galaxies are faint blue low mass starbursts . approximately 3 out of 14 star formimg galaxies show emission line ratios indicative of an agn . a similar fraction was found by @xcite in their uv selected sample . the masses of the galaxies are typically lower than what is found locally in the sdss spectroscopic sample . the range of @xmath107 for the deimos sample spans from @xmath108 to @xmath109 , whereas the median of the sdss spectroscopic sample is @xmath110 . + + 4 . the sfrs of the galaxies at @xmath62 are roughly an order of magnitude greater than the sfrs for the galaxies at @xmath61 . besides three of the most massive , and reddest in nuv -r color , the remaining galaxies show evidence of a starburst in the last 100 myr , with @xmath111 . fifteen of the galaxies in the lower mass range of the sample could have formed more than 20% of their stellar mass in bursts of star formation within the last 100 myr . our sample has similar velocity dispersions , sfrs , and b luminosities to previous samples of faint blue galaxies , though the galaxies in our present study are 2 mag fainter in surface brightess . _ galex _ is a nasa small explorer , launched in april 2003 . we gratefully acknowledge nasa s support for construction , operation , and science analysis for the galex mission , developed in cooperation with the centre national detudes spatiales of france and the korean ministry of science and technology . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . the analysis pipeline used to reduce the deimos data was developed at uc berkeley with support from nsf grant ast-0071048 . abazajian , k. et al . 2004 , , 128 , 502 baldwin , j. a. , phillips , m. m. , & terlevich , r. 1981 , pasp , 93 , 5 bertin , 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apj , 619 , 15 wyder , t. k. 2006 , in preparation 587725578037494738 & 0.474 & 7.23 @xmath81 5.29 & 2.11 @xmath81 0.51 & 2.54 @xmath81 0.29 & * * * @xmath81 * * * & * * * @xmath81 * * * & 2.83 @xmath81 0.72 & * * * @xmath81 * * * + 587725578037494286 & 0.134 & * * * @xmath81 * * * & 2.05 @xmath81 0.20 & 2.57 @xmath81 0.22 & 4.51 @xmath81 0.05 & 3.46 @xmath81 0.13 & 1.37 @xmath81 0.18 & 0.25 @xmath81 0.01 + 587725591459201372 & 0.615 & 4.63 @xmath81 1.24 & 3.02 @xmath81 0.50 & 3.74 @xmath81 0.33 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.46 @xmath81 0.28 & * * * @xmath81 * * * + 587725578037495014 & 0.213 & * * * @xmath81 * * * & 6.16 @xmath81 4.88 & 4.83 @xmath81 4.78 & 58.32 @xmath81 30.70 & 3.91 @xmath81 16.30 & 1.12 @xmath81 1.38 & 0.98 @xmath81 0.60 + 587725578037494283 & 0.084 & * * * @xmath81 * * * & 0.82 @xmath81 0.25 & 1.17 @xmath81 0.25 & 2.36 @xmath81 0.05 & 1.68 @xmath81 0.10 & 1.84 @xmath81 0.69 & 0.27 @xmath81 0.02 + 587725591459201726 & 0.439 & 5.21 @xmath81 0.35 & 3.17 @xmath81 0.18 & 3.34 @xmath81 0.06 & * * * @xmath81 * * * & * * * @xmath81 * * * & 4.95 @xmath81 0.30 & * * * @xmath81 * * * + 587725591459201125@xmath113 & 0.066 & * * * @xmath81 * * * & 7.74 @xmath81 0.19 & 2.74 @xmath81 0.06 & 3.57 @xmath81 0.01 & 3.13 @xmath81 0.02 & 1.40 @xmath81 0.05 & 0.29 @xmath81 0.01 + 587725591459201562 & 0.068 & * * * @xmath81 * * * & 0.81 @xmath81 0.82 & 1.51 @xmath81 0.75 & 2.66 @xmath81 0.19 & 1.17 @xmath81 0.51 & 2.93 @xmath81 3.32 & 0.14 @xmath81 0.06 + 587725591459201436 & 0.066 & * * * @xmath81 * * * & * * * @xmath81 * * * & 2.28 @xmath81 0.10 & 2.25 @xmath81 0.03 & 1.65 @xmath81 0.12 & * * * @xmath81 * * * & 0.14 @xmath81 0.010 + 587725591459201670 & 0.651 & 6.22 @xmath81 0.58 & 3.66 @xmath81 0.77 & 5.06 @xmath81 0.21 & * * * @xmath81 * * * & * * * @xmath81 * * * & 3.98 @xmath81 0.84 & * * * @xmath81 * * * + 587725591459201656 & 0.157 & * * * @xmath81 * * * & 2.04 @xmath81 0.51 & 2.10 @xmath81 0.11 & 2.53 @xmath81 0.12 & 1.60 @xmath81 1.65 & 5.81 @xmath81 1.47 & 0.02 @xmath81 0.02 + 587725591459201666 & 0.078 & * * * @xmath81 * * * & 1.03 @xmath81 1.80 & 1.08 @xmath81 0.62 & 2.10 @xmath81 0.11 & 1.50 @xmath81 0.51 & 2.36 @xmath81 4.33 & 0.18 @xmath81 0.06 + 587725591459201614 & 0.188 & * * * @xmath81 * * * & 2.62 @xmath81 0.40 & 2.69 @xmath81 0.15 & 3.38 @xmath81 0.10 & 2.02 @xmath81 0.83 & 3.01 @xmath81 0.49 & 0.08 @xmath81 0.03 + 587725591459136404 & 0.220 & * * * @xmath81 * * * & 0.74 @xmath81 0.59 & 3.43 @xmath81 0.57 & 4.95 @xmath81 0.23 & 2.77 @xmath81 0.67 & 7.21 @xmath81 5.93 & 0.18 @xmath81 0.04 + 587725591459136351 & 0.319 & 1.34 @xmath81 1.16 & 2.38 @xmath81 0.72 & 0.76 @xmath81 0.45 & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.34 @xmath81 0.23 & * * * @xmath81 * * * + 587725591459136031 & 0.192 & * * * @xmath81 * * * & 0.25 @xmath81 0.22 & 0.59 @xmath81 0.34 & 2.98 @xmath81 0.12 & 2.79 @xmath81 0.18 & 2.42 @xmath81 2.55 & 0.63 @xmath81 0.05 + 587725591459136024@xmath113 & 0.245 & * * * @xmath81 * * * & 2.00 @xmath81 0.44 & 1.81 @xmath81 0.47 & 3.87 @xmath81 0.12 & 2.54 @xmath81 0.32 & 0.85 @xmath81 0.29 & 0.23 @xmath81 0.03 + 587725591459136330 & 0.565 & 8.01 @xmath81 0.95 & 3.13 @xmath81 0.32 & 3.43 @xmath81 0.11 & * * * @xmath81 * * * & * * * @xmath81 * * * & 18.69 @xmath81 1.78 & * * * @xmath81 * * * + 587725591459135913 & 0.293 & * * * @xmath81 * * * & 2.32 @xmath81 0.61 & 2.23 @xmath81 0.47 & 2.76 @xmath81 0.09 & 2.18 @xmath81 0.26 & 1.29 @xmath81 0.44 & 0.19 @xmath81 0.02 + 587725591459136277 & 0.290 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.81 @xmath81 1.07 & 0.82 @xmath81 0.44 & 2.80 @xmath81 0.41 & * * * @xmath81 * * * & 3.97 @xmath81 2.21 + 587725591459136339 & 0.188 & * * * @xmath81 * * * & 2.97 @xmath81 0.35 & 2.69 @xmath81 0.35 & 5.10 @xmath81 0.07 & 5.15 @xmath81 0.17 & 0.95 @xmath81 0.17 & 0.36 @xmath81 0.01 + 587725578037166749 & 0.320 & * * * @xmath81 * * * & 2.30 @xmath81 0.35 & 2.45 @xmath81 0.86 & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.59 @xmath81 0.22 & * * * @xmath81 * * * + 587725578037166468 & 0.330 & * * * @xmath81 * * * & 1.49 @xmath81 0.20 & 0.94 @xmath81 0.17 & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.62 @xmath81 0.14 & * * * @xmath81 * * * + 587725578037166557 & 0.168 & * * * @xmath81 * * * & 2.47 @xmath81 0.11 & 3.06 @xmath81 0.07 & 4.11 @xmath81 0.03 & 3.06 @xmath81 0.09 & 2.39 @xmath81 0.12 & 0.20 @xmath81 0.01 + 587725578037166705 & 0.192 & * * * @xmath81 * * * & 1.54 @xmath81 0.35 & 2.71 @xmath81 0.29 & 2.50 @xmath81 0.11 & 1.24 @xmath81 0.50 & 2.94 @xmath81 0.73 & 0.06 @xmath81 0.03 + 587725578037166672 & 0.189 & * * * @xmath81 * * * & 3.85 @xmath81 0.15 & 2.92 @xmath81 0.20 & 5.48 @xmath81 0.03 & 5.96 @xmath81 0.07 & 0.59 @xmath81 0.05 & 0.34 @xmath81 0.01 + 587725578037166295 & 0.560 & 7.13 @xmath81 0.52 & 5.94 @xmath81 0.38 & 5.37 @xmath81 0.29 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.29 @xmath81 0.11 & * * * @xmath81 * * * + 587725578037166628 & 0.652 & 0.95 @xmath81 0.65 & 3.54 @xmath81 0.43 & 0.86 @xmath81 0.45 & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.17 @xmath81 0.09 & * * * @xmath81 * * * + 587725578037166629 & 0.321 & 2.15 @xmath81 4.43 & 2.93 @xmath81 0.17 & 3.21 @xmath81 0.07 & * * * @xmath81 * * * & * * * @xmath81 * * * & 3.02 @xmath81 0.19 & * * * @xmath81 * * * + 587725578037100839 & 0.561 & 5.25 @xmath81 0.34 & 2.84 @xmath81 0.15 & 4.40 @xmath81 0.25 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.70 @xmath81 0.13 & * * * @xmath81 * * * + 587725578037101267 & 0.293 & * * * @xmath81 * * * & 7.99 @xmath81 8.21 & 6.65 @xmath81 0.68 & 2.60 @xmath81 1.68 & 0.17 @xmath81 0.51 & * * * @xmath81 * * * & 0.10 @xmath81 0.30 + 587725578037101221 & 0.518 & 5.79 @xmath81 0.95 & 3.31 @xmath81 0.35 & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * + 587725578037100922 & 0.168 & * * * @xmath81 * * * & 1.24 @xmath81 0.44 & 1.06 @xmath81 0.45 & 3.54 @xmath81 0.11 & 2.82 @xmath81 0.20 & 0.85 @xmath81 0.47 & 0.48 @xmath81 0.04 + 587725578037101176 & 0.281 & * * * @xmath81 * * * & 2.28 @xmath81 0.29 & 3.52 @xmath81 0.27 & 2.49 @xmath81 0.08 & * * * @xmath81 * * * & 2.07 @xmath81 0.31 & * * * @xmath81 * * * + 587725591458873892 & 0.281 & * * * @xmath81 * * * & 2.49 @xmath81 0.21 & 3.14 @xmath81 0.26 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.21 @xmath81 0.14 & * * * @xmath81 * * * + 587725578037100775@xmath114 & 0.176 & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.86 @xmath81 0.11 & 1.07 @xmath81 0.08 & * * * @xmath81 * * * & 1.30 @xmath81 0.20 + 587725591458808530 & 0.427 & 2.53 @xmath81 0.96 & 3.58 @xmath81 0.27 & 3.92 @xmath81 0.38 & * * * @xmath81 * * * & * * * @xmath81 * * * & 0.94 @xmath81 0.11 & * * * @xmath81 * * * + 587725591458808528 & 0.598 & 5.42 @xmath81 0.31 & 3.57 @xmath81 0.20 & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * & * * * @xmath81 * * * + 587725578037101077 & 0.387 & 6.51 @xmath81 1.41 & 3.96 @xmath81 0.33 & 3.12 @xmath81 0.13 & * * * @xmath81 * * * & * * * @xmath81 * * * & 2.40 @xmath81 0.22 & * * * @xmath81 * * * + 587725578037101473 & 0.496 & 4.81 @xmath81 1.31 & 2.44 @xmath81 0.52 & 2.95 @xmath81 0.13 & * * * @xmath81 * * * & * * * @xmath81 * * * & 4.70 @xmath81 1.01 & * * * @xmath81 * * * + 587725578037166675 & 0.498 & 7.79 @xmath81 0.92 & 3.15 @xmath81 0.23 & 3.32 @xmath81 0.14 & * * * @xmath81 * * * & * * * @xmath81 * * * & 1.39 @xmath81 0.11 & * * * @xmath81 * * * lccllcclll 587725578037166705 & 0.192 & 17@xmath27 37@xmath28 30.681@xmath29 & 57@xmath31 20@xmath32 8.70@xmath33 & 22.53 & 23.11 & 1.51 & 8.69 & -0.42 & -0.09 + 587725578037166675 & 0.498 & 17@xmath27 37@xmath28 34.409@xmath29 & 57@xmath31 21@xmath32 13.71@xmath33 & * * * & 22.62 & 0.97 & 9.50 & 0.50 & -0.07 + 587725578037166672 & 0.189 & 17@xmath27 37@xmath28 39.053@xmath29 & 57@xmath31 21@xmath32 30.10@xmath33 & * * * & 23.04 & 3.36 & 10.05 & 0.15 & -0.55 + 587725578037166749 & 0.320 & 17@xmath27 37@xmath28 41.177@xmath29 & 57@xmath31 18@xmath32 46.29@xmath33 & 22.87 & 22.12 & 1.88 & 9.91 & 0.65 & -0.14 + 587725578037100839 & 0.561 & 17@xmath27 37@xmath28 43.542@xmath29 & 57@xmath31 24@xmath32 5.51@xmath33 & * * * & 22.19 & 1.19 & 10.40 & 0.85 & -0.32 + 587725578037166468 & 0.330 & 17@xmath27 37@xmath28 45.923@xmath29 & 57@xmath31 19@xmath32 17.19@xmath33 & 22.38 & 21.50 & 2.15 & 10.85 & 0.48 & -0.84 + 587725578037166557 & 0.168 & 17@xmath27 37@xmath28 58.250@xmath29 & 57@xmath31 20@xmath32 16.80@xmath33 & 20.61 & 20.12 & 1.18 & 9.47 & 0.53 & -0.08 + 587725578037166295 & 0.560 & 17@xmath27 37@xmath28 59.495@xmath29 & 57@xmath31 23@xmath32 21.80@xmath33 & * * * & 22.16 & 0.89 & 9.70 & 0.79 & -0.07 + 587725578037166628 & 0.652 & 17@xmath27 38@xmath28 2.622@xmath29 & 57@xmath31 23@xmath32 26.99@xmath33 & * * * & 22.73 & 1.51 & 10.51 & 1.11 & -0.24 + 587725578037166629 & 0.321 & 17@xmath27 38@xmath28 7.756@xmath29 & 57@xmath31 23@xmath32 34.90@xmath33 & * * * & 22.32 & 1.04 & 9.09 & 0.28 & -0.05 + 587725578037101267 & 0.293 & 17@xmath27 38@xmath28 22.192@xmath29 & 57@xmath31 25@xmath32 2.82@xmath33 & * * * & 23.36 & 1.66 & 9.16 & -0.06 & -0.18 + 587725578037100922 & 0.168 & 17@xmath27 38@xmath28 23.628@xmath29 & 57@xmath31 27@xmath32 56.42@xmath33 & 21.48 & 21.97 & 2.67 & 9.97 & -0.24 & -0.76 + 587725578037101473 & 0.496 & 17@xmath27 38@xmath28 27.876@xmath29 & 57@xmath31 26@xmath32 33.90@xmath33 & 22.91 & 22.28 & 1.22 & 9.76 & 0.68 & -0.10 + 587725578037101077 & 0.387 & 17@xmath27 38@xmath28 36.526@xmath29 & 57@xmath31 30@xmath32 38.59@xmath33 & * * * & 22.32 & 0.52 & 9.11 & 0.51 & -0.01 + 587725578037101221 & 0.518 & 17@xmath27 38@xmath28 37.317@xmath29 & 57@xmath31 26@xmath32 53.92@xmath33 & * * * & 22.50 & 1.09 & 10.07 & 0.62 & -0.26 + 587725578037100775@xmath114 & 0.176 & 17@xmath27 38@xmath28 37.646@xmath29 & 57@xmath31 29@xmath32 13.99@xmath33 & 21.03 & 20.34 & 3.08 & 11.08 & 0.69 & -0.88 + 587725578037101176 & 0.281 & 17@xmath27 38@xmath28 41.873@xmath29 & 57@xmath31 28@xmath32 9.30@xmath33 & * * * & 22.33 & 0.99 & 9.24 & -0.09 & -0.19 + 587725591458873892 & 0.281 & 17@xmath27 38@xmath28 48.259@xmath29 & 57@xmath31 29@xmath32 10.40@xmath33 & 22.69 & 22.23 & 1.80 & 9.76 & 0.43 & -0.13 + 587725591458808530 & 0.427 & 17@xmath27 38@xmath28 50.596@xmath29 & 57@xmath31 29@xmath32 54.31@xmath33 & * * * & 22.88 & 2.89 & 10.50 & 2.12 & 0.00 + 587725591458808528 & 0.598 & 17@xmath27 38@xmath28 54.873@xmath29 & 57@xmath31 30@xmath32 5.80@xmath33 & * * * & 22.58 & 1.83 & 10.37 & 1.33 & -0.09 + 587725578037494286 & 0.134 & 17@xmath27 39@xmath28 45.205@xmath29 & 56@xmath31 40@xmath32 2.20@xmath33 & 20.87 & 20.47 & 1.17 & 9.66 & -0.15 & -0.28 + 587725578037494409 & 0.355 & 17@xmath27 39@xmath28 51.035@xmath29 & 56@xmath31 39@xmath32 13.11@xmath33 & * * * & 23.23 & 1.78 & 9.14 & 0.36 & -0.04 + 587725578037495014 & 0.213 & 17@xmath27 39@xmath28 51.343@xmath29 & 56@xmath31 39@xmath32 58.89@xmath33 & * * * & 22.73 & 0.95 & 8.18 & -0.66 & -0.02 + 587725578037494283 & 0.084 & 17@xmath27 39@xmath28 53.130@xmath29 & 56@xmath31 40@xmath32 18.91@xmath33 & 22.24 & 22.00 & 2.34 & 9.17 & -0.57 & -0.35 + 587725578037494050 & 0.077 & 17@xmath27 39@xmath28 56.243@xmath29 & 56@xmath31 38@xmath32 17.20@xmath33 & * * * & 22.11 & 5.46 & 10.76 & -0.80 & -1.91 + 587725578037494494 & 0.356 & 17@xmath27 39@xmath28 56.287@xmath29 & 56@xmath31 37@xmath32 21.00@xmath33 & * * * & 22.20 & 1.96 & 9.99 & 1.14 & -0.03 + 587725578037494738 & 0.474 & 17@xmath27 39@xmath28 56.704@xmath29 & 56@xmath31 37@xmath32 53.80@xmath33 & * * * & 22.72 & 0.86 & 9.67 & 0.38 & -0.16 + 587725591459201436 & 0.066 & 17@xmath27 40@xmath28 1.663@xmath29 & 56@xmath31 44@xmath32 3.12@xmath33 & 20.89 & 20.74 & 2.20 & 9.21 & -0.41 & -0.35 + 587725591459201125@xmath113 & 0.066 & 17@xmath27 40@xmath28 3.853@xmath29 & 56@xmath31 41@xmath32 59.82@xmath33 & 20.37 & 19.99 & 1.96 & * * * & * * * & * * * + 587725591459201656 & 0.157 & 17@xmath27 40@xmath28 6.724@xmath29 & 56@xmath31 43@xmath32 49.51@xmath33 & 22.64 & 22.12 & -0.52 & 8.68 & -0.97 & -0.24 + 587725591459201627 & 0.079 & 17@xmath27 40@xmath28 8.196@xmath29 & 56@xmath31 44@xmath32 57.80@xmath33 & 22.18 & 21.68 & 1.51 & 8.48 & -0.61 & -0.09 + 587725591459201372 & 0.615 & 17@xmath27 40@xmath28 8.328@xmath29 & 56@xmath31 39@xmath32 39.82@xmath33 & * * * & 22.68 & 1.80 & 10.53 & 0.81 & -0.51 + 587725591459201929 & 0.436 & 17@xmath27 40@xmath28 15.117@xmath29 & 56@xmath31 46@xmath32 4.70@xmath33 & 22.36 & 22.16 & 0.24 & 9.27 & 0.22 & -0.07 + 587725591459201726 & 0.439 & 17@xmath27 40@xmath28 17.307@xmath29 & 56@xmath31 41@xmath32 31.09@xmath33 & * * * & 22.42 & 0.94 & 9.98 & 0.37 & -0.22 + 587725591459136339 & 0.188 & 17@xmath27 40@xmath28 17.468@xmath29 & 56@xmath31 48@xmath32 5.50@xmath33 & 21.23 & 20.57 & 0.76 & 9.98 & -0.06 & -0.47 + 587725591459201670 & 0.651 & 17@xmath27 40@xmath28 19.175@xmath29 & 56@xmath31 43@xmath32 39.18@xmath33 & * * * & 22.46 & 0.14 & 8.93 & 0.61 & 0.29 + 587725591459201562 & 0.068 & 17@xmath27 40@xmath28 20.969@xmath29 & 56@xmath31 42@xmath32 43.30@xmath33 & * * * & 22.77 & 2.90 & 8.77 & -1.06 & -0.53 + 587725591459201614 & 0.188 & 17@xmath27 40@xmath28 23.225@xmath29 & 56@xmath31 45@xmath32 42.52@xmath33 & 22.37 & 21.50 & 0.59 & 8.72 & -0.06 & -0.04 + 587725591459136404 & 0.220 & 17@xmath27 40@xmath28 23.708@xmath29 & 56@xmath31 46@xmath32 34.10@xmath33 & 22.53 & 21.76 & 0.79 & 9.59 & -0.47 & -0.55 + 587725591459135913 & 0.293 & 17@xmath27 40@xmath28 29.685@xmath29 & 56@xmath31 50@xmath32 27.71@xmath33 & 21.64 & 21.93 & 1.18 & 9.55 & 0.12 & -0.21 + 587725591459136024@xmath113 & 0.245 & 17@xmath27 40@xmath28 32.498@xmath29 & 56@xmath31 49@xmath32 12.51@xmath33 & 22.73 & 20.99 & -0.08 & * * * & * * * & * * * + 587725591459201666 & 0.078 & 17@xmath27 40@xmath28 33.193@xmath29 & 56@xmath31 44@xmath32 5.32@xmath33 & * * * & 20.82 & 1.06 & 9.00 & -0.90 & -0.42 + 587725591459136277 & 0.290 & 17@xmath27 40@xmath28 35.691@xmath29 & 56@xmath31 50@xmath32 29.29@xmath33 & 22.66 & 22.23 & 3.27 & 10.99 & 0.49 & -0.98 + 587725591459136330 & 0.565 & 17@xmath27 40@xmath28 46.362@xmath29 & 56@xmath31 49@xmath32 13.40@xmath33 & * * * & 22.18 & 1.33 & 10.03 & 1.06 & -0.08 + 587725591459136031 & 0.192 & 17@xmath27 40@xmath28 56.177@xmath29 & 56@xmath31 49@xmath32 15.38@xmath33 & 20.94 & 20.09 & 2.45 & 10.92 & 0.97 & -0.47 + 587725591459136351 & 0.319 & 17@xmath27 40@xmath28 56.594@xmath29 & 56@xmath31 48@xmath32 52.20@xmath33 & * * * & 21.35 & 2.15 & 10.90 & 0.75 & -0.60 + + + 587725578037100834 & 1.515 & 17@xmath27 38@xmath28 9.360@xmath29 & 57@xmath31 25@xmath32 21.36@xmath33 & * * * & 23.40 & 2.63 & * * * & * * * & * * * + 587725591459201473 & 1.387 & 17@xmath27 40@xmath28 9.836@xmath29 & 56@xmath31 40@xmath32 7.68@xmath33 & * * * & 22.67 & 1.14 & * * * & * * * & * * * + 587725591459136108 & 1.632 & 17@xmath27 40@xmath28 43.682@xmath29 & 56@xmath31 48@xmath32 45.36@xmath33 & * * * & 23.05 & 1.67 & * * * & * * * & * * * + 587725591459135981@xmath114 & 1.028 & 17@xmath27 40@xmath28 49.197@xmath29 & 56@xmath31 47@xmath32 23.65@xmath33 & 22.62 & 21.20 & 1.94 & * * * & * * * & * * *

fainter than the sloan digital sky survey ( sdss ) spectroscopic survey . 43 are starforming galaxies with , 3 have emission line ratios indicative of agn with , and 4 objects with are qsos , 3 of which are not previously cataloged . we compare our sample to a much larger sample of,000 matched galex / sdss galaxies with sdss spectroscopy ; while our survey is shallow , the optical counterparts to our sources reach magnitudes fainter in sdss _ our sample has sfrs , luminosities , and velocity dispersions that are similar to the samples of faint compact blue galaxies studied previously in the same redshift range by , , & .

we report results from a pilot program to obtain spectroscopy for objects detected in the _ galaxy evolution explorer _ ( _ galex _ ) medium imaging survey ( mis ) . our study examines the properties of galaxies detected by _ galex _ fainter than the sloan digital sky survey ( sdss ) spectroscopic survey . this is the first study to extend the techinques of to estimate stellar masses , star formation rates ( sfr ) and the b ( star formation history ) parameter for star - forming galaxies out to . we obtain redshifts for 50 _ galex _ mis sources reaching ( ab mag ) , having counterparts in the sdss data release 4 ( dr4 ) . of our sample , 43 are starforming galaxies with , 3 have emission line ratios indicative of agn with , and 4 objects with are qsos , 3 of which are not previously cataloged . we compare our sample to a much larger sample of,000 matched galex / sdss galaxies with sdss spectroscopy ; while our survey is shallow , the optical counterparts to our sources reach magnitudes fainter in sdss _ r _ than the sdss spectroscopic sample . we use emission line diagnostics for the galaxies to determine that the sample contains mostly star - forming galaxies . the galaxies in the sample populate the blue sequence in the vs color - magnitude diagram . the derived stellar masses of the galaxies range from 10 to 10 m and derived sfrs are between 10 and 10 m . our sample has sfrs , luminosities , and velocity dispersions that are similar to the samples of faint compact blue galaxies studied previously in the same redshift range by , , & . however , our sample is mag fainter in surface brightness than the compact blue galaxies . we find that the star - formation histories for a majority of the galaxies are consistent with a recent starburst within the last 100 myr .

quant-ph9805076

r

figure [ fig : apparat ] provides a general overview of the apparatus , indicating the schematic arrangement of various components to be described below . the diode laser setup for forming the cs mot is not shown . we use a fabry - perot high - finesse microcavity ( `` physics cavity '' ) consisting of two spherical mirrors with 1 m radius of curvature @xcite . the cavity was constructed with a mean length @xmath56 @xmath2 m , which we inferred from the cavity s measured free spectral range of @xmath57 hz . the measured @xmath58 and specified radii of curvature geometrically determine the cavity s electromagnetic mode volume for tem@xmath59 modes near 852 nm @xcite . together with the dipole decay rate @xmath60 mhz for the cs 6p@xmath61 level @xcite , this determines our optimal coupling constant @xmath62 to be @xmath63 mhz for @xmath64 transistions ( specifically the @xmath65 ) and @xmath66 mhz for @xmath67 transitions ( @xmath68 ) within the d2 zeeman manifold @xcite . in order to allow cold atoms to fall into such a short cavity , we found it necessary to have the mirror manufacturer reduce the substrate diameters from the standard value of 7.75 mm down to 3 mm @xcite . this reduced the `` sagittal depth '' of the curved mirror substrates and allowed us to maintain a gap of @xmath69 @xmath2 m around the edge of the cavity . machining of the mirror substrates was performed _ after _ they had been superpolished and coated , but this process did not seem to degrade the mirror reflectivities significantly . the nominal combined transmission and loss per mirror , before machining , was @xmath70 . direct measurements of the cavity finesse yield @xmath71 at an optical wavelength of 852.36 nm , consistent with a combined mirror transmission and loss @xmath72 . this value of @xmath73 is inferred from the measured value of @xmath58 and the measured cavity hwhm @xmath74 mhz . the cavity used throughout the work described in this paper suffers from a rather pronounced birefringence , which for tem@xmath59 modes near 852 nm induced a splitting of @xmath75 mhz between linearly - polarized eigenmodes . it is not entirely clear whether this birefrigence is a result of the substrate machining for diameter - reduction , a property of the coatings , or something associated with the mirror - mounting procedure used for this particular cavity . we note that recent efforts by other members of our group @xcite have produced a cavity of approximately the same finesse with greatly - reduced birefringence ( by a factor @xmath76 ) , using mirrors from a different coating run and with great care taken to minimize cavity misalignments and stress on the mirror substrates . our two mirror substrates are mounted in vee - grooves atop independent aluminum blocks , with a piezoelectric actuator between the blocks for active servo - control of the mirror separation ( cavity length ) . the cavity mount sits on a stack of alternating ofhc copper blocks and viton o - rings for passive vibration isolation , all within an ion - pumped vacuum chamber whose background pressure was typically @xmath77 torr ( inferred from the ion pump current ) . in order to bring the mot as close as possible to the central axis of the physics cavity , we had to use a rather open ( and non - magnetic ) mount design , leading to some compromises in the way of mechanical stability . sitting on the vibration - isolation stack and under vacuum , we found that the native noise spectrum of the cavity length extended out to about 4 khz , with one prominent resonance at 50 hz ( which we attribute to a transmission resonance of the isolation stack ) . due to a set of pzt - actuator resonances above 10 khz , we have ultimately been limited to a unity - gain bandwidth @xmath78 khz for the cavity stabilization servo . although the principle aim for this experiment is to stabilize the cavity length at some precise offset @xmath79 mhz from the cs d2 resonance at 852.359 nm , the strong atom - cavity coupling places severe restrictions on the optical power that can be used for the purpose of generating an error signal . on resonance , the saturation intracavity photon number for our cavity is as small as @xmath80 which sets a fiducial cavity throughput of @xmath81 pw . with such low optical power it would be extremely difficult to obtain a high - quality error signal for locking the physics cavity . other experiments performed in our group have circumvented this problem by using a chopped locking scheme , in which a strong `` lock beam '' alternates with a weak `` probe beam '' at 50% duty cycle and @xmath82 khz frequency @xcite . however , such a strategy inherently limits the servo unity - gain bandwidths to @xmath69 hz at best , and would not be appropriate for future experiments with atoms trapped inside the cavity for long periods of time . in this work we have developed an alternative locking scheme for the physics cavity , which employs an auxilliary diode laser at 836 nm to monitor the cavity length on a different longitudinal mode than that which couples strongly to intracavity cs atoms . we use a commercial grating - stabilized diode produced by new focus ( santa clara , california ) . with a 16 nm detuning , we can send @xmath83 nw through the cavity and incur an ac stark shift of only @xmath84 khz for the atomic resonance at @xmath85 . using an eg&g avalanche - photodiode / transimpedance amplifier module ( model c30998 ) for ac detection of transmitted 836 nm light , we obtain an fm error signal ( modulation frequency 3.8 mhz ) with signal - to - noise ratio ( snr ) @xmath86 at 30 khz bandwidth . the 836 nm diode laser is stabilized to an auxilliary `` transfer cavity , '' which consists of a pair of 25 cm radius - of - curvature mirrors at @xmath87 cm separation . one of the mirrors is mounted on a piezoelectric actuator to allow cancellation of dc drift and low - frequency noise . the transfer cavity has a linewidth @xmath88 khz at both 836 nm and 852 nm , with an overall mode spacing @xmath89 mhz . the transfer cavity is also used for pre - stabilization of the ti : sapphire laser , and some of the ti : sapphire light is used in a cs modulation - transfer spectrometer @xcite to provide an absolute reference for the transfer cavity length . from run to run we used one or two acoustooptic modulators to offset the ti : sapphire / transfer - cavity lock point by + 140 , + 87 , or + 43 mhz relative to the cs 6s@xmath90 6p@xmath91 transition . by comparison of the ti : sapphire and diode laser error signals in their respective locks to the transfer cavity , we infer that the relative rms jitter between them is @xmath92 khz . for both laser locks we use the pound - drever - hall technique @xcite of detecting an fm signal in reflection from the tranfser cavity . the stability of the transfer cavity resonances with respect to atomic cs lines in a vapor cell was such that we did not see any relative jitter beyond the measurement noise in our modulation - transfer spectrometer ( snr @xmath93 in 30 khz bandwidth ) . the ti : sapphire stabilization employs two feedback loops , one with @xmath94 khz bandwidth to the tweeter inside the ring laser and another with @xmath69 khz bandwidth to a vco - driven , double - passed acoustooptic modulator ( aom ) just outside the laser cavity @xcite . the mean frequency of the aom is 76 mhz , and the error signal going to the vco has a lower cutoff of @xmath94 khz to prevent dc drifts . we note that use of the aom is crucial for achieving high stability of the ti : sapphire frequency . the diode laser servo utilizes both feedback to the grating pzt and direct modulation of the injection current , achieving an overall unity - gain bandwidth @xmath95 mhz . having locked both the diode laser and ti : sapphire to modes of the transfer cavity , which itself is locked to cs , we use a travelling - wave electrooptic modulator to generate an rf sideband of the diode laser at @xmath96 mhz . either the upper or lower sideband is used to derive an fm error signal for locking the physics cavity by dithering @xmath97 at 3.8 mhz , thus allowing us to achieve arbitrary placement of the physics cavity mode near 852 nm via the tunability of @xmath97 . our basic requirement for the quality of the physics - cavity servo was that relative jitter of the cavity resonance and the probe laser frequency should not contribute a significant amount of noise in the heterodyne photocurrent . hence the relevant comparison to make is between the noise in both quadratures of a demodulated beatnote and the photocurrent fluctuations produced by the local oscillator alone . at 200 khz bandwidth and with a probe beam strength such that @xmath98 in the empty cavity , the standard deviations of the phase and amplitude quadratures of the transmitted probe beam were measured to be 1.01 and 1.39 ( respectively ) relative to those of the local oscillator alone . note that we have estimated the standard deviation of the quadrature - amplitude signals produced by our optical local oscillator to be only a factor of 1.05 above the theoretical shot - noise limit ( see below ) . we therefore believe that our overall excess noise factor @xmath99 . by taking some simultaneous recordings of the heterodyne photocurrent and the physics - cavity error signal , we were able to verify directly that the atomic transits do not affect the physics cavity servo . to provide a source of cold cs atoms , we used a standard magnetooptic trap loaded directly from a thermal beam @xcite . our choice of thermal - beam loading , as opposed to loading from a background vapor , was driven by an attempt to prevent accidental coating of the physics cavity mirrors with cs . in more than two years of service , we did not detect any significant ( @xmath100 ) change in the cavity finesse . pre - cooling of the cs beam was not necessary for this experiment , as we required only a very low rate of delivering single cold atoms into the cavity mode volume . our mot employs a six - beam configuration , and we orient the anti - helmholtz coils for the trap so that their symmetry axis is parallel to that of the optical cavity . this leads to a mot laser beam geometry with one beam axis running parallel to and just above the cavity , plus two beam axes in the plane of the mirror surfaces ( figure [ fig : motconfig ] ) . the light for the mot was provided by a pair of grating - stabilized diode lasers ( sdl 5421-g2 ) , one tuned to the cs 6s@xmath906p@xmath91 cycling transition for trapping and the other to 6s@xmath1016p@xmath102 for repumping . each trapping beam had @xmath95 cm diameter and anywhere from 40 @xmath2w to 4 mw of optical power , depending on how many atoms we were trying to send into the physics cavity . we typically used a cs reservoir temperature of 60 - 80 c for the thermal beam , which effused through a 200 @xmath2 pinhole and travelled an overall distance of @xmath84 cm to the trapping region ( with a cold mechanical collimator in the way to reduce loading of the ion pump ) . with an anti - helmholtz field of around 25 g / cm , we could load up to @xmath103 atoms into a millimeter - sized cloud , whose mean temperature we estimate to be @xmath69 @xmath2k based on fluorescent imaging of free expansion . this temperature estimate is also supported by the spread in arrival times of individual atoms falling into the cavity . when running the experiment we would load the mot for about 0.5 s , then drop it by quickly turning off the trapping beams with an aom ( using an rf switch with @xmath104 db attenuation ) . after the trapping beams were thus extinguished , we would ramp down the anti - helmholtz field according to an rc - filtered step with @xmath105 ms time constant . the repumping beam was left on all the time , so that falling atoms would be shelved in the @xmath106 ground hyperfine level before entering the cavity . no specific preparation was performed with respect to the atomic zeeman states . dropping @xmath103 atoms we would generally see 30 - 50 atoms falling through the central part of the cavity mode volume , so for single - atom transit data we had to reduce the trapping beam power by a factor of @xmath107 to reach 0 - 2 atoms per drop . the overall repitition rate for the trap - drop cycle was typically 0.6 hz . we used a balanced - heterodyne setup in order to achieve high - efficiency , zero - background photodetection of @xmath95 pw levels of 852 nm light transmitted through the physics cavity . the frequency difference between cavity probe light and the optical local oscillator for heterodyne detection was between 40 - 190 mhz , depending upon our choice for the atom - probe detuning . the probe light was generated from the ti : sapphire output by cascading a + 200 mhz aom and a tunable travelling - wave electrooptic modulator , which was driven between -245 mhz and -440 mhz to produce the desired atom - probe detuning . this indirect method was required to prevent contamination of the heterodyne photocurrent by electronic noise at the heterodyne frequency . light leaving the physics cavity first hit a color - separation mirror which reflected @xmath108 of the 852 nm light but transmited @xmath109 of the 836 nm light , allowing us to recover an error signal for locking the physics cavity ( see above ) without compromising the overall detection efficiency for the probe field . residual 836 nm light going to the heterodyne setup amounted to only @xmath14 nw and had negligible effect on the photocurrent of interest . the local oscillator ( lo ) for the optical heterodyne was spatially cleaned by a @xmath110 fabry - perot cavity ( linewidth @xmath95 mhz ) , which also served to strip off spectral noise at 76 mhz associated with the aom servo for stabilization of the ti : sapphire frequency . the cleaning cavity was locked using the pound - drever - hall method @xcite with fm sidebands at 24 mhz , which likewise had to be kept weak in order not to saturate the ac gain of the heterodyne photodetectors . we used a total of @xmath111 mw in the lo , which generated a shot - noise level @xmath112 db above the electronic noise of the photodetectors in the frequency range of interest . the difference photocurrent from the balanced heterodyne detectors was amplified up to -50 dbm or higher , then divided by a @xmath113 rf splitter . an independent signal generator was used to produce an rf local oscillator at the heterodyne frequency , and it was halved using a @xmath114 rf splitter . the two identical copies of the photocurrent were mixed with the in - phase and quadrature copies of the rf lo to produce an orthogonal pair of quadrature amplitude ( qa ) signals at baseband . the qa signals were further amplified , and passed through 300 khz analog filters with a roll - off of 12 db / octave . we used a 12-bit adc to sample both qa s simultaneously at a rate of 10 mhz per channel , which is sufficiently high to avoid signal aliasing completely . following each drop of the trap , we continuously recorded both qa s for a data acquisition window of 50 ms and streamed the data to a hard drive for offline processing following the experimental run . ideally , we would like the data acquisition procedure just described to yield directly the amplitude and phase quadrature amplitudes of light transmitted through the cavity . if we write the transmitted optical field as @xmath115 , where @xmath116 is a slowly - varying complex amplitude , the amplitude @xmath117 and phase @xmath118 quadrature - amplitudes are defined by @xmath119 . with respect to the quantum - mechanical theory of the master equation ( [ eq : me ] ) , @xmath120 . note that we define @xmath121 to have zero phase when the cavity is empty , so that @xmath118 should have zero mean when there are no intracavity atoms . given the way that we generate the probe beam , however , we have no way of generating a phase - locked rf local oscillator to recover @xmath117 and @xmath118 directly . the phase of the heterodyne photocurrent differs from the phase that the light has just after it leaves the cavity because of fluctuations in the relative optical path length travelled by the signal beam and optical local oscilator in reaching the photodetectors . so the two signals produced by mixing the photocurrent with the shifted and unshifted copies of our rf local oscillator correspond to an orthognal , but _ rotated _ pair of quadrature amplitudes @xmath122 , @xmath123 : @xmath124 luckily , the characteristic timescales for fluctuations in the phase @xmath125 are quite long ( @xmath126 ms , corresponding to acoustic disturbances ) compared to the 250 @xmath2s duration of an individual atom - transit signal . in processing the recorded data to produce the plots discussed below , we have therefore used an `` adaptive '' definition of the amplitude and phase quadrature amplitudes . within a window of 2 ms preceding the signal of interest , we estimate the instantaneous value of @xmath125 by determining the rotation of @xmath122,@xmath123 that produces one quadrature @xmath127 with zero mean and one quadrature @xmath128 with positive mean . then @xmath127 is operationally defined to be the phase quadrature photocurrent , and @xmath128 is the amplitude quadrature photocurrent . figure ( [ fig : hmtlong ] ) shows an example of a 15 ms segment of our quadrature amplitude data . note that some excess low - frequency noise can still be seen in the phase quadrature , which constrains the lower end of our measurement bandwidth to @xmath95 khz . six prominent atom - transit signals , characterized by a sharp drop in the amplitude quadrature and a simultaneous increase in the phase quadrature , can be seen between @xmath129 sec and @xmath130 sec . in our subsequent discussions of the data , we shall focus on individual signal `` events '' of this type .

we ultimately hope to be able to implement some recently - proposed `` applications '' of the continuous observation of dissipative quantum dynamics , in fields such as quantum measurement , quantum chaos , and quantum feedback control . we obtain phase - contrast signals induced by individual atomic transits , corresponding to a regime of strong but dispersive coupling .

we report the use of broadband heterodyne spectroscopy to perform continuous measurement of the interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . we achieve a fractional sensitivity to variations in within a measurement bandwidth that covers 2.5 decades of frequency ( 1300 khz ) . our basic procedure is to drop cold cesium atoms into the cavity from a magnetooptic trap while monitoring the cavity s complex optical susceptibility with a weak probe laser . the instantaneous value of the atom - cavity interaction energy , which in turn determines the coupled system s optical susceptibility , depends on both the atomic position and ( zeeman ) internal state . measurements over a wide range of atom - cavity detunings reveal the transition from resonant to dispersive coupling , via the transfer of atom - induced signals from the amplitude to the phase of light transmitted through the cavity . by suppressing all sources of excess technical noise , we approach a measurement regime in which the broadband photocurrent may be interpreted as a classical record of _ conditional _ quantum evolution in the sense of recently - developed quantum trajectory theories . = 10000 optical cavity quantum electrodynamics ( qed ) in the strong coupling regime provides a unique experimental paradigm for _ real - time _ observation of quantum dynamical processes at the _ single - atom _ level . while spectacular advances have certainly been made in the preparation and tomography of quantum states of motion for a single trapped ion , all such experiments have involved the accumulation of ensemble - averaged data over many successive realizations of the process being studied . recent studies of single - molecule dynamics have likewise demonstrated the `` immediate '' detection of photochemical or conformational events , but such experiments presently lack the potential that cavity qed provides for observing quantum processes on a timescale that makes coherent control / intervention a tangible possibility . we wish here to look beyond the mere detection of quantum jumps , and to focus on the development of a broadband , _ single - shot _ measurement technique that achieves signal - to - noise ratio over a bandwidth that includes all characterstic frequencies of a quantum dynamical process . real - time observation of quantum dynamics in _ many - atom _ systems has recently become an important theme in atomic physics , with notable demonstrations involving vibrational excitations of a trapped bose - einstein condensate and the decay of coherent oscillations of an ensemble of atoms in an optical lattice . in contrast to programs like these , for which the scientific emphasis lies on noninvasive observation of a system s intrinsic dynamical processes , experiments in single - atom cavity qed hold great potential for enabling precise investigations of how measurement backaction _ alters _ the dynamical behavior of a continuously - observed open quantum system . a sophisticated theoretical basis for understanding such issues is presently maturing in the form of quantum trajectory theories , but significant technical challenges remain to be solved before definitive experiments can be performed in the lab . our purpose in the present work is to report substantial progress towards surmounting such obstacles in the context of cavity qed , and hence towards achieving the essential experimental capabilities required to perform quantitative tests of measurement - based stochastic master equations . we ultimately hope to be able to implement some recently - proposed `` applications '' of the continuous observation of dissipative quantum dynamics , in fields such as quantum measurement , quantum chaos , and quantum feedback control . this article focuses on a detailed description of our recent experiments that record the complete time - evolution of interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . with characteristic atom - cavity interaction energies mhz , we achieve measurement sensitivities khz over a bandwidth that covers the dominant rates of variation in ( 1300 khz ) . unlike typical pump - probe measurements of scattering dynamics in real ( _ e.g. _ diatomic ) molecular systems , our experiments on the jaynes - cummings `` molecule '' yield a continuous time - domain record of the atom - cavity coupling during each individual `` scattering '' event ( transit ) . the data clearly illustrate variations caused by atomic motion through the spatial structure of the cavity eigenmode and/or optical pumping among the atomic internal ( zeeman ) states . in certain parameter regimes of the detuning and probe power , distinctive indications of the quantum - mechanical nature of the atom - cavity coupling can be seen in the photocurrent recorded from just a _ single _ atomic transit . for large ( mhz ) atom - cavity detunings we obtain phase - contrast signals induced by individual atomic transits , corresponding to a regime of strong but dispersive coupling . phase - quadrature measurements of atomic motion have been widely discussed in the quantum optics literature , but the present work provides the first experimental demonstration at the single - atom level . because of the standing - wave spatial structure of the cavity eigenmode , and the corresponding rapid varation of the atom - cavity coupling strength over sub - wavelength distances , our data should in principle display a _ sensitivity _ of m/ to atomic displacements along the cavity axis . unfortunately we can not realize this figure as a _ precision _ for monitoring the atomic position , as we do not presently have any means of separating signal variations due to motion through the standing wave from `` background '' contributions due to transverse motion or optical pumping . in our concluding section , we shall briefly discuss our motivations for further work to disambiguate the nature of rapid variations in our data .

quant-ph9805076

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in summary , we have described the details of our recent experimental work to perform continuous measurement of the interaction energy @xmath241 between one atom and an optical cavity during individual transit events . we displayed heterodyne transit signals in two complementary formats , one of which highlights the large bandwidth and nearly quantum - noise limited signal - to - noise ratio achieved in tracking the time - evolution of the amplitude and phase quadratures ( @xmath242 ) of light transmitted through the cavity . the second data format ( transit phasors ) displays the correlation induced between @xmath128 and @xmath127 by the atom - cavity interaction , and our experimental results show that we are able to distinguish unambiguously between quantum and semiclassical models of cavity qed in only a few ( or even just one ) atomic transits . we have furthermore presented the results of rudimentary numerical simulations of atomic motion under the influence of mechanical forces and momentum diffusion associated with the strong atom - cavity coupling , and we examined the interpretations suggested by these simulations for certain qualitative features of our experimental data ( _ i.e. _ steps and asymmetries ) . the primary conclusion we wish to draw in comparing the simulation results with our experimental data is that we have experimentally reached a regime of measurement sensitivity and bandwidth in which details of the atomic center - of - mass trajectories really should be visible . even though we have no incontrovertible means of proving that steps and asymmetries seen in our experimental data should be associated with dynamical processes like channeling and diffusive escape , we are now motivated in our continuing work to develop some means of _ actively influencing _ the atomic motion _ while _ it is still inside the cavity . this would allow us to produce deliberate displacements of an atom along the cavity standing wave , and to examine the induced variations of the heterodyne signal in order to verify our inferred displacement sensitivity of @xmath10 m/@xmath11 . we anticipate that the combined abilities of monitoring and influencing atomic position relative to the cavity standing wave will enable the investigation of schemes for _ real - time feedback control _ of quantized atomic center - of - mass motion . finally , let us note that the standard quantum limit for overall observation time of the position of a single atom with sensitivity @xmath10 m/@xmath11 and 300 khz bandwidth should be @xmath243 @xmath2s @xcite . this implies that quantitative experimental investigations of conditional quantum dynamics ( as described in @xcite ) should indeed become possible in our cavity qed system once we are able to reliably prepare individual atoms in well - defined initial states of motion . the ideal situation in this regard would be to trap and localize atoms _ within _ the cavity , releasing them at a node or antinode of the standing wave , on the cavity axis , and with an initial position uncertainty that is small compared to @xmath205 . current efforts in our group focus on trying to achieve this level of control via optical dipole - force traps and/or far - detuned optical lattices inside the cavity . we wish to acknowledge q. a. turchette s vital participation in the early stages of this work , and to thank a. c. doherty , c. j. hood , and t. w. lynn for valuable discussions . much of the numerical work described in this paper was performed on resources located at the advanced computing laboratory of the los alamos national laboratory . this research was supported by the national science foundation under grant no . phy97 - 22674 , by the onr , and by darpa through the quic initiative ( administered by aro ) . jun ye is supported by an r. a. millikan fellowship from the california institute of technology . h. j. kimble : in _ cavity quantum electrodynamics_. san deigo , academic press : 1994 d. m. meekhof , c. monroe , b. e. king , w. m. itano , d. j. wineland : phys . lett . * 76 * , 1796 ( 1996 ) d. leibfried , d. m. meekhof , b. e. king , c. monroe , w. m. itano , d. j. wineland : phys . rev . lett . * 77 * , 4281 ( 1996 ) w. e. moerner : science * 265 * , 46 ( 1994 ) b. c. stipe , m. a. rezaei , w. ho : science * 279 * , 1907 ( 1998 ) m. r. andrews , d. m. kurn , h. j. miesner , d. s. durfee , c. g. townsend , s. inouye , w. ketterle : phys . rev . * 79 * , 553 ( 1997 ) m. kozuma , k. nakagawa , w. jhe , m. ohtsu : phys . a * 57 * , r24 ( 1998 ) s. guibal , c. triche , l. guidoni , p. verkerk , g. grynberg : opt * 131 * , 61 ( 1996 ) c. m. caves , g. j. milburn : phys . a * 36 * , 5543 ( 1987 ) h. m. wiseman : quantum semiclass * 8 * , 205 ( 1996 ) a. m. herkommer , h. j. carmichael , w. p. schleich : quantum semiclass * 8 * , 189 ( 1996 ) a. c. doherty , a. s. parkins , s. m. tan , d. f. walls : phys . a ( in press ) h. j. carmichael , _ an open systems approach to quantum optics_. berlin , springer : 1993 h. m. wiseman , g. j. milburn : phys . a * 47 * , 642 ( 1993 ) h. m. wiseman , g. j. milburn : phys . a * 47 * , 1652 ( 1993 ) p. zoller , c. w. gardiner : in _ quantum fluctuations , session lxiii of lecole dete de physique des houches_. amsterdam , north - 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layer dielectric coatings fabricated by research electrooptics in boulder , co. a. e. siegman : _ lasers_. mill valley , university science books : 1986 . r. j. rafac , c. e. tanner , a. e. livingston , k. w. kukla , h. g. berry , c. a. kurtz : phys . a * 50 * , r1976 ( 1994 ) o. schmidt , k .- knaak , r. wynands , d. meschede : appl . b * 59 * , 167 ( 1994 ) q. a. turchette , r. j. thompson h. j. kimble : appl . phys . b * 60 * , s1 ( 1995 ) j. h. shirley : opt . * 7 * 537 ( 1982 ) r. w. p. drever , j. l. hall , f. v. kowalski , j. hough , g. m. ford , a. j. munley , h. ward : appl . b * 31 * , 97 ( 1983 ) w. vassen , c. zimmermann , r. kallenbach , t. w. hnsch : opt . commun . * 75 * , 455 ( 1990 ) t. l. boyd , h. j. kimble : opt * 16 * , 808 ( 1991 ) a. cable , m. prentiss , n. p. bigelow : opt . lett . * 15 * , 507 ( 1990 ) e. s. polzik , j. carri , h. j. kimble : appl b * 55 * , 279 ( 1992 ) g. rempe , r. j. thompson , h. j. kimble : opt . * 17 * , 363 ( 1992 ) c. w. gardiner : _ quantum noise_. berlin , springer : ( 1991 ) s. marksteiner , k. ellinger , p. zoller : phys . rev . a * 53 * , 3409 ( 1996 ) a. c. doherty : private communication ( 1996 ) h. katori , s. schlipf , h. walther : phys . lett . * 79 * , 2221 ( 1997 ) a. c. doherty , a. s. parkins , s. m. tan , d. f. walls : phys . rev . a * 56 * , 833 ( 1997 ) q. a. turchette , c. j. hood , w. f. lange , h. mabuchi , h. j. kimble : phys . lett . * 75 * 4710 ( 1995 ) m. brune , f. schmidt - kaler , a. maali , j. dreyer , e. hagley , j. m. raimond , s. haroche : phys . lett . * 76 * , 1800 ( 1996 ) r. j. thompson , q. a. turchette , o. carnal , h. j. kimble : phys . a * 57 * , 3084 ( 1998 ) h. mabuchi , j. ye , and h. j. kimble : in preparation h. mabuchi : phys . a ( in press )

we report the use of broadband heterodyne spectroscopy to perform continuous measurement of the interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . this article focuses on a detailed description of our recent experiments that record the complete time - evolution of interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . with characteristic atom - cavity interaction energies mhz , we achieve measurement sensitivities the data clearly illustrate variations caused by atomic motion through the spatial structure of the cavity eigenmode and/or optical pumping among the atomic internal ( zeeman ) states . in certain parameter regimes of the detuning and probe power ,

we report the use of broadband heterodyne spectroscopy to perform continuous measurement of the interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . we achieve a fractional sensitivity to variations in within a measurement bandwidth that covers 2.5 decades of frequency ( 1300 khz ) . our basic procedure is to drop cold cesium atoms into the cavity from a magnetooptic trap while monitoring the cavity s complex optical susceptibility with a weak probe laser . the instantaneous value of the atom - cavity interaction energy , which in turn determines the coupled system s optical susceptibility , depends on both the atomic position and ( zeeman ) internal state . measurements over a wide range of atom - cavity detunings reveal the transition from resonant to dispersive coupling , via the transfer of atom - induced signals from the amplitude to the phase of light transmitted through the cavity . by suppressing all sources of excess technical noise , we approach a measurement regime in which the broadband photocurrent may be interpreted as a classical record of _ conditional _ quantum evolution in the sense of recently - developed quantum trajectory theories . = 10000 optical cavity quantum electrodynamics ( qed ) in the strong coupling regime provides a unique experimental paradigm for _ real - time _ observation of quantum dynamical processes at the _ single - atom _ level . while spectacular advances have certainly been made in the preparation and tomography of quantum states of motion for a single trapped ion , all such experiments have involved the accumulation of ensemble - averaged data over many successive realizations of the process being studied . recent studies of single - molecule dynamics have likewise demonstrated the `` immediate '' detection of photochemical or conformational events , but such experiments presently lack the potential that cavity qed provides for observing quantum processes on a timescale that makes coherent control / intervention a tangible possibility . we wish here to look beyond the mere detection of quantum jumps , and to focus on the development of a broadband , _ single - shot _ measurement technique that achieves signal - to - noise ratio over a bandwidth that includes all characterstic frequencies of a quantum dynamical process . real - time observation of quantum dynamics in _ many - atom _ systems has recently become an important theme in atomic physics , with notable demonstrations involving vibrational excitations of a trapped bose - einstein condensate and the decay of coherent oscillations of an ensemble of atoms in an optical lattice . in contrast to programs like these , for which the scientific emphasis lies on noninvasive observation of a system s intrinsic dynamical processes , experiments in single - atom cavity qed hold great potential for enabling precise investigations of how measurement backaction _ alters _ the dynamical behavior of a continuously - observed open quantum system . a sophisticated theoretical basis for understanding such issues is presently maturing in the form of quantum trajectory theories , but significant technical challenges remain to be solved before definitive experiments can be performed in the lab . our purpose in the present work is to report substantial progress towards surmounting such obstacles in the context of cavity qed , and hence towards achieving the essential experimental capabilities required to perform quantitative tests of measurement - based stochastic master equations . we ultimately hope to be able to implement some recently - proposed `` applications '' of the continuous observation of dissipative quantum dynamics , in fields such as quantum measurement , quantum chaos , and quantum feedback control . this article focuses on a detailed description of our recent experiments that record the complete time - evolution of interaction energy between one atom and a high - finesse optical cavity , during individual transit events ofs duration . with characteristic atom - cavity interaction energies mhz , we achieve measurement sensitivities khz over a bandwidth that covers the dominant rates of variation in ( 1300 khz ) . unlike typical pump - probe measurements of scattering dynamics in real ( _ e.g. _ diatomic ) molecular systems , our experiments on the jaynes - cummings `` molecule '' yield a continuous time - domain record of the atom - cavity coupling during each individual `` scattering '' event ( transit ) . the data clearly illustrate variations caused by atomic motion through the spatial structure of the cavity eigenmode and/or optical pumping among the atomic internal ( zeeman ) states . in certain parameter regimes of the detuning and probe power , distinctive indications of the quantum - mechanical nature of the atom - cavity coupling can be seen in the photocurrent recorded from just a _ single _ atomic transit . for large ( mhz ) atom - cavity detunings we obtain phase - contrast signals induced by individual atomic transits , corresponding to a regime of strong but dispersive coupling . phase - quadrature measurements of atomic motion have been widely discussed in the quantum optics literature , but the present work provides the first experimental demonstration at the single - atom level . because of the standing - wave spatial structure of the cavity eigenmode , and the corresponding rapid varation of the atom - cavity coupling strength over sub - wavelength distances , our data should in principle display a _ sensitivity _ of m/ to atomic displacements along the cavity axis . unfortunately we can not realize this figure as a _ precision _ for monitoring the atomic position , as we do not presently have any means of separating signal variations due to motion through the standing wave from `` background '' contributions due to transverse motion or optical pumping . in our concluding section , we shall briefly discuss our motivations for further work to disambiguate the nature of rapid variations in our data .

astro-ph9904248

i

the most important difference between mm and cm interferometry is the effect of the troposphere at mm wavelengths . the optical depth of the troposphere becomes significant below 1 cm , leading to increased system temperatures due to atmospheric emission , and increased demands on gain calibration due to variable opacity ( yun et al . , 1998 , kutner and ulich 1981 ) . even more dramatic is the effect of the troposphere on interferometer phases . variations in the tropospheric water vapor column density lead to variations in electronic pathlength , and hence variations in interferometric phase . this can cause loss of amplitude of the cross correlations , or ` visibilities ' , over the integration time ( ` coherence ' ) , reduced spatial resolution ( ` seeing ' ) , and pointing errors ( ` anomalous refraction ' ) . until recently , mm interferometric arrays have been restricted to maximum baselines of a few hundred meters . diffraction limited resolution images at mm wavelengths can be made on such baselines , since the tropospheric phase fluctuations on such baselines at good observatory sites are typically one radian or less under good weather conditions . however , many existing mm arrays are expanding to baselines of 1 km or more , and the planned large millimeter array facility at the chajnantor site in chile will have baselines as long at 10 km . even at this premium site , phase fluctuations due to the troposphere will be larger than 1 radian at 230 ghz on these baselines , except under the best weather conditions . hence , tropospheric seeing will preclude diffraction limited resolution imaging at frequencies of 230 ghz for arrays larger than about 1 km , even at the best possible sites , if no corrections are made for tropospheric phase noise . at higher frequencies , the maximum baselines which would permit uncorrected observations would be even shorter . in this paper we review the theory of tropospheric phase noise in mm interferometry , along with examples showing tropospheric induced phase fluctuations and their effect on images made with interferometric arrays . we then consider three techniques for reducing tropospheric phase noise : ( i ) fast switching phase calibration , ( ii ) paired array phase calibration , and ( iii ) radiometric phase calibration . the first two techniques entail using celestial calibration sources near the target source , with either a calibration cycle time fast enough to ` stop ' the troposphere ( fast switching ) , or by using some of the antennas as a tropospheric ` calibration array ' ( paired array ) . we present extensive observational data using the very large array ( vla ) in socorro , nm , usa , at 22 ghz and 43 ghz designed to test the efficacy of these first two techniques on baselines longer than a few km . the radiometric phase correction technique entails real - time estimation of the precipitable water vapor content along each antenna s line of sight through the troposphere via a radiometric measurement of the brightness temperature of the atmosphere above each antenna . a number of issues are addressed , including : ( i ) the required radiometric sensitivity as a function of frequency and site quality , ( ii ) the constraints on ancillary data , such as atmospheric data and models , in order to perform an absolute radiometric phase correction , and ( iii ) the limitations to making radiometric phase corrections by calibrating the relationship between brightness temperature fluctuations and interferometric phase using celestial sources .

we review millimeter interferometric phase variations caused by variations in the precipitable water vapor content of the troposphere , and we discuss techniques proposed to correct for these variations . we present observations with the very large array at 22 ghz and 43 ghz designed to test these techniques . we consider the technique of tropospheric phase correction using a measurement of the precipitable water vapor content of the troposphere via a radiometric measurement of the brightness temperature of the atmosphere . the stability requirement is 450 for the cooled system at the vla at 22 ghz . to perform absolute radiometric phase corrections

we review millimeter interferometric phase variations caused by variations in the precipitable water vapor content of the troposphere , and we discuss techniques proposed to correct for these variations . we present observations with the very large array at 22 ghz and 43 ghz designed to test these techniques . we find that both the fast switching and paired array calibration techniques are effective at reducing tropospheric phase noise for radio interferometers . in both cases , the residual rms phase fluctuations after correction are _ independent of baseline length for b b . _ these techniques allow for diffraction limited imaging of faint sources on arbitrarily long baselines at mm wavelengths . we consider the technique of tropospheric phase correction using a measurement of the precipitable water vapor content of the troposphere via a radiometric measurement of the brightness temperature of the atmosphere . required sensitivities range from 20 mk at 90 ghz to 1 k at 185 ghz for the mma , and 120 mk for the vla at 22 ghz . the minimum gain stability requirement is 200 at 185 ghz at the mma assuming that the astronomical receivers are used for radiometry . this increases to 2000 for an uncooled system . the stability requirement is 450 for the cooled system at the vla at 22 ghz . to perform absolute radiometric phase corrections also requires knowledge of the tropospheric parameters and models to an accuracy of a few percent . it may be possible to perform an ` empirically calibrated ' radiometric phase correction , in which the relationship between fluctuations in brightness temperature differences with fluctuations in interferometric phases is calibrated by observing a strong celestial calibrator at regular intervals . a number of questions remain concerning this technique , including : ( i ) over what time scale and distance will this technique allow for radiometric phase corrections when switching between the source and the calibrator ? and ( ii ) how often will calibration of the t - relationship be required ?

0911.4115

i

the scattering and absorption of cold and ultracold neutrons ( ucn ) at slightly rough surfaces resembles the roughness problem in light and x - ray optics [ 1 ] . surface roughness induces losses in neutron guide tubes and affects the behavior of a ucn gas in a trap . we investigate especially the relation between a realistic account of roughness in computer simulations of ucn storage and a reliable data interpretation with respect to the neutron lifetime . the issue has gained added importance since a new ucn storage based lifetime value six standard deviation away from the world average value [ 2 ] was published in 2005 [ 3 ] . most theoretical analyses of diffuse cold and ultracold neutron scattering at surfaces with small roughness ( e.g. , [ 4 - 7 ] ) are based on first - order perturbation theory . a possible extension to macroscopic ray optics was presented in [ 4 ] . carrying the analysis to second order perturbation theory , ignatovich [ 7 ] derived the roughness effect on the loss coefficient for reflection at a slightly absorbing wall material . the analysis was complex , and the result has , apparently , not been numerically evaluated and applied so far . we used a more direct approach , verified and quantified the result of [ 7 ] , and in the process obtained a derivation of the `` debye - waller factor '' ( describing the attenuation of the specular beam due to roughness ) , that is consistent with standard expressions but requires fewer assumptions about the roughness characteristics . this appears important since in practical cases very little is known about the roughness parameters of a given surface . finally , we address the question to what extent a transition to a macroscopic picture is possible .

the results are used in a computer simulation of neutron storage in a recent neutron lifetime experiment that reported a large discrepancy of neutron lifetime with the current particle data value . our partial re - analysis suggests the possibility of systematic effects that were not included in this publication . + * keywords : * ultracold neutrons , monte carlo simulations , neutron lifetime

we review the diffuse scattering and the loss coefficient in ultracold neutron reflection from slightly rough surfaces , report a surprising reduction in loss coefficient due to roughness , and discuss the possibility of transition from quantum treatment to ray optics . the results are used in a computer simulation of neutron storage in a recent neutron lifetime experiment that reported a large discrepancy of neutron lifetime with the current particle data value . our partial re - analysis suggests the possibility of systematic effects that were not included in this publication . + * keywords : * ultracold neutrons , monte carlo simulations , neutron lifetime

astro-ph0210292

c

we have reviewed the astro - f all sky survey and its expected results . astro - f will carry out the first all sky survey at infrared wavelengths for 20 years and will probe down to sensitivities between 10 - 1000 times deeper than the iras mission to more than 5 times the angular resolution in 4 far - ir bands from 50 - 200@xmath6 m and 2 mid - ir bands at 9 & 20@xmath6 m . expected numbers of sources range from 10 s millions in the longest wavelength bands where they will be source confusion limited , to 10,000 at mid - ir wavelengths ( a number of an order of magnitude higher than that detected by iras or iso at mid - ir wavelengths ) . most of the sources detected in the far - infrared bands will be dusty ligs & uligs of which , in the longest wavelengths bands , @xmath350@xmath16 will be at redshifts greater than unity . the ultimate goal of the astro - f all sky survey is to achieve approximately 95@xmath16 sky coverage by the end of the survey to a reliability of @xmath399@xmath16 for bright sources . absolute flux uncertainties of 10 and 20@xmath16 are expected for point and diffuse sources respectively . pointing accuracy is hoped to be @xmath200 . note that the orbit of astro - f will be sun - synchronous polar with the fov always perpendicular to the sun . this will have significant effects on the visibility of sources . sources near the ecliptic plane will be visible only 2 days ( 29 orbits ) every half year whereas targets near the ecliptic poles will be will be observable on many orbits . the north ecliptic pole is indeed under investigation as a target area for deep pointed surveys with the irc @xcite and will complement well with the proposed planck deep nep survey . ultimately , it is expected that the astro - f all sky survey will produce several catalogue products which could then serve as input catalogues and cross correlation databases for later missions such as herschel @xcite & planck ( including the all sky survey with hfi @xcite ) due for launch in 2007 . these catalogues can be broken down as follows ; 1 . _ astro - f flux of known sources _ - measurement of sources used for the input source catalogue and fluxes of iras point sources . 2 . _ bright source catalogue _ - a catalogue of sources that can be extracted easily such as bright sources or those at high ecliptic latitude . 3 . _ faint source catalogue _ - the all sky point source catalogue to the optimum sensitivity . image maps _ - crude maps , square degree imagelets and 10 s sq.deg . image atlases . the astro - f surveyor mission should be seen as supplementing not supplanting the sirtf observatory mission . the two are complementary . sirtf will cover relatively small areas ( 1-70sq.deg . ) to high sensitivity while astro - f will cover huge areas to more moderate sensitivities . in the study of large scale structure sirtf - swire will be sensitive to small scales over large redshift while conversely astro - f will probe larger scales to shallower depths . however , one of many clear distinctions between the two missions is that the astro - f all sky survey is the only way that the infrared dipole work carried out with iras can be checked and extended ( yahil et al . , rowan - robinson et al . , rowan - robinson et al . ) . astro - f will also provide an ideal companion to planck which will survey the whole sky at sub - mm wavelengths and also down to 200@xmath6 m which will provide an important longer wavelength channel to join fir measurements by astro - f . further associations and cross correlations with large scale surveys at other wavelengths ( swire , pos - ii , ukss , sdss , nvss , galex , rosat , ukidss , 6df , 2mass , lmt , etc . , see tables [ followup ] , [ redsurvey ] ) will result in a fully comprehensive unified view of galaxy evolution and star formation from radio - mm - ir - optical - uv - x - ray wavelengths .

astro - f will be the first survey of the entire sky at infrared wavelengths since the iras mission almost 20 years ago . astro - f will survey the entire sky in 4 far - infrared bands from 50 - 200microns and 2 mid - infrared bands at 9 and 20microns to sensitivities of 10 - 1000 times deeper than the iras satellite at angular resolutions of 25 - 45arcsec ( c.f . we predict that astro - f will detect of the order of 10 s millions of sources in the far - infrared wavelength bands , most of which will be dusty lig / uligs of which as many as half will lie at redshifts greater than unity .

we review the next generation japanese infrared space mission , astro - f . astro - f will be the first survey of the entire sky at infrared wavelengths since the iras mission almost 20 years ago . astro - f will survey the entire sky in 4 far - infrared bands from 50 - 200microns and 2 mid - infrared bands at 9 and 20microns to sensitivities of 10 - 1000 times deeper than the iras satellite at angular resolutions of 25 - 45arcsec ( c.f . iras 2 - 5arcmins ) . astro - f can be considered a super - iras . using the galaxy evolution model of pearson ( 2001 ) we produce expected numbers of sources under 3 different cosmological world models . we predict that astro - f will detect of the order of 10 s millions of sources in the far - infrared wavelength bands , most of which will be dusty lig / uligs of which as many as half will lie at redshifts greater than unity . we produce number - redshift distributions , flux - redshift and colour - colour diagrams for the survey and discuss various segregation and photometric redshift techniques . furthermore , we investigate the large scale structure scales that will be accessed by astro - f , discovering that astro - f and sirtf - swire probe both different scales and redshift domains and concluding that the 2 missions will supplement rather than supplant one another . [ firstpage ] cosmology : source counts infrared : source counts , surveys galaxies : evolution .

1508.01658

i

in the context of ads / cft , entanglement entropy of the boundary quantum field theory can be calculated using the ryu - takayanagi @xcite prescription and its generalizations to higher curvature gravity theories . the derivation of this holographic entanglement entropy for two derivative einstein gravity was proposed by lewkowycz and maldacena in @xcite . this derivation allows one to obtain a surface equation ( for static situations ) for the entangling surface which minimizes an entropy functional . there were attempts to extend this calculation to find the entangling surface equation in higher curvature theories in @xcite and the corresponding entropy functionals were argued to be different from the wald entropy @xcite . in particular , for lovelock theories the entropy functional is the so - called jacobson - myers ( jm ) @xcite one while for general four derivative theories , it coincides with the fursaev - patrushev - solodukhin ( fps ) entropy functional @xcite . however , there still exist problems in finding the entangling surface using the lewkowycz - maldacena method and there are potential ambiguities related to higher order extrinsic curvature terms in the entropy functionals . moreover , it leads one to wonder if such entropy functionals could arise independent of ads / cft from different and perhaps more fundamental considerations . wald and collaborators @xcite had established the first law for black hole mechanics for any diffeomorphism invariant theory of gravity and proposed that the entropy of a black hole is a noether charge associated with the killing isometry generating the horizon . the wald entropy suffers from various ambiguities @xcite and therefore does not provide a unique answer for the horizon entropy . although , none of these ambiguities contribute to black hole entropy of a stationary killing horizon with regular bifurcation surface , the study of the second law of black hole mechanics beyond general relativity ( gr ) shows that these ambiguities need to be carefully included in the expression of black hole entropy to obtain an increase theorem similar to hawking area theorem in gr . in fact , for black holes in lovelock gravity , it is the jm functional which leads to an increase theorem for linearized perturbations @xcite . recently , it has been pointed out that the 2nd law for spherically symmetric black holes is satisfied at linear order in perturbations in general four derivative theories of gravity by the holographic entanglement entropy ( hee ) functionals @xcite . this has been also generalized beyond spherical symmetry and to generic perturbations up to linear order @xcite and a detailed construction of the entropy functionals has been proposed for any metric theory of gravity such that the linearized second law holds true . for theories with higher curvature terms , the construction produces the hee functionals . this is a remarkable result since it allows for a way independent of ads / cft of deriving entropy functionals these same entropy functionals therefore find applications in diverse settings . however , what still needs to be addressed is if only the hee functionals alone do this job . in this paper , we first show that at linear order in perturbations only the hee functionals can satisfy the second law . we start with an expression for horizon entropy with all possible ambiguous terms relevant for linear order in perturbation . we fix these terms by demanding the validity of the linearized second law and the final entropy coincides with hee functionals . to be clear , since our analysis is going to be perturbative , we will not be able to rule out higher order extrinsic curvature terms in the functionals ( e.g. @xmath0 in the fps functional)see section 5 . we will tackle the question keeping in mind two different motivations . first , we are interested in what happens in the case of asymptotically flat black holes . we will consider two different types of perturbations the first kind will be due to radially symmetric , slowly falling matter and the second kind being a shear perturbation . we will find that for the gauss - bonnet ( gb ) theory , if we go to second order in perturbations , the second law is automatically satisfied for regular horizons if the gb coupling is positive . if the gb coupling is negative then a certain lower bound on the horizon radius ensures that the second law is satisfied ; since this suggests that such black holes can not be formed from collapsing matter , one can take this as an indication that the negative coupling is disfavoured . if we consider a ricci - square theory then we find that similar extra conditions on the mass of the black hole may be needed for the second law to hold . second , we are interested in what happens in the context of ads / cft . we will find that for the gb theory , the second order analysis leads to a bound on the gauss - bonnet coupling . for black branes , this bound coincides with the absence of sound channel instabilities at the black hole horizon . a similar analysis for the ricci- square theory bounds the corresponding coupling constant . for gb topological black holes @xcite , for the zero mass case we find that the second law bound coincides with the tensor channel causality constraint @xcite . this bound is what leads to the lower bound on the ratio of shear viscosity to entropy density in the dual plasma and agrees with the lower bound on the @xmath1 ratio in 4d cfts @xcite with @xmath2 supersymmetry . we also investigate quadratic theories with @xmath3 and @xmath4 terms . in these theories , the causality constraints following from @xcite are trivial whereas the second law bound in certain examples we study is nontrivial . using the hee entropy functionals and the raychaudhuri equation , we then turn to the question of holographic c - theorems . we will argue that the holographic c - functions found in @xcite arise naturally from such a consideration provided the matter sector satisfies the null energy condition . in @xcite , a derivation for the c - functions in einstein gravity , found in @xcite , was given using the raychaudhuri equation . in @xcite an attempt was made to extend this to higher curvature theories using the iyer - wald prescription . unfortunately the resulting functions do not give the correct central charge ( namely the a - type anomaly coefficient in even dimensions ) . in @xcite it was observed that in all sensible holographic models , which can be constructed by demanding the absence of higher derivative terms in the radial direction ( to ameliorate the problem of ghosts ) allow for a simple c - function which at the fixed points coincide with the a - type anomaly coefficient in even dimensions . this c - function was monotonic under rg flow provided the matter sector satisfied the null energy condition . we will find that using the hee entropy functionals and considering the raychaudhuri equation naturally leads to the same c - functions as in @xcite . the organization of the paper as follows : in the next section we briefly describe the ambiguities in wald s noether charge construction . in the section [ second - set ] set up for proving second law has been described . next , we determine the coefficients of the ambiguous terms in wald s construction using linearized second law . in section [ beyond ] , we go beyond linear order in perturbation to study the gb theory and determine bound on the coupling parameter using ads black hole solution with different horizon topologies as background . we also consider various other examples like critical gravity theories and put bounds on the couplings in those theories . in section 6 , we derive holographic c - functions using the hee functionals and the raychaudhuri equation . we end this paper by discussing several follow - up questions . we use @xmath5 signature and set @xmath6 throughout the paper .

we show that for a general four derivative theory of gravity , only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations . for the five dimensional gauss - bonnet theory in the context of ads / cft , the bound arising from black branes coincides with there being no sound channel instability close to the horizon . repeating the analysis for topological black holes , the bound coincides with the tensor channel causality constraint ( which is responsible for the viscosity bound ) . furthermore , we show how to recover the holographic c - theorems in higher curvature theories from similar considerations based on the raychaudhuri equation .

we show that for a general four derivative theory of gravity , only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations . we also derive bounds on the higher curvature couplings in several examples , demanding the validity of the second law for higher order perturbations . for the five dimensional gauss - bonnet theory in the context of ads / cft , the bound arising from black branes coincides with there being no sound channel instability close to the horizon . repeating the analysis for topological black holes , the bound coincides with the tensor channel causality constraint ( which is responsible for the viscosity bound ) . furthermore , we show how to recover the holographic c - theorems in higher curvature theories from similar considerations based on the raychaudhuri equation .

cond-mat0605350

i

in recent years , ultracold atomic systems have served as a controlled and tunable toolbox for studying many - body quantum phenomena . the continuous tunability of the interaction by feshbach resonances makes these systems ideal candidates to study the crossover from momentum space pairing in the bardeen schrieffer ( bcs ) theory to bose - einstein condensate ( bec ) of fermions bound into molecules . this bcs - bec crossover has been one of the most studied problems in recent experiments in both magnetic or optical traps @xcite and optical lattices @xcite . tuning across the feshbach resonance , one traverses the whole range of the gas parameter @xmath3 , where @xmath4 is the fermi momentum and @xmath5 is the s - wave scattering length . the regime of @xmath6 ( negative @xmath5 ) is described by bardeen schrieffer ( bcs ) theory . at @xmath7 ( positive @xmath5 ) fermions pair into bosonic molecules and form a bose - einstein condensate ( bec ) . at the microscopic scale , the bcs and bec regimes are radically different ; however , the macroscopic , and , in particular , critical behaviour is supposed to be qualitatively the same for the whole range of @xmath3 : the system undergoes the superfluid ( sf ) phase transition at a certain critical temperature . separating the bcs and bec extremes is the so - called unitarity point @xmath8 . it is worth noting that the unitarity regime is approximately realized in the inner crust of the neutron stars , where the neutron - neutron scattering length is nearly an order of magnitude larger than the mean interparticle separation @xcite . the fermi gas at unitarity is a peculiar case of a strongly interacting system with no interaction - related energy scale : the divergent scattering length and any related energy scale drop out completely . this gives rise to universality of the dilute gas properties , in the sense that the only relevant energy scale left in the system is given by the density , @xmath9 . because of this universality one obtains a unified description of such diverse systems as cold atoms in magnetic or optical traps , fermi - hubbard model in optical lattices and inner crusts of neutron stars . the theoretical description of the fermi gas in the bcs - bec crossover regime is a major challenge , since the system features no small parameter on which one could build a theory in a rigorous way . the original analytical treatments were confined to zero temperature and were based on the extension of the bcs - type many - body wave function @xcite . most of the subsequent elaborations are also of mean - field type ( with or without remedies for the effects of fluctuations ) @xcite . the accuracy and reliability of such approximations is questionable since they inevitably involve an uncontrollable approximation . numerical investigations of the unitary fermi gases are hampered by the sign problem , inherent to any monte carlo ( mc ) simulations of fermion systems @xcite . one way of avoiding the sign problem at the expense of a systematic error is the fixed - node monte carlo framework , which has been used to study the ground state @xcite . the systematic error of the fixed - node monte carlo depends on the quality of the variational ansatz for the nodal structure of the many - body wave function and is not known precisely . only in a few exceptional cases can the sign problem be avoided without incurring systematic errors . one of such cases is given by fermions with attractive contact interaction , for which a number of sign - problem - free schemes has been introduced @xcite . fortunately , this system can be tuned to the unitarity regime . still , despite a number of calculations at finite temperature @xcite , an accurate description of the finite - temperature properties of the unitary fermi gas is missing . in the present paper , we simulate the fermi - hubbard model in the unitary regime by means of a determinant diagrammatic monte carlo method . by studying the dilute limit of the model , we extract properties of the homogeneous continuum fermi gas . a brief summary of the main results has been given in ref . @xcite . here we provide a detailed description of the monte carlo scheme and methods of data analysis . we also report new results relevant to experimental realizations of the fermi - hubbard model in optical lattices and trapped fermi gases . the fermi - hubbard model is defined by the hamiltonian @xmath10 @xmath11 @xmath12 here @xmath13 is a fermion creation operator , @xmath14 , @xmath15 is the spin index , @xmath16 enumerates @xmath17 sites of the three - dimensional ( 3d ) simple cubic lattice with periodic boundary conditions , the quasimomentum @xmath18 spans the corresponding brillouin zone , @xmath19 is the single - particle tight - binding spectrum , @xmath20 and @xmath21 are the lattice spacing and the hopping amplitude , respectively , @xmath22 stands for the chemical potential and @xmath23 is the on - site attraction . without loss of generality we henceforth set @xmath20 and @xmath21 equal to unity ; the effective mass at the bottom of the band is then @xmath24 . in sec . [ sec:2body ] we will study the two - body problem at zero temperature , show how the hubbard model can be used to study the continuum unitary gas and investigate the functional structure of lattice corrections to the continuum behaviour . in sec.[sec : ddmc ] we discuss the finite - temperature diagrammatic expansion for the hubbard model ( sec . [ ssec : matsubara ] ) , and give a qualitative description of the monte carlo procedure to sum the diagrammatic series ( sec.[ssec : mc ] ) , with details of the updating procedures given in appendix [ sec : updates ] . in order to extract the thermodynamic limit properties from mc data , we use finite - size scaling analysis described in sec . [ sec : sense ] . section [ sec : thermodynamics ] gives an overview of the scaling functions describing thermodynamics of the unitary gas , and results are presented and discussed in sec . [ sec : results ] .

we simulate the dilute attractive fermi - hubbard model in the unitarity regime using a diagrammatic determinant monte carlo algorithm with worm - type updates . we obtain the dependence of the critical temperature on the filling factor and , by extrapolating to , determine the universal critical temperature of the continuum unitary fermi gas in units of fermi energy : . we also determine the thermodynamic functions and show how the monte carlo results can be used for accurate thermometry of a trapped unitary gas .

we simulate the dilute attractive fermi - hubbard model in the unitarity regime using a diagrammatic determinant monte carlo algorithm with worm - type updates . we obtain the dependence of the critical temperature on the filling factor and , by extrapolating to , determine the universal critical temperature of the continuum unitary fermi gas in units of fermi energy : . we also determine the thermodynamic functions and show how the monte carlo results can be used for accurate thermometry of a trapped unitary gas .

1407.7915

i

in summary , we investigated the metastability , excitations , fluctuations , and swallowtail structures of the bec with a uniformly moving defect in a two - dimensional torus system . we first calculated the total energy and the total momentum as functions of the driving velocity of the moving defect . a negative effective - mass region appears near the critical velocity , as is the case for optical lattice systems . in contrast to optical lattice systems , the negative effective - mass states are metastable . this difference comes from that the di in the optical lattice systems is due to the formation of the long - period structures , such as the period - doubling states and the bright gap solitons , which are prohibited in the torus systems . we also found gvps in stationary states in the presence of a strong defect . using the results of the gp equation , we solved the bogoliubov equation and obtained the excitation spectra . we determined that near the critical velocity , the scaling of the energy gap followed a one - fourth power law . this implies an algebraic divergence of the characteristic time scale toward the critical velocity and a violation of the adiabaticity condition at the critical velocity . from wave functions of the excited states @xmath33 and @xmath34 , we obtained the fluctuation properties and showed that the density ( amplitude of the order parameter ) fluctuations are enhanced near the critical velocity . we also calculated the qd and found that it increased near the critical velocity . we confirmed the validity of the gp and the bogoliubov approximations on the basis of these results . we found unconventional swallowtail structures ( multiple - swallowtail structure ) by the direct calculations of the unstable solutions . we discussed that the number of unstable branches depends on the width of the superflow path and expect that the multiple - swallowtail structure reduces to the conventional one in the narrow superflow path limit . we discussed the bifurcation structure of the system . the results for the one - fourth power - law scaling near the critical velocity and the unstable branches imply that the hsn bifurcation occurs in the system , which describes the disappearance of the energy barrier that protects a metastable state . we pointed out that the same scaling law appears in the attractive bec in a harmonic trap near the collapse point . we also discussed the effects of the multiple - swallowtail structure on the calculations for the phase slip rate . in future work , we will attempt to determine why the hamiltonian saddle - node bifurcation appears at the critical velocity and to derive the normal form from the gp and bogoliubov equations . the energy landscape away from the critical velocity remains open . full knowledge of the energy landscape of the multiple - swallowtail structures will serve as the understanding of the breakdown of the superfluidity due to the vortex nucleations . a possible further extension of the present work is to study the effects of quantum fluctuations on the metastability of superfluidity . in particular , these effects are crucial for cases that are not weakly interacting and that are near the critical velocity . in fact , a nonzero drag force acting on a defect below the critical velocity in a one - dimensional system has been reported in ref . this phenomenon is due to quantum fluctuations . it is important to understand the effects of quantum fluctuations on vortex nucleation . another extension of the present work is to study multicomponent systems , such as spinor becs @xcite , and to reveal the effects of the internal degrees of freedom on the metastability of the superfluidity . we thank s. watabe and i. danshita for fruitful discussions and d. yamamoto for useful comments . we also thank an anonymous referee for his or her indication of the unstable solutions , which trigger the findings of the multiple - swallowtail structures . m. k. acknowledges the support of a grant - in - aid for jsps fellows ( grant no . this work is supported by jpsj kakenhi ( grant no . 24543061 ) .

we solve the gross - pitaevskii ( gp ) and bogoliubov equations to investigate the metastability of superfluidity in a bose - einstein condensate in the presence of a uniformly moving defect potential in a two - dimensional torus . we calculate the total energy and momentum as functions of the driving velocity of the moving defect and find metastable states with negative effective - mass near the critical velocity . we also find that the first excited energy ( energy gap ) in the finite - sized torus closes at the critical velocity , that it obeys one - fourth power - law scaling , and that the dynamical fluctuation of the density ( amplitude of the order parameter ) is strongly enhanced near the critical velocity . we find an unconventional swallowtail structure ( multiple - swallowtail structure ) through calculations of the unstable stationary solutions of the gp equation .

we solve the gross - pitaevskii ( gp ) and bogoliubov equations to investigate the metastability of superfluidity in a bose - einstein condensate in the presence of a uniformly moving defect potential in a two - dimensional torus . we calculate the total energy and momentum as functions of the driving velocity of the moving defect and find metastable states with negative effective - mass near the critical velocity . we also find that the first excited energy ( energy gap ) in the finite - sized torus closes at the critical velocity , that it obeys one - fourth power - law scaling , and that the dynamical fluctuation of the density ( amplitude of the order parameter ) is strongly enhanced near the critical velocity . we confirm the validity of our results near the critical velocity by calculating the quantum depletion . we find an unconventional swallowtail structure ( multiple - swallowtail structure ) through calculations of the unstable stationary solutions of the gp equation .

1703.03338

i

the communication paradigm of cooperative relaying has recently received considerable attention due to its effectiveness in alleviating the effects of multipath fading , pathloss and shadowing , and its ability to deliver improved performance in cognitive radio systems and wireless sensor networks . relay - assisted cellular networks are a promising solution for enhancing coverage and are included in standards , such as ieee 802.16j / m and long term evolution - advanced ( lte - a ) . several protocols for cooperative relaying were presented in @xcite where the gains in transmit and receive diversity were studied . in multi - relay networks , simultaneous transmissions by the relays are in general difficult to handle ; towards this end , opportunistic relay selection has been suggested in @xcite to improve the resource utilization and to reduce the hardware complexity . stemming from the relay selection concept , many studies have proposed improved selection techniques ( see , _ e.g. _ , @xcite ) . traditional hd relaying schemes partition the packet transmission slot into two phases , where the transmission on the source - relay @xmath0 link happens in the first phase , and the transmission on the relay - destination @xmath1 link occurs in the second phase . however , this relaying scheme limits the maximum achievable multiplexing gain to @xmath2 , which also results in bandwidth loss . in order to overcome such multiplexing and bandwidth limitations , several techniques have been proposed in the literature ( see , for example , @xcite and references therein ) . among them , the successive relaying scheme in @xcite incorporates multiple relay nodes and allows concurrent transmissions between source - relay and relay - destination to mimic an ideal full - duplex transmission . however , this scheme targets scenarios with a long distance between the relays and thus inter - relay interference is not considered . an extension of this work is discussed in @xcite , where the authors assume that iri is strong ( in co - located or clustered relays ) and can always be decoded at the affected nodes ; this decoded iri is exploited in a superposition coding scheme that significantly improves the diversity - multiplexing trade - off performance of the system . in earlier studies , relays were assumed to lack data buffers and relay selection was mainly based on the @xmath3 criterion and its variations ( see , for example , @xcite ) . here , the relay that receives the source signal is also the one that forwards the signal to the destination . with the adoption of buffer - aided relays , this coupling is broken , since different relays could be selected for transmission and reception , thus allowing increased degrees of freedom . buffering at the relay nodes has been shown to be a promising solution for cooperative networks and motivates the investigation of new protocols and transmission schemes ( see @xcite and @xcite for an overview ) . @xcite proposed a novel criterion based on @xmath4 relay selection ( mmrs ) , in which the relay with the best source - relay @xmath0 link is selected for reception and the relay with the best relay - destination @xmath1 link is selected for transmission on separate slots . in @xcite , at each slot the best link is selected among _ all _ the available @xmath0 and @xmath1 links , as a part of the proposed @xmath5 policy , thus offering an additional degree of freedom to the network , while buffer - aided link selection was studied in topologies with source - destination connectivity ( see , _ e.g. , _ in @xcite ) , resulting in improved diversity and throughput . more recently , to alleviate the throughput loss of hd relaying , significant focus has been given to minimizing the average packet delay . towards this end , various works have proposed hybrid solutions combining the benefits of mmrs and @xmath5 @xcite , the use of broadcasting in the @xmath0 link @xcite , the prioritization of @xmath1 transmissions @xcite or the selection of the relay with the maximum number of packets residing in its buffer @xcite . however , it was shown that a trade - off exists between delay performance and the diversity of transmission as the number of relays with empty or full buffers increases . to improve throughput and reduce average packet delays , a number of works proposed to employ non - orthogonal successive transmissions by the source and a selected relay . in order to recover the hd multiplexing loss , @xcite suggests to combine mmrs with successive transmissions ( sfd - mmrs ) . as the proposed topology aims to mimic full - duplex relaying , different relays are selected in the same time slot ; however , relays are assumed to be isolated and the effect of iri is ignored . more practical topologies were studied in @xcite where iri exists and is not always possible to be cancelled . for fixed rate transmission , the proposed @xmath6 solution proposed in @xcite , combining power adaptation and interference cancellation , provides a performance close to the upper bound of sfd - mmrs . in addition , kim and bengtsson @xcite proposed buffer - aided relay selection and beamforming schemes taking the iri into consideration ; they consider a model which can be regarded as an example of relay - assisted device - to - device ( d2d ) communications , where the source and destination are low - cost devices with a single antenna and the base stations comprise more powerful relays with buffers and multiple antennas . numerical results show that their approach outperforms sfd - mmrs when interference is taken into consideration , and when the number of relays and antennas increases they approach the performance of the interference - free sfd - mmrs , herein called the _ ideal _ sfd - mmrs . finally , the use of buffer aided relays has been considered in topologies wth full - duplex ( fd ) capabilities @xcite and decoupled non - orthogonal uplink and downlink transmissions @xcite , showing that throughput can be significantly improved due to the increased scheduling flexibility . in many practical considerations ( _ e.g. _ , wireless sensors ) , the relay nodes are hardware - limited to be hd while the source can be a more powerful wireless device with large buffers and multiple antennas . although this observation is not always true ( _ e.g. _ , in d2d communications @xcite ) , it is a reasonable and common practical scenario . towards this end , we study a network which consists of a buffer - aided source with one or multiple antennas , multiple hd buffer - aided relays and a destination . with this setup , we are able to approach ( achieve ) the performance of the ideal sfd - mmrs by adopting a buffer - aided source whose buffer retains replicas of the relay buffers , successfully transmitted data from the source to relays , to facilitate iri mitigation ( cancellation ) ; we relax the assumption of knowing the full csi and instead we allow for csir and limited feedback from the receiver to the transmitter ; under these conditions we propose a relay pair selection scheme that is based on partial phase alignment of signals . the rest of the paper is organized as follows . in section [ sec : model ] , the system model is outlined . the proposed relaying schemes for variable and fixed rate are presented in sections [ sec : policy1 ] and [ sec : policy2 ] , respectively . the performance of the proposed relaying policies in terms of outage and average throughput , along with comparisons with other state - of - the - art relaying schemes are presented in section [ sec : numerical ] . finally , conclusions and a discussion on future possible directions are drawn in section [ sec : conclusions ] . vectors are written in bold lower case letters and matrices in bold capital letters . @xmath7 , @xmath8 and @xmath9 denote the sets of real numbers , complex and natural numbers , respectively . for a matrix @xmath10 ( @xmath11 ) , @xmath12 denotes the entry in row @xmath13 and column @xmath14 . matrix @xmath15 denotes the identity matrix of appropriate dimensions . the trace of a square matrix @xmath16 is denoted by @xmath17 . @xmath18 and @xmath19 denote the transpose and hermitian transpose operations , respectively ; @xmath20 denotes the @xmath21-norm operation . the complex conjugate of a complex number @xmath22 is denoted by @xmath23 ; the real and imaginary parts of a complex number @xmath22 are denoted by @xmath24 and @xmath25 , respectively . we denote by @xmath26 the set of all possible relay - pairs in the relay network , and by @xmath27 its cardinality . a relay pair , denoted by @xmath28 belongs to set @xmath26 if and only if @xmath29 , the receiving relay @xmath30 is not full and the transmitting relay @xmath31 is not empty .

we study a cooperative network with a buffer - aided multi - antenna source , multiple half - duplex ( hd ) buffer - aided relays and a single destination . such a setup could represent a cellular downlink scenario , in which the source can be a more powerful wireless device with a buffer and multiple antennas , while a set of intermediate less powerful devices are used as relays to reach the destination . we show that the detrimental effect of iri can be alleviated by precoding at the source , mitigating or even fully canceling the interference . a cooperative relaying policy is proposed that employs a joint precoding design and relay - pair selection . when channel state information is only available at the receiving side ( csir ) , we propose a relay selection policy that employs a phase alignment technique to reduce the iri . the performance of the two proposed relay pair selection policies are evaluated and compared with other state - of - the - art relaying schemes in terms of outage and throughput .

we study a cooperative network with a buffer - aided multi - antenna source , multiple half - duplex ( hd ) buffer - aided relays and a single destination . such a setup could represent a cellular downlink scenario , in which the source can be a more powerful wireless device with a buffer and multiple antennas , while a set of intermediate less powerful devices are used as relays to reach the destination . the main target is to recover the multiplexing loss of the network by having the source and a relay to simultaneously transmit their information to another relay and the destination , respectively . successive transmissions in such a cooperative network , however , cause inter - relay interference ( iri ) . first , by assuming global channel state information ( csi ) , we show that the detrimental effect of iri can be alleviated by precoding at the source , mitigating or even fully canceling the interference . a cooperative relaying policy is proposed that employs a joint precoding design and relay - pair selection . note that both fixed rate and adaptive rate transmissions can be considered . for the case when channel state information is only available at the receiving side ( csir ) , we propose a relay selection policy that employs a phase alignment technique to reduce the iri . the performance of the two proposed relay pair selection policies are evaluated and compared with other state - of - the - art relaying schemes in terms of outage and throughput . the results show that the use of a powerful source can provide considerable performance improvements . cooperative networks , opportunistic relaying , buffer - aided relays , precoding , interference cancellation .

1702.05719

i

consider a two - player and zero - sum game between alice and bob . the game is played once . a nash equilibrium assigns a strategy to alice and bob such that no player has any incentive to unilaterally change his strategy @xcite . it is proven that if the players can randomize on their pure strategies set according to _ any _ probability distribution , then the game has at least one nash equilibrium in the randomized mixed strategies . however , assume that alice has restrictions on implementing probability distributions when choosing his mixed strategy . more specifically , assume that alice can only choose a mixed action with entropy at most a given number @xmath0 . for instance , if @xmath1 , alice is only allowed to play pure actions . we are interested in the maximum payoff that alice can secure with mixed actions of entropy at most @xmath0 ( regardless of the action of bob ) . let us denote this by @xmath2 . equivalently , we may ask : in order to guarantee average payoff of @xmath3 , how much randomness needs to be utilized by alice ? let us denote the minimum entropy of the randomness consumed by alice to guarantee payoff @xmath3 by @xmath4 . we may call @xmath4 , the _ min - entropy function_. observe that @xmath5 is the inverse function of @xmath6 . even though @xmath2 is defined in a one - shot setting , the ( upper concave envelope ) of @xmath2 finds an operational meaning in @xcite in the context of repeated games as the payoff that alice can secure in the long run . for instance , gossner and vieille @xcite study a repeated game in which alice can not randomize freely , but has access to an external i.i.d . source @xmath7 which are revealed symbol by symbol ( causally ) to alice as the game is played out . they show that the entropy of the source @xmath8 characterizes the payoff that alice can secure in the long run , and the answer is given in terms of @xmath9 . this is similar to shannon s compression formula @xmath8 which is defined on a single copy of the source ( _ single letter _ ) , but gives the ultimate compression limit when multiple copies of the source are observed . another motivation for @xmath2 is given in @xcite , arguing that limitation on random strategies of players stems from simplicity of humans ; that humans are known to be bad at generating random - like sequences " . to compute @xmath4 , one has to first consider the set of distributions on the action of alice that would secure a payoff @xmath3 for her . this set will be a polytope in the space of all probability distributions . then , one should solve an entropy minimization problem over this polytope in the space of probability distributions . in fact , minimizing and maximizing entropy arises in a wide range of contexts . computing maximum entropy under a set of linear constraints is a well - studied problem with a wide range of applications , _ see @xcite@xcite and the principle of maximum entropy . it is shown in @xcite that computing the minimum entropy can be also quite important . furthermore , many algorithms for clustering and pattern recognition are essentially solving entropy minimization problems @xcite . an important special case of the entropy minimization problem ( with its own applications ) is that of finding a joint probability of minimum entropy given its marginal distributions ( the marginal distribution is a linear constraint on the joint probability distribution ) @xcite . finally , the quantum version of the entropy minimization problem is of key theoretical importance.@xcite while the calculation of the function @xmath4 has received attention in the game theory literature , entropy minimization problem are known to be an np - hard non - convex optimization problem @xcite . since the entropy is a concave function over the probability simplex , its minimum occurs at a vertex of the feasible domain . as a result , computation of @xmath10 leads to a search problem over an exponentially large set . even though the algorithm of @xcite can be used to compute @xmath4 , but it has no guarantee of success . our contributions can be summarized as follows : * we study the properties of @xmath10 and give a number of easy - to - compute bounds on the value of @xmath10 . one of the bounds on @xmath10 is expressed in term of a linear program ; this linear program has a quite general form . we employ _ probabilistic tools _ to study this linear program to prove the following explicit lower bound on @xmath4 : @xmath11 where @xmath12 and @xmath13 are the minimum and maximum entries of the entries of the payoff table ; @xmath14 is the payoff that alice can guarantee with deterministic strategies ( pure - strategy security level ) and @xmath15 is the nash value of the game for alice ( payoff that alice can guarantee with no restriction on her action s entropy ) . because the linear program we consider has a quite general form ( and can be converted to other linear programs with a change of variables ) , our use of probabilistic tools for studying linear programs is novel . * we give and utilize new results on the set of mixed strategies that guarantee a certain security level . while the literature on game theory makes extensive use of total variation distance between distributions , we propose and illustrate the use of the @xmath16divergence ( or the tsallis divergence of order two ) in game theoretic contexts . the @xmath16divergence is defined as @xmath17 , where @xmath18 and @xmath19 are two probability distributions . to see the applicability of this divergence measure , consider a zero - sum game between alice and bob . fix an arbitrary ( mixed ) strategy for bob . let @xmath20 and @xmath21 be two probability distributions for the action of alice . let @xmath22 and @xmath23 denote the payoff of alice when she plays according to @xmath20 and @xmath21 respectively . then , @xmath24 $ ] and @xmath25 $ ] are the payoffs secured by @xmath20 and @xmath21 . also @xmath26 $ ] is a natural object , the risk associated to @xmath20 . then , as we see later in lemma [ lemmavar ] , these natural objects in a game come together as follows : @xmath27-\mathbb{e}[{w_2}])^2}{\mathsf{var}[w_1]}.\end{aligned}\ ] ] * the min - entropy function @xmath4 finds its operational interpretation in a repeated game ( e.g. , the result of gossner and vieille in @xcite ) . we simplify and generalize the proof of gossner and vieille in section [ sec:5op ] . the generalized setup considers the possibility of leackage of alice s random source sequence to bob in the zero - sum game . more specifically , we assume an i.i.d . sequence of pairs @xmath28 , @xmath29 distributed according to a given @xmath30 . the sequence @xmath31 is revealed symbol by symbol ( causally ) to alice as the game is played out , while the sequence @xmath32 is revealed symbol by symbol to bob . we can view @xmath33 as the side information that bob obtains about alice s observation . as before , alice can not randomize freely and can only use the randomness in the sequence @xmath31 . we show that the upper concave envelope of @xmath2 , at @xmath34 is the maximum payoff that alice can secure regardless of bob s actions ; furthermore , bob can ensure that alice does not get more than this payoff . this result is a generalization of the result of gossner and vieille since when @xmath35 is a constant random variable , the conditional entropy @xmath36 reduces to the unconditional entropy @xmath8 . the rest of this paper is organized as follows : in section [ s : prob_state ] we give a mathematical definition of the problem under study ; in section [ s : results ] we express the main results . finally , in section [ s : proofs ] we give the proofs . some of the details are left for the appendices . add notation of @xmath37 and @xmath38 .

more precisely , we consider the maximum payoff that the maximizer ( alice ) can secure with limited randomness . this problem finds an operational interpretation in the context of repeated games with non - ideal sources of randomness as shown by gossner and vieille , and neyman and okada . we begin by simplifying the proof of gossner and vieille and also generalize their result . then , we turn to the computational aspect of the problem , which has not received much attention in the game theory literature . we observe the equivalence of this problem with entropy minimization problems in other scientific contexts . next , we provide two explicit lower bounds on the entropy - payoff tradeoff curve . to do this , we provide and utilize new results for the set of distribution that guarantee a certain payoff for alice ( mixed strategies corresponding to a security level for alice ) . in particular , we study how this set of distribution shrinks as we increase the security level . while the use of total variation distance is common in game theory , our derivation indicates the suitability of utilizing the renyi - divergence of order two .

we study a two - player zero - sum game in which one of the players is restricted to mixed strategies with limited randomness . more precisely , we consider the maximum payoff that the maximizer ( alice ) can secure with limited randomness . this problem finds an operational interpretation in the context of repeated games with non - ideal sources of randomness as shown by gossner and vieille , and neyman and okada . we begin by simplifying the proof of gossner and vieille and also generalize their result . then , we turn to the computational aspect of the problem , which has not received much attention in the game theory literature . we observe the equivalence of this problem with entropy minimization problems in other scientific contexts . next , we provide two explicit lower bounds on the entropy - payoff tradeoff curve . to do this , we provide and utilize new results for the set of distribution that guarantee a certain payoff for alice ( mixed strategies corresponding to a security level for alice ) . in particular , we study how this set of distribution shrinks as we increase the security level . while the use of total variation distance is common in game theory , our derivation indicates the suitability of utilizing the renyi - divergence of order two .

0801.0845

i

in this paper we have studied higher - dimensional gauge / gravity theories with compact extra dimension(s ) . in section [ sec : abelian ] we have investigated the pure abelian gauge theory with extra compact @xmath9-dimensions in the @xmath5 gauge , and found that the gauge - fixed action possesses the residual global symmetries between unphysical component of the gauge fields and the would - be scalar ng bosons . the @xmath1-dependent mass - matrix of this multiplet is exactly the super - hamiltonian and the residual global symmetry is generated by the supercharge found in the analysis of the mass spectrum . in section [ sec : gravity ] we have extended the analysis to five - dimensional pure gravity to quadratic order as perturbation to the randall - sundrum background . we have established the one - parameter family of gauge choices for 5d gravity analogous to the @xmath5 gauge in spontaneously broken gauge theories . in this @xmath5 gauge we have shown that the gauge - fixed action exhibits the three independent residual global symmetries . as in the pure abelian gauge theory with extra dimensions , it is the symmetries between unphysical component of the graviton field and the would - be vector and scalar ng bosons . however , as opposed to the pure abelian gauge theories with extra dimensions , one of these residual symmetry transformations can not be expressed in terms of the first - order differential supercharges but the second - order differential supercharge . in section [ sec : amplitude ] , to see the validity of our @xmath5 gauge we have computed the one graviton exchange amplitude in the lowest tree - level approximation , and confirmed that it is indeed @xmath1-independent . using this result we also found that for the process of a gravitational interaction between two conserved energy - momentum tensors residing on the uv and ir branes , the famous vdvz - discontinuity does not arise even in the lowest tree - level approximation .

we study compactified pure gauge / gravitational theories with gauge - fixing terms and show that these theories possess quantum mechanical susy - like symmetries between unphysical degrees of freedom . these residual symmetries are global symmetries and generated by quantum mechanical supercharges . also , we establish new one - parameter family of gauge choices for higher - dimensional gravity , and calculate as a check of its validity one graviton exchange amplitude in the lowest tree - level approximation . we also give a simple interpretation of the vdvz - discontinuity , which arises in the lowest tree - level approximation , from the supersymmetric point of view .

we study compactified pure gauge / gravitational theories with gauge - fixing terms and show that these theories possess quantum mechanical susy - like symmetries between unphysical degrees of freedom . these residual symmetries are global symmetries and generated by quantum mechanical supercharges . also , we establish new one - parameter family of gauge choices for higher - dimensional gravity , and calculate as a check of its validity one graviton exchange amplitude in the lowest tree - level approximation . we confirm that the result is indeed-independent and the cancellation of the-dependence is ensured by the residual symmetries . we also give a simple interpretation of the vdvz - discontinuity , which arises in the lowest tree - level approximation , from the supersymmetric point of view .

1501.06030

i

a fractional quantum hall ( qh ) system of filling fraction @xmath3 has edge channels that support fractional charges obeying fractional braiding statistics @xcite . at @xmath4 , the edge states are decomposed into a @xmath5 charge mode and a counterpropagating neutral mode @xcite . they originate from renormalization of two counterpropagating charge modes @xcite , @xmath6 and @xmath7 , and stabilize at low temperature under strong disorder . neutral modes have attracted much attention , as they are charge neutral and carry energy . they have been recently detected through shot noise measurements @xcite , and their properties such as energy and decay length have been extensively studied @xcite . electron interaction is a dominant source of dephasing at low temperature @xcite . it leads to electron fractionalization @xcite in quantum wires ; an electron , injected into a wire , splits into constituents ( spin - charge separation , charge fractionalization ) , showing reduction of interference visibility or dephasing @xcite . interestingly , when the wire is finite , the constituents recombine after bouncing at wire ends , resulting in coherence revival @xcite . fractionalization was detected @xcite in a non - chiral wire , and studied in the integer qh edge @xcite . coherent transport , as well as dephasing , can be tackled through the study of low energy dynamics at the edge . this is particularly important in the context of the fractional qh regime . the present study implies that the presence of neutral modes could be a dominant source of dephasing . note that neutral modes have been observed in almost all fractional qh systems @xcite . at the same time there is no uncontested observation of anyonic interference oscillations in the pure aharonov - bohm regime of a fractional qh interferometer . the present study of the @xmath4 qh regime emphasizes two dephasing mechanisms by fractionalization of an electron into charge and neutral components , _ plasmonic dephasing _ and _ topological dephasing_. concerning the plasmonic dephasing mechanism , the overlap between the plasmonic parts of the charge and neutral components decreases with time , as the two components propagate with different velocities in the opposite directions . the resulting dephasing is similar to the plasmonic dephasing that takes place in a quantum wire or in integer qh edges . on the other hand , the topological dephasing is a new mechanism unnoticed so far . it occurs because the zero - mode parts of the components , satisfying fractional statistics , may braid with thermally excited anyons . thermal average of the resulting braiding phase leads to dephasing that occurs only in the interfering processes characterized by particular values of topological winding numbers . , coupled to lead edge states of @xmath4 ( black solid lines ) through quantum point contacts ( qpcs ) at @xmath8 . electron ( rather than fractional quasiparticle ) tunneling occurs through the qpcs ( dotted lines ) . following the tunneling , each electron ( and the hole left behind in the lead edge ) fractionalizes into a charge component propagating at velocity @xmath9 ( solid blue arrow ) and a neutral component counterpropagating at velocity @xmath10 ( dashed red ) . the magnetic flux in the dot area is @xmath11 . ] our analysis addresses the ab oscillation of differential conductance @xmath12 through a quantum dot ( qd ) in the @xmath4 qh regime . we focus on linear response of electron sequential tunneling into the qd . @xmath12 is decomposed into the harmonics of the ab flux @xmath11 in the qd , @xmath13 where @xmath14 is a flux quantum ; see fig . [ setup1 ] . semiclassically , @xmath15 represents the relative winding number of a fractionalized charge component , around the circumference @xmath16 of the qd , between two interfering paths : an electron , after tunneling into the qd , fractionalizes into charge and neutral components ; see fig . [ setup1 ] . the charge ( neutral ) component has propagation velocity @xmath17 , spatial width @xmath18 at temperature @xmath19 , level spacing @xmath20 , and scaling dimension @xmath21 ( @xmath22 ) in the electron tunneling operator at low temperatures . @xmath23 is determined by the overlaps of the components of the same kind between two interfering paths of relative charge winding @xmath15 . we find two mechanisms suppressing @xmath24 , the plasmonic dephasing and the topological dephasing ; the former ( latter ) involves plasmon ( zero - mode ) parts of the components . in the plasmonic dephasing , @xmath23 is contributed from the two interfering paths whose charge components overlap maximally between the paths . but , their neutral components overlap only partially between the interfering paths , reducing @xmath23 ; similar dephasing occurs in other fractionalizations @xcite . the topological dephasing additionally occurs , but depending on @xmath15 , in contrast to the other known mechanisms . when @xmath25 @xcite , the first harmonics @xmath26 is suppressed at @xmath27 ( namely , @xmath28 ) . it is because the charge component gains thermally fluctuating fractional braiding phase of @xmath29 ( leading to @xmath30 ) , while it winds once ( @xmath31 ) around @xmath32 electronic or anyonic thermal excitations on the qd edge or in the bulk . by contrast , the second harmonics @xmath33 is not affected by the topological dephasing ( as braiding phase @xmath34 and @xmath35 are trivial ) and dominates @xmath12 , resulting in @xmath2 ab oscillations . these above findings occur in both the regimes of strong disorder and weak disorder in the edge of the qd . note that the topological dephasing does not occur in the coulomb dominated regime @xcite where coulomb interactions between the bulk and edge of the qd is strong , as discussed later .

tunneling , dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot . in particular , when the charge mode moves much faster than the neutral mode , and at temperatures higher than the level spacing of the dot , electron fractionalization combined with the fractional statistics of the charge mode leads to the dephasing selectively suppressing aharonov - bohm oscillations but not oscillations , resulting in oscillation - period halving .

we study dephasing in electron transport through a large quantum dot ( a fabry - perot interferometer ) in the fractional quantum hall regime with filling factor . in the regime of sequential tunneling , dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot . in particular , when the charge mode moves much faster than the neutral mode , and at temperatures higher than the level spacing of the dot , electron fractionalization combined with the fractional statistics of the charge mode leads to the dephasing selectively suppressing aharonov - bohm oscillations but not oscillations , resulting in oscillation - period halving .

hep-lat0605012

i

in two seminal papers svetitsky and yaffe have tentatively linked the finite - temperature phase transitions in ` hot ' gauge theories to the simpler order - disorder phase transitions of spin models @xcite . in the general case their conjecture may be stated as follows : the effective theory describing finite - temperature yang - mills theory with gauge group @xmath3 in @xmath4 dimensions is a spin model in @xmath5 dimensions with a global symmetry group given by the centre @xmath6 of the gauge group . a somewhat stronger version of the conjecture can be formulated if the phase transitions in questions are of second order . in this case yang - mills theory and spin model fall into the same universality class and the critical exponents coincide . this has been convincingly demonstrated for @xmath7 @xcite in @xmath8 . however , continuous phase transitions in hot gauge theories are not generic and hence the universality statement is almost empty at least in 3 + 1 dimensions @xcite . on the other hand , the more general version of the statement has already been used by svetitsky and yaffe to argue that the phase transition for @xmath9 yang - mills theory must be first order for @xmath8 as there is no @xmath0 rg fixed point in this case . since then this has been firmly established by a number of lattice calculations @xcite . the conjecture implies that the effective theories may be formulated as ` polyakov loop models ' @xcite . for @xmath3 this means that the macroscopic dynamical variables have to reflect the complete gauge invariant information contained in the ( untraced ) polyakov loop , which in lattice notation is given by @xmath10 \equiv \prod_{t=1}^{n_{\tau } } u_{t,{\mbox{\scriptsize\boldmath$x$}};0 } \ ; .\ ] ] this is a temporal holonomy winding around the compact euclidean time direction of extent @xmath11 . for gauge groups with nontrivial centre the traced polyakov loop , @xmath12 with the trace being taken in the defining representation for the ease of later notation . ] serves as an order parameter for the deconfinement phase transition . the phase transition goes along with spontaneous breaking of the centre symmetry resulting from _ non - periodic _ gauge transformations under which @xmath13 the deconfined broken - symmetry phase at sufficiently large wilson coupling @xmath14 is characterised by @xmath15 ( see @xcite for a review ) . recently it has been found that gauge groups with trivial centre may also lead to a deconfinement transition depending on the _ size _ of the gauge group @xcite . at this point the choice of dynamical variables needs to be addressed . under _ periodic _ gauge transformations @xmath16 the holonomy ( [ eq : utrpoldef ] ) transforms as @xmath17 which leaves its eigenvalues and , as a consequence , its trace ( [ eq : trpoldef ] ) invariant . the eigenvalues are permuted arbitrarily by gauge transformations corresponding to weyl reflections @xcite . this invariance is taken into account by constructing symmetric polynomials in the @xmath18 eigenvalues . from unimodularity the product of the eigenvalues is @xmath19 and there are only @xmath20 independent polynomials , for example the traces @xmath21 for @xmath22 . these in turn are in one - to - one correspondence with the characters of the @xmath23 fundamental representations ( see below ) . hence , for @xmath7 @xmath24 ( which is real ) is sufficient while @xmath9 requires @xmath24 and @xmath25 , the latter being a linear combination of @xmath26 and @xmath27 . only for @xmath28 traces of higher powers of @xmath29 are needed as independent dynamical variables @xcite . in two recent papers @xcite we have studied polyakov loop models on the lattice for the simplest non - abelian gauge group @xmath7 . the models have been derived using strong - coupling techniques at small wilson coupling @xmath30 and a newly developed inverse monte carlo ( imc ) method which works for arbitrary values of @xmath30 . the latter method allows for a mapping of yang - mills theory at a certain value of @xmath30 to any appropriately chosen polyakov loop model of the form @xmath31 where the summation is over nearest neighbours and group representations @xmath32 , @xmath33 . the group character @xmath34 is the trace of the polyakov loop in representation @xmath32 , @xmath35 \equiv { \text{tr}}_i \ , { \mathfrak{p}_{{\mbox{\footnotesize\boldmath$x$ } } } } \ ; .\ ] ] all characters @xmath34 are polynomials in the characters corresponding to the fundamental representations . for @xmath7 the simplest model is of ising type , @xmath36 as first suggested in @xcite ( see also @xcite ) . the output of the imc routines are the @xmath30-dependent effective couplings @xmath37 . even without particular knowledge of these one may study the models ( [ eq : polmodel ] ) in their own right as statistical field theories . the svetitsky - yaffe conjecture may then be utilised to deduce information about the yang - mills phase transition . for @xmath7 we have been able to show that the mean - field analysis of the effective models yields a surprisingly good agreement with the monte carlo analysis of both the model itself and the underlying yang - mills dynamics . it should be stressed at this point that the models ( [ eq : polmodel ] ) are not just simple scalar field theories with a linear target space as all characters ( [ eq : chars ] ) take values in a compact space parametrised by the @xmath38 fundamental characters . hence , in the lattice path integral each lattice site is endowed with the reduced haar measure on the gauge group rather than a lebesgue measure . this paper presents our first steps to generalise the results of @xcite to the gauge group @xmath9 . we label the characters by two integers @xmath39 and @xmath40 which count the numbers of fundamental and conjugate representations ( ` quarks ' and ` antiquarks ' in the @xmath9 flavour language ) required to construct the representation @xmath41 . equivalently , these integers characterise the horizontal extensions of @xmath9 young tableaux ( see fig . [ fig : pq ] ) . character labels and @xmath9 young tableaux . ] under the @xmath0 centre transformations the characters transform according to the rule @xmath42 so that the most general centre - symmetric effective action with nearest - neighbour interaction may be written as @xmath43 = \sum_{\substack{{\langle}{\mbox{\scriptsize\boldmath$x$ } } { \mbox{\scriptsize\boldmath$y$}}{\rangle } , \ , pq , \ , p'q ' \\ p + p ' = q + q ' \ , \mathrm{mod } \ , 3 } } \lambda_{pq , p'q ' } \ , \big ( \chi_{pq } ( { \mbox{\boldmath$x$ } } ) \ , \chi_{p'q ' } ( { \mbox{\boldmath$y$ } } ) + \text{h.c . } \big ) \\ + \sum_{\substack{{\mbox{\scriptsize\boldmath$x$ } } , \ , pq \\ \mathrm{mod } \ , 3 } } \lambda_{pq,00 } \ , \big ( \chi_{pq } ( { \mbox{\boldmath$x$ } } ) + \text{h.c . } \big ) \ ; .\end{gathered}\ ] ] this coincides with the ansatz suggested by dumitru et al.@xcite . the first sum in the effective action consists of hopping terms involving monomials of the form @xmath44 or @xmath45 ( and h.c . ) while the second sum is a ` potential ' term containing only powers @xmath46 ( and h.c . ) localised at single sites . the remainder of the paper is organised as follows . in section [ sec : sce ] we confirm the ansatz ( [ eq : ssu3 ] ) by means of a strong coupling ( small-@xmath30 ) expansion for @xmath47 $ ] . for a restricted set of couplings ( and hence representations ) we investigate the resulting @xmath0 models by minimising the classical action ( section [ sec : qca ] ) followed by an improved mean field analysis in section [ sec : mf ] . in agreement with the svetitsky - yaffe conjecture we find a first order phase transition from the symmetric to a ferromagnetic phase . our improved mean field analysis already reveals an interesting phase structure with four different phases : two distinct ferromagnetic phases , one symmetric and one anti - ferromagnetic phase . besides the first order transitions we detect second order transitions from the symmetric to an anti - ferromagnetic and to a ferromagnetic phase . the continuous transition from the symmetric to the anti - ferromagnetic phase is to be expected since the models reduce to the @xmath48-state potts model for polyakov - loops having values in the centre of the gauge group . section [ sec : mcsim ] contains the results of our extensive monte carlo simulations performed on a linux cluster where we have implemented the powerful package jenlatt . similarly as for @xmath7 the mean field and numerical results are in surprisingly good agreement . this is presumably due to the existence of ( three ) tricritical points . depending on the order of the transition we localise the critical lines with either a metropolis , a multicanonical or a modified cluster algorithm . in addition we have checked that the critical exponents @xmath1 and @xmath2 at the second order transition to the anti - ferromagnetic phase agree with those of the @xmath48-state potts model in @xmath48 dimensions . finally , in section [ sec : so ] we wrap up with discussion and conclusions .

we study effective lattice actions describing the polyakov loop dynamics originating from finite - temperature yang - mills theory . starting with a strong - coupling expansion we find excellent agreement of both approaches concerning the phase structure of the theories . the phase diagram exhibits both first and second order transitions between symmetric , ferromagnetic and anti - ferromagnetic phases with phase boundaries merging at three tricritical points . the critical exponents and at the continuous transition between symmetric and anti - ferromagnetic phases are the same as for the 3-state potts model .

we study effective lattice actions describing the polyakov loop dynamics originating from finite - temperature yang - mills theory . starting with a strong - coupling expansion the effective action is obtained as a series of-invariant operators involving higher and higher powers of the polyakov loop , each with its own coupling . truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved . to this end we employ a modified mean field approximation and monte carlo simulations based on a novel cluster algorithm . we find excellent agreement of both approaches concerning the phase structure of the theories . the phase diagram exhibits both first and second order transitions between symmetric , ferromagnetic and anti - ferromagnetic phases with phase boundaries merging at three tricritical points . the critical exponents and at the continuous transition between symmetric and anti - ferromagnetic phases are the same as for the 3-state potts model .

1105.4291

i

cyg x-1 is an archetypical and well studied persistent black - hole binary . its companion is the ob supergiant hde 226868 . cyg x-1 is both a radio and x - ray source , and the fluxes in these two bands are strongly correlated ( e.g. , @xcite , hereafter paper i ) . the likely cause of the correlation is the jet in this system ( @xcite , hereafter s01 ) being formed by the matter of an inner hot accretion flow @xcite . the radio emission is modulated at the orbital period @xcite , which is caused by free - free absorption in the stellar wind from the massive companion . as shown by @xcite ( hereafter sz07 ) , the observed modulation levels imply that the average radio fluxes are substantially absorbed , which then , as discussed in paper i , modifies the form of the observed radio / x - ray correlation . in this work , we study in detail the free - free absorption of radio emission in winds of massive stars in high - mass x - ray binaries ( hereafter hmxbs ) . we derive formulae for the optical depth measured from the point of emission along the jet . we also consider emission of counter - jets and compton scattering by the wind . then , we apply our results to cyg x-1 , taking into account the strong anisotropy of its stellar wind , found by @xcite , as well as the radio emission being extended ( s01 ) . this yields strong constraints on the structure of the jet in cyg x-1 , in particular it implies that a major part of this emission takes place at distances comparable to the binary orbit . based on the results of this application , we estimate the effect of the free - free absorption on the form of the radio / x - ray correlation in cyg x-1 .

we study free - free absorption of radio emission by winds of massive stars . we derive formulae for the optical depth through the wind measured from a point of emission along a jet , taking into account compton and photoionization heating and compton , recombination , line and advection cooling . based on the finding of the flux - dependent orbital modulation , we are able to estimate a range of the possible changes of the form of the radio / x - ray correlation in cyg x-1 due to free - free absorption .

we study free - free absorption of radio emission by winds of massive stars . we derive formulae for the optical depth through the wind measured from a point of emission along a jet , taking into account compton and photoionization heating and compton , recombination , line and advection cooling . we apply the developed formalism to radio monitoring data for cyg x-1 , which allows us to obtain strong constraints on the structure of its inner jet . with the data at 15 ghz , and taking into account an anisotropy of the stellar wind in cyg x-1 , we estimate the location of the peak of that emission along the jet at about one orbital separation , i.e. , cm . given a previous determination of the turnover frequency in cyg x-1 , this implies the location of the base of the jet at gravitational radii . we also obtain corresponding results at 8.3 ghz and 2.25 ghz , which roughly follow the standard conical partially self - absorbed jet model . furthermore , we find that the level of the orbital modulation depends on the radio flux , with the modulation being substantially stronger when the radio flux is lower . this is explained by the height of the radio emission along the jet decreasing with the decreasing radio flux , as predicted by jet models . based on the finding of the flux - dependent orbital modulation , we are able to estimate a range of the possible changes of the form of the radio / x - ray correlation in cyg x-1 due to free - free absorption . we also derive predictions for the orbital modulation and flux attenuation at frequencies beyond the 2.2515 ghz range . [ firstpage ] accretion , accretion discs radio continuum : stars stars : individual : cyg x-1 stars : individual : hde 226868 x - rays : binaries x - rays : stars .

1105.4291

c

we have studied free - free absorption in an optically - thin x - ray irradiated stellar wind . we have taken into account compton heating and cooling , photoionization heating , bremsstrahlung and line cooling , and advection . we have derived relatively simple formulae for the free - free optical depth , in section [ wind ] . we have also considered constraints from eclipses , counter - jets ( appendix [ eclipses ] ) and compton scattering ( appendix [ scattering ] ) . we have then considered the current constraints on the parameters of the cyg x-1 binary and its stellar wind ( section [ pars ] ) . as found by @xcite , the wind is strongly anisotropic , with the density close to the orbital plane and in the region shadowed by the donor much higher than that in the polar regions , which are responsible for absorption of the radio emission of the jet . in section [ radio ] , we have discussed the radio data , including the available information about the extended character of the emission . it appears that a relatively high fraction of the radio emission is emitted far away from the binary orbit , and thus it is not orbitally modulated by the wind . this effect needs to be taken into account in modelling of the modulation . in section [ cygx1 ] , we have applied the formalism of section [ wind ] to the available radio data from monitoring of cyg x-1 , taking into account the extended character of the emission . in the hard spectral state , the radio light curves show significant modulation at the orbital period , which is due free - free absorption in the wind . we have fitted the folded and averaged light curves at 15 ghz , 8.3 ghz and 2.25 ghz , and obtained the location of the bulk of the emission regions along the jet . in the units of the separation , our best models gave @xmath3391.2 , 1.82.8 , 6.28.8 , respectively . the height at 15 ghz corresponds to @xmath340 , and that at 2.25 ghz is about 10 times higher . these locations , corresponding to the heights at which the jet becomes optically thin to free - free absorption , appear to follow a law relatively close to @xmath341 , expected theoretically ( bk79 ) . on the other hand , @xcite in his estimates of the power of the jet in cyg x-1 based on the model of bk79 used the vlba images of s01 , which imply that 50 per cent of the 8.4 ghz emission comes from distances @xmath342 cm , which is @xmath343 . if the entire jet would follow the emission profile of bk79 , only a tiny fraction of the emission would take place at @xmath245 ( see fig . 1 of @xcite ) , and the resulting orbital modulation would be tiny and probably unobservable , whereas it is at the level @xmath20910 per cent . given that the distance of the emission should scale as @xmath344 ( bk79 ) , it would have been even more difficult to explain the @xmath20930 per cent modulation of the 15 ghz emission . a likely solution to this problem is that the observed resolved emission comes from a secondary dissipation event in the jet whereas the emission of the inner jet , at @xmath245 , is comparable to the resolved one , and it may follow the model of bk79 . this would also solve the problem of that jet power calculated by @xcite being much lower than that inferred from the observed large - scale optical nebula , presumably powered by the jet @xcite . furthermore , this would solve the problem of the jet base inferred from the vlba measurements being an order of magnitude higher than that theoretically expected @xcite . recently , @xcite have calculated the location the jet base in cyg x-1 ( defined by the lowest distance at which significant emission takes place ) at @xmath345 . using the measurement of the turnover frequency of @xmath170 ev of @xcite , and assuming @xmath341 ( bk79 ) , gives a location of the 15 ghz emission in agreement with our results . our best data , at 15 ghz , allow us to study the orbital modulation as a function of the radio flux . we have found a strong dependence of the modulation depth , changing from @xmath346 to @xmath271 when the flux increases by a factor of about 2 . this is naturally interpreted as the height corresponding to the bulk of the emission increasing with the radio flux as a consequence of the corresponding increase of the jet power . in our case , we find @xmath63 approximately proportional to the power of about @xmath347 of the intrinsic radio flux ( i.e. , that before free - free absorption ) , which dependence is somewhat stronger than the relation in the bk79 model . based on the above results , we have estimated the effect of free - free absorption on the form of the hard - state radio / x - ray correlation in cyg x-1 , which correlation was the subject of paper i. we find the absorption has a substantial effect , but , given the uncertainty about the wind density in the polar regions of cyg x-1 , we can not accurately quantify this effect . this effect changes the correlation index , @xmath348 ( defined as @xmath349 ) , from about 1.7 , found in paper i , to about 0.71.3 . thus , cyg x-1 may have a similar correlation to that of the lmxb h1743322 , which has @xmath350 @xcite , or a number of other lmxbs , e.g. , gx 3394 @xcite and v404 cyg @xcite , where the correlation index is @xmath3510.8 . we also discuss predictions for the orbital modulation and attenuation by free - free absorption of radio emission at frequencies higher than 15 ghz . given the relatively low density of the polar wind in cyg x-1 , these effects are likely to be much weaker than estimated before ( in sz07 ) , which may explain the apparent lack of orbital modulation at @xmath352 ghz , and the 2220 ghz radio spectrum of cyg x-1 being represented by a single power law @xcite . still , it would be highly desirable to actually measure the modulation depth at high frequency , which would give us significant constraints on the structure of both the wind and the jet in cyg x-1 . in particular , this would test the possible location of the high - frequency radio emission within the focused wind component . finally , we mention that another high - mass x - ray binary with strong wind , cyg x-3 ( which is likely to contain a black - hole ) does not show any orbital modulation of its very strong radio emission . as discussed by sz07 , this may be due to the binary orbit of that system being @xmath20910 times smaller than that in cyg x-1 . if the jet of cyg x-3 is similar in size to that of cyg x-1 , this would imply values of @xmath66 @xmath20910 times higher , which is likely to reduce the depth of the radio modulation to unobservable values .

we apply the developed formalism to radio monitoring data for cyg x-1 , which allows us to obtain strong constraints on the structure of its inner jet . with the data at 15 ghz , and taking into account an anisotropy of the stellar wind in cyg x-1 , we estimate the location of the peak of that emission along the jet at about one orbital separation , i.e. , cm . this is explained by the height of the radio emission along the jet decreasing with the decreasing radio flux , as predicted by jet models . we also derive predictions for the orbital modulation and flux attenuation at frequencies beyond the 2.2515 ghz range .

we study free - free absorption of radio emission by winds of massive stars . we derive formulae for the optical depth through the wind measured from a point of emission along a jet , taking into account compton and photoionization heating and compton , recombination , line and advection cooling . we apply the developed formalism to radio monitoring data for cyg x-1 , which allows us to obtain strong constraints on the structure of its inner jet . with the data at 15 ghz , and taking into account an anisotropy of the stellar wind in cyg x-1 , we estimate the location of the peak of that emission along the jet at about one orbital separation , i.e. , cm . given a previous determination of the turnover frequency in cyg x-1 , this implies the location of the base of the jet at gravitational radii . we also obtain corresponding results at 8.3 ghz and 2.25 ghz , which roughly follow the standard conical partially self - absorbed jet model . furthermore , we find that the level of the orbital modulation depends on the radio flux , with the modulation being substantially stronger when the radio flux is lower . this is explained by the height of the radio emission along the jet decreasing with the decreasing radio flux , as predicted by jet models . based on the finding of the flux - dependent orbital modulation , we are able to estimate a range of the possible changes of the form of the radio / x - ray correlation in cyg x-1 due to free - free absorption . we also derive predictions for the orbital modulation and flux attenuation at frequencies beyond the 2.2515 ghz range . [ firstpage ] accretion , accretion discs radio continuum : stars stars : individual : cyg x-1 stars : individual : hde 226868 x - rays : binaries x - rays : stars .

nucl-th0101035

i

the study of a new form of strongly interacting matter , the so - called quark - gluon plasma , is at the core of current and future experimental programs at relativistic heavy ion collider ( rhic ) at brookhaven national laboratory ( bnl ) @xcite and large hadron collider ( lhc ) at cern @xcite . although colliders give well - known advantages compared to the fixed target experiments , the kinematics of ultrarelativistic heavy - ion collisions at colliders creates certain complications in the beam monitoring as well as in the identification of collision events . due to the geometrical factor @xmath3 , where @xmath4 is the impact parameter , the number of central nuclear collisions ( @xmath5 ) is relatively very small in the whole set of the collisions with nuclear overlap , @xmath6 ( @xmath7 and @xmath8 are the nuclear radii ) . moreover , in peripheral collisions without direct overlap of nuclear densities , @xmath9 , one or both nuclei may be disintegrated by the long - range electromagnetic forces . this process of electromagnetic dissociation ( ed ) is a well - known phenomenon @xcite . the properties of central and peripheral collisions are very different and then should be studied separately . the ed events are less violent than the collisions with the participation of strong interactions . namely , the average particle multiplicities are essentially lower @xcite and the main part of nucleons and mesons is produced in projectile and target fragmentation regions , very far from the mid - rapidity region . calculations show @xcite that the ed cross section in collisions of heavy nuclei at rhic and lhc by far exceeds the dissociation cross section due to the direct nuclear overlap . in @xmath10 and @xmath11 collisions at such energies many neutrons can be produced in the ed process @xcite . among other interesting phenomena one may expect a complete disintegration of nuclei induced by the electromagnetic fields of collision partners @xcite . this phenomenon is very well known in nuclear reactions under the name of `` multifragmentation '' @xcite . several operational problems of heavy - ion colliders are connected with the high rate of the ed process . on the one hand , the ed process reduces the lifetimes of heavy ion beams in colliders as compared with the proton - proton accelerator mode @xcite . on the other hand , the process of simultaneous neutron emission from the collision partners , where the ed process plays a dominant role , can be useful for the luminosity monitoring @xcite . the luminosity monitoring method based on mutual dissociation has several advantages @xcite . in particular , the beam - residual - gas interaction events can be strongly suppressed in favour of the beam - beam events by the condition that a pair of neutrons should be detected in coincidence by each arm of the calorimeter . the cross section of mutual neutron emission can be calculated in the framework of conventional theoretical models designed for describing the heavy ion disintegration in peripheral collisions . corresponding nuclear data , especially photoneutron emission cross sections , may be used as numerical input for such calculations . therefore , the neutron counting rates in zero degree ( very forward ) calorimeters may provide an accurate measure for the heavy - ion collider luminosity . in the present paper the neutron emission in peripheral collisions of ultrarelativistic heavy ions is considered with the aim of providing the theoretical basis for the luminosity monitoring method proposed in refs . the uncertainties in results originating from uncertainties in input nuclear data and in the theoretical model itself are carefully examined . a brief review of corresponding photonuclear data is given with special attention to the publications describing data evaluation and re - measurement . model predictions for the @xmath12 and @xmath13 fragmentation cross sections are compared with recent experimental data obtained in fixed target experiments at cern sps with the highest energies available thus far . this serves as an important test before extrapolating our methods to the rhic and lhc energies .

earlier this process was proposed for beam luminosity monitoring via simultaneous registration of forward and backward neutrons in zero degree calorimeters at relativistic heavy ion collider . good description of cern sps experimental data on au and pb dissociation gives confidence in predictive power of the model for auau and pbpb collisions at rhic and lhc . e - mail : pshenichnov@nbi.dk + e - mail : ventura@bologna.enea.it + enea guest researcher + pacs : 25.75.-q , 25.20.-x , 29.27.-a + key words : ultrarelativistic heavy ions , photonuclear reactions , beams in particle accelerators +

we study mutual dissociation of heavy nuclei in peripheral collisions at ultrarelativistic energies . earlier this process was proposed for beam luminosity monitoring via simultaneous registration of forward and backward neutrons in zero degree calorimeters at relativistic heavy ion collider . electromagnetic dissociation of heavy ions is considered in the framework of the weizscker - williams method and simulated by the reldis code . photoneutron cross sections measured in different experiments and calculated by the gnash code are used as input for the calculations of dissociation cross sections . the difference in results obtained with different inputs provides a realistic estimation for the systematic uncertainty of the luminosity monitoring method . contribution to simultaneous neutron emission due to grazing nuclear interactions is calculated within the abrasion model . good description of cern sps experimental data on au and pb dissociation gives confidence in predictive power of the model for auau and pbpb collisions at rhic and lhc . e - mail : pshenichnov@nbi.dk + e - mail : ventura@bologna.enea.it + enea guest researcher + pacs : 25.75.-q , 25.20.-x , 29.27.-a + key words : ultrarelativistic heavy ions , photonuclear reactions , beams in particle accelerators +

1502.03082

i

condensed matter systems are an endless resource of emergent physical phenomena and associated quasiparticles . majorana fermions , which are particles that are their own antiparticles and which have been first proposed as particles in the context of high energy physics , emerge beautifully as zero energy excitations in condensed matter setups @xcite . specifically , they are predicted to occur as zero energy excitations in solid - state systems , such as genuine @xmath0-wave superconductors @xcite , or engineered from topological insulators @xcite , semiconductor wires in a magnetic field @xcite , or in chains of magnetic atoms @xcite , all in the proximity of @xmath1-wave superconductors . these exotic objects are robust against local perturbations and , moreover , they obey non - abelian statistics @xcite under braiding operations , thus recommending them as qubits for the implementation of topological quantum computation . electronic transport is the foremost experimental tool for investigating the majorana fermions physics but alternative , _ non - invasive _ , methods that preserve the quantum states would be highly desired to address these objects . cavity quantum electrodynamics ( cavity qed ) has been established as an extremely versatile tool to address equilibrium and out - of - equilibrium electronic and spin systems non - invasively @xcite . majorana fermions , too , have been recently under theoretical scrutiny in the context of cavity qed physics @xcite . however , most of these studies dealt with effective low energy models that involved majorana fermions only , leaving the bulk physics , which is at the heart of the majorana physics , largely unexplored . and @xmath2 , respectively , and measuring the field at the end with @xmath3 and @xmath4 . the difference between the two gives a direct access to the electronic correlation function in the wire ( see text ) . the presence of majorana end modes in the finite wire ( black curves ) is also signaled in the cavity response . ] the basic idea behind cavity qed with electronic system is that it allows one to extract various properties of the latter , such as its spectrum and its electronic distribution function , from photonic transport measurements , as opposed to electronic transport . such photonic transport is quantified by the complex transmission coefficient @xmath5 that relates the output and input photonic fields as depicted in fig . [ fig : scheme ] . in the weakly coupled limit , one finds @xcite , appendix [ inputoutput ] : @xmath6 where @xmath7 and @xmath8 are the frequency and the escape rate of the cavity , respectively , while @xmath9 is an electronic correlation function that depends on the actual coupling between the two systems , and which contains information about the spectrum of the electronic system . the phase and amplitude response of the cavity close to resonance @xmath10 are related to the susceptibility @xmath9 as follows : @xmath11 and @xmath12 , where @xmath13 , @xmath14 , and @xmath15 $ ] ( @xmath16 $ ] ) is the real ( imaginary ) part of the susceptibility . in this paper , we evaluate the function @xmath9 first for the simple case of a one - dimensional ( 1d ) @xmath0-wave superconductor described by the kitaev chain and then for more realistic model of a 1d topological semiconducting wire in proximity of a superconductor . we assume in both cases that these 1d systems are coupled to a microwave cavity , as showed schematically in fig . [ fig : scheme ] . we address various physical situations for this coupling and show that such a method allows us to ascertain the topological phase transition point , the occurrence of majorana fermions , and the parity of the ground state , all in a _ global _ and _ non - invasive _ fashion . the paper is structured as follows . in sec . [ sec2 ] , we describe our model hamiltonians for the two systems under consideration and discuss the coupling between the microwave photons and the electrons in the 1d topological systems . in sec . [ sec3 ] , we show how the optical transmission through the cavity is able to probe the topological phase transition . in [ sec4 ] , we demonstrate that the cavity allows to detect the occurrence of majorana fermions and the parity of the majorana fermionic state in a non - invasive fashion . finally , in sec . [ sec5 ] we provide a brief summary of our results . technical details of the calculations are given in the appendices .

, one can reveal the electronic susceptibility of the-wave superconductor . we analyze two superconducting systems : the prototypical kitaev chain , and a topological semiconducting wire . for both systems , we show that the photonic measurements , via the electronic susceptibility , allows us to determine the topological phase transition point , the emergence of the majorana fermions , and the parity of their ground state .

we study one - dimensional-wave superconductors capacitively coupled to a microwave stripline cavity . by probing the light exiting from the cavity , one can reveal the electronic susceptibility of the-wave superconductor . we analyze two superconducting systems : the prototypical kitaev chain , and a topological semiconducting wire . for both systems , we show that the photonic measurements , via the electronic susceptibility , allows us to determine the topological phase transition point , the emergence of the majorana fermions , and the parity of their ground state . we show that all these effects , which are absent in effective theories that take into account the coupling of light to majorana fermions only , are due to the interplay between the majorana fermions and the bulk states of the superconductors .

cond-mat9806367

i

models of strongly correlated electrons in two dimensions have been much studied in recent years as part of a search for a minimal model of the high - t@xmath6 superconducting cuprates , and other fascinating new antiferromagnetic systems@xcite . the @xmath0 model , defined by the hamiltonian @xmath7 has become a generic model for mobile electrons / holes in doped antiferromagnets . in this expression the @xmath8 , @xmath9 are the usual electron creation and destruction operators , @xmath10 are the electron spin operators and the sum is over nearest neighbors pairs . @xmath11 is a projection operator which ensures that doubly occupied states are excluded . the @xmath0 model originally was derived@xcite as the strong correlation limit of the hubbard model , with @xmath12 , but it is now generally treated as an effective hamiltonian in its own right , with @xmath13 and @xmath14 independent parameters . for the cuprates it is estimated@xcite that @xmath15 , which is well outside the region of validity of the hubbard mapping . an independent `` derivation '' of the @xmath0 model as an effective hamiltonian for the cuprates has been presented by zhang and rice@xcite . at exactly half - filling ( one electron per site ) the kinetic term vanishes because of the single - occupancy restriction and the model reduces to an antiferromagnetic insulator . it is known from a variety of numerical and analytic calculations@xcite that this model , on the square lattice , has nonzero long range antiferromagnetic ( nel ) order , reduced by strong quantum fluctuations . removal of a small number of electrons ( by doping ) will allow mobility of holes and will reduce the antiferromagnetic order . the physics of a small number of holes in a dynamic antiferromagnetic background remains a challenging problem . previous studies of the @xmath0 model at @xmath1 have used a variety of approaches . exact diagonalization methods have been used extensively on clusters up to 32 sites@xcite , but suffer from substantial finite - size corrections and an inability to treat extended excitations . green s function monte carlo calculations have been performed for larger lattices , up to @xmath16@xcite , and show , for example , a significant decrease of the two - hole binding energy with increasing lattice size . a variety of variational approaches and analytic many body methods have also been employed@xcite . the picture that emerges from this body of work is roughly as follows . for one hole the ground state energy is given by @xmath17 where the coefficients are approximate numerical estimates . the dispersion curve for 1-hole states is qualitatively similar from different methods , with minima at @xmath18 and equivalent points . the bandwidth from the largest diagonalizations scales as @xmath19 where the coefficients are again estimates and are not known with great precision . the spectral function for 1-hole states has been calculated@xcite and shows a clear quasiparticle peak , together with a continuum at higher energies . for two holes the binding energy , spectral function and pair susceptibility have been computed . the results support the existence of a bound state with @xmath20 and d - wave symmetry for @xmath21 , with @xmath22 although not all methods agree and this is still controversial . the dispersion curve for two - hole bound states is also of interest @xmath23 to our knowledge the only calculation of this is due to eder@xcite . the aim of the present work is to study the physics of one - hole and two - hole states in the half - filled @xmath0 model at zero temperature via linked - cluster series expansions . this approach has been developed extensively in recent years by our group@xcite and others@xcite . most of the applications to date have been to spin systems , although we have included fermions in lattice gauge calculations . shi and singh@xcite have used this approach to study the hubbard model at half filling , via an expansion about an additional ising term included in the hamiltonian . for completeness we also mention the use of high - temperature expansions to study the @xmath0 model@xcite . the present work of course addresses different questions which can not be probed by high - temperature series . the plan of the paper is as follows . in sec . ii , the series expansion method is briefly reviewed , and the results for one - hole properties of the @xmath0 model are presented . in sec . iii , we study the dispersion relation and the binding energy for two - hole bound states . in sec . iv , we study the one - hole and two - hole properties of the @xmath5 model . v is devoted to a summary and discussion .

the dispersion curve for one hole excitations is calculated and found to be qualitatively similar to that obtained by other methods , but the bandwidth for small is some 20% larger than given previously . we also obtain the binding energy and dispersion relation for two hole bound states . we also make a similar study for the model .

we study one and two hole properties of the model at half - filling on the square lattice using series expansion methods at . the dispersion curve for one hole excitations is calculated and found to be qualitatively similar to that obtained by other methods , but the bandwidth for small is some 20% larger than given previously . we also obtain the binding energy and dispersion relation for two hole bound states . the lowest bound state as increases is found to be first-wave , and then-wave , in accordance with predictions based upon the kohn - luttinger effect . we also make a similar study for the model .

0706.2515

i

the study of the intersections of stable and unstable manifolds of maps and flows has a strong influence on dynamical systems . in particular , the existence of a transverse intersection is associated with the onset of chaos , and gave rise to the famous horseshoe construction of smale . the poincar - melnikov method @xcite is a widely used technique for detecting such intersections . given a system with a pair of saddles and a degenerate heteroclinic or saddle connection between them , the classical melnikov function computes the rate at which the distance between the manifolds changes with a perturbation . there have been many formulations of the melnikov method for two - dimensional maps or flows @xcite and for higher - dimensional symplectic mappings @xcite . recently , the geometric content of melnikov s method was exploited in order to detect heteroclinic intersections of lagrangian manifolds for the case of perturbed hamiltonian flows @xcite . here it was shown that the heteroclinic orbits are in correspondence with the zeros of a geometric object , the so - called melnikov one - form . for maps , the melnikov function is an infinite sum whose domain is a saddle connection between two hyperbolic invariant sets . as usual , a simple zero of this function corresponds to a transverse intersection of stable and unstable manifolds of a perturbation of the original map . melnikov s method can also be used to compute transport fluxes . in particular , a _ resonance zone _ for a two - dimensional mapping is a region bounded by alternating segments of stable and unstable manifolds that are joined at primary intersection points @xcite . because the intersection points are primary , a resonance zone is bounded by a jordan curve and has exit and entry sets @xcite . the images of these sets completely define the transport properties of the resonance zone . moreover , the integral of the melnikov function between two neighbouring primary intersection points is the first order approximation to the geometric flux escaping from the resonance zone @xcite . the method has also been applied to the case of periodically time - dependent , volume - preserving flows @xcite and more generally to volume - preserving maps with fixed points @xcite and invariant circles @xcite . volume - preserving maps provide perhaps the simplest , natural generalization of the class of area - preserving maps to higher dimensions . moreover , they naturally arise in applications as the time - one poincar map of incompressible flows even when the vector field of the flow is nonautonomous . thus the study of the dynamics of volume - preserving maps has application both to fluids and magnetic fields . our goal in this paper is to develop , based on the theory of deformations , a general , geometrical description of the melnikov displacement and to compare our theory to classical results . deformation theory was first introduced in the theory of singularities @xcite , but was soon used in the contexts of volume and symplectic geometry . its application to dynamical systems in @xcite provide results that are close to our goals . let @xmath0 be a smooth family of diffeomorphisms such that the unperturbed map @xmath1 has a saddle connection @xmath2 between a pair of compact @xmath3-normally hyperbolic invariant manifolds . let @xmath4 be the algebraic normal bundle of the saddle connection . we show that there exists a canonical @xmath5 section @xmath6 , called the _ melnikov displacement _ , that measures the splitting of the saddle connection in first - order . we will prove that the melnikov displacement is given by the absolutely convergent series @xmath7 where @xmath8 is the vector field defined by @xmath9 . these sums do not converge in the tangent space @xmath10 , but only in the algebraic normal bundle @xmath11 . the use of the algebraic normal bundle in the study of normally hyperbolic manifolds goes back to @xcite . the fact that ( [ mainformula ] ) always converges also addresses the question of how to deal with melnikov s method when the original pair of compact @xmath3-normally hyperbolic invariant manifolds ( that are connected with the saddle connection ) are not fixed with the perturbation . in addition , we will also show that the melnikov displacement has a number of geometric properties . the main result in this direction is that any change of coordinates acts on the displacement by its pullback . this result will be used to obtain the natural action of any symmetries , reversing symmetries or integrals of the dynamical system on the displacement . similarly , if the map preserves a symplectic or volume form , this gives additional structure to the displacement . for example , if @xmath0 is a family of exact symplectic maps and the normally hyperbolic invariant manifolds are fixed points , then we will show that there exists a function @xmath12 , the _ melnikov potential _ , such that @xmath13 , where @xmath14 is the symplectic two - form . this relation is reminiscent of the definition of globally hamiltonian vector fields . when the normally hyperbolic invariant manifolds are not fixed points ( or isolated periodic points ) , its stable and unstable manifolds are coisotropic , but not isotropic , and so the relation @xmath13 makes no sense . we complete this introduction with a note on the organization of this paper . the general theory is developed in [ sec : melnikovdisplacement ] . in [ sec : classical ] , we show how our theory reproduces the classical methods of poincar and melnikov . the study of exact symplectic maps and volume - preserving maps is contained in [ sec : symp ] and [ sec : volume ] , respectively .

we study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds . this function is defined to be a section of the normal bundle of the saddle connection . we show how our definition reproduces the classical methods of poincar and melnikov and specializes to methods previously used for exact symplectic and volume - preserving maps . we use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the melnikov displacement .

we study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds . we develop a first - order deformation calculus for invariant manifolds and show that a generalized melnikov function or _ melnikov displacement _ can be written in a canonical way . this function is defined to be a section of the normal bundle of the saddle connection . we show how our definition reproduces the classical methods of poincar and melnikov and specializes to methods previously used for exact symplectic and volume - preserving maps . we use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the melnikov displacement .

quant-ph0611234

i

the theory of games provides a general structure within which both cooperation and competition among independent entities may be modeled , and provides powerful tools for analyzing these models . applications of this theory have fundamental importance in many areas of science . this paper considers games in which the players may exchange and process quantum information . we focus on competitive games , and within this context the types of games we consider are very general . for instance , they allow multiple rounds of interaction among the players involved , and place no restrictions on players strategies beyond those imposed by the theory of quantum information . while classical games can be viewed as a special case of quantum games , it is important to stress that there are fundamental differences between general quantum games and classical games . for example , the two most standard representations of classical games , namely the _ normal form _ and _ extensive form _ representations , are not directly applicable to general quantum games . this is due to the nature of quantum information , which admits a continuum of pure ( meaning extremal ) strategies , imposes bounds on players knowledge due to the uncertainty principle , and precludes the representation of general computational processes as trees . in light of such issues , it is necessary to give special consideration to the incorporation of quantum information into the theory of games . a general theory of quantum games has the potential to be useful in many situations that arise in quantum cryptography , computational complexity , communication complexity , and distributed computation . this potential is the primary motivation for the work presented in this paper , which we view as a first step in the development of a general theory of quantum games . the following facts are among those proved in this paper : * every multiple round quantum strategy can be faithfully represented by a single positive semidefinite operator acting only on the tensor product of the input and output spaces of the given player . this representation is a generalization of the choi - jamiokowski representation of super - operators . the set of all operators that arise in this way is precisely characterized by the set of positive semidefinite operators that satisfy a simple collection of linear constraints . * if a multiple round quantum strategy calls for one or more measurements then its representation consists of one operator for each of the possible measurement outcomes . the probability of any given pair of measurement outcomes for two interacting strategies is given by the inner product of their associated operators . * the maximum probability with which a given strategy can be forced to output a particular result is the _ minimum _ value of @xmath1 for which the positive semidefinite operator corresponding to the given measurement result is bounded above ( with respect to the lwner partial order ) by the representation of a valid strategy multiplied by @xmath1 . we give the following applications of these facts : * a new and conceptually simple proof of kitaev s bound for strong coin - flipping , which states that every quantum strong coin - flipping protocol allows a bias of at least @xmath2 . * the exact characterization @xmath0 of the class of problems having quantum refereed games ( i.e. , quantum interactive proof systems with two competing provers ) . this establishes that quantum and classical refereed games are equivalent in terms of expressive power : @xmath3 . it is appropriate for us to comment on the relationship between the present paper and a fairly large collection of papers written on a topic that has been called _ quantum game theory_. meyer s _ pq penny flip _ game @xcite is a well - known example of a game in the category these papers consider . the work of eisert , _ et al . _ @xcite is also commonly cited in this area . some controversy exists over the interpretations drawn in some quantum these papers see , for instance , refs . @xcite . a key difference between our work and previous work on quantum game theory is that our focus is on multiple - round interactions . understanding the actions available to players that have quantum memory is therefore critical to our work , and to our knowledge has not been previously considered in the context of quantum game theory . a second major difference is that , in most of the previous quantum game theory papers we are aware of , the focus is on rather specific examples of classical games and on identifying differences that arise when so - called quantum variants of these games are considered . as a possible consequence , it may arguably be said that none of the results proved in these papers has had sufficient generality to be applicable to any other studies in quantum information . in contrast , our interest is not on specific examples of games , but rather on the development of a general theory that holds for all games . it remains to be seen to what extent our work will be applied , but the applications that we provide suggest that it may have interesting uses in other areas of quantum information and computation . a different context in which games arise in quantum information theory is that of _ nonlocal games _ @xcite , which include _ pseudo - telepathy games _ @xcite as a special case . these are cooperative games of incomplete information that model situations that arise in the study of multiple - prover interactive proof systems , and provide a framework for studying bell inequalities and the notion of nonlocality that arises in quantum physics . while such games can be described within the general setting we consider , we have not yet found an application of the methods of the present paper to this type of game . possibly there is some potential for further development of our work to shed light on some of the difficult questions in this area .

we study properties of _ quantum strategies _ , which are complete specifications of a given party s actions in any multiple - round interaction involving the exchange of quantum information with one or more other parties . this new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces . various facts about such representations are established , and two applications are discussed : the first is a new and conceptually simple proof of kitaev s lower bound for strong coin - flipping , and the second is a proof of the exact characterization of the class of problems having quantum refereed games .

we study properties of _ quantum strategies _ , which are complete specifications of a given party s actions in any multiple - round interaction involving the exchange of quantum information with one or more other parties . in particular , we focus on a representation of quantum strategies that generalizes the choi - jamiokowski representation of quantum operations . this new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces . various facts about such representations are established , and two applications are discussed : the first is a new and conceptually simple proof of kitaev s lower bound for strong coin - flipping , and the second is a proof of the exact characterization of the class of problems having quantum refereed games .

1309.3065

i

the anomalous magnetic moment of the muon , @xmath4 , ( muon @xmath0 ) has been measured very precisely @xcite . it is compared with the standard model ( sm ) prediction , and the latest result is @xmath5 where ref . @xcite is referred to for contributions of the hadronic vacuum polarization , and the hadronic light - by - light contribution is from ref . similarly , ref . @xcite provides @xmath6 . therefore , there is discrepancy at more than @xmath7 confidence levels . it is noticed that the difference is as large as sm electroweak contributions , @xmath8 @xcite . if this is a signature of physics beyond the sm , and if the new physics exists in the tev scale , new physics contributions to the muon @xmath0 are necessarily enhanced by some mechanisms , because they are naively estimated as @xmath9 , which is required to be comparable to @xmath10 . the supersymmetry ( susy ) is a good candidate for such new physics models . the model can provide sizable contributions to the muon @xmath0 @xcite , which are enhanced by @xmath11 . the muon @xmath0 anomaly is solved if the superparticles ( muonic sleptons , neutralinos and/or charginos ) have a mass around @xmath12 for @xmath13 . they are light enough to be produced at the lhc experiments . recently , lhc phenomenology of the superparticles that are relevant for the muon @xmath0 has been studied in ref . it has been shown that they can be discovered in the near future in most of the parameter regions , especially in regions where the susy contributions to the muon @xmath0 are dominated by chargino sneutrino diagrams . however , the searches rely on the assumption that the wino is light . this assumption is not necessary to explain the muon @xmath0 discrepancy , when the susy contribution is mainly from bino smuon diagrams . if the wino is heavy , collider searches differ significantly from those in ref . @xcite . in this paper , we study searches for the models in which only the bino and the left- and right - handed smuons are light , while the other superparticles including the wino are decoupled from the lhc sensitivity . smuon contribution is enhanced when the left - right mixing of the smuon is large . if the left - right mixing were allowed to be arbitrarily large , the superparticles could be extremely heavy while keeping the contribution to the muon @xmath0 , thereby escaping any collider searches . however , too large left - right mixing spoils stability of the electroweak vacuum . hence , the superparticle masses are bounded from above . we will show that , when staus and smuons have comparable masses to each others , upper bounds on the slepton masses are within the reach of lhc / ilc . if the staus are much heavier than smuons , the mass bounds are relaxed , while lepton flavor violations ( lfv ) and cp violations ( cpv ) generically become too large . therefore , we will show that almost all the parameter regions can be tested in future complementarily by lhc / ilc and lfv / cpv , if the muon @xmath0 anomaly is solved by the bino and the left- and right - handed smuons . the rest of the paper is organized as follows . the mass spectrum is provided in sec . [ sec : setup ] . the susy contributions to the muon @xmath0 and the vacuum stability conditions are explained in sec . [ sec : pheno ] . in sec . [ sec : search ] , experimental searches are studied . [ sec : conclusion ] is devoted to the conclusion .

we study susy models in which bino contributions solve the muon anomaly . , there are upper bounds on masses of sleptons and bino . it is within the reach of lhc and ilc . if the stau is heavier than the smuon , the bound can be as large as .

we study susy models in which bino contributions solve the muon anomaly . the contributions are enhanced by large left - right mixing of the smuons . however , it is constrained by the vacuum stability condition of the slepton higgs potential . therefore , there are upper bounds on masses of sleptons and bino . when the slepton soft masses are universal , the upper bound on the smuon mass becomes in order to solve the anomaly at the level . it is within the reach of lhc and ilc . if the stau is heavier than the smuon , the bound can be as large as . such non - universal slepton mass spectrum generically predicts too large lfv / cpv . we show that the models are expected to be probed by lhc / ilc and lfv / cpv complementarily in future . ut1334 2.7 cm * probing bino contribution to muon * .85 in * motoi endo * , * koichi hamaguchi * , + * teppei kitahara * , * and * * takahiro yoshinaga * 0.25 in _ department of physics , university of tokyo , tokyo 113 - 0033 , japan _ .75 in

1207.2725

i

the aim of this paper is to study the asymptotic behaviour of the solutions to a sequence of gradient flows ( in a suitable metric setting ) , when the governing energies and metric - dissipation potentials give raise in the limit to a rate - independent evolution or , more generally , to an evolution driven by a dissipation potential with linear growth . in order to explain the problem , let us start from a simple example in a finite dimensional manifold @xmath3 ( see e.g. the motivating discussion in @xcite ) . we fix a time interval @xmath4 $ ] , we denote by @xmath5 the product space @xmath6\times { \mathscr{x}}$ ] , and we consider a sequence of smooth energies @xmath7 indexed by @xmath8 . we are also given a sequence of smooth dissipation potentials @xmath9 of the form @xmath10 smoothly depending on @xmath11 and @xmath12 typical examples are @xmath13 for given initial data @xmath14 we can consider the solutions @xmath15\to { \mathscr{x}}$ ] of the cauchy problem for the doubly nonlinear differential equations @xmath16 in the parameter @xmath8 affects the limit behaviour of the initial data @xmath17 , of the energies @xmath18 in @xmath5 , of the norms @xmath19 on @xmath20 , and of the dissipation potentials @xmath21 on @xmath22 . assuming that ( in a suitable sense that we will describe later on ) @xmath23 , @xmath24 , @xmath25 , @xmath26 as @xmath27 , it is then natural to investigate if a limit curve @xmath28 ( possibly up to subsequence ) of the solutions @xmath29 still satisfies the corresponding limit equation of . we want to address here the singular situation when the limit dissipation potential @xmath30 loses the superlinear growth ; let us focus here on the @xmath2-homogeneous case when @xmath31 corresponding e.g.to @xmath32 or @xmath33 in ( in that cases @xmath34 ) . the limit problem is formally the differential inclusion @xmath35,\quad u(0)=\bar u,\ ] ] where the presence of the subdifferential @xmath36 is motivated by the lack of differentiability of the norm @xmath37 at @xmath38 . since @xmath39 is @xmath2-positively homogeneous , describes a rate - independent evolution and its solutions exhibit a different behavior with respect to the viscous flows . in particular , jumps can occur even for smooth energies @xmath40 and various kinds of solutions have been proposed in the literature ( we refer to the surveys @xcite , the overall presentation in @xcite and the references therein ) . here we focus on the notion of bv solution , proposed in @xcite : for the sake of simplicity , in this introductory section we consider the simplest case of a piecewise smooth curve @xmath28 with a finite number of jump points @xmath41 $ ] ; @xmath42 will denote the left and the right limit of @xmath28 at each @xmath43 ( see also @xcite for an explicit characterization in a one - dimensional setting ) in this case a bv solution @xmath28 can be characterized by two conditions : 1 . in each interval @xmath44 the velocity vector field @xmath45 satisfies the differential inclusion , which yields in particular the local stability condition @xmath46\setminus { { \mathrm j}}_u\ ] ] and the energy dissipation @xmath47 where @xmath48 and @xmath49 denotes the dual norm of the ( opposite ) differential of the energy , @xmath50 it turns out that in the smooth regime and are equivalent to . 2 . at each jump point @xmath43 it is possible to find an optimal transition path @xmath51\to { \mathscr{x}}$ ] , @xmath52 , such that @xmath53 , @xmath54 , @xmath55 in @xmath56 $ ] , and @xmath57 notice that the choice of the interval @xmath58 $ ] is not essential , since the integrals in are invariant with respect to monotone time rescaling . the minimum problem in characterizes the minimal transition cost at each jump point @xmath43 to connect in @xmath59 with @xmath60 passing through @xmath61 . such a cost is influenced both by the norms @xmath62 and by the slope @xmath49 of the energy : we will denote it by @xmath63 . it is a remarkable fact , highlighted in @xcite , that the refined structure given in ( bv1,bv2 ) can be captured by simply imposing the local stability condition and a single energy - dissipation inequality , namely @xmath64 it turns out that is in fact an identity , since the opposite inequality is always satisfied along _ any _ piecewise smooth curve @xmath28 . if holds , then @xmath28 is forced to satisfy along its smooth evolution , and the optimal transition paths obtained by solving the minimum problem in provide the right energy balance between @xmath42 . the link of with the gradient flow becomes more transparent if , following @xcite , one notices that also can be formulated as a energy - dissipation inequality . in fact , setting as before @xmath65 it is not difficult to check ( see the informal discussion in the next section ) that a @xmath66 curve @xmath67 with @xmath68 satisfies if and only if the @xmath21 energy - dissipation inequality holds @xmath69 where @xmath70 is the legendre transform of @xmath21 . [ [ a - more - general - formulation - in - metric - spaces . ] ] a more general formulation in metric spaces . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + here we want to show that the metric - variational approach to gradient flows and rate - independent problems provides a natural framework to study this singular perturbation problem and suggests a robust and general strategy to pass to the limit in a much more general setting where * @xmath3 is a topological space endowed with a family of complete extended distances @xmath71 , * the terms like @xmath72 are replaced by the _ metric velocity _ induced by @xmath71 , * the functions @xmath73 can be characterized as an _ irreversible couple of upper gradients _ in terms of the behaviour of the energies @xmath18 along arbitrary absolutely continuous curves with values in @xmath74 , and * @xmath30 is a general metric dissipation function with linear growth . postponing to the next two sections a more precise review of motivations and definitions , we just remark that whenever sufficiently strong a priori estimates are available to guarantee the pointwise convergence of @xmath67 to some limit function @xmath75;({\mathscr{x}},{{\sf d}}))}$ ] , then the heart of the problem consists in deriving ( in a suitably extended form allowing countably many jumps and cantor - like terms in the metric velocity ) , starting from the viscous inequality . assuming convergence in energy of the initial data , i.e.@xmath76 , some lower - upper semicontinuity conditions on @xmath77 and @xmath78 along arbitrary sequences @xmath79 with equibounded energy and converging to @xmath80 in a fixed reference topology @xmath81 of @xmath3 are naturally suggested by the structure of the main inequalities and : @xmath82 the most challenging point is provided by the limit behaviour of the integral term @xmath83 which has been typically studied by a clever re - parametrization technique , introduced by @xcite and then extended in various directions by @xcite . this approach leads to the notion of the so - called _ parametrized solutions _ to the rate - independent evolution and the crucial assumption concerns the validity of the @xmath84-@xmath85 space - time estimate for the slopes @xmath86 in the present paper we propose a different technique , which avoids parametrized solutions and thus allows for more general non - homogenous dissipation potentials like @xmath87 our approach involves weak convergence of measures to deal with concentrations of the time derivative and blow - up around jump points of the limit solution to recover the variational structure of the transition . in this way , an easier rescaling is sufficient to construct the optimal transition paths ( see ) from the converging family @xmath29 and to obtain the bv energy - dissipation inequality . [ [ particular - cases . ] ] particular cases . + + + + + + + + + + + + + + + + + let us remark that various particular cases of the present setting are interesting by themselves and have been considered from many different points of view . a. a first important case for applications is when @xmath3 is a hilbert space , @xmath88 , and the norms @xmath89 are independent of @xmath90 and coincide with the norm @xmath91 of @xmath3 . in this case we are dealing with the convergence of gradient flows and a typical situation arises when @xmath92 . it is well known , since the pioneering contributions of @xcite , that convexity ( or @xmath93-convexity for some @xmath94 independent of @xmath90 ) of the energies makes it possible to reduce to the simpler mosco - convergence @xcite of @xmath18 ( see e.g. @xcite or @xcite for the connection with the graph - convergence of the differential operators ) . the link between @xmath84-convergence of the energies and convergence of the gradient flows in a metric setting has been considered in @xcite . b. another relevant situation is when both the energies and the distances depend on @xmath90 : in the quadratic case a convergence result can be deduced by a joint @xmath84-convergence , see e.g. @xcite . the role of the @xmath84-@xmath85 condition on the slopes as in in general non - convex setting has been clarified in @xcite . a very general stability result has been given in @xcite . an interesting example where the limit of gradient flows gives raise to a singular limit in a new geometry is discussed in @xcite . c. the particular case when the @xmath90-dependence affects only the dissipation potential @xmath30 and gives raise to a rate - independent problem in the limit has been studied in @xcite . the @xmath84-limit of rate - independent evolutions , in the framework of energetic solutions , has been studied in @xcite . [ [ plan - of - the - paper . ] ] plan of the paper . + + + + + + + + + + + + + + + + + + in the next section we give more details on the simple finite - dimensional example we introduced before , in order to motivate the abstract metric approach , whose setting is explained in section [ sec : preliminaries ] . section [ sec : main ] contains our main results , concerning compactness ( theorem [ thm : compactness ] ) and convergence ( theorem [ thm : convergence ] ) of gradient flows in a general setting . a few examples are briefly presented at the end of the paper .

we study the asymptotic behaviour of families of gradient flows in a general metric setting , when the metric - dissipation potentials degenerate in the limit to a dissipation with linear growth . we present a general variational definition of bv solutions to metric evolutions , showing the different characterization of the solution in the absolutely continuous regime , on the singular cantor part , and along the jump transitions . by using tools of metric analysis , bv functions and blow - up by time rescaling , we show that this variational notion is stable with respect to a wide class of perturbations involving energies , distances , and dissipation potentials . as a particular application , we show that bv solutions to rate - independent problems arise naturally as a limit of-gradient flows , , when the exponents converge to .

we study the asymptotic behaviour of families of gradient flows in a general metric setting , when the metric - dissipation potentials degenerate in the limit to a dissipation with linear growth . we present a general variational definition of bv solutions to metric evolutions , showing the different characterization of the solution in the absolutely continuous regime , on the singular cantor part , and along the jump transitions . by using tools of metric analysis , bv functions and blow - up by time rescaling , we show that this variational notion is stable with respect to a wide class of perturbations involving energies , distances , and dissipation potentials . as a particular application , we show that bv solutions to rate - independent problems arise naturally as a limit of-gradient flows , , when the exponents converge to .

cond-mat0404126

i

in the last few years graph theoretic approach has been of great value to characterize complex systems found in social , informational and biological areas . here , a complex system is represented as a graph or network whose vertices and edges stand for its constituents and interactions . a simplest model for such is the random graph model proposed by erds and rnyi ( er ) @xcite . in the er model , @xmath0 number of vertices are present from the beginning and edges are added one by one in the system , connecting pairs of vertices selected randomly . due to the randomness , the distribution of the number of edges incident on each vertex , called the degree distribution , is poissonian . however , many real - world networks such as the world - wide web , the internet , the coauthorship , the protein interaction networks and so on display power - law behaviors in the degree distribution . such networks are called scale - free ( sf ) networks @xcite . thanks to recent extensive studies of sf networks , various properties of sf network structures have been uncovered @xcite . there have been a few attempts to describe scale - free networks in the framework of equilibrium statistical physics , even though the number of vertices grows with time in many real - world networks @xcite . in this approach , various mathematical tools developed in equilibrium statistical physics may be used to understand network structures . to proceed , one needs to define equilibrium network ensembles with appropriate weights , where one graph corresponds to one state of the ensemble . in a canonical ensemble , the number of edges @xmath11 is fixed : given a degree distribution , @xmath12 , the mean degree @xmath13 is obtained . then the number of edges obtained through the relation , @xmath14 , can be fixed . a degree sequence specifies the number of vertices with degree @xmath15 as @xmath16 @xcite . a grandcanonical ensemble can be also defined , where the number of edges is also a fluctuating variable while keeping the sf nature of the degree distributions . the grandcanonical ensemble for sf random graphs is realized in the static model introduced by goh _ et al . _ @xcite or in its generalized version investigated in refs . the name ` static ' originates from the fact that the number of vertices is fixed from the beginning . here each vertex @xmath1 has a prescribed weight @xmath2 summed to 1 and an edge can connect vertices @xmath1 and @xmath3 with rate @xmath4 @xcite . a chemical potential - like parameter @xmath17 that can be regarded as time " in the process of attaching edges controls the mean number of edges so that @xmath18 increases with increasing @xmath17 . as the parameter @xmath17 increases , a giant cluster , or giant component , forms in the system . here the giant cluster means the largest cluster of connected vertices whose size is @xmath19 . often such a giant cluster appears at the percolation transition point . in equilibrium statistical physics , the percolation problem can be studied through a spin model , the @xmath6-state potts model in the @xmath5-limit @xcite . using the relation , in this paper , we study the evolution of sf random graphs from the perspective of equilibrium statistical physics . to be specific , we construct the @xmath6-state potts model , where the interaction strength between each pair of vertices is inhomogeneous on the complete graph . in this formulation , since the interaction strength @xmath17 is tunable , the mean number of edges @xmath20 varies . thus , the grandcanonical ensemble is taken in the network representation . however , since the number of spins ( vertices ) is fixed , the formulation corresponds to a canonical ensemble in the spin - model representation . note that our model is different from the one studied by dorogovtsev _ et al . , _ @xcite where the potts model is defined as a given fixed network so that each edge represents homogeneous interactions . the formulation of the spin model facilitates explicit derivation of various properties of the sf network . thus we derive the formula for the giant cluster size , the mean cluster size , and in particular , the number of loops and clusters . these quantities are explicitly evaluated analytically for the static model with @xmath21 , @xmath22 in the thermodynamic limit as a function of the edge density , and their critical properties are also studied . the degree exponent @xmath23 is related to @xmath24 by @xmath25 . moreover , their finite - size scaling behaviors are obtained using the _ finite _ largest cluster size for finite @xmath0 that in turn is evaluated from the cluster size distribution . from these , we are able to elucidate the process of formation of the giant cluster . while for the case @xmath9 , the giant cluster forms abruptly at the percolation transition point @xmath26 , for the case @xmath27 where most real world networks belong to , however , the formation of the giant cluster is gradual and the mean cluster size for finite @xmath0 show double peaks . in fact , the percolation problem of sf networks has been studied , but in a different way , that is , by removing vertices one by one as well as their attached edges from an existing sf network @xcite . the percolation transition was understood by using the branching process approach , which is supposed to be valid near the percolation transition point , where the network is sparse . in this paper , we provide the criterion for the validity of the branching process approach for a general degree distribution , and show that the branching process and the potts model approaches are equivalent for the static model . finally , note that while the branching process approach can not count the number of loops , the potts model formalism we use here enables us to count it . this paper is organized as follows . we introduce in sec . [ sec : static ] an ensemble of random graphs where each vertex is weighted , and present in sec . [ sec : potts ] the potts model formulation to derive graph theoretical quantities from its free energy . in sec . [ sec : bp ] , the connection between the potts model formulation and the branching process approach is discussed . the general results of sec . [ sec : potts ] are applied to the static model in sec . [ sec : thermo ] to obtain explicitly the giant cluster size , the mean cluster size and the mean number of loops and clusters as a function of @xmath17 . the cluster size distribution and the largest cluster size in finite size systems are obtained in sec . [ sec : distribution ] . the finite - size scaling is presented and compared with numerical simulation results in sec . [ sec : fss ] . finally sec . [ sec : summary ] contains summary and discussion .

we study the bond percolation problem in random graphs of weighted vertices , where each vertex has a prescribed weight and an edge can connect vertices and with rate . we apply this approach to the static model having so that the resulting graph is scale - free with the degree exponent . the number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density , and their associated critical exponents are also obtained . finite - size scaling behaviors are derived using the largest cluster size in the critical regime , which is calculated from the cluster size distribution , and checked against numerical simulation results . we find that the process of forming the giant cluster is qualitatively different between the cases of and . while for the former , the giant cluster forms abruptly at the percolation transition , for the latter , however , the formation of the giant cluster is gradual and the mean cluster size for finite shows double peaks . ,

we study the bond percolation problem in random graphs of weighted vertices , where each vertex has a prescribed weight and an edge can connect vertices and with rate . the problem is solved by the limit of the-state potts model with inhomogeneous interactions for all pairs of spins . we apply this approach to the static model having so that the resulting graph is scale - free with the degree exponent . the number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density , and their associated critical exponents are also obtained . finite - size scaling behaviors are derived using the largest cluster size in the critical regime , which is calculated from the cluster size distribution , and checked against numerical simulation results . we find that the process of forming the giant cluster is qualitatively different between the cases of and . while for the former , the giant cluster forms abruptly at the percolation transition , for the latter , however , the formation of the giant cluster is gradual and the mean cluster size for finite shows double peaks . ,

1301.1092

i

topological insulators are a new class of materials that attract much interest recently.@xcite they are band insulating in the bulk but conducting along the surface due to the gapless surface state . in three - dimensional strong topological insulators , the surface state involves an odd number of massless dirac cones in the surface brillouin zone and is protected by time - reversal invariance.@xcite for the simplest case with a single dirac cone , such as on the surface of bi@xmath0se@xmath1 , sb@xmath0te@xmath1 and bi@xmath0te@xmath1,@xcite the surface state near the dirac cone can be described by the rashba spin - orbit coupling@xcite and hence exhibits helicity.@xcite the metallic and helical surface state has been proposed to have much potential for the application in spintronics.@xcite the spin helicity of surface state in topological insulators has been experimentally measured by spin - angle resolved photoemission spectroscopy.@xcite however , it has not been clearly evidenced by the electrical transport experiment . this might be caused by the difficulty in seperating the bulk and surface conduction as both of them are usually involved simultaneously , and also the influence of the stray field from the ferromagnetic electrode when the spins are injected via the ferromagnetic contact . to overcome these circumvents and confirm the spin - momentum locking in the topological surface state , a scheme of transport experiment by injecting spin polarized electrons into the topological surface state via silicon has been proposed very recently.@xcite in spite of the experimental difficulties , the understanding of charge and spin transport on the surface of topological insulators is necessary . in fact , theoretically , this issue has been preliminarily studied , with electric field being small ( @xmath20.1 kv / cm,@xcite under which the electrons are near equilibrium ) , the fermi level located deep enough in the conduction band and the fully occupied valence band being irrelevant.@xcite moreover , even in the microscopic study based on kinetic equations by culcer _ _ , only the electron - impurity scattering is considered.@xcite the electron - phonon scattering , which can be very important,@xcite and also the electron - electron coulomb scattering are not incorporated . it is revealed that in the presence of driving by the electric field or diffusion by the density gradient , a transverse spin polarization is induced due to the spin - momentum locking,@xcite with the magnitude proportional to the electric field and momentum scattering time.@xcite besides , due to the spin - momentum locking again , the spin polarization relaxes in a time scale of momentum scattering in the absence of an electric field.@xcite the transport on the surface of topological insulators under large electric fields ( @xmath21 kv / cm ) , which can drive the carriers far away from the equilibrium,@xcite has been rarely investigated so far . here we perform this study on the surface of bi@xmath0se@xmath1 by means of the kinetic spin bloch equation ( ksbe ) approach,@xcite with the electric field up to several kv / cm . bi@xmath0se@xmath1 is expected to have a 300 mev direct band gap at the zone center@xcite and is usually @xmath3-type due to the charged se vacancies . however , the electron density can be adjusted by counterdoping with ca@xcite or partially substituting bi with sb to reduce se vacancies.@xcite particularly , employing cd doping in combination with a se - rich growth condition , even a @xmath4-type bi@xmath0se@xmath1 can be obtained.@xcite for the thin - layer structure with a thickness @xmath210 nm , the electron density is also controllable by the gate voltage.@xcite due to the large relative static dielectric constant,@xcite the dominant scattering on the surface is the electron - surface optical phonon scattering.@xcite in this work , we take into account both the @xmath3-doped degenerate and intrinsic nondegenerate cases before turning on the electric field , by including both the conduction and valence bands . our study reveals that due to the joint effects of the driving of the electric field and the inter - band precession as well as inter - band electron - phonon scattering , electrons can be transferred from the valence band to the conduction one . this effect is more pronounced when the scattering is weak and the electric field is strong . moreover , the variation in electron density for each band is linear in the electric field when the latter is strong for both the @xmath3-doped and intrinsic cases . the induced spin polarization is linear in the electric field when the latter is small and deviates from the linear relation when the latter becomes large enough . besides , at high temperature , the induced spin polarization is sensitive to the temperature but insensitive to the electron density . we also find that the electron - electron coulomb scattering is too weak to establish a drifted fermi distribution with a unified hot - electron temperature under the electric field . after turning off the electric field , the hot carriers cool down in a time scale of 100 - 1000 ps while the spin polarization relaxes in a time scale of momentum scattering , which is of the order of 0.01 - 0.1 ps . this paper is organized as follows . in sec . ii , we introduce the model and ksbes . in sec . iii , we analytically solve the ksbes under a small electric field in the presence of electron - impurity and electron - phonon scatterings , with the latter treated in the elastic scattering approximation . in sec . iv we present the numerical results from full calculation based on the ksbes . we summarize in sec .

the electron density in each band varies with the electric field linearly when the electric field is strong . due to the spin - momentum locking , a transverse spin polarization , with the magnitude proportional to the momentum scattering time , the induced spin polarization depends on the electric field linearly when the latter is small . our investigation also reveals that due to the large relative static dielectric constant , the coulomb scattering is too weak to establish a drifted fermi distribution with a unified hot - electron temperature in the steady state under the electric field . after turning off the electric field in the steady state , the hot carriers cool down in a time scale of energy relaxation which is very long ( of the order of 100 - 1000 ps ) while the spin polarization relaxes in a time scale of momentum scattering which is quite short ( of the order of 0.01 - 0.1 ps ) .

we study the charge and spin transport under high electric field ( up to several kv / cm ) on the surface of topological insulator bise , where the electron - surface optical phonon scattering dominates except at very low temperature . due to the spin mixing of conduction and valence bands , the electric field not only accelerates electrons in each band , but also leads to inter - band precession . in the presence of the electric field , electrons can transfer from the valence band to the conduction one via the inter - band precession and inter - band electron - phonon scattering . the electron density in each band varies with the electric field linearly when the electric field is strong . due to the spin - momentum locking , a transverse spin polarization , with the magnitude proportional to the momentum scattering time , is induced by the electric field . the induced spin polarization depends on the electric field linearly when the latter is small . moreover , its magnitude is inversely proportional to the temperature and is insensitive to the electron density at high temperature . our investigation also reveals that due to the large relative static dielectric constant , the coulomb scattering is too weak to establish a drifted fermi distribution with a unified hot - electron temperature in the steady state under the electric field . after turning off the electric field in the steady state , the hot carriers cool down in a time scale of energy relaxation which is very long ( of the order of 100 - 1000 ps ) while the spin polarization relaxes in a time scale of momentum scattering which is quite short ( of the order of 0.01 - 0.1 ps ) .

1301.1092

r

the analytical study in the previous section only applies to the small electric field . in order to take into account the large electric field , as well as all the scatterings explicitly , we carry out the numerical calculation based on the ksbes . in the calculation , we first apply the electric field along the @xmath32-axis to study the charge and spin transport , and then turn off the electric field after reaching the steady state to look into the cooling of the hot carriers and the relaxation of the previously induced spin polarization . we consider both the intrinsic nondegenerate and @xmath3-doped degenerate cases , starting from the initial equilibrium state with @xmath95 and a given @xmath127 respectively . in our study @xmath127 is chosen to be of the order of 10@xmath128 @xmath129 or even smaller , to avoid entering the bulk states in the presence of high electric field and also ensure the validity of hamiltonian @xmath18 [ eq . ( [ h0 ] ) ] without involving the terms square or cubic in momentum.@xcite we also do not consider the intrinsic case under low temperature as for such case the carrier density is quite low and the fluctuation ( e.g. , the effect of puddles@xcite ) , which is beyond the scope of this work , becomes important . in semiconductors with a large band gap , the electron and hole densities in the conduction and valence bands remain unchanged under the static electric field . however , here on the surface of topological insulator , due to the spin mixing of the two bands , the static electric field leads to inter - band precession,@xcite and also , due to the zero band gap , the inter - band electron - phonon scattering is easy to take place . therefore , electrons can be transferred from the valence band to the conduction one under the influence of the electric field , with the difference in the densities of electrons and holes in the two bands , @xmath130 , keeping constant due to the particle conservation . this redistribution of electrons between two bands under the electric field has also been revealed in a similar system , the gapless graphene.@xcite in principle , the auger process of the coulomb scattering , during which one and only one of the two scattered electrons transfers between two bands,@xcite may also lead to the redistribution of electrons between two bands under the electric field . however , this process is actually forbidden when the dynamic screening under random phase approximation ( rpa)@xcite ( refer to appendix [ ap1 ] ) is adopted.@xcite the redistribution of electrons in the two bands can not be revealed by the analytical study presented in sec . [ ana ] , which fails to incorporate the inter - band precession [ due to the replacement of @xmath28 by @xmath131 in terms proportional to @xmath69 ] as well as the inter - band scattering ( due to the elastic scattering approximation ) . however , this process can be revealed by fully solving the ksbes , as stated in the following . with @xmath133 kv / cm , @xmath134 k and @xmath135 @xmath129 . during calculation , the electron - impurity scattering is not included while the intra - band electron - phonon scattering ( labeled as intra - ep ) is always present . ( a ) : the chain curve is calculated without the inter - band precession ( labeled as ip ) and inter - band electron - phonon scattering ( labeled as inter - ep ) , the dashed ( dotted ) one with only the inter - band electron - phonon scattering ( inter - band precession ) , while the solid one with both the inter - band precession and inter - band electron - phonon scattering . the double - dotted chain curve is calculated with the inter - band precession , inter - band electron - phonon scattering and also the electron - electron coulomb scattering ( labeled as ee ) . ( b ) : temporal evolution of @xmath136 with the electron - phonon scattering artificially strengthened . the inter - band precession is always included . the solid curve is calculated with both the intra- and inter - band electron - phonon scatterings strengthened by a factor @xmath137 , while the dotted ( double - dotted chain ) one with only the intra - band ( inter - band ) electron - phonon scattering strengthened by a factor 2 . the crosses ( with scales on the top and right - hand side of the frame ) are the relative variation of @xmath138 reached in the steady state , @xmath139 , against the modulation factor @xmath140 ranging from 1 to 4 . the chain curve ( with scales on the top and right - hand side of the frame ) is the function @xmath141|_{\chi_{\rm ep}=1}/\chi_{\rm ep}^{2}$].,title="fig:",width=332 ] we take an @xmath3-type degenerate case with @xmath134 k and @xmath135 @xmath129 ( the corresponding fermi energy is @xmath142 mev and the fermi momentum is @xmath143 nm@xmath60 ) as an example to show the temporal evolution of the relative change of electron density in the conduction band , @xmath136 , under electric field @xmath133 kv / cm . it is seen in fig . [ figzw1](a ) that when both the inter - band precession and inter - band electron - phonon scattering are excluded , @xmath144 remains almost unchanged ( chain curve ) . however , once the inter - band precession is included , electrons can be effectively transferred from the lower band to the higher one ( dotted curve ) . the scenario is that , the electrons are precessed from the states below the dirac point to the ones above and then driven away to higher - energy states by the electric field . the transfer of electrons can also be alternatively realized with the assistance of phonons ( dashed curve ) . around the dirac point ( with @xmath145 nm@xmath60 ) , when electrons in the conduction band are driven away to higher - energy states , electrons in the valence band tend to enter the conduction band by _ absorbing _ phonons . however , the above two effects are not definitely superimposed when both of them are present . when the inter - band precession transfers electrons between two bands effectively , i.e. , leads to substantial nonequilibrium between the two bands ( such as the case presented here ) , electrons in the conduction band tend to fall back to the valence band by _ emitting _ phonons . therefore , when both the inter - band scattering and inter - band precession are included , the steady - state electron density in the conduction band decreases compared to the case with only the inter - band precession ( compare the solid and dotted curves ) . as pointed out above , the inter - band precession and inter - band scattering open channels for electron transfer between the two bands . however , the steady state of the two - band system is determined by the balance between the rates of energy gain from electric field and the energy loss to phonons . the former is determined by @xmath146 [ refer to eq . ( [ current ] ) ] . if the steady state is not far away from the equilibrium , one approximately has @xmath147 in the presence of electron - phonon scattering only . the dominant channel of the energy loss is the intra - band electron - phonon scattering . that is because the inter - band electron - phonon scattering is limited to a small finite region @xmath148 in momentum space , and also , with such small momentum , the scattering is weak as the rate is @xmath149 . a rough estimation gives that the rate of energy loss due to the intra - band electron - phonon scattering for the degenerate case with both low temperature and electron density is @xmath150 required by @xmath151 . based on eq . ( [ nv ] ) , it is found that the strengthening of the electron - phonon scattering , especially the intra - band part , leads to the decrease in @xmath139 . in fig . [ figzw1](b ) we numerically verify this by performing similar calculation as in ( a ) but with the electron - phonon scattering artificially strengthened . it is shown by the solid curve that when the total electron - phonon scattering is strengthened by a factor @xmath137 ( solid curve ) , @xmath139 substantially decreases compared to the genuine case [ solid curve in ( a ) ] . when only either the intra- or inter - band electron - phonon scattering is strengthened ( dotted and double - dotted chain curves , respectively ) , @xmath139 also decreases . however , the decrease is not obvious when only the inter - band electron - phonon scattering is strengthened ( double - dotted chain curve ) , indicating that the contribution to the energy loss by the inter - band electron - phonon scattering is indeed relatively weak . we further show the steady - state value , @xmath139 , against @xmath152 ranging from 1 to 4 by the crosses ( the scales are on the top and right - hand side of the frame ) . it is seen that approximately @xmath153 , satisfying eq . ( [ nv ] ) [ as a guide to the eye , a function proportional to @xmath154 , @xmath141|_{\chi_{\rm ep}=1}/\chi_{\rm ep}^{2}$ ] , is plotted by the chain curve in ( b ) ] . at last we briefly address the effect of electron - impurity and electron - electron coulomb scatterings on the redistribution of electrons . although neither of them leads to energy loss directly , both of them can limit the charge current and hence the energy injection rate of the electric field . the effect of impurities on charge current is apparent , as also explicitly indicated here by the combination of eqs . ( [ ana - eq ] ) and ( [ current ] ) . the coulomb scattering is usually deemed to preserve the charge current . this is indeed the case in semiconductors with _ parabolic _ energy spectrum where both momentum and current are conserved during the coulomb scattering . however , here with _ linear _ energy spectrum , only the momentum but not the current is conserved during the coulomb scattering . this particular feature also exists in graphene with linear dispersion as well.@xcite in fact , the effect of the coulomb scattering can be conjectured based on our analytical study , which indicates that @xmath155 [ eqs . ( [ current ] ) and ( [ sk0 ] ) ] . with the addition of the coulomb scattering , the momentum scattering time @xmath25 is reduced and hence the charge current decreases . consequently , with the inclusion of the electron - impurity and/or electron - electron coulomb scattering , the current and hence the energy injection rate of electric field decreases , resulting in less obvious redistribution of electrons . nevertheless , due to the large relative static dielectric constant , the effect of the electron - impurity and electron - electron coulomb scatterings is expected to be weak except when the temperature is low . in fig . [ figzw1](a ) , we add the double - dotted chain curve calculated with the coulomb scattering included . in the absence of impurities and under low temperature , the contribution of the coulomb scattering is visible , with which the variation in @xmath138 decreases compared to the coulomb scattering - free case ( solid curve there ) . in the following , we systematically investigate the charge and spin transport under the electric field , first in the low electric field regime and then the large one . we first focus on the low electric field regime with @xmath156 kv / cm and compare the numerical results with the analytical study in sec . we consider three cases , ( i ) @xmath3-doped case with @xmath134 k and @xmath135 @xmath129 , ( ii ) @xmath3-doped case with @xmath157 k and @xmath158 @xmath129 and ( iii ) intrinsic case with @xmath157 k and @xmath95 [ correspondingly @xmath159 @xmath129 ] . corresponding to these three cases , in figs . [ figzw2](a)-(c ) , we show the dependence of @xmath139 on the electric field with different impurity densities ( note that the @xmath112-axes are in different scales in the three figures ) . for case ( i ) with low temperature @xmath134 k , @xmath138 increases obviously with the electric field , due to the small initial electron density in the conduction band @xmath127 as well as the weak electron - phonon scattering . moreover , @xmath138 increases with @xmath69 faster with a smaller impurity density as the electron - impurity scattering weakens . besides , it is shown that when @xmath69 is small ( @xmath161 kv / cm ) , @xmath139 roughly exhibits a square dependence on @xmath69 , consistent with eq . ( [ nv ] ) . for case ( ii ) , which is highly degenerate and with strong electron - phonon scattering due to both high temperature and electron density , the electron density remains almost unchanged in the low electric field regime under investigation ( the relative variation is of the order of @xmath162 ) . nevertheless , for the intrinsic case ( iii ) , it becomes relatively easier for electrons to transfer due to the less occupancy of electrons in the conduction band , when compared to case ( ii ) . finally , figs . [ figzw2](b ) and ( c ) show that the effect of impurities is negligible at @xmath157 k. , against the electric field @xmath69 for cases ( i)-(iii ) , respectively , with different impurity densities . @xmath163 @xmath129 . ( d)-(f ) : the induced spin polarization @xmath164 against the electric field @xmath69 for cases ( i)-(iii ) with different impurity densities ( the scale is on the right - hand side of the frame).,title="fig:",width=328 ] the induced spin polarizations in the steady state @xmath164 against the electric field @xmath69 for the three cases ( i)-(iii ) are plotted in figs . [ figzw2](d)-(f ) , respectively . it is shown that @xmath164 increases with @xmath69 much faster at 50 k than those at 300 k , mainly due to the weaker electron - phonon scattering . for case ( i ) with @xmath134 k , the electron - impurity scattering is important and @xmath138 increases with @xmath69 effectively [ refer to fig . [ figzw2](a ) ] , therefore the rate of the increase in @xmath164 with @xmath69 shows impurity density dependence and also a slight electric field dependence [ refer to eq . ( [ ana - eq ] ) ] . however , for cases ( ii ) and ( iii ) with @xmath157 k and hence the strong electron - phonon scattering , @xmath165 increases with @xmath69 linearly , with almost the identical rate under different impurity and electron densities . this is consistent with the analytical study : when the electron - phonon scattering dominates , the spin polarization increases with the electric field linearly in a rate solely determined by temperature [ refer to eq . ( [ ana - eq ] ) and the discussion there ] . in the steady state against impurity density @xmath49 for cases ( i)-(iii ) , in ( a)-(c ) respectively . the triangles are obtained by numerically solving the full ksbes , while the crosses are calculated without the electron - electron coulomb scattering ( labeled as ee ) . the solid curves are from the analytical result [ eq . ( [ ana - eq ] ) ] . , title="fig:",width=245 ] in the following , we compare the induced steady - state spin polarization numerically obtained to the analytical one at @xmath166 kv / cm , with which all the three cases ( i)-(iii ) are close to the equilibrium . in fig . [ figzw3 ] , the impurity density dependence of the spin polarization from the numerical calculation with all the scatterings explicitly included is shown by triangles for the three cases . we also plot the numerical results without the coulomb scattering by crosses . it is shown that the effect of the coulomb scattering can only be visible when the impurity density approaches zero and the temperature is low . for comparison , the analytical calculation based on eq . ( [ ana - eq ] ) is plotted by the solid curves in the figure . one finds that the analytical formula primarily captures the numerical results . we point out that at 300 k where the elastic scattering approximation for electron - phonon scattering is more reasonable ( @xmath167 ) , the best fit to the numerical results by eq . ( [ ana - eq ] ) requires @xmath168 . finally , figs . [ figzw3](b ) and ( c ) indicate more clearly that at room temperature the electron - impurity scattering is negligible even when @xmath49 reaches @xmath169 @xmath129 . in fact , according to the analytical study in sec . [ ana1 ] , the momentum scattering times are estimated to be @xmath170 ps and @xmath171 ps for case ( i ) , @xmath172 ps and @xmath173 ps for case ( ii ) , and @xmath174 ps and @xmath175 ps for case ( iii ) ( in the estimation the impurity density is set as @xmath176 @xmath129 ) . these values quantitatively support the dominance of the electron - phonon scattering at high temperature . after investigating the low field regime and comparing with the analytical study , we proceed with the large electric field regime ( @xmath69 is upto 7 kv / cm ) . both the intrinsic nondegenerate and @xmath3-type degenerate cases under 150 k and 300 k are considered . for the degenerate case , we set @xmath177 @xmath129 . the impurity density is fixed at @xmath176 @xmath129 , with which the electron - impurity scattering is in fact negligible under the temperature investigated . we first present the electric field dependence of the steady - state electron density in the conduction band , @xmath178 , for the intrinsic and @xmath3-type cases at different temperatures . figure [ figzw4 ] indicates that @xmath178 increases with @xmath69 almost linearly for both cases , except in the low electric field region @xmath179 kv / cm for the degenerate situation where the pauli blocking is important . in fact , a nearly linear increase of electron density in conduction band with electric field is also observed in intrinsic graphene when @xmath180 kv / cm.@xcite it is also noted that here in the nearly linear regime , the rate of the increase in @xmath178 with @xmath69 is determined by temperature and is insensitive to the electron density . it is believed that this linear relation as well as the temperature dependent increasing rate are attributed to the dominant electron - phonon scattering with almost constant scattering matrix element . as a comparison , we recalculate the intrinsic case at 300 k by artificially setting @xmath181 and @xmath182 ev@xmath56nm@xmath58 in the electron - phonon scattering matrix element [ eq . ( [ ep - me ] ) ] . the result is shown in the figure by dots . it is seen that it deviates from the linear relation obviously . finally , we also present the calculation without the electron - electron coulomb scattering for the intrinsic case at 150 k by the closed squares . the comparison between the closed and open squares indicates that the influence of the coulomb scattering is marginal when the electric field is low and relatively effective when the electric field is high . for the intrinsic nondegenerate ( solid curves ) and @xmath3-type degenerate ( dashed curves ) cases under different temperatures . the dots are calculated for the intrinsic case at @xmath157 k by setting @xmath181 and @xmath182 ev@xmath56nm@xmath58 in the electron - phonon scattering matrix element [ eq . ( [ ep - me ] ) ] . the closed squares are calculated without the electron - electron coulomb scattering for the intrinsic case at 150 k.,title="fig:",width=245 ] -type degenerate ( dashed curves ) cases at different temperatures . the dotted and chain curves are obtained from eq . ( [ ana - eq ] ) with @xmath168 at 150 k and 300 k , respectively . the closed squares are calculated without the electron - electron coulomb scattering for the intrinsic case at 150 k.,title="fig:",width=245 ] we then look into the steady - state spin polarization @xmath164 induced by the electric field . in fig . [ figzw5 ] the electric field dependence of @xmath164 for the intrinsic and @xmath3-type cases at different temperatures is plotted . strikingly , in this whole large electric field region with the electron - phonon scattering being dominant , @xmath165 is solely determined by temperature , as previously revealed in the low electric field regime . moreover , with the same electric field @xmath69 , @xmath164 at 150 k is about 2 times as large as that at 300 k , approximately satisfying the analytical relation @xmath183 at high temperature . in the figure we also plot the @xmath164-@xmath69 relation given by eq . ( [ ana - eq ] ) ( with modified @xmath168 ) at 150 k ( dotted curve ) and 300 k ( chain curve ) , respectively . it is seen that the analytical formula for @xmath164 can approximately apply up to @xmath184 kv / cm ( 4 kv / cm ) at 150 k ( 300 k ) . when @xmath69 exceeds @xmath185 , the electron heating becomes important . therefore , with the occupation of larger - momentum states , the electron - phonon scattering is strengthened . at the same time , the momentum dependence of the electron - phonon scattering matrix element [ arising from the term @xmath186 in eq . ( [ ep - me ] ) ] also plays a role and further enhances the electron - phonon scattering . as a result , @xmath164 tends to decrease and hence deviates from the linear relation against @xmath69 . finally , the result obtained without the electron - electron coulomb scattering for the intrinsic case at 150 k is also plotted by the closed squares . again , the effect of the coulomb scattering on spin polarization is also shown to be marginal , especially in the low electric field regime . we now turn to study the mobility of the two - band system . according to eq . ( [ current ] ) , the steady - state charge current under the electric field is immediately obtained as @xmath187 . therefore , the steady - state mobility of the electron - hole system can be determined by @xmath188 $ ] . in fig . [ figzw6 ] we plot @xmath189 against @xmath69 for the intrinsic and @xmath3-type cases at different temperatures . it is shown that @xmath189 is around the order of @xmath190 cm@xmath58/(v@xmath56s ) , in consistence with the experimental data.@xcite @xmath189 decreases with @xmath69 as electrons and holes are heated to occupy large - momentum states where strong electron - phonon scattering takes place . moreover , with the increase of temperature from 150 to 300 k , @xmath189 decreases as well . in fact , we roughly have @xmath192 as both @xmath193 and @xmath194 are close to linear functions of @xmath69 . here @xmath195 is determined by the increasing rates of @xmath178 and @xmath194 with @xmath69 , both of which are only sensitive to temperature when @xmath69 is large ( as indicated by figs . [ figzw4 ] and [ figzw5 ] ) . therefore , in the large electric field regime , @xmath196 , with @xmath195 determined by the temperature . this feature is manifested in fig . [ figzw6 ] when @xmath197 kv / cm . -type ( dashed curves ) cases at different temperatures.,title="fig:",width=245 ] now we turn to see the effect of the coulomb scattering on the steady state established in the presence of electric field . it has been revealed in the previous section that due to the large relative static dielectric constant , the influence of the coulomb scattering is marginal in the presence of electron - phonon and electron - impurity scatterings . with the weak coulomb scattering , electrons in two bands fail to reach the drifted fermi distribution with a unified hot - electron temperature in the steady state . to reveal this , we take the intrinsic case with @xmath157 k and @xmath198 kv / cm as an example to plot the dependence of function @xmath199 on @xmath200 along the @xmath32-axis in fig . [ figzw7 ] , with different coulomb scattering strengths adjusted artificially.@xcite the comparison among these sets of data indicates that only when the coulomb scattering is strong enough ( e.g. , with the coulomb scattering term rescaled by a factor @xmath201 ) , in the steady state the drifted fermi distribution @xmath202 + 1\}$ ] is reached . here @xmath203 is the unified hot - electron temperature and @xmath204 is the shift of the momentum center limited by the scattering . both can be obtained from the slope of the wings of the `` v '' shape and the position of the valley , respectively ( refer to the solid curve as a guide to the eye ) . @xmath205 are chemical potentials for the two bands . for the intrinsic case as presented here , @xmath206 , due to the symmetry between the two bands . in the inset of the figure we plot both @xmath207 ( closed circles ) and @xmath208 ( open circles ) for the genuine case ( with @xmath209 ) in a small momentum scale . although the drifted fermi distribution is not established , the symmetry between the conduction and valence bands is clearly indicated by the inset . against momentum @xmath200 along the @xmath32-axis in the steady state , evolving from the intrinsic case with @xmath157 k and @xmath198 kv / cm . the dots are obtained from the calculation for the genuine case , while the open squares , triangles and closed squares are from the calculation with the coulomb scattering term multiplied by @xmath210 , 10 and 50 , respectively . the solid line is plotted as a guide to the eye by fitting the closed squares with hot - electron temperature @xmath211 k. inset : function @xmath212 [ closed ( open ) circles are for electrons in conduction ( valence ) band with @xmath213 ( @xmath214 ) ] against momentum @xmath200 along the @xmath32-axis in a small momentum scale in the steady state for the genuine case.,title="fig:",width=264 ] against the initial spin polarization @xmath215 for the intrinsic ( solid curves ) and @xmath3-type ( dashed curves ) cases at different temperatures . the temporal evolution of @xmath216 is plotted in the inset for two cases , with @xmath215 initialized from the intrinsic situation at 150 k under electric field 1 ( solid curve ) and 7 kv / cm ( dashed curve ) , respectively . the dotted ( chain ) curve is the exponential fit to the rapid decay in the beginning of the solid ( dashed ) curve . , title="fig:",width=257 ] finally , we start from the steady - state spin polarization reached previously under the electric field , to study the spin relaxation by turning off the electric field . the zero point of time , @xmath217 , is reset to be the moment at which the electric field is turned off . beginning at @xmath217 , the heated electrons cool down to the original fermi distribution in the time scale of energy relaxation , which is as long as @xmath2100 - 1000 ps , mainly due to the weak inter - band electron - phonon scattering . however , the spin polarization relaxes in the time scale of momentum scattering which is quite short.@xcite according to eq . ( [ sr ] ) , @xmath218 relaxes approximately in the exponential form when @xmath219 . the total spin polarization @xmath220 , containing a summation of @xmath218 over momentum , does not definitely relax in a fine exponential form . our calculation shows that @xmath221 against @xmath222 decays first very fast to about @xmath223 but then slowly . the slowly - decaying tail with small magnitude is determined by the low - energy states near the dirac point with long momentum relaxation times . as an example , in the inset of fig . [ figzw8 ] , we plot the dependence of @xmath216 against @xmath222 for two cases by the solid and dashed curves . in these two cases @xmath215 are initialized from the intrinsic situation at 150 k under electric field 1 ( solid curve ) and 7 kv / cm ( dashed curve ) , respectively . to obtain the spin relaxation time @xmath224 , we fit the rapid decaying part in the beginning by an exponential function , as illustrated by the dotted and chain curves in the inset . the spin relaxation time @xmath224 against the initial spin polarization @xmath215 for the intrinsic and @xmath3-type cases at different temperatures is plotted in fig . [ figzw8 ] . it is shown that the spin relaxation time is of the order of 0.01 - 0.1 ps , mainly limited by the electron - phonon scattering . in fact , a momentum relaxation time of the similar order is given from both estimation and experiment by butch _ et al._.@xcite the decrease of @xmath224 with the increase of @xmath215 is due to the fact that the larger @xmath215 is initialized by the higher electric field , with which the electrons and holes occupy larger - momentum states and hence exhibit faster momentum relaxation . besides , with higher temperature , the spin relaxation time also decreases as the electron - phonon scattering is strengthened .

not only accelerates electrons in each band , but also leads to inter - band precession . in the presence of the electric field , electrons can transfer from the valence band to the conduction one via the inter - band precession and inter - band electron - phonon scattering .

we study the charge and spin transport under high electric field ( up to several kv / cm ) on the surface of topological insulator bise , where the electron - surface optical phonon scattering dominates except at very low temperature . due to the spin mixing of conduction and valence bands , the electric field not only accelerates electrons in each band , but also leads to inter - band precession . in the presence of the electric field , electrons can transfer from the valence band to the conduction one via the inter - band precession and inter - band electron - phonon scattering . the electron density in each band varies with the electric field linearly when the electric field is strong . due to the spin - momentum locking , a transverse spin polarization , with the magnitude proportional to the momentum scattering time , is induced by the electric field . the induced spin polarization depends on the electric field linearly when the latter is small . moreover , its magnitude is inversely proportional to the temperature and is insensitive to the electron density at high temperature . our investigation also reveals that due to the large relative static dielectric constant , the coulomb scattering is too weak to establish a drifted fermi distribution with a unified hot - electron temperature in the steady state under the electric field . after turning off the electric field in the steady state , the hot carriers cool down in a time scale of energy relaxation which is very long ( of the order of 100 - 1000 ps ) while the spin polarization relaxes in a time scale of momentum scattering which is quite short ( of the order of 0.01 - 0.1 ps ) .

1301.1092

c

in conclusion , we have studied the charge and spin transport under the influence of high electric field ( up to several kv / cm ) on the surface of topological insulator bi@xmath0se@xmath1 , by means of the ksbes . we assume that the fermi level , adjustable by doping,@xcite is located in the bulk gap . therefore the bulk states are excluded from our study . with moderate electron and hole densities , the surface state around the dirac point can be depicted by the rashba spin - orbit coupling . in our study , both the conduction and valence bands of the surface state are considered , with the inter - band coherence explicitly included . apart from the driving effect in each band , due to the spin mixing of conduction and valence bands , the electric field also leads to inter - band precession . this differs from the semiconductors with parabolic energy spectrum . in bi@xmath0se@xmath1 , the relative static dielectric constant is as large as 100 , indicating weak electron - impurity and electron - electron coulomb scatterings . with the weak coulomb scattering , electrons in the two bands fail to establish a drifted fermi distribution with a unified hot - electron temperature under the driving of the electric field . the electron - surface optical phonon scattering dominates in a large temperature region . moreover , the electron - phonon scattering matrix element is approximately constant due to its marginal dependence on momentum . this feature leads to particular properties of charge and spin transport on the surface of bi@xmath0se@xmath1 . our study reveals that in the presence of driving of the electric field , both the inter - band precession and inter - band electron - phonon scattering cause electrons to transfer from the valence band to the conduction one . due to the dominant electron - phonon scattering , the variation in electron density for each band is linear in the electric field when the latter is high , despite whether the initial state is degenerate or nondegenerate . it is also found that due to the spin - momentum locking from the rashba spin - orbit coupling , a transverse spin polarization is induced by the electric field , with the magnitude proportional to the momentum scattering time . besides , the spin polarization is linear in the electric field when the latter is small but deviates from the linear relation when the latter is large enough as the electron - phonon scattering is enhanced due to the heating of electrons . moreover , a very interesting feature is that at high temperature , the spin polarization is inversely proportional to the temperature but insensitive to the electron density . the cooling of hot carriers and the relaxation of spin polarization induced by the electric field are investigated by turning off the electric field after reaching the steady state . it is found that the hot carriers cool down in a time scale of energy relaxation , which is quite long and is of the order of 100 - 1000 ps . however , due to the spin - momentum locking again , the spin polarization relaxes in a time scale of momentum scattering . the spin polarization is mainly contributed by the states with large momentum . therefore , it decays rapidly within the time of the order of 0.01 - 0.1 ps . following this rapid decay , there is a slowly damping tail . this tail is attributed to the low - energy states near the dirac point where the momentum scattering is weak . this work was supported by the national basic research program of china under grant no.2012cb922002 and the strategic priority research program of the chinese academy of sciences under grant no . one of the authors ( pz ) would like to thank m. q. weng for valuable discussions .

we study the charge and spin transport under high electric field ( up to several kv / cm ) on the surface of topological insulator bise , where the electron - surface optical phonon scattering dominates except at very low temperature . due to the spin mixing of conduction and valence bands , the electric field is induced by the electric field . moreover , its magnitude is inversely proportional to the temperature and is insensitive to the electron density at high temperature .

we study the charge and spin transport under high electric field ( up to several kv / cm ) on the surface of topological insulator bise , where the electron - surface optical phonon scattering dominates except at very low temperature . due to the spin mixing of conduction and valence bands , the electric field not only accelerates electrons in each band , but also leads to inter - band precession . in the presence of the electric field , electrons can transfer from the valence band to the conduction one via the inter - band precession and inter - band electron - phonon scattering . the electron density in each band varies with the electric field linearly when the electric field is strong . due to the spin - momentum locking , a transverse spin polarization , with the magnitude proportional to the momentum scattering time , is induced by the electric field . the induced spin polarization depends on the electric field linearly when the latter is small . moreover , its magnitude is inversely proportional to the temperature and is insensitive to the electron density at high temperature . our investigation also reveals that due to the large relative static dielectric constant , the coulomb scattering is too weak to establish a drifted fermi distribution with a unified hot - electron temperature in the steady state under the electric field . after turning off the electric field in the steady state , the hot carriers cool down in a time scale of energy relaxation which is very long ( of the order of 100 - 1000 ps ) while the spin polarization relaxes in a time scale of momentum scattering which is quite short ( of the order of 0.01 - 0.1 ps ) .

0908.0068

c

we studied the soliton excitations in the classical f - af model with the easy - axis anisotropy . the f - af model has two parameters : the frustration parameter @xmath401 and the anisotropy @xmath60 . we found that in a weakly anisotropic limit ( @xmath402 ) the behavior of the soliton solutions for small frustration parameter @xmath11 is qualitatively similar to that for the exactly solvable easy - axis xxz chain ( @xmath25 case ) . however , the situation drastically changes near the it point ( @xmath88 , @xmath12 ) , where the transition from the ferromagnetic to the spiral ground state takes place in the isotropic case . in the vicinity of the it point the corresponding energy functional in the continuum approximation qualitatively changes and does not admit the exact solution . the analysis of the derived energy functional allowed us to estimate the behavior of the transition line between the ferromagnetic to the spiral ground state in ( @xmath403 ) plane near the it point . we mainly interested in the behavior of the solitons in the vicinity of the it point . we showed that these localized states are separated from the ferromagnetic state by a finite gap . the dependence of the soliton energy ( the gap ) on model parameters near the it point was established on a base of the scaling arguments . as a result we found that the soliton energy is proportional to @xmath404 and is expressed by the scaling function ( [ escal ] ) depending on three scaling parameters : @xmath405 , the scaled soliton size @xmath180 and the momentum @xmath197 . the analysis of the asymptotic solutions of the corresponding equation of motion provided us with the necessary conditions of the soliton stability . it was shown that solitons of all sizes and any momentum exist when @xmath234 , while in the region @xmath145 there are definite restrictions on the soliton size @xmath180 and the momentum @xmath197 . the distribution of the allowable values of the soliton parameters in ( @xmath179 ) plane for @xmath145 has very complicated form , which can be determined numerically only . for example , the static solitons ( @xmath199 ) only of the middle size @xmath243 are stable at @xmath242 . nevertheless , some facts about the soliton existence region was ascertained analytically and then confirmed by numerical calculations . in particular , small static ( @xmath199 ) solitons are unstable for @xmath145 , while small solitons with non - zero momentum exist for any @xmath110 . large solitons ( @xmath181 ) exist for @xmath246 and , therefore , they survive in the part of the spiral phase @xmath406 . though the soliton excitations in the spiral phase lie in the high - energy part of the spectrum , they can play an essential role in the magnetization processes . in the isotropic limit ( @xmath249 ) only small solitons with non - zero momentum survive and the maximal allowable size of these solitons increases when the frustration parameter tends to the critical value @xmath407 . such a dependence of the soliton size on the frustration parameter is qualitatively similar to the observation that the size of the multimagnon bound complexes with @xmath254 in the quantum f - af model grows when @xmath407 . we found that the frustration reveals itself in the oscillating shape of solitons . the amplitude of the oscillations grows at approaching to the spiral phase and further inside of it . generally , at some value of @xmath110 the solution starts to oscillate without the decay at infinity , i.e. , soliton - like solution with given values of @xmath180 and @xmath197 disappears . we studied the finite - size effects on the soliton solutions . it was shown that the soliton solution on finite ring originates in the uniform ( non - localized ) state . the transition from the uniform to the soliton - like state occurs at the critical value of the anisotropy @xmath408 , below which the uniform solution is realized . this finite - size effect is similar to the well - known gross - pitaevskii transition in the bose - systems . in order to establish a connection between the properties of the solitons and the multi - magnon complexes of the quantum counterpart of this model we used the dyson - maleev mapping of the spin model to the bose one . it turned out that the dependence of the energy of boson bound complexes on model parameters represents a particular case of the found scaling expression for the classical soliton energy . moreover , the energy of the bound magnon complexes for quantum spin-@xmath2 model found by us before perfectly coincides with the scaling equation for soliton energy . therefore , we believe that the bound energy of multi - magnon complex for a quantum spin-@xmath13 model near the it point is characterized by the same critical exponents and by the identical scaling parameters as the soliton energy , though the corresponding scaling functions are different for different @xmath13 . it is known that such a resemblance takes place for the heisenberg ferromagnetic chain with an easy - axis anisotropy . our study shows that the multi - magnon complexes behave substantially as the classical objects for the frustrated model as well . for future it would be interesting to study the behavior of the classical spin model deeply in the spiral phase . we believe that it can help in understanding of unusual magnetization processes and shed light on the behavior of the multi - magnon complexes at high magnetic fields . mikeska and a. k. kolezhuk , in _ quantum magnetism _ , lecture notes in physics vol . * 645 * , edited by u. schollwck , j. richter , d. j. j. farnell , and r. f. bishop , eds . ( springer - verlag , berlin , 2004 ) , p. 1 . r. d. somma and a. a. aligia , phys . b * 64 * , 024410 ( 2001 ) ; r. jafari and a. langari , phys . rev . b * 76 * , 014412 ( 2007 ) ; a. avella , f. mancini , and e. plekhanov , eur . j. : cond . matter , * 66 * , 295 ( 2008 ) . r. kanamoto , h. saito , and m. ueda , phys . a * 67 * , 013608 ( 2003 ) ; g. m. kavoulakis , phys . rev . a * 67 * , 011601(r ) ( 2003 ) ; k. sakmann , a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . a * 72 * , 033613 ( 2003 ) .

the dependence of the soliton energy on small anisotropy parameter is established using scaling estimates and numerical minimization of the energy functional . it is shown that solitons survive in the spiral phase though with some restrictions on their size . the influence of the finite - size effects on the soliton states is studied and it is shown that the localized solitons originate from the uniform state when the system size exceeds some critical value depending on the anisotropy .

we study the classical anisotropic ferromagnetic spin chain with frustration . the behavior of soliton and kink solutions in the vicinity of the ground state phase transition from the ferromagnetic to the spiral phase is studied . the dependence of the soliton energy on small anisotropy parameter is established using scaling estimates and numerical minimization of the energy functional . conditions of the existence of the solitons are determined . it is shown that solitons survive in the spiral phase though with some restrictions on their size . a comparison of the energies of the classical solitons and the bound magnon complexes in the quantum model shows the functional similarity between them . the influence of the finite - size effects on the soliton states is studied and it is shown that the localized solitons originate from the uniform state when the system size exceeds some critical value depending on the anisotropy .

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nature is not perfect and various types of disorder are ubiquitous . disorder often causes large changes in the properties of condensed matter systems as predicted on the basis of naive idealized models that assume perfect regularity . electron properties in two - dimensional @xcite and three - dimensional disordered media @xcite , crystalline lattices with structural defects @xcite , spin glasses with random interactions @xcite and systems exhibiting criticality modified by the presence of disorder @xcite , are all instances of pronounced disorder effects in the bulk of the materials that can fundamentally change the behavior of idealized model systems . apart from their fundamental importance in modifying the bulk properties , disorder effects at surfaces and interfaces are particularly important in the context of the solid - electrolyte interphases @xcite relevant also for energy generation and storage technologies @xcite . the structural disorder in the charge distribution and/or dielectric response spatial profile in the vicinity of the material interfaces couple to long - range electrostatic interactions , leading effectively to long - range disorder effects as well @xcite , that can not be understood in terms of the usual assumptions of piecewise homogeneous charge distribution and/or dielectric properties , underpinning so much of colloid science and electrochemistry @xcite . the coupling between electrostatic interactions and disorder has been already noted and discussed in other important cases @xcite , including surfactant - coated surfaces @xcite , random polyelectrolytes and polyampholytes @xcite , and contaminant adsorption onto macroscopic surfaces or in amorphous films showing grain structure after being deposited on crystalline substrates @xcite . in all these cases the charge distribution often shows a fundamentally disordered component that often remains unaltered after the assembly or fabrication of the materials , thus exhibiting a frozen , or _ quenched _ , type of disorder ( see , e.g. , refs . @xcite for examples of surfaces with _ annealed _ charge distributions that will not be considered in this paper ) . this charge disorder coupled to the long - range electrostatic interactions can then leave its fingerprint also on the interactions between macromolecular surfaces that in their turn can play a fundamental role in the stability of colloidal systems @xcite . in fact , this coupling between disorder and coulomb interactions has been suggested to underly the anomalously long - ranged interactions observed in ultrahigh sensitivity experiments on casimir - van der waals interactions between surfaces _ in vacuo _ @xcite . the intricate experimental details of accurate measurements of these interactions can be properly accounted for only if one considers also the disordered nature of charges on and within the interacting surfaces by invoking the so - called _ patch effect _ @xcite , where the disorder stems , for instance , from the adsorption of charged contaminants and/or impurities that can give rise to monopolar random surface charges , and/or the variation of the local crystallographic axes of the exposed surface of a clean polycrystalline sample and the corresponding electron work function that can cause a variation of the local surface potential . such random distributions of surface charges can be measured directly by kelvin force microscopy measurements @xcite . the salient features of electrostatic interactions themselves , even for homogeneous charge distributions in the absence of any disorder , are however quite involved ( see , e.g. , refs . @xcite and references therein ) . it has been recognized some time ago that electrostatic interactions in fact come in several varieties , depending on the strength of electrostatic coupling in the system @xcite . in the presence of mobile monovalent counterions , they are standardly described by the poisson - boltzmann ( pb ) theory stemming from the mean - field , collective description of coulomb fluids @xcite that gives rise to pronounced repulsive interactions between like - charged macromolecules ( such as polymers , colloids and nano - particles ) . on the contrary , in the presence of multivalent counterions , electrostatic interactions exhibit basically a single - particle character and mediate strong attractive interactions between like - charged macromolecules this attraction led to a new understanding of the theory of electrostatic interactions in colloidal domain based on the _ strong - coupling ( sc ) limit _ @xcite , devised to describe the equilibrium properties of coulomb fluids when charges involved become large . in the simple case of a counterion - only system , the transition from the mean - field pb description , dubbed also the _ weak - coupling ( wc ) limit _ , to the sc limit is governed by a single dimensionless _ electrostatic coupling parameter _ @xcite , being a ratio of the bjerrum length , which identifies coulomb interaction between counterions themselves , and the gouy - chapman length , which describes electrostatic interaction between the counterions and the charged ( macromolecular ) surfaces . the emerging picture of equilibrium properties of coulomb fluids has thus become much richer than conveyed for many years by the standard dlvo paradigm of colloid science @xcite . however , this is still not the complete story . the most relevant case of a coulomb fluid is in fact not a counterion - only system , but an asymmetric mixture of multivalent ions in a bathing solution of monovalent ions , a particularly relevant situation specifically in the context of bio - macromolecules , where multivalent ions together with the screening properties of the monovalent salt are believed to play a key role in the stability of macromolecular aggregates such as liquid crystalline mesophases of semiflexible biopolymers @xcite , or dna condensates that form in the bulk @xcite or within viruses or virus - like nano - capsids @xcite . in an asymmetric mixture , multivalent counterions and monovalent ions are coupled differently to the macromolecular charges : multivalent ions strongly , while monovalent ions only weakly , as evidenced from their respective electrostatic coupling parameters . since usually multivalent ions are present at very low concentrations , e.g. , around just a few mm , their behavior is expected to be properly described within the virial expansion in powers of their fugacity ( or bulk concentration ) @xcite . a _ dressed multivalent - ion theory _ then emerges naturally within this context @xcite since the degrees of freedom due to weakly coupled monovalent ions can be traced out from the partition function , leading to an effective formalism based on screened interactions between the remaining dressed multivalent ions and fixed macromolecular charges . the dressed multivalent - ion theory for complicated asymmetric mixtures of multivalent ions in a bathing solution of monovalent ions can then seamlessly bridge between the standard wc and sc limits @xcite . these baroque features of electrostatic interactions furthermore give their imprint also on the effects of disordered charge distribution along macromolecular interfaces @xcite . while on the wc level and for homogeneous planar systems the quenched disorder effects are nonexistent @xcite , they can lead to qualitative changes in the stability properties of the system once the dielectric contrast between the solution and macromolecular interfaces ( or the inhomogeneous distribution of salt ions ) is taken fully into account @xcite . nevertheless , it is in the sc limit that the coupling between electrostatic interactions and the quenched disorder in the external interfacial charge distributions gives rise to fundamentally novel and unexpected phenomena @xcite . while studying the interaction between two disordered charged surfaces it was noticed @xcite that disorder can in fact lead to a lowering of the effective temperature of the system , engendering a distribution of the multivalent counterions between the interacting surfaces that is characterized by less effective entropy . this is intuitively difficult to foresee , as one would perhaps naively assume that thermal and externally imposed charge disorder would somehow enhance one another . in order to properly understand and identify all salient features of the coupling between quenched charge disorder and long - range electrostatic interactions , we now proceed to characterize more closely the consequences of coupling between charge disorder and _ electrostatically strongly coupled _ multivalent counterions immersed in a monovalent salt solution bath . in particular , we will identify the defining feature of this strongly coupled , disordered system as belonging to the _ anti - fragility _ @xcite exhibited by this system . in the present context , anti - fragility simply refers to the fact that an externally imposed , quenched charge disorder , effectively diminishes the intrinsic thermal disorder in the system , forcing its behavior to be more ` ordered ' . we will show that this behavior stems from the interplay between the _ translational entropy _ of the multivalent counterions and the _ configurational entropy _ due to the averaging over different realizations of the quenched disorder . in the particular example of the counterion - only model ( with no monovalent salt ions and no interfacial dielectric discontinuity ) , we show that multivalent counterions experience an additional logarithmic attraction towards the surface due to the presence of the surface charge disorder in a way that their density profile exhibits an algebraically singular behavior at the surface with an exponent that depends on the disorder strength ( variance ) . this behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact - value theorem @xcite . in the presence of an interfacial dielectric discontinuity , depleting the counterion layer at the surface , the charge disorder still generates a much enhanced counterion density further away from the surface . likewise , the charge inversion and/or overcharging of the surface are predicted to occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder . the organization of the paper is as follows : in section [ sec : model ] , we introduce our model and then in section [ sec : formal ] present the theoretical formalism that will be used to study the distribution of multivalent counterions next to a randomly charged dielectric interface . we then proceed to present our results in section [ sec : results ] , where we discuss the case of counterion - only systems and the effects due to the presence of a bathing salt solution , an interfacial dielectric discontinuity , and also the overcharging and charge - inversion phenomena in the system . we conclude our discussion in section [ sec : discussion ] .

this behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact - value theorem , reflecting the _ anti - fragility _ effects of the disorder that drive the system towards a more ` ordered ' state . in the presence of an interfacial dielectric discontinuity , depleting the counterion layer at the surface , the charge disorder still generates a much enhanced counterion density further away from the surface . likewise , the charge inversion and/or overcharging of the surface occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder .

we study the distribution of multivalent counterions next to a dielectric slab , bearing a quenched , random distribution of charges on one of its solution interfaces , with a given mean and variance , both in the absence and in the presence of a bathing monovalent salt solution . we use the previously derived approach based on the _ dressed multivalent - ion theory _ that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework . the presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the density of multivalent counterions in its vicinity . in the counterion - only model ( with no monovalent salt ions ) , the surface disorder generates an additional logarithmic attraction potential and thus an algebraically singular counterion density profile at the surface . this behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact - value theorem , reflecting the _ anti - fragility _ effects of the disorder that drive the system towards a more ` ordered ' state . in the presence of an interfacial dielectric discontinuity , depleting the counterion layer at the surface , the charge disorder still generates a much enhanced counterion density further away from the surface . likewise , the charge inversion and/or overcharging of the surface occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder . overall , the presence of quenched surface charge disorder leads to sizable effects in the distribution of multivalent counterions in a wide range of realistic parameters and typically within a distance of a few nanometers from the charged surface .

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we have investigated the distribution of multivalent counterions close to a dielectric slab bearing a quenched , random distribution of monopolar surface charges on one of its solution interfaces with set mean value and variance , both in the absence and in the presence of an asymmetric coulomb fluid , comprised of a mixture of multivalent counterions in a bathing solution of monovalent ions . such asymmetric coulomb fluids are commonplace in many experimental examples such as in the condensation of dna by multivalent cations in the bulk @xcite or in viruses and virus - like nano - capsids @xcite . our analysis is done within the framework of the _ dressed multivalent - ion theory _ , which reproduces the strong - coupling theory of multivalent counterions @xcite in the zero salt limit and takes into account the surface - counterion as well as counterion - image correlations on the leading order and in the presence of a bathing salt solution as discussed in detail elsewhere @xcite . ( note that in the opposite regime of weak coupling , where , e.g. , all ions are monovalent , the quenched charge disorder effects turn out to be small and do not lead to any qualitatively new features in the behavior of the system @xcite . ) in the case of counterions only , we show that a randomly charged surface generates a singular density profile for multivalent counterions with an algebraically diverging behavior at the surface ; the latter is characterized by an exponent which is determined by the disorder strength ( variance ) . thus , multivalent counterions are predicted to accumulate strongly in the immediate vicinity of the randomly charged surface in a way that violates the contact - value theorem , which describes the behavior of counterions at uniformly charged surfaces and predicts a finite contact density @xcite . this behavior stems from the interplay between the translational entropy of the solution ions and the ( non - thermal ) configurational entropy due to the averaging over different realizations of the quenched disorder . therefore , by introducing an external ( quenched ) disorder component , we find that the system is driven towards a more ` ordered ' state characterized by a diminished intrinsic thermal ` disorder ' in the system . it thus seems appropriate to characterize this response of the system to an externally imposed quenched disorder as the _ anti - fragile behavior _ @xcite of multivalent counterions in the presence of quenched charge disorder . it is to be noted that , in the presence of disorder , the system also attains a thermodynamically more stable state because the internal energy of the system drops in a way that leads to a lowered free energy . the singular behavior of multivalent counterions persists also when counterions are immersed into a bath of a monovalent salt solution and there are no dielectric inhomogeneities in the system . in this case , the slab defines an ion - excluded region , creating salt image effects . the interplay between the disorder - induced attraction and the salt - image depletion leads to a non - monotonic density profile for counterions close to the surface . the amount of multivalent counterions accumulated near the surface is again enhanced strongly when the surface is randomly charged . this holds also in the case of a finite discontinuity in the dielectric constant ( even though dielectric image charges , unlike salt images , eliminate the singularity and create a counterion - depleted zone in the immediate vicinity of the charged surface ) and/or when the multivalent counterions have a finite size ( that prevents them from probing the singular point of the single - particle interaction energy on the charged surface ) . the charge disorder can thus make the overcharging and/or charge inversion of the mean surface charge highly pronounced . our results are presented in terms of rescaled ( dimensionless ) parameters such as the rescaled screening parameter and the electrostatic and disorder coupling parameters , which can be mapped to a wide range of values for counterion and salt bulk concentration , mean surface charge density , counterion valency , etc . a few examples of the actual values for these latter quantities ( corresponding to the typical values of the rescaled parameters that were used to plot the figures in the previous sections ) are shown in table [ table ] . note that other sets of actual parameter values than those given in the table ( e.g. , using divalent and trivalent counterions ) are just as conceivable , as long as they correspond to the same set of dimensionless parameters . the typical values of the disorder coupling parameter that we used in our study , e.g. , @xmath184 , correspond to a relatively small degree of charge disorder on the surface @xmath185nm@xmath186 . assuming that the disorder originates from a quenched , random distribution of positive and negative impurity charges , @xmath187 , residing on the surface with a surface density of @xmath188 , we find @xmath189 @xcite . therefore , the above - mentioned values of @xmath190 can be obtained by relatively small densities @xmath191nm@xmath186 of impurity charges as compared with the mean number of surface charges ( typically @xmath192nm@xmath186 ) and can be thus easily realized in actual systems . hence , we conclude that the effects due to charge randomness , even at such small amounts , can be quite significant ! we should emphasize that our results are valid strictly in the case of highly asymmetric coulomb fluids , where the dressed multivalent - ion approach can be justified @xcite . the dressed multivalent - ion theory , that was implemented here , follows as a limiting single - particle theory from the virial expansion of the partition function up to the leading order in the fugacity of multivalent counterions and , as such , is expected to be applicable in two distinct regimes @xcite : ( i ) when the electrostatic interactions are strong enough giving rise , on the leading order , to a strong - coupling , single - particle behavior for multivalent counterions next to an oppositely charged boundary ( typically at low salt concentrations or in counterion - only systems ) @xcite , and ( ii ) when multi - particle interactions between counterions are sufficiently weak due , e.g. , to high salt screening effects , allowing again for a single - particle description ( typically at moderate to high salt concentrations ) @xcite . this analytical approach is thus expected to be valid only at relatively small bulk concentrations of multivalent counterions around , for instance , just a few mm , which is in fact often the case in experiments ( see , e.g. , refs . @xcite ) . the dressed multivalent - ion theory has been tested extensively against implicit- and explicit - ion simulations @xcite and turns out to have a wide range of validity in the parameter space when the surfaces bear uniform charge distributions . similar simulations are still missing in the case of randomly charged surfaces with multivalent ions mostly because of a significantly large increase in the computational time , which would be required in oder to produce reliable quenched disorder averages . our results , however , produce concrete predictions that can be tested against simulations . the fingerprints of charge disorder are expected to show up in appropriately designed experiments as well @xcite , although one should note that experiments on systems containing solutions of multivalent ions face certain difficulties as is , for instance , the case @xcite in electrophoresis measurements conducted to show the charge inversion effect ( see refs . @xcite for other recent methods such as streaming currents or atomic force microscopy measurements ) . in general , we expect that the previously determined regimes of validity of the dressed multivalent - ion theory @xcite roughly hold also for the present case with disordered surfaces . one particular case that should be treated with caution in systems containing added monovalent salt is the situation where the mean electrostatic potential near the randomly charged surface becomes large , e.g. , when the disorder strength is very large and/or the dielectric discontinuity parameter is small , in which case the validity of the underlying dh approximation used for the monovalent ions can break down @xcite . another case that goes beyond the present approach is the situation where nonlinear charge renormalization and/or bjerrum pairing effects become relevant ( see , e.g. , refs . @xcite ) ; however , these effects turn out to be negligible in the regime of parameters that is of concern here @xcite . also , while we expect that the predicted boundaries of the parameter space pertaining to the onset of the charge inversion and/or overcharging would be relatively accurate , the single - particle approximation that lies at the heart of the dressed multivalent - ion description is not expected to be adequate in the regime of parameters deeply within the regime of charge inversion and/or overcharging due to non - negligible many - body contributions @xcite . these considerations and the role of other possible factors such as higher - order virial corrections @xcite , the discrete nature and the finite size of monovalent salt ions @xcite and the ion - ion excluded - volume repulsions @xcite , etc , that are expected to become relevant especially at intermediate electrostatic couplings and/or within the regime of charge inversion / overcharging , remain to be assessed further in future simulations . our model is based on a few simplifying assumptions and , as such , neglects several other factors including solvent structure ( see , e.g. , refs . @xcite and references therein ) , the polarizability of mobile ions ( see , e.g. , refs . @xcite and references therein ) , specific surface ion - adsorption effects @xcite , etc . we have also neglected the internal structure of counterions that can introduce higher - order multipolar effects ( see , e.g. , refs . @xcite and references therein ) ; these effects can be relevant especially for multivalent counterions that have an extended structure such as rod - like polyamines like the trivalent spermidine and tetravalent spermine with chain lengths of up to 1 - 1.5 nm @xcite . on the other hand , we have assumed that the charge disorder is distributed according to a gaussian weight and that it is uncorrelated in space . spatial correlations can be included in our formalism in a straightforward manner @xcite and will be considered in future works . it is important to note that the precise statistical characteristics of charge disorder in real systems can be highly sample and material dependent , involving also the method of preparation , features that should all be considered if the theoretical findings are to be compared with experiments . furthermore , annealed as opposed to quenched disordered surfaces , containing mobile surface charges that are in thermal equilibrium with the rest of the system @xcite , as well as surfaces containing partially quenched or partially annealed charge distributions @xcite , and also charge regulating surfaces @xcite constitute other interesting examples that can be studied in the present context . all of these additional features we plan to address in the future . another interesting problem , which is closely related to the present work and can be studied using similar methods , is the strong - coupling interaction between randomly charged surfaces immersed in an asymmetric coulomb fluid @xcite . it is also worth mentioning that some of the key findings in the present study , such as the singular behavior of the density profile of multivalent ions , remain valid even in the case of _ net - neutral _ surfaces that carry no mean charge density but only a finite charge disorder variance . the case of net - neutral surfaces has been studied recently in a series of works in the context of casimir interactions @xcite and the role of an asymmetric coulomb fluid in this case will be discussed elsewhere @xcite . a.n . acknowledges partial support from the royal society , the royal academy of engineering , and the british academy ( uk ) . acknowledges support from the school of physics , institute for research in fundamental sciences ( ipm ) , where she stayed as a short - term visiting researcher during the completion of this work . r.p . acknowledges support from the arrs through grants no . p1 - 0055 and j1 - 4297 . we thank m. kandu and e. mahgerefteh for useful comments and discussions . kim , m. brown - hayes , d.a.r . dalvit , j.h . brownell and r. onofrio , phys . a * 78 * , 020101(r ) ( 2008 ) ; * 79 * , 026102 ( 2009 ) ; r.s . decca , e. fischbach , g.l . klimchitskaya , d.e . krause , d. lpez , u. mohideen and v.m . mostepanenko , phys . a * 79 * , 026101 ( 2009 ) ; s. de man , k. heeck and d. iannuzzi , phys . a * 79 * , 024102 ( 2009 ) . lukatsky , s.a . safran , a.w.c . lau and p.a . pincus , europhys . lett . * 58 * , 785 ( 2002 ) . henle , c.d . santangelo , d.m . patel and p.a . pincus , europhys . lett . * 66 * , 284 ( 2004 ) . w. pezeshkian , n. nikoofard , d. norouzi , f. mohammad - rafiee and h. fazli , phys . e * 85 * , 061925 ( 2012 ) .

we study the distribution of multivalent counterions next to a dielectric slab , bearing a quenched , random distribution of charges on one of its solution interfaces , with a given mean and variance , both in the absence and in the presence of a bathing monovalent salt solution . we use the previously derived approach based on the _ dressed multivalent - ion theory _ that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework . the presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the density of multivalent counterions in its vicinity . in the counterion - only model ( with no monovalent salt ions ) , the surface disorder generates an additional logarithmic attraction potential and thus an algebraically singular counterion density profile at the surface . overall , the presence of quenched surface charge disorder leads to sizable effects in the distribution of multivalent counterions in a wide range of realistic parameters and typically within a distance of a few nanometers from the charged surface .

we study the distribution of multivalent counterions next to a dielectric slab , bearing a quenched , random distribution of charges on one of its solution interfaces , with a given mean and variance , both in the absence and in the presence of a bathing monovalent salt solution . we use the previously derived approach based on the _ dressed multivalent - ion theory _ that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework . the presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the density of multivalent counterions in its vicinity . in the counterion - only model ( with no monovalent salt ions ) , the surface disorder generates an additional logarithmic attraction potential and thus an algebraically singular counterion density profile at the surface . this behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact - value theorem , reflecting the _ anti - fragility _ effects of the disorder that drive the system towards a more ` ordered ' state . in the presence of an interfacial dielectric discontinuity , depleting the counterion layer at the surface , the charge disorder still generates a much enhanced counterion density further away from the surface . likewise , the charge inversion and/or overcharging of the surface occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder . overall , the presence of quenched surface charge disorder leads to sizable effects in the distribution of multivalent counterions in a wide range of realistic parameters and typically within a distance of a few nanometers from the charged surface .

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reaction rates controlled by collisions between diffusing particles depend on the distribution of distances between particles as well as on the density of particles . in particular , as noyes stated in 1961 _ any rigorous treatment of chemical kinetics in solution must consider concentration gradients that are established by the existence of the reaction itself _ " . @xcite here , we study the dynamics of point particles in one dimension , nucleated at random positions and times , then diffusing until colliding with and annihilating another particle . competition between nucleation and annihilation produces a statistically steady state with a well - defined mean density of particles and distribution of distances between particles . we shall contrast two types of nucleation : _ unpaired _ , in which particles are deposited at random locations at random times , and _ paired _ , in which _ pairs _ of particles are deposited at random locations . the dynamics is as follows : 1 . particles are nucleated in pairs with initial separation @xmath0 ; 2 . nucleation occurs at random times and positions with rate @xmath1 ; 3 . once born , all particles diffuse independently with diffusivity @xmath2 ; and 4 . particles annihilate on collision . a portion of a typical realization of these dynamics is shown in fig . [ spacetime ] . for unpaired nucleation ( i ) and ( ii ) are replaced by 1 . particles are nucleated at random times and positions with rate @xmath3 . = 4.0 in an existing method of analysis , based on a truncated hierarchy of correlation functions , is developed and extended in this article to the case of paired nucleation , yielding expressions for the correlation functions in the steady state , and for the time scales for relaxation towards the steady state . we also introduce a different method of analysis that yields an _ exact _ explicit expression for the steady - state density and for the time dependence of the density starting from arbitrary initial conditions . our analytical predictions are compared with the results of direct numerical simulations . in the simulations , large numbers of diffusing particles are simultaneously evolved in continuous space , with annihilation whenever two paths cross and nucleation ( paired or unpaired ) at random times and positions . a striking difference between paired and unpaired nucleation is the scaling of the steady state density of particles , @xmath4 , with the nucleation rate : @xmath5 ( paired ) versus @xmath6 ( unpaired ) . here , we shall exhibit the crossover between these two cases in terms of the following dimensionless quantity : @xmath7 for @xmath8 , the dynamics described by ( i)(iv ) is equivalent to that described by ( i ) , ( iii)(iv ) with the replacement @xmath9 the paper is arranged as follows . in the remainder of this section we summarize published results for reaction - diffusion systems . in sec . [ vk ] we analyze the dynamics using a hierarchy of equations for particle density functions , called `` reduced distribution functions '' by van kampen @xcite . derivation of the reaction kernel leads to an exact relation between the density of particles and the derivative of the correlation function . we also explore the linear response to a perturbation away from the steady state to establish the time scales for relaxation . in sec . [ exact ] , by introducing a function that satisfies a closed linear partial differential equation , we present exact expressions for the steady - state density and for the time evolution of the density with arbitrary initial conditions . in particular , analytical results are presented describing the rapid initial annihilation that transforms an initially random distribution into one characterized by an effective repulsion between particles . analysis of diffusion - limited reaction dates back to m. von smoluchowski . his _ mathematische theorie der raschen koagulation _ @xcite considered reaction between diffusing particles resulting in merger , with the reaction taken to occur immediately whenever two particles are a distance @xmath10 apart . he introduced a diffusion equation for the density of particles relative to the position of a test particle and noted that the density is zero at all times at radius @xmath10 @xcite . for many years it was assumed that the final result of a complete calculation following the procedure outlined by smoluchowski would be an equation for the mean density of particles , @xmath11 , of the form @xcite @xmath12 where @xmath3 is the rate ( per unit length and time ) of appearance of new particles and @xmath13 is constant . this would imply , for the case _ without nucleation _ ( @xmath14 ) , that the density is proportional to @xmath15 for @xmath16 . however , arguments based on dimensional analysis and scaling show that this is not true in one dimension @xcite . in 1983 , torney and mcconnell studied this case and published an exact solution for the mean density as a function of time @xcite . starting from an initial random distribution of particles , they found @xmath17 in particular , @xmath18 for @xmath16 . a rederivation of the result of torney and mcconnell was provided by spouge @xcite , whose insight was that an annihilation process is equivalent to a coagulation process if coagulants made up of an even number of particles are considered as diffusing `` ghosts . '' derivations based on reflection principle @xcite and field theory @xcite methods have also been published . in discrete models of diffusion - limited reaction , diffusion is approximated by hopping between neighboring sites on a lattice . here , too , the density of particles without nucleation is proportional to @xmath19 for @xmath16 @xcite . moreover , with unpaired nucleation , the steady state density is proportional to the third power of the nucleation rate @xcite . this can be interpreted as evidence for a time - dependent rate constant @xmath13 in , or as requiring to be replaced by an equation of the form @xmath20 however , no polynomial equation for the density can describe both the steady state with nucleation and the long - time decay of the density without nucleation @xcite . an exact solution has been found in one dimension for a discrete coagulation model with one fixed source . the latter solution is related to the probability that a given spin in an ising chain with random initial conditions does not change its value before time @xmath21 @xcite . for discrete and continuous coagulation models , exact results are available not only for the density but also for the spectrum of relaxation rates , @xcite the distribution of interparticle distances , @xcite and correlation functions . @xcite they are obtained by considering the function @xmath22 , defined as the probability that an arbitrarily chosen segment of @xmath23 consecutive sites contains no particles , satisfying a closed kinetic equation . it has , however , not proven possible to extend this method to the case of annihilation on contact , because the function @xmath22 does not satisfy a closed equation @xcite . the `` coefficient of recombination '' of two particles initially close together was introduced in the study of subatomic particles @xcite . the relative motion of two diffusing particles is equivalent to a problem of brownian motion of one particle . @xcite a discrete model that corresponds to paired nucleation is the ising model , with nucleation at neighboring sites . its dynamics was studied analytically by glauber in 1963 @xcite ; the nucleation rate is proportional to the square of the steady state density for nucleation rates sufficiently small that excluded volume effects can be neglected @xcite . computer simulations of a discretized reaction - diffusion model @xmath24 , published in 1987 @xcite , contrasted the scalings of the steady state density according to whether nucleation occurred at random sites or in pairs at neighboring sites . in the latter case , the scaling @xmath25 was found . a different approach to diffusion - limited reaction was recently introduced in the context of kink dynamics in a stochastic partial differential equation ( pde ) @xcite . there , the dynamics was termed `` mesoscopic '' because it was an approximate model that ignored the internal structure of kinks and antikinks , treating them simply as particles that happen to be nucleated in pairs . the treatment was based on classifying particles according to whether they are annihilated in a collision with their nucleation partner ( recombination ) or with a different particle ( nonrecombinant annihilation ) . the steady - state density @xmath4 is related to the mean lifetime of a particle , @xmath26 , by @xmath27 the mean lifetime @xmath26 was estimated directly by averaging over the possible histories of a pair of particles born together . this approximate analysis yielded the estimate @xmath28 .

we study the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation ( creation of particles ) with constant probability per unit time and length . the nucleation rate is proportional to the square of the steady - state density . for unpaired nucleation , and for paired nucleation at sufficiently large initial separation , the nucleation rate is proportional to the cube of the steady - state density .

we study the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation ( creation of particles ) with constant probability per unit time and length . the cases of nucleation of single particles and nucleation in pairs are considered . a new method of analysis permits exact calculation of the steady - state density and its time evolution in terms of the three parameters describing the microscopic dynamics : the nucleation rate , the initial separation of nucleated pairs , and the diffusivity of a particle . for paired nucleation at sufficiently small initial separation the nucleation rate is proportional to the square of the steady - state density . for unpaired nucleation , and for paired nucleation at sufficiently large initial separation , the nucleation rate is proportional to the cube of the steady - state density .

astro-ph0501131

i

binary stars play a fundamental role in the evolution of globular clusters for at least two important reasons . first , the evolution of stars in binaries , whether in a cluster or in the galactic field , can be very different from the evolution of the same stars in isolation . in a dense environment like a globular cluster , this difference is exacerbated by dynamical encounters , which affect binaries much more than single stars . second , binary stars crucially affect the dynamical evolution of globular clusters , providing ( through inelastic collisions ) the source of energy that supports them against gravothermal collapse @xcite . in the `` binary burning '' phase , a cluster can remain in quasi - thermal equilibrium with nearly constant core density and velocity dispersion for many relaxation times , in a similar way to that in which a star can maintain itself in thermal equilibrium for many kelvin - helmholtz times by burning hydrogen in its core . the binary fraction ( and the initial , primordial binary fraction in particular ) , is therefore one of the most important parameters that determine the evolution of globular clusters . however , most previous dynamical studies of globular clusters even those including binaries have neglected stellar evolution , which can significantly impact the properties and survival of binaries and hence the reservoir of energy they provide . at present , there are very few direct measurements of binary fractions in clusters . however , even early observations showed that binary fractions in globular cluster cores are smaller than in the solar neighborhood ( e.g. , * ? ? ? * ) . recent hubble space telescope ( hst ) observations have provided further constraints on the binary fractions in many globular clusters @xcite . the measured binary fractions in dense cluster cores are found to be _ very small_. as an example , the upper limit on the core binary fraction of ngc 6397 is only 5 - 7% @xcite . on the other hand , in very sparse clusters , like ngc 288 @xcite , but also in some other `` core - collapsed '' clusters , like ngc 6752 @xcite , the upper limit for the binary fraction can be as high as @xmath1 . for the _ initial _ binary fraction in globular clusters , there are of course no direct measurements . however , there are no observational or theoretical arguments suggesting that the formation of binaries and hierarchical multiples in dense stellar systems should be significantly different from other environments like open clusters , the galactic field , or star - forming regions . binary frequencies @xmath2 are found in the solar neighborhood and in open clusters . t tauri stars also have a very high binary fraction @xcite . for the range of separations between 120 and 1800 au , their binary fraction is comparable to that of main sequence stars in the solar neighborhood , while at shorter periods it is higher . furthermore , many stars are formed in systems of multiplicity 3 or higher : in the field their abundance is no less than 40% for inner periods @xmath3 days @xcite . all this suggests that , in dense stellar systems as well , most stars could be formed in binary and multiple configurations . most dynamical interactions in dense cluster cores tend to _ destroy _ binaries ( the possible exception is tidal capture , which may form binaries , but turns out to play a negligible role ; see 5.2 ) . soft binaries ( with orbital speeds lower than the cluster velocity dispersion ) can be disrupted easily by any strong encounter with another passing star or binary . even hard binaries can be destroyed in resonant binary binary encounters , which typically eject two single stars and leave only one binary remaining @xcite , or produce physical stellar collisions and mergers @xcite . in addition , many binary stellar evolution processes lead to disruptions ( e.g. , following a supernova explosion of one of the stars ) or mergers ( e.g. , following a common envelope phase ) . these evolutionary destruction processes can also be enhanced by dynamics . for example , more common envelope systems form as a result of exchange interactions @xcite , and the orbital shrinkage and the development of high eccentricities through hardening encounters may lead to the coalescence of binary components @xcite . it is therefore natural to ask whether the small binary fractions measured in old globular clusters today result from these many destruction processes , and what the _ initial binary fraction _ must have been to explain the current numbers . we address these questions in this paper by performing calculations that combine binary star evolution with a treatment of dynamical interactions in dense cluster cores . in 3 we describe in detail the method we use , following a brief overview of the theoretical background in 2 . we test our simplified dynamical model by comparing it against full monte carlo @xmath0-body simulations in 4.1 . in 4.2 we use semi - analytical estimates to predict the upper limit for the final binary fraction in dense clusters . in 4.3 we estimate the lower limit for the final binary fraction and analyse which mechanisms of binary destruction are most efficient as a function of cluster age . in 5 we present our numerical results for the evolution of the binary fraction in dense cluster cores , and we compare these results with observations . in particular , using our theoretically predicted period distribution , we re - examine observations of 47 tuc and re - derive constraints on the core binary fraction . in the final discussion ( 6 ) , we point out how our results may be helpful in interpreting observations of core binary fractions in other clusters , and we discuss the required initial conditions for simulations of clusters with binaries , as well as which methods are best suited for these simulations .

the _ maximum _ binary fraction today in the core of a typical dense cluster like 47 tuc , assuming an initial binary fraction of 100% , is only about 510% . binaries : close binaries : general methods :-body simulations globular clusters : general globular cluster : individual ( ngc 104 , 47 tucanae ) stellar dynamics .

we study the evolution of binary stars in globular clusters using a new monte carlo approach combining a population synthesis code ( startrack ) , and a simple treatment of dynamical interactions in the dense cluster core using a new tool for computing 3-body and 4-body interactions ( fewbody ) . we find that the combination of stellar evolution and dynamical interactions ( binary single and binary binary ) leads to a rapid depletion of the binary population in the cluster core . the _ maximum _ binary fraction today in the core of a typical dense cluster like 47 tuc , assuming an initial binary fraction of 100% , is only about 510% . we show that this is in good agreement with recent _ hst _ observations of close binaries in the core of 47 tuc , provided that a realistic distribution of binary periods is used to interpret the results . our findings also have important consequences for the dynamical modeling of globular clusters , suggesting that `` realistic models '' should incorporate much larger initial binary fractions than has usually been done in the past . [ firstpage ] binaries : close binaries : general methods :-body simulations globular clusters : general globular cluster : individual ( ngc 104 , 47 tucanae ) stellar dynamics .

0901.0699

i

we study a directed polymer model introduced by huse and henley ( in dimension @xmath0 ) @xcite with the purpose of investigating impurity - induced domain - wall roughening in the 2d - ising model . the first mathematical study of directed polymers in random environment was made by imbrie and spencer @xcite , and was followed by numerous authors @xcite ( for a review on the subject see @xcite ) . directed polymers in random environment model , in particular , polymer chains in a solution with impurities . in our set up the polymer chain is the graph @xmath2 of a nearest neighbor path in @xmath3 , @xmath4 starting from zero . the equilibrium behavior of this chain is described by a measure on the set of paths : the impurities enter the definition of the measure as _ disordered potentials _ , given by a typical realization of a field of i.i.d . random variables @xmath5 ( with associated law @xmath6 ) . the polymer chain will tend to be attracted by larger values of the environment and repelled by smaller ones . more precisely , we define the hamiltonian @xmath7 we denote by @xmath8 the law of the simple symmetric random walk on @xmath3 starting at @xmath9 ( in the sequel @xmath10 , respectively @xmath11 , will denote the expectation with respect to @xmath8 , respectively q ) . one defines the polymer measure of order @xmath12 at inverse temperature @xmath13 as @xmath14 where @xmath15 is the normalization factor which makes @xmath16 a probability measure @xmath17 we call @xmath15 the _ partition function _ of the system . in the sequel , we will consider the case of @xmath18 with zero mean and unit variance and such that there exists @xmath19 $ ] such that @xmath20 finite exponential moments are required to guarantee that @xmath21 . the model can be defined and it is of interest also with environments with heavier tails ( see e.g. @xcite ) but we will not consider these cases here . in order to understand the role of disorder in the behavior of @xmath16 , as @xmath12 becomes large , let us observe that , when @xmath22 , @xmath16 is the law of the simple random walk , so that we know that , properly rescaled , the polymer chain will look like the graph of a @xmath23-dimensional brownian motion . the main questions that arise for our model for @xmath24 are whether or not the presence of disorder breaks the diffusive behavior of the chain for large @xmath12 , and how the polymer measure looks like when diffusivity does not hold . many authors have studied diffusivity in polymer models : in @xcite , bolthausen remarked that the renormalized partition function @xmath25 has a martingale property and proved the following zero - one law : @xmath26 a series of paper @xcite lead to @xmath27 and a consensus in saying that this implication is an equivalence . for this reason , it is natural and it has become customary to say that _ weak disorder _ holds when @xmath28 converges to some non - degenerate limit and that _ strong disorder _ holds when @xmath28 tends to zero . carmona and hu @xcite and comets , shiga and yoshida @xcite proved that strong disorder holds for all @xmath13 in dimension @xmath29 and @xmath30 . the result was completed by comets and yoshida @xcite : we summarize it here [ strdis ] there exists a critical value @xmath31 $ ] ( depending of the law of the environment ) such that * weak disorder holds when @xmath32 . * strong disorder holds when @xmath33 . moreover : @xmath34 \text { for } d\ge 3 . \end{split}\ ] ] we mention also that the case @xmath35 can only occur when the random variable @xmath36 is bounded . in @xcite and @xcite a characterization of strong disorder has been obtained in term of localization of the polymer chain : we cite the following result ( * ? ? ? * theorem 2.1 ) if @xmath37 and @xmath38 are two i.i.d . polymer chains , we have @xmath39 moreover if @xmath40 there exists a constant @xmath41 ( depending on @xmath13 and the law of the environment ) such that for @xmath42 one can notice that has a very strong meaning in term of trajectory localization when @xmath28 decays exponentially : it implies that two independent polymer chains tend to share the same endpoint with positive probability . for this reason we introduce now the notion of free energy , we refer to ( * ? ? ? * proposition 2.5 ) and ( * ? ? ? * theorem 3.2 ) for the following result : the quantity @xmath43 exists @xmath6-a.s . , it is non - positive and non - random . we call it the _ free energy _ of the model , and we have @xmath44 moreover @xmath45 is non - increasing in @xmath13 . we stress that the inequality @xmath46 is the standard _ annealing _ bound . in view on , it is natural to say that _ very strong disorder _ holds whenever @xmath47 . one can moreover define @xmath48 the critical value of @xmath13 for the free energy i.e. : @xmath49 let us stress that , from the physicists viewpoint , @xmath48 is the natural critical point because it is a point of non - analyticity of the free energy ( at least if @xmath50 ) . in view of this definition , we obviously have @xmath51 . it is widely believed that @xmath52 , i.e. that there exists no intermediate phase where we have _ strong disorder _ but not _ very strong disorder_. however , this is a challenging question : comets and vargas @xcite answered it in dimension @xmath0 by proving that @xmath53 . in this paper , we make their result more precise . moreover we prove that @xmath54 . the first aim of this paper is to sharpen the result of comets and vargas on the @xmath0-dimensional case . in fact , we are going to give a precise statement on the behavior of @xmath45 for small @xmath13 . our result is the following [ pasgaussi ] when @xmath55 and the environment satisfies , there exist constants @xmath41 and @xmath56 ( depending on the distribution of the environment ) such that for all @xmath57 we have @xmath58 \le p({\beta})\le -c { \beta}^4.\ ] ] we believe that the logarithmic factor in the lower bound is an artifact of the method . in fact , by using replica - coupling , we have been able to get rid of it in the gaussian case . [ gaussi ] when @xmath55 and the environment is gaussian , there exists a constant @xmath41 such that for all @xmath59 . @xmath60 these estimates concerning the free energy give us some idea of the behavior of @xmath16 for small @xmath13 . indeed , carmona and hu in ( * ? ? ? * section 7 ) proved a relation between @xmath45 and the overlap ( although their notation differs from ours ) . this relation together with our estimates for @xmath45 suggests that , for low @xmath13 , the asymptotic contact fraction between independent polymers @xmath61 behaves like @xmath62 . the second result we present is that @xmath54 . as for the @xmath0-dimensional case , our approach yields an explicit bound on @xmath45 for @xmath13 close to zero . [ 1 + 2uplb ] when @xmath63 , there exist constants @xmath41 and @xmath64 such that for all @xmath65 , @xmath66 so that @xmath67 and @xmath9 is a point of non - analyticity for @xmath45 . after the appearance of this paper as a preprint , the proof of the above result has been adapted by bertin @xcite to prove the exponential decay of the partition function for _ linear stochastic evolution _ in dimension @xmath30 , a model that is a slight generalisation of directed polymer in random environment . unlike in the one dimensional case , the two bounds on the free energy provided by our methods do not match . we believe that the second moment method , that gives the lower bound is quite sharp and gives the right order of magnitude for @xmath68 . the method developped in @xcite to sharpen the estimate on the critical point shift for pinning models at marginality adapted to the context of directed polymer should be able to improve the result , getting @xmath69 for all @xmath59 for any @xmath70 . the various techniques we use have been inspired by ideas used successfully for another polymer model , namely the polymer pinning on a defect line ( see @xcite ) . however the ideas we use to establish lower bounds differ sensibly from the ones leading to the upper bounds . for this reason , we present first the proofs of the upper bound results in section [ rough ] , [ onedim ] and [ twodim ] . the lower bound results are proven in section [ lb11 ] , [ dim11 ] and [ dim12 ] . to prove the lower bound results , we use a technique that combines the so - called _ fractional moment method _ and change of measure . this approach has been first used for pinning model in @xcite and it has been refined since in @xcite . in section [ rough ] , we prove a non - optimal upper bound for the free energy in the case of gaussian environment in dimension @xmath0 to introduce the reader to this method . in section [ onedim ] we prove the optimal upper bound for arbitrary environment in dimension @xmath0 , and in section [ twodim ] we prove our upper bound for the free energy in dimension @xmath1 which implies that _ very strong disorder _ holds for all @xmath13 . these sections are placed in increasing order of technical complexity , and therefore , should be read in that order . concerning the lower bounds proofs : section [ lb11 ] presents a proof of the lower bound of theorem [ pasgaussi ] . the proof combines the second moment method and a directed percolation argument . in section [ dim11 ] the optimal bound is proven for gaussian environment , with a specific gaussian approach similar to what is done in @xcite . in section [ dim12 ] we prove the lower bound for arbitrary environment in dimension @xmath1 . these three parts are completely independent of each other .

we study the free energy of the directed polymer in random environment model in dimension and . for dimension one + 2000 _ mathematics subject classification : 82d60 , 60k37 , 82b44 _ + + _ keywords : free energy , directed polymer , strong disorder , localization , fractional moment estimates , quenched disorder , coarse graining . _

we study the free energy of the directed polymer in random environment model in dimension and . for dimension one , we improve the statement of comets and vargas in concerning very strong disorder by giving sharp estimates on the free energy at high temperature . in dimension two , we prove that very strong disorder holds at all temperatures , thus solving a long standing conjecture in the field . + 2000 _ mathematics subject classification : 82d60 , 60k37 , 82b44 _ + + _ keywords : free energy , directed polymer , strong disorder , localization , fractional moment estimates , quenched disorder , coarse graining . _

0804.0803

i

the spectrum of an unobscured , radio - quiet ( rq ) agn in the energy band is best characterized by a single power - law continuum of the form @xmath8 , where @xmath2 , hereafter the photon index in the energy band , typically lies in the range @xmath71.52.5 . a corona of hot electrons is assumed to produce the hard- emission via compton upscattering of uv soft- photons from the accretion disk , and @xmath2 is predicted to be only weakly sensitive to large changes in the electron temperature and the optical depth in the corona ( e.g. , haardt & maraschi 1991 ; zdziarski et al . 2000 ; kawaguchi et al . 2001 ) . the relatively narrow range of @xmath2 values in rq agns has been reported in numerous studies ( e.g. , nandra & pounds 1994 , reeves & turner 2000 ; page et al . 2005 ; shemmer et al . 2005 ; vignali et al . 2005 ; just et al . 2007 ) , and typically no strong dependence of @xmath2 on redshift or luminosity has been detected across the widest possible ranges of these parameters . on the other hand , a strong anticorrelation between @xmath2 and the full width at half - maximum intensity ( fwhm ) of the broad emission - line region ( belr ) component of h@xmath9 has been found , first by brandt et al . ( 1997 ) . the remarkable dependence between and optical spectroscopic properties has been suggested to arise from a more fundamental correlation between @xmath2 and the accretion rate ( e.g. , brandt & boller 1998 ; laor 2000 ) . a high accretion rate is expected to soften ( steepen ) the hard- spectrum by increasing the level of disk emission , resulting in the production of softer photons , which increase the compton cooling of the corona . using recent scaling relations for the belr size , luminosity , and the width of the broad h@xmath9 emission line from reverberation - mapping studies , it is clear that the normalized accretion rate ( i.e. , @xmath10/@xmath11 , hereafter @xmath1 , where @xmath10 is the bolometric luminosity ) is proportional to fwhm(h@xmath9)@xmath12 , at least for low moderate luminosity agns in the local universe ( e.g. , kaspi et al . 2000 ) . subsequent studies of nearby ( @xmath130.5 ) unobscured rq agns have confirmed the brandt et al . ( 1997 ) anticorrelation ( e.g. , leighly 1999 ; reeves & turner 2000 ; porquet et al . 2004 ; piconcelli et al . 2005 ; brocksopp et al . 2006 ) , and others have found significant correlations between @xmath2 and @xmath1 ( e.g. , lu & yu 1999 ; porquet et al . 2004 ; wang et al . 2004 ; bian 2005 ) . however , all these studies were not able to disentangle the strong dependence . recently , shemmer et al . ( 2006 ; hereafter s06 ) have suggested that this degeneracy can be removed if highly luminous sources are included in the analysis . this can be achieved by obtaining high - quality near - ir spectroscopy of the h@xmath9spectral region , to obtain @xmath1 ( e.g. , shemmer et al . 2004 ) , as well as accurate measurements of @xmath2 using and _ chandra _ for highly luminous agns found at 1@xmath133 . within the limits of their sample of 30 sources , spanning three orders of magnitude in luminosity , s06 have shown that @xmath2 does not depend on luminosity or black - hole ( bh ) mass ( @xmath4 ) . they have also shown that the @xmath2 values of the five highly luminous sources in their sample , while consistent with the values expected from their normalized accretion rates ( @xmath1 ) , are significantly higher than expected from the widths of their broad h@xmath9 emission lines . this has enabled , for the first time , breaking of the fwhm(h@xmath9)-@xmath1degeneracy and has provided evidence that @xmath2 depends primarily on the accretion rate . however , the number of highly luminous sources was small , and as explained below , some uncertainties remained . in this work , we double the number of highly luminous sources at high redshift and reinforce the s06 results . we show that @xmath2 can be considered a reliable accretion - rate indicator for moderate high luminosity rq agns , and that the combination of @xmath2 and luminosity may provide a useful probe for tracing the history of bh growth in the universe . we also discuss the spectral and temporal properties of luminous , high - accretion rate agns at high redshift as well as the dependence of the optical spectral energy distribution ( sed ) on luminosity and @xmath1 . in [ sec_observations ] we describe our sample selection , and present the new observations and their analysis . our results are presented and discussed in [ sec_results ] , where we focus on the correlation between the hard- photon index and the normalized accretion rate in rq agns and its implications for probing bh growth in the universe . a summary of our main findings is given in [ sec_conclusions ] . throughout this work we consider only rq agns to avoid any contribution from jet - related emission to the spectra . luminosity distances are computed using the standard cosmological model with @xmath14 , @xmath15 , and @xmath16 ^ -1 km s@xmath17mpc@xmath17 .

we study the hard- spectral properties of ten highly luminous radio - quiet ( rq ) active galactic nuclei ( agns ) at , including new observations of four of these sources . we find a significant correlation between the normalized accretion rate ( ) and the hard- photon index ( ) for 35 moderate high luminosity rq agns including our ten highly luminous sources . within the limits of our sample , this may provide a useful probe for tracing the history of bh growth in the universe , utilizing samples of -selected agns for which and have not yet been determined systematically . it may prove to be a useful way to probe bh growth in distant compton - thin type 2 agns .

we study the hard- spectral properties of ten highly luminous radio - quiet ( rq ) active galactic nuclei ( agns ) at , including new observations of four of these sources . we find a significant correlation between the normalized accretion rate ( ) and the hard- photon index ( ) for 35 moderate high luminosity rq agns including our ten highly luminous sources . within the limits of our sample , we show that a measurement of and can provide an estimate of and black - hole ( bh ) mass ( ) with a mean uncertainty of a factor of 3 on the predicted values of these properties . this may provide a useful probe for tracing the history of bh growth in the universe , utilizing samples of -selected agns for which and have not yet been determined systematically . it may prove to be a useful way to probe bh growth in distant compton - thin type 2 agns . we also find that the optical spectral slope ( ) depends primarily on optical uv luminosity rather than on in a sample of rq agns spanning five orders of magnitude in luminosity and over two orders of magnitude in . we detect a significant compton - reflection continuum in two of our highly luminous sources , and in the stacked spectrum of seven other sources with similar luminosities , we obtain a mean relative compton reflection of and an upper limit on the rest - frame equivalent width of a neutral line of 105ev . we do not detect a significant steepening of the power - law spectrum below rest - frame 2kev in any of our highly luminous sources , suggesting that a soft - excess feature , commonly observed in local agns , either does not depend strongly on , or is not accessible at high redshifts using current detectors . none of our highly luminous sources displays flux variations on timescales ofhr , supporting the idea that the timescale of variability depends inversely on and does not depend on .

0804.0803

c

we present spectroscopy for five highly luminous rq agns at @xmath0 , with accurate fwhm(h@xmath9 ) measurements that allow determinations of their @xmath4 and @xmath1 values . analysis of the spectra provided measurements of the hard- photon index in the rest - frame 2kev band and @xmath5 . we have combined these data with the s06 sample of 30 moderate high luminosity sources with similar properties , while doubling the number of highly luminous sources in their sample . our main goal was to test the s06 claim that @xmath2 can serve as an accretion - rate indicator in rq agns . we have also tested whether any additional properties of our highly luminous sources depend on @xmath1 . our main results are summarized as follows : 1 . our new highly luminous sources with fwhm(h@xmath9 ) measurements have allowed us to break the degeneracy between the dependence of @xmath2 on fwhm(h@xmath9 ) and on @xmath1 , suggesting that the accretion rate largely determines the hard- spectral slope across four orders of magnitude in agn luminosity ( i.e. , @xmath169 { \raisebox{-.5ex}{$\;\stackrel{<}{\sim}\;$}}48 $ ] ) . 2 . we found a significant correlation between @xmath1 and @xmath2 with a best - fit line of the form @xmath170 , and an acceptable uncertainty of a factor of 3 on a predicted value of @xmath1 . 3 . utilizing a sample of 91 sources from steffen et al . ( 2006 ) and this work , we find that @xmath5 depends strongly on optical uv luminosity and only weakly on @xmath1 ; the ( weak ) correlation with @xmath1 is probably due to the strong dependence . we discuss possible explanations for this result including the possibility that @xmath5 can not be used as an accretion - rate indicator based on its current definition . we find a significant compton - reflection feature in two of our sources , and the mean relative reflection for seven other sources is @xmath171 . by setting rather loose constraints on the strengths of emission lines in our highly luminous sources , we can neither confirm nor rule out a suggested anticorrelation between ew ( ) and either luminosity or @xmath1 ; the upper limit on the mean rest - frame ew ( ) for seven of these sources that do not show compton - reflection features is 105ev . we have not detected any signature of a soft - excess component in any of our highly luminous sources , including two sources at @xmath172 where our rest - frame coverage extends to @xmath75kev , suggesting that the soft excess does not depend strongly on the accretion rate . although one of our highly luminous sources , lbqs0109@xmath210213 , exhibits long - term ( i.e. , on timescales of years ) variations , rapid variations on timescales of @xmath71hr have not been detected in any of our highly luminous ( and high-@xmath4 ) sources , supporting the idea that variability timescale depends inversely on @xmath4 and does not depend on @xmath1 . the strong correlation between @xmath2 and @xmath1 may serve as a useful probe for tracing the history of bh growth in the universe . it may provide @xmath1 and @xmath4 estimates for -selected agns , with the possibility of estimating these properties for compton - thin type2 agns for the first time . this work is based on observations obtained with , an esa science mission with instruments and contributions directly funded by esa member states and the usa ( nasa ) . we thank an anonymous referee for a helpful report that assisted in improving the presentation of this work . we are also grateful to franz bauer , george chartas , brandon kelly , and aaron steffen for useful comments and fruitful discussions . we gratefully acknowledge the financial support of nasa grants and ( o.s , w.n.b ) , nasa ltsa grant ( o.s , w.n.b ) , and the zeff fellowship at the technion ( s.k ) . this work is supported by the israel science foundation grant 232/03 .

we show that a measurement of and can provide an estimate of and black - hole ( bh ) mass ( ) with a mean uncertainty of a factor of 3 on the predicted values of these properties . we detect a significant compton - reflection continuum in two of our highly luminous sources , and in the stacked spectrum of seven other sources with similar luminosities , we obtain a mean relative compton reflection of and an upper limit on the rest - frame equivalent width of a neutral line of 105ev . we do not detect a significant steepening of the power - law spectrum below rest - frame 2kev in any of our highly luminous sources , suggesting that a soft - excess feature , commonly observed in local agns , either does not depend strongly on , or is not accessible at high redshifts using current detectors . none of our highly luminous sources displays flux variations on timescales ofhr , supporting the idea that the timescale of variability depends inversely on and does not depend on .

we study the hard- spectral properties of ten highly luminous radio - quiet ( rq ) active galactic nuclei ( agns ) at , including new observations of four of these sources . we find a significant correlation between the normalized accretion rate ( ) and the hard- photon index ( ) for 35 moderate high luminosity rq agns including our ten highly luminous sources . within the limits of our sample , we show that a measurement of and can provide an estimate of and black - hole ( bh ) mass ( ) with a mean uncertainty of a factor of 3 on the predicted values of these properties . this may provide a useful probe for tracing the history of bh growth in the universe , utilizing samples of -selected agns for which and have not yet been determined systematically . it may prove to be a useful way to probe bh growth in distant compton - thin type 2 agns . we also find that the optical spectral slope ( ) depends primarily on optical uv luminosity rather than on in a sample of rq agns spanning five orders of magnitude in luminosity and over two orders of magnitude in . we detect a significant compton - reflection continuum in two of our highly luminous sources , and in the stacked spectrum of seven other sources with similar luminosities , we obtain a mean relative compton reflection of and an upper limit on the rest - frame equivalent width of a neutral line of 105ev . we do not detect a significant steepening of the power - law spectrum below rest - frame 2kev in any of our highly luminous sources , suggesting that a soft - excess feature , commonly observed in local agns , either does not depend strongly on , or is not accessible at high redshifts using current detectors . none of our highly luminous sources displays flux variations on timescales ofhr , supporting the idea that the timescale of variability depends inversely on and does not depend on .

0809.2314

i

under confinement in disordered mesoporous materials , the characteristic time scale for relaxation of a fluid can become extremely long . as a result , and although not always appreciated , equilibrium is often not attained and , accordingly , _ bona fide _ thermodynamic transitions such as the liquid - gas transition in one - component fluids or macroscopic phase separation in mixtures , are unobservable . `` capillary condensation '' in disordered solids is an out - of - equilibrium phenomenon , as illustrated by the irreversibility and hysteresis effects found in experiments . one typically observes a hysteresis loop that describes the isothermal evolution of the amount of fluid adsorbed in the porous solid as a function of the applied pressure , with branches that differ on adsorption ( filling ) and on desorption ( draining ) . this hysteresis loop appears rate - independent , and its size and shape vary with temperature as well as with the characteristics of the solid ( _ e.g. _ its porosity ) or those of the solid - fluid interaction potential . such a phenomenon is related to the existence of a large number of `` metastable states '' in which the system can be trapped on the experimental time scale ; evolution from one metastable state to another then only occurs as a result of the action of the applied pressure ( or equivalently , chemical potential ) and it proceeds through a sequence of irreversible cooperative condensation ( or evaporation ) events , generically denoted as `` avalanches''.@xcite the fact that the location and the shape of the hysteresis loop are reproducible in experiments indicates that the observation time is smaller than the time to reach the global equilibrium state , but is larger than local equilibration processes by which the system settles in one metastable state . as a result , the behavior of a fluid during filling or draining in disordered mesoporous materials can be rationalized by envisaging the evolution of the system in a free - energy landscape characterized by many local minima , _ i.e. _ metastable states.@xcite the above picture of gas adsorption in disordered porous media brings in a strong analogy with the out - of - equilibrium response of systems driven by an external force in the presence of impurities or other types of quenched disorder . this is for example the case of magnetization cycles in ferromagnetic materials when a magnetic field is ramped up and down and of hysteretic martensitic transformations in alloys;@xcite in both examples , avalanches can be detected through some `` crackling noise'',@xcite magnetic barkhausen noise in the former , acoustic emission in the latter . in such driven disordered systems , one expects the occurrence of out - of - equilibrium phase transitions as one changes , on top of the driving force , some external parameters such as the temperature or the characteristics of the intrinsic disorder ( _ e.g. _ the porosity in a porous solid).@xcite the branches of the hysteresis loop , in particular the adsorption and the desorption isotherms , may then display jumps ( discontinuities ) : indications for such behavior are for instance seen in the adsorption of helium in very light aerogels.@xcite such discontinuities and out - of - equilibrium phase transitions , however , are theoretically predicted on the basis of a grand - canonical set - up ( for gas adsorption ) in which the gas reservoir is infinite . in real experiments , the reservoir has a finite size which may not always be large enough for considering that the fluid inside the porous material is in a grand - canonical ensemble with fixed chemical potential . what should be expected in such situations ? the evolution of the system among metastable states may depend on the specific experimental set - up . as far as we know , there has been no systematic experimental study of the effect of changing the size of the gas reservoir ( relative to that of the porous medium ) and no estimate of the condition under which a grand - canonical situation is approximately reached . answering these questions is the primary goal of the present paper . the question of the dependence of the hysteretic response on the chosen control parameter has been a little more studied in other driven disordered systems . two extreme cases have been considered : the response of an extensive quantity to a change in the ( conjugate ) `` force '' and the response of an intensive quantity ( a force ) to a change in the conjugate extensive quantity ; the former is akin to the grand - canonical situation for a fluid in which the chemical potential ( or actually , the pressure in the gas reservoir ) is controlled and the latter to a canonical situation in which the number of adsorbed fluid molecules is controlled . examples of such studies are found in the context of martensitic transformations in which either stress or strain is controlled@xcite and in that of barkhausen noise in which either magnetic field or , via some feed - back mechanism , magnetization is controlled.@xcite in all cases , the loop obtained with the extensive variable as control parameter appears as reentrant when compared to that obtained with the force as control parameter . ( for a theoretical study , see ref . @xcite ) one anticipates that the influence of the relative size of the reservoir@xcite on the adsorption isotherms of a fluid in a disordered porous material is intimately connected to the organization of the metastable states in the adsorbed - density / chemical - potential plane . indeed , when the isotherms are smooth both on adsorption and on desorption , one may experimentally probe metastable states located inside the main hysteresis loop by studying ascending and descending `` scanning curves '' , which involve partial filling or draining.@xcite these curves lead to a variety of hysteretic subloops that provide direct evidence for the presence of metastable states inside the main loop.@xcite actually , metastable states are expected everywhere inside the latter . the situation is quite different , however , when the adsorption or the desorption branch displays a jump ( in a grand - canonical setting with a very large reservoir ) . a discontinuity prevents the realization of scanning curves in some portion of the isotherm . as a result , part of the interior of the main hysteresis loop is now inaccessible . in the present work we address the above questions , namely the effect of the relative size of the gas reservoir on the adsorption isotherms of a fluid in a disordered or inhomogeous porous solid and the connection to the distribution of metastable states inside the hysteresis loop . we show that even when the grand - canonical isotherms display discontinuous jumps , there are branches of metastable states inside the main hysteresis loop and that many of these states can be reached by varying the relative size of the reservoir , the smaller the reservoir the larger the extent to which the branches of metastable states are probed . in particular , the extent is maximal when the reservoir is so small that the fluid inside the porous solid behaves as in a canonical situation of fixed number of adsorbed molecules . when compared to the loop obtained for an infinite reservoir ( grand - canonical situation ) and plotted as the amount adsorbed versus the chemical potential , the hysteresis loop for a finite reservoir size then appears as reentrant . on the contrary , when the isotherms are smooth ( continuous ) , there is no influence of the size of the reservoir . the rest of the paper is organized as follows : in section ii , we introduce the two models that have been investigated and give some details on the methods used to compute the adsorption isotherms . we have considered : ( i ) an atomistic model of a fluid in simple , yet structured pore , whose adsorption isotherms are computed by molecular simulation , and ( ii ) a coarse - grained model for adsorption in a disordered mesoporous material , studied by a density functional approach in a local mean - field approximation . in both cases , the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied . the overall system composed of the sample plus the reservoir is taken in the canonical ensemble , with the total number of molecules as control parameter . in section iii , we present the results for the atomistic model . the simplicity of the system allows one to get a clear interpretation of the physical nature of the branches of metastable states , whose number is limited . the existence of metastable states is a direct consequence of the intrinsic inhomogeneity of the pore space . as the relative size of the gas reservoir is varied , we find that the exploration of the branches changes , the isotherm displaying larger jumps in the adsorbed density as the size increases . section iv is devoted to the coarse - grained model of a disordered porous material . the number of metastable states is now enormous , since it is likely to increase exponentially with the size of the sample . we find a drastic change of behavior between the `` strong - disorder '' regime for which the isotherm is continuous and the `` weak - disorder '' one for which the isotherm , here the adsorption isotherm on which we focus our study , displays a jump corresponding to a macroscopic avalanche . in the former regime , the isotherm does not display any dependence on the relative size of the reservoir whereas in the latter , it is reentrant for finite reservoir sizes , the more so as one decreases the reservoir size , and it shows increasing jumps in adsorbed density with increasing reservoir size . finally , we summarize our main results and give our conclusions in section v. in particular , we discuss the relevance of our study to experimental situations and we stress the important role of the intrinsic inhomogeneity induced by the solid matrix .

we study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids . we consider both an atomistic model of a fluid in a simple , yet structured pore , whose adsorption isotherms are computed by molecular simulation , and a coarse - grained model for adsorption in a disordered mesoporous material , studied by a density functional approach in a local mean - field approximation . in both cases , the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied , and the control parameter is the total number of molecules present in the porous sample and in the reservoir . varying the relative sizes of the reservoir and the sample may change the shape of the hysteretic isotherms , leading to a `` reentrant '' behavior compared to the grand - canonical isotherm when the latter displays a jump in density . we relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density .

we study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids . we consider both an atomistic model of a fluid in a simple , yet structured pore , whose adsorption isotherms are computed by molecular simulation , and a coarse - grained model for adsorption in a disordered mesoporous material , studied by a density functional approach in a local mean - field approximation . in both cases , the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied , and the control parameter is the total number of molecules present in the porous sample and in the reservoir . varying the relative sizes of the reservoir and the sample may change the shape of the hysteretic isotherms , leading to a `` reentrant '' behavior compared to the grand - canonical isotherm when the latter displays a jump in density . we relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density .

astro-ph9908099

i

galaxy interactions are likely to play a key role in determining the morphology and the structural properties of galaxies and in driving evolution at all epochs and in widely - varying environments . the importance of environmental conditions on the properties of populations of galaxies has been recognized for a long time ( hubble & humason 1931 ) and observational studies have now firmly established relationships between the relative abundance of galaxies of different morphological types and the density of the environment ( see e.g. dressler 1980 , dressler et al . 1997 ) , their location in clusters ( oemler 1974 ) as well as the evolution of the morphology of galaxies in clusters at different epochs ( butcher & oemler 1978 , 1984 ) . in particular , the ratio of early to late - type galaxies has been shown to be an increasing function of density and a decreasing function of the distance from the center of a cluster . in addition , hst observations show that the relative number of spirals to elliptical and s0 galaxies tend to increase in distant clusters , pointing to a time evolution of the morphology of galaxies from spirals to ellipticals ( see e.g. dressler et al . 1994a , 1994b , couch et al . 1998 ) . altogether , these results suggest that environmental disturbances due to interactions with other galaxies and with a cluster tidal field can lead to dramatic changes in the structure of galaxies . simulations have explored strong encounters and mergers . our recent work suggests that relatively weak encounters can give rise to significant asymmetries as well . to study weaker galaxy interactions and quantify their importance , we compute the response of a spherical stellar system to the perturbation induced by another system during a fly - by , focusing our attention on the morphology and the persistence of the distortions produced during the encounter . the range of orbital parameters considered encompasses the typical environmental conditions for field galaxies , for galaxies in groups and in clusters . our perturbative solution for these distortions provides quantitative and qualitative predictions in low to moderate amplitude that are difficult to reach by simulation . this approach nicely reveals the underlying dynamics without being masked or swamped by n - body fluctuation noise . on the other hand , numerical feasibility restricts the complexity of possible geometries and the perturbative assumption limits its validity for large amplitudes . our investigation is relevant for galactic dark halos or for spheroidal galaxies over a range of environments . we explore the possibility that the halo distortions produced during a fly - by could in turn lead to a significant and observable distortion in an embedded stellar disk ( see e.g. weinberg 1995 , 1998b , murali & tremaine 1998 , murali 1998 ) . in particular the deformations produced in a dark halo during an encounter could be one of the culprits for distorted morphologies like those observed in lopsided and warped galactic disks ( see e.g. richter & sancisi 1994 , zaritsky & rix 1997 , rudnick & rix 1998 , swaters et al . 1998 , haynes et al . 1998 , kornreich , haynes & lovelace 1998 ) . as recently shown by weinberg ( 1995 , 1998b ) , this could be the case for the milky way in which the deformations induced in the dark halo by the magellanic clouds could be responsible for the observed warp in the galactic disk . in a recent investigation , reshetnikov & combes ( 1998 , 1999 ) have found that about 40% of a sample of 540 galaxies have warped planes and their analysis revealed that warped galaxies tend to be located in denser environments supporting a scenario in which interactions would play an important role in the formation of warps . distortions of spheroidal galaxies are directly observable . our results show that in low velocity dispersion and dense environments , where low - velocity close encounters are more likely to occur , even low - mass perturbers can lead to significant asymmetries in the primary galaxy . recent morphological studies of both local and very distant galaxies have yielded comparisons of the frequencies of systems with distorted morphologies in different environments and at different distances ( see e.g. zepf & whitmore 1993 , mendes de oliveira & hickson 1994 , abraham et al . 1996a,1996b , van den bergh et al . 1996 , naim , ratnatunga & griffiths 1997 , brinchmann et al . 1998 , marleau & simard 1998 , conselice & bershady 1998 , conselice & gallagher 1999 ) . on the theoretical side , the efforts have been largely concentrated on numerical @xmath2-body simulations aimed at investigating the fate and the evolution of merging galaxies ( see e.g. barnes & hernquist 1992 , barnes 1998 and references therein ) and the distortions and the morphological alterations produced in galaxies in clusters and groups by the ensemble of `` tidal shocks '' with other members ( moore et al . 1996 , 1998 ) . this mechanism can drive the evolution of spiral galaxies into spheroidal systems and it is a strong candidate explanation for the difference in the relative number of spiral to elliptical galaxies in clusters at different redshifts . the plan of the paper is the following . in 2 we outline the method adopted for this investigation while the mathematical details are described in the appendix . in 3 we show the results obtained for initial conditions typical of galactic dark halos and their dependence on the orbital parameters of the perturber . in 4 initial conditions relevant for spheroidal galaxies and a survey of orbital parameters of the perturber typical of different environments are considered . overall , our results quantify the relationship between the interaction rate for the environment and the probability of observing irregular morphologies , aiding interpretation of any trend in the fraction of asymmetric galaxies at different redshifts . this latter aspect is of particular interest as data on the morphology of distant galaxies are now available from hst observations in the hubble deep field and in the medium deep survey projects ( abraham et al . 1996a , 1996b ) . in order to facilitate the comparison of our theoretical results with observational data , we will quantify the distortions produced by means of the asymmetry parameter @xmath0 ( abraham et al . 1996a ) which has been determined for a number of local and distant galaxies . we will also introduce a generalized asymmetry parameter @xmath1 which will provide an important information on the radial structure of the asymmetry produced by the mechanism we have considered and which will allow to test the theory presented here . the main conclusions are summarized and discussed in 5 .

we study the internal response of a galaxy to an unbound encounter and present a survey of orbital parameters covering typical encounters in different galactic environments . overall , we conclude that relatively weak encounters by low - mass interloping galaxies can cause observable distortions in the primaries any distortion produced in a dark halo can distort the embedded stellar disk , possibly leading to the formation of lopsided and warped disks . we find that high - density , low - velocity dispersion environments are more likely to host galaxies with significant asymmetries . finally , we propose a generalized asymmetry parameter which provides detailed information on the radial structure of the asymmetry produced by the mechanism explored in our work .

we study the internal response of a galaxy to an unbound encounter and present a survey of orbital parameters covering typical encounters in different galactic environments . overall , we conclude that relatively weak encounters by low - mass interloping galaxies can cause observable distortions in the primaries . the resulting asymmetries may persist long after the interloper is evident . we focus our attention on the production of structure in dark halos and in cluster ellipticals . any distortion produced in a dark halo can distort the embedded stellar disk , possibly leading to the formation of lopsided and warped disks . we show that distant encounters with pericenters in the outer regions of a halo can excite strong and persistent features in the inner regions . features excited in an elliptical are directly observable and we predict that asymmetries in the morphologies of these systems can be produced by relatively small perturbers . for example , a fly - by on an orbit with pericenter equal to the half - mass radius of the primary system and velocity of 200 km / s ( a value typical for groups ) can result in a significant dipole distortion for perturbers with mass as small as 5% of primary s mass . we use these detailed results to predict the distribution of the parameter defined by abraham et al . ( sensitive to lopsidedness ) and the shift between the center of mass of the primary system and the position of the peak of density for a range of environments . we find that high - density , low - velocity dispersion environments are more likely to host galaxies with significant asymmetries . our distribution for the parameter is in good agreement with the range spanned by the observed values for local galaxy clusters and for distant galaxies in the medium deep survey and in the hubble deep field . assuming that primordial galaxies were located in dense environments with previrialized low velocity dispersions , our conclusions are consistent with the observational results showing a systematic trend for galaxies at larger redshifts to be more asymmetric than local galaxies . finally , we propose a generalized asymmetry parameter which provides detailed information on the radial structure of the asymmetry produced by the mechanism explored in our work .

1507.00082

i

let @xmath2 be a convex closed smooth hyper - surface . we consider the following spherical radon transform @xmath3 of a function @xmath4 defined in @xmath5 @xmath6 here , @xmath7 is the sphere centered at @xmath8 of radius @xmath9 , and @xmath10 is its surface measure . this transform appears in several imaging modalities , such as thermo / photoacoustic tomography ( e.g. , @xcite ) , ultrasound imaging ( e.g. , @xcite ) , sonar ( e.g. , @xcite ) , and inverse elasticity ( e.g. , @xcite ) . for example , in thermo / photoacoustic tomography ( tat / pat ) , @xmath4 is the initial ultrasound pressure generated by the thermo / photo - elastic effect . it contains useful information about the inner structure of the tissue , which can be used , e.g. , for cancer detection . on the other hand , the knowledge of @xmath11 can be extracted from the ultrasound signals collected by a transducer located at @xmath12 , which is called the * observation * surface . one , therefore , can concentrate on finding @xmath4 given @xmath13 . the same problem also arises in other aforementioned image modalities . it is commonly assumed that @xmath4 is supported inside the bounded domain @xmath14 whose boundary is @xmath15 . let us discuss an inversion formula under this assumption . let @xmath16 be the pseudo - differential operator defined by @xmath17 and @xmath18 be the back - projection type operator @xmath19 when @xmath15 is an @xmath20-dimensional ellipsoid , one has the following inversion formula @xcite @xmath21 we note here that formula ( [ e : inversion ] ) was written in other forms in the above references . the above form , presented in @xcite , is convenient to analyze from the microlocal point of view . another advantage of the above form is that it can be implemented straight forwardly : 1 ) @xmath22 can be computed fast by using fast fourier transform ( fft ) and 2 ) @xmath23 only involves a simple integration on @xmath15 . [ fig : full - circle ] is the result of our implementation when @xmath24 and @xmath15 is the unit circle . the image size is @xmath25 pixels . the sampling data has the resolution of @xmath26 for the spatial ( angular ) variable @xmath27 and radial variable @xmath28 $ ] . the reconstruction is almost perfect . when @xmath15 is a general convex surface , the operator on the right hand side of ( [ e : inversion ] ) might not be the identity . however , it only differs from the identity by a compact operator ( see @xcite ) , which is a pseudo - differential operator of order @xmath29 ( as shown in @xcite ) . moreover , from the numerical experiments , we observe that @xmath30 and @xmath4 are very close , even when @xmath15 is not any ellipse / ellipsoid . for example , in fig . [ fig : full - polar ] we present the reconstruction using @xmath31 for @xmath15 being the polar curve defined by @xmath32 the reconstruction is almost perfect . in this article , we are interested in the limited data problem . that is , the knowledge of @xmath3 is only available on a closed proper subset @xmath33 with smooth boundary @xmath34 and nontrivial interior @xmath35 ( see , e.g. , @xcite ) . it is natural to consider the following formula @xmath36 where @xmath37 is the characteristic function of @xmath38 . as we observe from fig . [ fig : limited - cir ] , formula ( [ no_smoothing ] ) reconstructs some singularities and also smoothens out some singularities of the original image . moreover , it also creates some artifacts ( added singularities ) into the picture . more detailed discussion will be presented in sections [ s:2d ] and [ s:3d ] ( see also section [ s : num ] for numerical demonstrations ) . the operator @xmath39 reconstructs all the visible singularities . however , the artifacts it generates are quite strong . we now introduce a generalization of @xmath39 in order to reduce the artifacts . let us consider @xmath40 here , @xmath41 and @xmath42 on @xmath43 . moreover , we assume further that @xmath44 on the interior @xmath35 of @xmath38 and @xmath45 vanishes to order @xmath0 on the boundary @xmath34 . of course , @xmath46 if @xmath47 . in this article , we will study formula ( [ e : mt ] ) . namely , we will analyze which singularities are reconstructed and how strong the reconstructed singularities are , compared to the original ones . moreover , we will describe how the artifacts are generated by ( [ e : mt ] ) and how strong they are . let us discuss here the main idea of our analysis . we first follow the approach in @xcite to represent @xmath48 as an oscillatory integral . to that end , let @xmath49 be the schwartz kernel of @xmath48 . then , it can be written as ( see @xcite ) @xmath50 by the simple change of variables @xmath51 , @xmath52 here , @xmath53 are the intersections of @xmath15 with the positive and negative rays @xmath54 to illuminate the idea , let us at the moment assume that @xmath45 vanishes to * infinite * order at the boundary of @xmath55 , then the functions @xmath56 are ( smooth ) symbols of order zero . then , due to ( * ? ? ? * theorem 3.2.1 ) , @xmath48 is a pseudo - differential operator ( @xmath57do ) of order zero whose principal symbol is ( see @xcite , and also @xcite , for the same result in a more general framework ) : @xmath58.\ ] ] one important consequence of @xmath48 being a @xmath57do is that it does not generate the artifacts into the picture . moreover , let us denote @xmath59 , the line passing through @xmath60 along direction @xmath61 . then , the following discussions hold . * let us denote @xmath62 then , any singularities @xmath63 of @xmath4 in this zone generates a corresponding singularity of on the observed data @xmath64 . it is , therefore , called the * visible zone * ( see , e.g. , @xcite ) . let @xmath65 , then either @xmath66 or @xmath67 . therefore , @xmath68 . that is , @xmath48 is an elliptic pseudo - differential operator of order @xmath69 near @xmath63 . due to the standard theory of pseudo - differential operators ( see lemma [ l : pet ] ) , @xmath70 if and only if @xmath71 . that is , all the visible singularities of @xmath4 are reconstructed by @xmath48 with the correct order . we notice that one visible singularity may be either visible in two directions , when both @xmath72 and @xmath73 belong to @xmath35 , or in one direction , when only one of @xmath74 or @xmath73 belongs to @xmath38 . we will say that they are * doubly * visible and * singly * visible , respectively . * on the other hand , let us denote @xmath75 then , @xmath76 is called * invisible zone * , since any singularity of @xmath4 in this zone does not generate any singularity of @xmath77 . a singularity of @xmath4 in this zone is called * invisible*. we notice that for each @xmath78 , then @xmath79 . that is , the full symbol of @xmath49 is zero near @xmath63 . therefore , due to the standard theory of pseudo - differential operators , @xmath80 , even if @xmath81 . that is , all the invisible singularities are completely smoothen out by @xmath48 . let us now consider the case of our interest : @xmath45 only vanishes to a * finite * order @xmath0 on the boundary of @xmath82 ( @xmath0 can be zero as in case of @xmath39 ) . then , @xmath48 is not a @xmath57do anymore , since @xmath83 are not smooth . therefore , @xmath48 may generate artifacts into the picture , as shown fig . [ fig : limited - cir ] where @xmath46 . our results ( see sections [ s:2d ] and [ s:3d ] ) , show that the effect of @xmath48 on the zones @xmath84 and @xmath76 is exactly what we discuss above for the case of infinitely smooth @xmath45 . this can be seen from the facts that @xmath85 are smooth on these two zones . the artifacts , on the other hand , come from the * boundary zone * where at least one of @xmath86 or @xmath87 is non - smooth : @xmath88 we will characterize how these artifacts are generated and how strong they are . to that end , we will make use of the formula ( [ e : mu - ori ] ) . compared to ( [ e : mu ] ) , the formula ( [ e : mu - ori ] ) still keeps track of the geometric information of @xmath89 , which is helpful to understand the generation artifacts . moreover , we will study ( [ e : mu - ori ] ) as a fourier integral operator , whose order determines the strength of artifacts ( compared to the original singularity generating them ) . in term of geometric description of the artifacts , we will take advantage of the technique developed in @xcite ( see also @xcite ) . in @xcite , the third author studied the strength of the artifacts in @xmath15 is a hyperplane ( that is , @xmath38 is flat ) . in this article , we study the problem for any convex smooth surface @xmath15 . we will restrict ourselves to the two and three dimensional problems ( i.e. , @xmath90 ) , since they are the most practical ones . we will follow the microlocal analysis technique in @xcite . however , due to the generality of the geometry involved , the arguments are more sophisticated . moreover , for the three dimensional problem , we introduce a new idea of lifting up the space , which is simple but interesting . it is worth mentioning that similar problem has been studied for the x - ray ( or classical radon ) transform @xcite . the article is organized as follows . in section [ s:2d ] , we state and prove the main results for the two dimensional problem . in section [ s:3d ] , we state and prove the results for three dimensional problem . we then present some numerical experiments for the two dimensional problem in section [ s : num ] . finally , we recall some essential background in microlocally analysis in the appendix .

we study the limited data problem of the spherical radon transform in two and three dimensional spaces with general acquisition surfaces . in such situations , we explicitly analyze a family of such inversion formulas , depending on a smoothing function that vanishes to order on the boundary of the acquisition surfaces . our analysis for three dimensional space contains an important idea of lifting up a space .

we study the limited data problem of the spherical radon transform in two and three dimensional spaces with general acquisition surfaces . in such situations , it is known that the application of filtered - backprojection reconstruction formulas might generate added artifacts and degrade the quality of reconstructions . in this article , we explicitly analyze a family of such inversion formulas , depending on a smoothing function that vanishes to order on the boundary of the acquisition surfaces . we show that the artifacts are orders smoother than their generating singularity . moreover , in two dimensional space , if the generating singularity is conormal satisfying a generic condition then the artifacts are even orders smoother than the generating singularity . our analysis for three dimensional space contains an important idea of lifting up a space . we also explore the theoretical findings in a series of numerical experiments . our experiments show that a good choice of the smoothing function might lead to a significant improvement of reconstruction quality .

1212.6689

i

quasars are routinely used as background sources to study the gaseous phases of intervening objects via absorption - line diagnostics . these absorption lines have their origins both in _ intervening _ objects ( i.e. , foreground galaxies , inter - galactic medium ( igm ) , quasar host galaxies ) and in sources that are _ intrinsic _ to the quasars . one of the most promising candidates for the intrinsic absorbers is an outflowing wind from the accretion disk of quasar central engines . the outflow is accelerated by magnetocentrifugal forces @xcite , radiation pressure in lines and continuum @xcite , and/or by thermal pressure force ( e.g. , @xcite ) . the outflowing winds play an important role in three ways : 1 ) the extraction of angular momenta from disks allows accretions to proceed ( e.g. , @xcite ) , leading to growth of black holes , 2 ) the disk outflow also provides energy and momentum feedback to interstellar media of host galaxies and to intergalactic media ( igm ) , and inhibits star formation activity ( e.g. , @xcite ) , 3 ) outflowing winds may induce the metal enrichment of the igm ( e.g. , @xcite ) . thus , the physical conditions of the outflow not only promote the evolution of quasars themselves , but greatly impact the surrounding environments . among absorption lines , broad features ( hereafter , bals ; fwhm @xmath4 2000 ) are easily identified as being intrinsic , because it is almost impossible for foreground objects to produce very broad and smooth line profiles . bals are detected in about 10 20% of optically selected quasars ( e.g. , @xcite ) , and their detection rate is slightly higher in radio - quiet quasars ( e.g. , @xcite ) . bals are thought to originate in the outflowing winds when our sight - line intersects this component . this idea is supported by the fact that there are no significant differences in the properties of quasars with bals ( bal qsos ) and those without bals ( non - bal qsos ) @xcite . moreover , quasar spectra tend to be redder when bal profiles , especially those with low ionization absorption lines ( i.e. , lobals and felobals ) , are observed , which is probably caused by dust reddening in the outflows ( e.g. , @xcite ) . thus , quasars with and without bals may intrinsically be a single population , although the evolutionary phase of quasars could also affect the detection rate of bals ( e.g. , @xcite ) . the only difference is whether the sight - line passes through the outflowing wind or not in this orientation scheme . thus , bal qsos have traditionally been the best targets for the study of outflows ( e.g. , @xcite ) . in addition to bals , a fraction of narrow absorption lines ( hereafter nals ; fwhm @xmath5 500 ) and mini - bals ( an intermediate category between bals and nals ) have also been suggested to be physically associated with quasars . however , the origin of nals and mini - bals are still under debate . each of the above classes of absorption features could represent either different lines of sight through the outflowing wind to the quasar continuum source or different stages in the evolution of the absorbing gas parcels ( e.g. , @xcite ) . the observed fraction of optically - selected quasars hosting bals ( @xmath01020 ) and nals ( @xmath02050% ; e.g. , @xcite ) constrains the solid angle subtended by the dense portion of the wind to the central engine . however , such a statistical treatment requires the assumption that all quasars are identical . this remains an assumption because in past studies , it has only been possible to trace _ single _ sight - lines ( i.e. , probe a one dimension profile ) toward the nucleus of each quasar . gravitationally lensed images of background quasars are our only tools for the study of the three - dimensional geometry of the absorbers ( e.g. , @xcite ) . indeed , this technique has frequently been applied for investigating intervening absorption lines , produced by galaxies or igm on scales of up to several kilo - parsecs . however , these traditional quasar lenses are not useful for multi - angle studies of the agns themselves because their separation angles ( @xmath1 @xmath0 a few arcsec ) are too small to separate internal structures in the vicinity of the quasars . on the other hand , @xcite discovered a lensed quasar , sdss j1004 + 4112 , with a maximum image separation of @xmath1 @xmath0 14@xmath2.6 , which is the first example of a quasar lensed by a cluster of galaxies rather than a single massive galaxy . if there exists outflow gas at a distance of @xmath01 kpc from the continuum source as measured for some specific quasars @xcite , the large separation angle of sdss j1004 + 4112 translates into a physical distance of @xmath60.1 pc , with which we may trace outflowing winds with different physical properties unless their transverse sizes are much larger than sub - parsec scale . taking advantage of this large image separation , @xcite proposed that the differences in emission lines between the lensed images seen in their follow - up spectra can be explained by differential absorptions along each sight - line , although the spectra do not show explicit intrinsic absorption features . the second large - separation lensed quasar sdss j1029 + 2623 @xcite has an image separation of @xmath1 @xmath0 22@xmath2.5 , and therefore is the largest quasar lens currently known . @xcite identified the third image of this lens system ( see figure [ f1 ] ) . as shown in figure [ f2 ] , all the spectra of quasar images a , b , and c have absorption features on the blue side of the emission lines , which implies that each sight - line passes through the outflowing wind . in what follows , we call this feature `` the associated absorption line '' . moreover , we see a clear difference in the absorption features between image a and images b / c . the former has a broader and shallower profile and an additional redshifted absorption line at @xmath04990 , while the latter two have narrower and deeper profiles ( figure [ f2 ] ) . after correcting for magnification , the eddington ratio of the quasar is estimated to be @xmath7 @xmath0 0.11 . this value is consistent with the typical eddington ratio of bright quasars , @xmath7 @xmath0 0.07 1.6 @xcite . in this paper , we discuss the origin of these differential absorption profiles in sdss j1029 + 2623 . the likely scenarios include ( i ) time - variation of a single absorber covering both sight - lines toward the quasar between the time - delay of images a and b / c , which is @xmath0744 days in the observed frame according to monitoring observations by @xcite ( hereafter , * scenario i * ) , ( ii ) each sight - line penetrating different absorbers or different regions of a single absorber toward the quasar as proposed by @xcite ( * scenario ii * ) , and ( iii ) micro - lensing ( * scenario iii * ) . among these , the last scenario has been already rejected because each image shows common ratios between radio , optical , and x - ray fluxes @xcite , which is not expected for micro - lensing . thus we concentrate on the viability of scenarios i and ii , based on our medium- and high - resolution spectroscopic observations of sdss j1029 + 2623 . the structure of this paper is as follows . in 2 , we describe the observations and data reduction . we present results in 3 , and discuss the results in 4 . we summarize our results in 5 . we adopt @xmath8 as the emission redshift of the quasar , which was estimated using broad uv emission lines by @xcite . time intervals between observations are given in the observed frame throughout the paper , unless otherwise noted .

we study the origin of absorption features on the blue side of the broad emission line of the large - separation lensed quasar sdss j1029 + 2623 at.197 . the quasar images , produced by a foreground cluster of galaxies , have a maximum separation angle of 22.5 . the large angular separation suggests that the sight - lines to the quasar central source can go through different regions of outflowing winds from the accretion disk of the quasar , providing a unique opportunity to study the structure of outflows from the accretion disk , a key ingredient for the evolution of quasars as well as for galaxy formation and evolution .

we study the origin of absorption features on the blue side of the broad emission line of the large - separation lensed quasar sdss j1029 + 2623 at.197 . the quasar images , produced by a foreground cluster of galaxies , have a maximum separation angle of 22.5 . the large angular separation suggests that the sight - lines to the quasar central source can go through different regions of outflowing winds from the accretion disk of the quasar , providing a unique opportunity to study the structure of outflows from the accretion disk , a key ingredient for the evolution of quasars as well as for galaxy formation and evolution . based on medium- and high - resolution spectroscopy of the two brightest images conducted at the subaru telescope , we find that each image has different intrinsic levels of absorptions , which can be attributed either to variability of absorption features over the time delay between the lensed images , 744 days , or to the fine structure of quasar outflows probed by the multiple sight - lines toward the quasar . while both these scenarios are consistent with the current data , we argue that they can be distinguished with additional spectroscopic monitoring observations .

1212.6689

c

in this section , we discuss the origin ( i.e. , intrinsic or intervening ) of the associated absorption lines ( [ sec4.1 ] ) , possible geometries toward images a and b ( [ sec4.2 ] ) , and models of single / multiple sight - line(s ) ( [ sec4.3 ] ) , respectively . while bals have high probability of being physically associated to the quasars , nals are difficult to classify as intrinsic or intervening . with our high - resolution spectra , the associated absorption line is deblended into multiple narrow components . as for and doublets ( whose absorption features are clearly detected without being affected by any data defects or line blending ) , we measure their physical parameters by performing voigt profile fitting with minfit . we have several observational results that support an intrinsic origin for these features , itemized below in order of relevance . * the associated nals show clear evidence of partial coverage ( see figure [ f4 ] and table [ t2 ] ) . covering factors are quite important for ascertaining the location of the absorbers . among 16 and 12 components in the spectra of images a and b , 6 and 6 components show partial coverage at the 4@xmath21 level ( i.e. , @xmath28 4@xmath21 ( ) @xmath29 1.0 ) , respectively . this supports the physical sizes of the absorbers being comparable to or even smaller than the size of the background source , suggesting that the system is intrinsic to the quasar itself ( e.g. , @xcite ) . interestingly , nals have higher values and are consistent with full coverage with only a few exceptions . covering factors are not necessarily identical for all ions from the same absorber , both in bals ( e.g. , @xcite ) and nals ( e.g. , @xcite ) . in the literature , ions in higher ionization states usually have larger , as is also the case for the associated system in sdss j1029 + 2623 . * the associated nals show the so - called line - locking phenomenon ( i.e. , blue components of doublets are aligned with red ones of the following doublets ; see figures [ f3 ] and [ f4 ] ) . chance coincidence of such alignments is negligibly small . this is naturally explained by radiative acceleration ( e.g. , @xcite ) . although several mechanisms have been proposed to explain the acceleration of outflowing winds , radiative acceleration almost always contributes substantially . line locking requires that the sight - lines be approximately parallel to the gas motion . * the velocity distribution of the associated and nals shows values beyond 1,000 , which is too large for an origin in igm , foreground galaxy , and ism of the host galaxy . intervening absorption lines are typically clustered in @xmath30 @xmath25 400 both for metal lines ( e.g. , @xcite ) and for lines ( e.g. , @xcite ) . the ism of most galaxies show velocities below this limit . a distribution with velocities @xmath4 1,000 strongly supports an intrinsic origin due to the outflow wind . * these nals have small ejection velocities from the quasar emission redshift , @xmath31 @xmath5 1600 . @xcite found that a high fraction ( @xmath021% ) of the associated nals within = 5,000 from the quasars , is time - variable ( i.e. , intrinsic lines ) . @xcite discovered an excess number density of nals in quasar vicinities , and concluded that almost half of absorbers at @xmath31 @xmath5 12000 are intrinsic to the quasars , with a peak value of @xmath0 80 % at @xmath31 @xmath0 2000 . based on multiple medium - resolution spectra , we confirmed that the associated absorption lines toward both images a and b retain their profiles unchanged , while their profiles are clearly different each other . this result was originally expected to reject the time - variation scenario ( i.e. , scenario i ) . however , with the high - resolution spectrograph , the associated absorption lines are deblended into multiple narrow components , of which two are foreground absorption lines of @xmath102344 and @xmath102600 at @xmath0 0.9187 . we confirmed that the differential absorption profiles between the lensed images seen in medium - resolution spectra are mainly due to these physically unrelated lines . thus , we can not distinguish different scenarios with medium - resolution spectra alone . high - resolution spectra taken with subaru / hds provide us with several important clues regarding the origin of the associated lines . first of all , the general profiles of the absorption lines toward images a and b are very similar to each other . this means that the size of the absorber must be larger than the transverse distance of the two sight - lines . in the extreme case , the absorber s location would be very close to the background flux source so as to make the separation angle almost negligible . second , we see a clear difference of absorption profiles between images a and b in various structures . for example , at @xmath0 0 200 , there exist additional absorption components in , , ly@xmath14 panels of figure [ f6 ] only in image a. this small difference , discovered only after taking high - resolution spectra , reminds us of the original question : what is the source of this difference ? finally , the most important clue is that a substantial fraction of absorption components show partial coverage , which means that the physical sizes of the absorbers are smaller than or comparable to the background source such as the continuum source and the belr . while some intrinsic absorption lines cover only the continuum source ( e.g. , @xcite ) , the covering factors toward the continuum source and the belr usually take specific values , depending on the relative strengths of their fluxes @xcite . in our case , the residual flux at @xmath10 @xmath0 4948 , at which the emission line peaks , is almost zero . this means that absorbers as a whole cover both the continuum source and the belr significantly . therefore , size estimation of the flux sources is important . we estimate the size of the belr ( @xmath32 ) using the empirical relation between @xmath32 and quasar luminosity . this relation was originally discovered through reverberation mapping @xcite and then extended to brighter quasars with monochromatic luminosities of @xmath2710@xmath33 ergs s@xmath12 to redshifts @xmath27 0.7 ( eq.[a4 ] in @xcite ) . the monochromatic luminosity of image a at @xmath34 = 3000 in the quasar rest - frame is measured in @xcite as @xmath35 = 46.21 ergs s@xmath12 . after correcting the magnification factor of image a , @xmath36 = 10.4 @xcite , we estimate @xmath32 to be @xmath0 0.09@xmath37 pc , where the main source of 1@xmath21 uncertainty comes from the scatter in the empirical relation in @xcite . as to the size of the continuum source ( @xmath38 ) , we take five times the schwarzschild radius , @xmath39 = 10@xmath40 , following @xcite , where @xmath41 and @xmath42 are the schwarzschild radius and mass of the central black hole . the virial mass of the central black hole is already calculated in @xcite using the luminosity and fwhm of broad emission lines of image a. again , after correcting for magnification , we obtain @xmath43 = 8.72 , and then @xmath38 is evaluated to be @xmath0 2.54@xmath44@xmath45 pc . this is almost 300 times smaller than @xmath32 . the size of the background flux source ( @xmath9 ) and the absorber s distance from the central flux source ( @xmath46 ) decide geometry , i.e. , a single sight - line or multiple sight - lines . the transverse distance of the two sight - lines ( @xmath47 ) can be calculated as @xmath47 = @xmath48 , where @xmath1 is the separation angle of the two sight - lines seen from the flux source ( which is very similar to the separation angle seen from us , @xmath1 @xmath0 22@xmath2.5 ) . at a distance , where @xmath9 @xmath5 @xmath47 (= @xmath48 ) is satisfied , the two sight - lines become fully separated with no overlap . we call this distance a boundary distance ( @xmath49 ) , hereafter ( see figure [ f7]a ) . the boundary distance is @xmath49 @xmath02.3 pc if only the continuum source is the flux source , and @xmath0788 pc if the belr is also the background source . the latter is comparable to the distance of outflowing gas measured by @xcite and @xcite for other quasars . the geometry also depends on the absorber s size ( @xmath50 ) . if the size of the absorber ( whose internal sub - structure is ignored here ) is much larger than the transverse distance ( i.e. , @xmath50 @xmath51 @xmath52 ) , a single sight - line scenario is applicable regardless of the absorber s distance from the flux source ( see figure [ f7]b ) . however , this geometry can not be applied to our case because the partial coverage we found in [ sec3.2 ] requires the size of each absorber to be comparable or smaller than the size of background source . on the other hand , if @xmath50 @xmath5 @xmath52 ( figure [ f7]c ) , we should analyze the condition in more detail . in the case of @xmath50 @xmath5 @xmath52 @xmath53 @xmath9 ( i.e. , the absorber s distance is smaller than the boundary distance ) , a substantial fraction of both sight - lines is covered by a single absorber although the fraction depends on the distance and the absorber s size . small differences of absorption profiles , seen in the high - resolution spectra of images a and b , can be explained either by i ) a different part of the absorber s outskirts covering each sight - line ( _ quasi-_scenario ii ) , or by ii ) time - variation ( scenario i ) . in the case of @xmath50 @xmath5 @xmath9 @xmath5 @xmath48 ( i.e. , the absorber s distance is larger than the boundary distance ) , this will be _ bona - fide _ scenario ii . one shortcoming of this model is that we can not reproduce common absorption profiles seen in the two sight - lines because the same absorber can not cover both sight - lines . we will discuss this problem later . @xcite claimed that nal absorbers should be located in a low gravity environment far from the central bh in order to maintain kinematic stability . their result suggests that the ejection velocity of nal absorbers is larger than the escape velocity so that the absorber is gravitationally unbound . if the nal absorbers in our target quasar are also in a similar kinematic condition , their radial distance from the central bh should be @xmath46 @xmath4 1.79 pc . this is close to the boundary distance in the case that only the continuum source is the background flux source . as a result , we do not have any conclusive evidence to either accept or reject scenarios i or ii . therefore , we will discuss the absorber s physical condition further assuming both scenarios in turn below . if scenario i represents reality , there are two possible origins of time variability , i ) a change of ionization condition of the absorber ( e.g. , @xcite ) and ii ) the absorber moving across our sight lines to change the covering factor ( e.g. , @xcite ) . neither situation is applicable for the case of intervening absorbers as discussed in @xcite . if a change in ionization is the origin of variation , we can place constraints on the electron density and the distance from the flux source following the procedure by @xcite and @xcite . we can not evaluate the specific ionization condition because a wide range of ionic species ( which is necessary for photoionization modeling ) are not detected in our spectra . therefore , by adopting the following assumptions ; i ) the gas is very close to ionization equilibrium , ii ) the change of ionizing flux is small , and iii ) is the dominant ionization stage of carbon , we estimate the electron density to be @xmath54 @xmath0 @xmath55 @xmath0 1.78@xmath4410@xmath56 @xmath57 by assuming a variation timescale in the quasar rest frame ( @xmath0233 days ) as a recombination time ( @xmath58 ) , where we use the recombination coefficient of @xmath59 in gas temperature of 20,000 k @xcite . because the variation timescale is an upper limit of the recombination time , we should regard the electron density as a lower limit . we can also evaluate the distance of the absorber from the flux source using the prescription of @xcite . the ionization parameter ( @xmath60 ) depends on the bolometric luminosity of the quasar , the continuum shape , distance from the flux source , and electron density . by adopting the continuum shape of @xcite , we estimate the distance of the absorber to be @xmath46 @xmath50.44 kpc , with an ionization parameter of @xmath60 = 0.02 ( in which is the dominant ionization stage ; @xcite ) , and the bolometric luminosity of the quasar of @xmath61 = 45.87 erg s@xmath12 @xcite . the limits on the electron density and the absorber s distance are consistent with the literature ( e.g. , @xcite ) . if the gas motion ( i.e. , crossing of our sight - line ) is the origin of variation , we can simply estimate the average crossing velocity ( @xmath62 @xmath0 @xmath63 ) to be @xmath0390 if the continuum source is the only background source . again , this is the minimum velocity because @xmath3 is an upper limit on the variability timescale . the belr should not be the flux source , because the corresponding crossing velocity , @xmath01.32@xmath4410@xmath64 , is comparable to the speed of light . thus , we conclude that the absorber covers primarily the uv continuum source with only a small part of the belr if the gas motion is the origin of variation . the main problem of the _ bona - fide _ scenario ii model , in which the absorber s size is smaller than the transverse distance of the two sight - lines , is that we can not reproduce closely similar absorption profiles seen in the two sight - lines because the same absorbers can not cover both sight - lines . a possible solution for this is that there exists a number of clumpy absorbers or fluctuations in gas density ( whose sizes are smaller than the background source ) constituting a filamentary ( or a sheet - like ) structure that covers both sight - lines ( figure [ f7]c ) . such a structure is well reproduced above the main body of the outflow by hydrodynamical simulations ( e.g , @xcite ) . here , we calculate the radial mass - outflow rate ( @xmath65 ) toward the two sight - lines summing contributions from all absorption components as @xmath66 where @xmath67(@xmath68 ) and @xmath69(@xmath68 ) are the total ( @xmath28 ) hydrogen column density and the radial depth of the @xmath68-th absorption component toward a sight - line . @xmath9 and @xmath70 are the size of background source and the proton mass . in [ sec3.2 ] , we measured ejection velocities of all and absorption components by applying voigt profile fitting . however , their absolute values could be underestimated because emission redshifts determined from broad uv emission lines are systematically blueshifted from the systemic redshift , as measured by narrow , forbidden lines ( see , e.g. , @xcite ) . @xcite find a mean blueshift of the broad uv emission lines relative to the systemic redshift of about 260 and that 90% of the blueshifts are between 0 and 650 . we therefore add 260 to the values given in table [ t2 ] for the calculation herein . because our spectra do not detect a wide range of ionic species ( which are necessary for photoionization modeling , as described in [ sec4.3.1 ] ) , we can measure neither the ionization condition nor the total hydrogen column density @xmath71(h ) . these parameters decide an absorber s metallicity and radial depth . therefore , we simply calculate @xmath65 assuming all absorption components have the same ionization condition , metallicity , and radial depth toward both the sight - lines as follows , @xmath72 where @xmath73 ( a metallicity - ionization correction ) for and are defined as follows , respectively , @xmath74 @xmath75 based on the and absorption lines , a difference of radial mass - outflow rates toward images a and b is only @xmath030 35% , which suggests that internal fluctuation of the nal absorber is almost negligible within the angular distance of @xmath1 @xmath0 22@xmath2.5 . because @xmath020 50% of quasars have at least one intrinsic nal absorber in their spectra @xcite , the global covering factor of the central flux source surrounded by nal absorbers can have values of @xmath76 @xmath5 0.8@xmath77 2@xmath77 in terms of solid angle . thus , small areas within @xmath00.002% 0.005% of the total solid angle for nal absorbers produce similar absorption profiles with the same order of total column densities . in other words , the outflow wind corresponding to the nal absorbers can be divided into @xmath520,000 50,000 small zones with common physical conditions .

based on medium- and high - resolution spectroscopy of the two brightest images conducted at the subaru telescope , we find that each image has different intrinsic levels of absorptions , which can be attributed either to variability of absorption features over the time delay between the lensed images , 744 days , or to the fine structure of quasar outflows probed by the multiple sight - lines toward the quasar . while both these scenarios are consistent with the current data , we argue that they can be distinguished with additional spectroscopic monitoring observations .

we study the origin of absorption features on the blue side of the broad emission line of the large - separation lensed quasar sdss j1029 + 2623 at.197 . the quasar images , produced by a foreground cluster of galaxies , have a maximum separation angle of 22.5 . the large angular separation suggests that the sight - lines to the quasar central source can go through different regions of outflowing winds from the accretion disk of the quasar , providing a unique opportunity to study the structure of outflows from the accretion disk , a key ingredient for the evolution of quasars as well as for galaxy formation and evolution . based on medium- and high - resolution spectroscopy of the two brightest images conducted at the subaru telescope , we find that each image has different intrinsic levels of absorptions , which can be attributed either to variability of absorption features over the time delay between the lensed images , 744 days , or to the fine structure of quasar outflows probed by the multiple sight - lines toward the quasar . while both these scenarios are consistent with the current data , we argue that they can be distinguished with additional spectroscopic monitoring observations .

1203.4233

i

many x - ray sources ( xrss ) are inside globular clusters ( gcs ; e.g. heinke 2011 ) , but only five of them unambiguosly host a black hole ( bh ; maccarone et al . 2007 , hereafter m07 ; brassington et al . 2010 ; shih et al . 2010 ; maccarone et al . 2011 ; irwin et al . 2010 , hereafter i10 ; see king 2011 for an alternative explanation ) . these five objects were observed as luminous xrss ( @xmath6 ) with strong variability ( so that blending is excluded ; kalogera et al . the spectra of at least two of their host gcs are quite peculiar . one of them , rz 2109 ( in the elliptical ngc 4472 ; zepf et al . 2007 , 2008 , and steele et al . 2011 ; hereafter z07 , z08 , s11 ) displays prominent and broad [ oiii]@xmath75007,4959 emission ( the fwhm of [ oiii]@xmath8 is @xmath9@xmath10 ; its flux is @xmath11 ; at @xmath12 it corresponds to @xmath13 ; see z08 ) , but no h line emission@xmath14 , [ nii]@xmath15 , [ sii]@xmath16 ) is detected , except perhaps [ oiii]@xmath17 . ] . the spectrum of the gc hosting the xrs cxoj033831.8 - 352604 ( in the elliptical ngc 1399 ; see i10 ) is somewhat similar in the absence of h and the presence of [ oiii ] lines ; but widths and luminosities are lower ( fwhm @xmath18 , @xmath19 ) , and [ nii ] @xmath76583,6548 emission is comparable to [ oiii ] . these observations are hard to explain , because of the high [ oiii]/h@xmath20 ratio ( z08 estimate @xmath21 ; i10 finds a 3@xmath22 lower limit of 5 ; both are very uncertain ) and of the large broadening , implying motions much faster than gc velocity dispersions ( @xmath23 ) . optical lines are too wide for a planetary nebula , and too narrow for a supernova remnant . z08 suggest that the [ oiii ] emission from rz 2109 might come from a strong wind originating around the bh , photoionized by the xrs . such scenario strongly favours a bh with mass @xmath24 , rather than an intermediate - mass bh ( imbh ) with mass in the 10@xmath25 - 10@xmath26m@xmath27 range . this was preferred to the hypothesis that the [ oiii]-emitting gas closely orbits ( @xmath28 ) an imbh , on the basis of considerations about the maximum possible emission from such a small volume . such argument is severely weakened if the orbiting gas is very metal - rich , e.g. as the result of the tidal disruption of a white dwarf ( wd ) by an imbh ( see i10 ) : according to porter ( 2010 ) , the cxoj033831.8 - 352604 data are compatible with this scenario , whereas in the case of rz 2109 the conflict remains ; however , clausen & eracleous ( 2011 ) showed that simulations of wd disruption can reproduce the [ oiii ] line profiles observed in rz 2109 . on the other hand , maccarone & warner ( 2011 ) argued that the line emission of cxoj033831.8 - 352604 might be better explained with the photoionization ( by the xrs ) of the wind from an r coronae borealis star in the same gc . in this paper , we examine a further possible scenario , and apply it to the case of rz 2109 : [ oiii ] lines might be associated with a recent nova eruption in the core of the gc . in particular , we discuss the case ( first mentioned by s11 ) where the [ oiii ] emission comes from the photoionization of the nova ejecta by the xrs . x - ray emission from novae is typically fainter ( @xmath29 , even though at least one nova was reported to reach @xmath30 - see henze et al . 2010 ) and shorter ( decay times @xmath31 ) than what is observed for these sources . thus , we assume that the nova eruption is _ not _ associated to the xrs , i.e. that the co - existence of the two phenomena in the same gc is serendipitous .

we study the possibility that the very broad ( 1500 km s ) and luminous ( ) [ oiii ] line emission observed in the globular cluster rz 2109 might be explained with the photoionization of nova ejecta by the bright ( ) x - ray source hosted in the same globular cluster . we find that such scenario is plausible and explains most of the features of the rz 2109 spectrum ( line luminosity , absence of h emission lines , peculiar asymmetry of the line profile ) ; on the other hand , it requires the nova ejecta to be relatively massive ( ) , and the nova to be located at a distance from the x - ray source .

we study the possibility that the very broad ( 1500 km s ) and luminous ( ) [ oiii ] line emission observed in the globular cluster rz 2109 might be explained with the photoionization of nova ejecta by the bright ( ) x - ray source hosted in the same globular cluster . we find that such scenario is plausible and explains most of the features of the rz 2109 spectrum ( line luminosity , absence of h emission lines , peculiar asymmetry of the line profile ) ; on the other hand , it requires the nova ejecta to be relatively massive ( ) , and the nova to be located at a distance from the x - ray source . we also predict the time evolution of the rz 2109 line emission , so that future observations can be used to test this scenario . novae , cataclysmic variables - galaxies : individual ( ngc 4472 ) - galaxies : star clusters : individual ( rz 2109 ) - x - rays : binaries - ism : jets and outflows

math0110081

i

in this paper we continue the study of the q - analogue of the knizhnik zamolodchikov bernard ( qkzb ) equations on elliptic curves and their solutions initiated in @xcite . in @xcite , hypergeometric solutions of qkzb equations were introduced . in @xcite , the monodromy of hypergeometric solutions was calculated , and a symmetry between equations and monodromies was discovered : the equations giving the monodromy are again qkzb equations but with modular parameter and step of the difference equations exchanged . in @xcite we introduced the @xmath0-analogue of the kzb heat equation , which governs the change in the modular parameter of the elliptic curve , proved that it is compatible with the other equations and explained how to recover the kzb heat equation in the semiclassical limit . in this paper we prove three results about our hypergeometric solutions in the case where the sum of highest weights is two : we show that the hypergeometric solutions also obeys the qkzb heat equation of @xcite , see theorem [ t - he1 ] . we give a formula ( theorem [ t - mod ] ) for the transformation properties of the hypergeometric solutions under the modular group @xmath4 . we prove a completeness result , corollary [ completeness ] , by showing that the associated `` fourier transform '' is invertible . then we show that these results are part of a bigger picture , in which the modular group combines with the transformation defined by the qkzb heat equation to give a set of quadratic identities for our generalized hypergeometric integrals . in fact , this picture can already be seen in a simpler situation , in which the elliptic gamma function @xcite , @xcite plays the role of the hypergeometric integral . the elliptic gamma function is a function @xmath5 of three complex variables obeying identities @xcite involving its values at points related by an action of @xmath6 . these identities mean that @xmath7 is a `` degree 1 '' generalization of a jacobi modular function , see @xcite . these identities are a scalar version of the identities obeyed by the hypergeometric solutions of the qkzb equation . their meaning is that the hypergeometric integrals define a discrete projectively flat @xmath1-connection ( i.e. , a lift of the action to the projectivization ) on a vector bundle over `` regular '' orbits of @xmath1 acting on the variety of pairs ( point in @xmath8 , plane through @xmath9 containing it ) . this is the content of theorem [ t - pf ] . the results on the elliptic gamma function are used in the proof , since the `` phase function '' which appears in the integrand of hypergeometric solutions is a ratio of gamma functions . in fact , we see `` experimentally '' that there seems to be a principle stating that to every identity obeyed by the gamma function , there corresponds an identity for hypergeometric integrals . the proofs of the identities consist in applying the gamma function identity to the phase function in the integrand , and then use a version of stokes theorem to relate the integrals . the second step is relatively simple in the case of the one - dimensional integrals to which we restrict ourselves here , but becomes exceedingly involved in the higher dimensional case . proving our identities in the higher dimensional case , i.e. , if the sum of highest weights is larger than two , remains a challenging open problem . an alternative approach to this problem is based on representation theory : in @xcite a representation - theoretic interpretation of a degenerate version of the qkzb equations was established . it was shown that traces of intertwining operators for quantum groups satisfy a version of the qkzb equations and are eigenfunctions of analogues of macdonald operators . this fact indicates that our theorem [ t - he1 ] is an elliptic analogue of the macdonald - mehta identities proved by cherednik , @xcite , @xcite , and the present work is a glimpse into an elliptic version of macdonald s theory . in fact theorem [ t - pf ] concerns the case of generic parameters , where an infinite - dimensional vector bundle is preserved by the projectively flat connection . in a next paper we will restrict our attention to special @xmath1-orbits . the projectively flat connection can be then defined on a finite - dimensional vector bundle of theta - functions which are a @xmath0-deformed version of the space of conformal blocks in conformal field theory . in this setting the analogy with macdonald s theory will appear more explicitly . another degeneration of the @xmath1 symmetry of our hypergeometric integrals are the @xmath1 symmetries of the ordinary fourier transform indicated in @xcite .

we study the properties of one - dimensional hypergeometric integral solutions of the-difference ( `` quantum '' ) analogue of the knizhnik zamolodchikov bernard equations on tori . we show that they also obey a difference kzb heat equation in the modular parameter , give formulae for modular transformations , and prove a completeness result , by showing that the associated fourier transform is invertible . these results are based on transformation properties parallel to those of elliptic gamma functions . _ chapel hill , nc 27599 - 3250 , usa _

we study the properties of one - dimensional hypergeometric integral solutions of the-difference ( `` quantum '' ) analogue of the knizhnik zamolodchikov bernard equations on tori . we show that they also obey a difference kzb heat equation in the modular parameter , give formulae for modular transformations , and prove a completeness result , by showing that the associated fourier transform is invertible . these results are based on transformation properties parallel to those of elliptic gamma functions . supported in part by the swiss national science foundation]supported in part by nsf grant dms-9801582 ] _department of mathematics , eth - zentrum , _ _ 8092 zrich , switzerland _ _department of mathematics , university of north carolina at chapel hill , _ _ chapel hill , nc 27599 - 3250 , usa _ october 2001

1011.4846

r

in the following we first discuss the correlations between the local galaxy densities @xmath109 and @xmath123 . we then investigate the colour - magnitude relation in bins of stellar mass and bins of local density , and show the behaviour of rest - frame colour @xmath6 and blue fraction of galaxies as a function of both local density ( @xmath124 ) and stellar mass ( @xmath125 ) . additionally , we test differences between galaxy properties in the high and low quartiles of the local density and stellar mass distributions respectively . we focus on the redshift range of @xmath55 , which has a reasonable surveyed volume and stellar mass completeness down to @xmath126 . as described above two different methods were used to estimate local galaxy densities , the fixed aperture density , @xmath92 , and the @xmath127 , @xmath128 and @xmath129 nearest neighbour density , @xmath130 , @xmath131 and @xmath132 . figure [ fig4 ] , left panel , shows the distribution of the different measures of relative overdensities : @xmath123 is plotted as a black dashed - dotted line and @xmath109 as a green solid line ( @xmath95 ) , red dotted line ( @xmath133 ) and blue dashed line ( @xmath134 ) . the figure shows the different dynamical range of the four methods : the nearest neighbour densities @xmath109 cover a wider range of relative densities , especially at the high density end . the @xmath127 nearest neighbour density has the widest range , since it is most sensitive to density variations on very small scales . the standard deviation of the @xmath123 distribution is @xmath135 , while @xmath136 . the good overall agreement between the four methods is shown in the right panel of figure [ fig4 ] , where @xmath109 is plotted against @xmath123 . the different symbols used are green crosses ( @xmath95 ) , red circles ( @xmath133 ) and blue triangles ( @xmath134 ) , while the one - to - one relation is shown as a black solid line . the four density estimates agree well on average , with an average spread of @xmath137 dex . this scatter reflects the average uncertainty of the local density measurements of @xmath138 dex obtained by the monte carlo simulations described in section [ mc ] . however , it also shows that the different methods trace galaxy environment on different scales and are not necessarily comparable . the different sensitivity of the different values of @xmath94 is visible at the low density end , where the higher @xmath94 traces the average densities on larger scales , rather than local underdensities , which we are interested in . at densities above @xmath139 the four methods agree best on average , while the higher sensitivity of densities measured with lower @xmath94 towards galaxy concentration on small scales becomes visible : high relative overdensities measured with @xmath95 ( green crosses in figure [ fig4 ] ) are partly recovered by @xmath133 but not detected using @xmath134 or the fixed aperture density . the @xmath140 nearest neighbour density is by construction a better tracer of the extremes in the local density distribution , since it uses an adaptive area and therefore is sensitive to galaxy concentrations at very small scales , that the fixed aperture can not probe . the lower the value of @xmath94 , the more sensitive the density measure is to local galaxy concentrations on small scales . these very local galaxy concentrations however are potentially influencing the evolution of a galaxy dramatically via merging or galaxy interactions . in the following we use the @xmath127 nearest neighbour density @xmath124 as a local density estimator , since - although it has slightly larger uncertainties than the other density estimates ( see section [ mc ] ) - it has a wider dynamical range and higher sensitivity to the most underdense and overdense environments and is therefore a better probe of the local environment . in the following we investigate the colour - magnitude relation of the gns sample in different redshift ranges . we investigate if the red sequence is already present at @xmath141 and if it is populated by high or low - mass galaxies . additionally we examine if the build - up of the red sequence preferentially takes place in a certain environment . for this purpose the sample is split up in four stellar mass bins and four local density bins . figure [ fig5 ] shows the @xmath6 - @xmath142 colour - magnitude relation ( cmr ) in three different redshift bins : @xmath143 , @xmath144 and @xmath145 . in the three top panels the sample is split in 4 stellar mass bins with a bin size of 0.5 dex ; the symbols are shaped and sized according to the galaxy s stellar mass : larger symbols represent higher stellar mass galaxies . in the three lower panels the sample is split in bins of local density with a bin size of 0.6 dex . here , larger symbols correspond to galaxies located in higher overdensities . the red solid lines indicate the expected location of the red sequence observed at @xmath10 , and evolved passively back in time according to the models of @xcite , as described in section [ completeness - colour ] . the blue long - dashed lines is the border to the blue cloud , defined as being 0.25 magnitudes bluer than the red sequence ( see section [ completeness - colour ] ) . the different slices in stellar mass are clearly separated in colour - magnitude space . the separation is perpendicular to the red sequence , and the distance from the expected red sequence increases with decreasing stellar mass . the different slices in local density on the other hand are not well separated in colour - magnitude space . the relation between colour and local density is much weaker than the relation between colour and stellar mass . this subject is further discussed in section [ colour - mass - density ] . , scaledwidth=48.0% ] as can be seen , massive red galaxies are already present at a redshift of @xmath146 , when the universe was only @xmath152 gyrs old . the location of these galaxies in the colour - magnitude diagram is consistent with the location expected from passively evolving back the red sequence found at @xmath10 ( see above ) . at @xmath147 this region in colour - magnitude space is populated mainly by the most massive galaxies ( @xmath148 ) , while at lower @xmath13 the range of galaxies on or close to the red sequence extends towards lower mass galaxies . note that these most massive galaxies are mostly star - forming ( bauer et al . , submitted ) and not red and dead " as their location in the colour - magnitude diagram close to the red sequence might suggest . galaxies close to or on the location of the red sequence span a wide range of local densities , and there is no clear preference for a certain environment , however , we do not see red galaxies uniquely located in the most overdense regions . this is opposite to what was found at lower redshifts up to @xmath12 ( see e.g. * ? ? ? * ) and might hint at an inversion of the colour - density relation at high @xmath13 , as discussed later in this paper ( section [ colour - mass - density ] and section [ highlow ] ) . clear evolution in @xmath142 is seen for the galaxies on or close to the expected red sequence , while the blue cloud remains basically unchanged . part of this evolution , as well as the lack of low - mass galaxies at high @xmath13 may be due to the fact that faint red galaxies become more difficult to detect with high @xmath13 than faint blue galaxies and we might miss some low surface brightness , low - mass red galaxies in our sample . however , the mass limit we adopt in this study is very conservative and our sample should not be affected by colour - dependent incompleteness . a more detailed discussion on the stellar mass completeness and stellar mass functions for blue and red galaxies will be presented in mortlock et al . ( submitted ) . a strong relation between rest - frame colour and stellar mass and the apparent lack of a strong relation between colour and local density was found in the colour - magnitude relation in the previous section . we now investigate these correlations in more detail . the same redshift ranges as already used for the analysis of the colour - magnitude relation are used here : @xmath143 , @xmath144 and @xmath145 . to quantify the correlation between two variables we compute spearman rank correlation coefficients @xmath74 . the value of @xmath74 ranges between @xmath149 , where @xmath150 ( @xmath151 ) means that two variables are perfectly correlated ( anti - correlated ) by a monotonic function . completely uncorrelated variables result in @xmath152 . taking into account the sample size in each bin we estimate the significance of the value of @xmath74 using the conversion from correlation coefficient to z - score @xcite . figure [ fig6 ] , shows rest - frame @xmath6 colour ( top ) and the fractions of blue and red galaxies ( bottom ) as a function of stellar mass in three redshift bins . the correlation between @xmath6 colour and stellar mass @xmath125 is highly significant at all redshifts . spearman rank correlation coefficients in the three redshift bins range between 0.7 - 0.8 , corresponding to a significance of @xmath153 at all redshifts . the colour - mass relation also does not appear to evolve strongly with redshift . the cross - over mass , i.e. the stellar mass at which there is an equal number of red and blue galaxies , stays roughly constant at @xmath154 . this is the same cross - over mass found at lower redshifts @xmath155 @xcite . note that in the computation of blue and red galaxy fractions we account for the passive reddening of galaxy colours with redshift ( see section [ completeness - colour ] ) . the fraction of blue galaxies over all stellar masses evolves with redshift from @xmath156 at @xmath0 to @xmath157 at @xmath7 . notice that the fading and reddening expected from passive evolution of a galaxy s stellar population is already accounted for in the definition of red and blue galaxies at each redshift . combining this with the above considerations of almost no evolution in the colour - stellar mass relation , the colour evolution is mainly taking place at low stellar masses of @xmath158 . the population of more massive galaxies already comprises a similar fraction of red galaxies at high redshifts up to @xmath0 compared to @xmath7 . the left panel of figure [ fig7 ] shows the relation between @xmath6 colour ( top row ) and the fraction of blue and red galaxies ( bottom row ) as a function of relative overdensity @xmath124 . we do not find a significant correlation between colour and overdensity in the data there is , however , a possible trend for a higher fraction of blue galaxies ( @xmath159 ) at the highest overdensities ( @xmath160 ) at all redshifts , where as the blue fraction at intermediate and low densities is around 80 - 90% . the trend of a lack of red galaxies at high overdensities noticed in the cmr in figure [ fig5 ] is visible , but not significant due to the low number of galaxies at high overdensities . to further check the significance of the higher fraction of blue galaxies at high overdensities we use monte carlo simulations . we perform 100 monte carlo runs based on the randomised photometric redshift input as described in section [ mc ] . the scatter between the individual runs represents the uncertainties in the local densities due to the photometric redshift error . the right panel of figure [ fig7 ] shows the result of the simulations . the average colour ( top panels ) and fraction of blue and red galaxies ( bottom panels ) as a function of local density in each monte carlo run is plotted . the large scatter in the high density end due to the low number of galaxies in extreme overdensities becomes visible . although , above densities of @xmath160 , and at all redshifts , the vast majority of monte carlo runs show a blue fraction of 100% , whereas at lower densities the blue fractions vary between 85 - 90% . the average and rms of all monte carlo runs at @xmath161 shows an average blue fraction of 85@xmath1622% in the two lower @xmath13 bins and 90@xmath1622% in the high @xmath13 bin . at the highest densities the average blue fraction is 95@xmath16213% , however , the distribution of average blue fractions at the highest overdensities is not gaussian and the standard deviation does not represent the distribution adequately . to estimate the probability that the difference between high and low density is caused by chance , we consider the number of times a monte carlo run gives a blue fraction at the highest densities which is lower than the average value plus 3@xmath26 at lower densities . in the lowest redshift bin about 90% of monte carlo runs result in @xmath163 , giving a @xmath164 probability that the difference between highest and lower densities is caused by chance . the intermediate and high redshift bin have a probability of @xmath165 . we conclude that the colour - density relation at @xmath141 is practically not existent or very weak . if a trend with local density persists it must be very minor , with a variation of the average @xmath6 colours of less than @xmath150.1 magnitudes between relative local densities that differ by a factor of 100 . there could be an environmental influence on the blue fractions of galaxies in the most extreme overdense environments . this difference in blue fractions amounts to about 10% and is not detectable at a statistically significant level with the low number of galaxies in our sample located at the highest overdensities ( 33 galaxies at @xmath160 between @xmath67 ) . in the following we compare the properties of galaxies in the low and high quartiles in the distribution of local density and stellar mass , i.e. 25% of galaxies at each extreme respectively . the high quartile of local density corresponds to galaxies located in overdense regions of @xmath166 , while the low quartile corresponds to underdense regions of @xmath167 . the stellar mass distribution has its low quartile at @xmath168 and the high quartile at @xmath169 . after dividing the sample into low and high quartiles a kolmogorov - smirnov ( k - s ) test between the different quartiles is used to investigate the statistical difference of the two subsamples . to increase the number statistics we consider the full redshift range of our sample at @xmath55 , instead of binning into the three redshift ranges used above . the stellar mass limit is kept at @xmath126 , as above . the k - s test gives the probability @xmath170 that the galaxy properties in the low and high quartile come from the same parent distribution . the statistical differences we find over the whole redshift range ( @xmath55 ) can be summarised as : + ( 1 ) galaxies in the low and high quartile of the local density distribution have marginally different colours ( @xmath171 , i.e. @xmath172 ) but not statistically different stellar masses ( @xmath173 , i.e. @xmath174 ) ; and + ( 2 ) galaxies in the low and high quartile of the stellar mass distribution have statistically different colours ( @xmath175 , i.e. @xmath176 ) , as well as marginally different local densities ( @xmath177 , i.e. @xmath178 ) . although the differences between the low and high stellar mass quartiles are much clearer than the differences in the local density quartiles , there is a difference at the 2 @xmath26 confidence level between the colours of galaxies in over and under - dense environments . we further investigate the reliability of this result by using the monte carlo simulations described in section [ mc ] . in figure [ fig8 ] and figure [ fig9 ] we plot galaxy properties in the low and high quartiles of local density and stellar mass distribution , respectively , as a function of redshift . the results of each of the 100 monte carlo runs are plotted as a single line . figure [ fig8 ] shows the median @xmath6 colour , blue fraction and median stellar mass in each redshift bin ( @xmath179 ) in the low quartile ( blue ) and high quartile ( red ) of local densities . figure [ fig9 ] shows median @xmath6 colour , and two different densities ( fixed aperture density @xmath123 and third nearest neighbour density @xmath124 ) in the low ( blue ) and high quartile ( red ) of stellar mass . the average of all monte carlo runs in each redshift slice is overplotted as big symbols , blue circles for the low quartile and red triangles for the high quartile . figure [ fig8 ] shows that there is barely any difference in colour , blue fraction or stellar mass between the low and high quartile of local density . we may see evidence for a weak trend of a lower blue fraction at high densities emerging at @xmath180 , as well as a correspondent peak in the average stellar mass in the high density quartile , which is probably responsible for the positive correlation found from the k - s test on the data described above . however , we conclude that we lack the number statistics to reliably confirm the presence of a difference between low and high density quartile and that our data is consistent with there being no difference . note however that the lack of a clear separation between the low and high density quartiles does not contradict the results from the colour - density relation in section [ colour - mass - density ] , where we possibly see evidence for a higher blue fraction in the most overdense environments above @xmath181 . the high density quartile includes all galaxies at densities above @xmath182 and does not comprise the extreme overdensities only , in which we see the higher blue fraction . since there is no relation with local density at densities below @xmath181 , we do not see any difference between the colours of galaxies in the low and high quartile of the density distribution . we conclude that in the redshift range of @xmath55 the highest local overdensities ( @xmath160 , i.e. , an overdensity of roughly a factor of 5 ) possibly show a higher fraction of blue galaxies . at densities below @xmath181 there is no correlation between rest - frame colours or fraction of blue galaxies with local density . this finding is different from the colour density relation found at lower redshifts ( up to @xmath11 ) , where higher density environments show a higher fraction of red galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . figure [ fig9 ] shows two different local densities @xmath124 and @xmath123 and @xmath6 colour in the low and high quartiles of the stellar mass distribution . the high quartile includes galaxies with @xmath169 ( red ) , while the low quartile corresponds to @xmath168 ( blue ) . there are strong differences in the rest - frame colour distributions of low- and high - mass galaxies at all redshifts . as already investigated in the previous section , high - mass galaxies have consistently redder colours ( @xmath183 magnitudes ) . these differences are highly significant . the colour difference of @xmath150.4 mag between the high- and low - mass quartile appears constant with redshift up to @xmath184 . the magenta line in the colour panel of figure [ fig9 ] shows the distinction between red and blue galaxies calculated from the red sequence at @xmath10 evolved back in time assuming passive evolution of the stellar populations ( see section [ completeness - colour ] ) . it corresponds to the position of the blue line at @xmath185 in the colour - magnitude diagrams in figure [ fig5 ] . at a redshift of @xmath184 the median colour of the high mass quartile decreases slightly towards the region occupied by the blue cloud however , a similar decrease is seen at redshifts below @xmath58 and is probably caused by the target selection of the gns , which favours the inclusion of very massive red galaxies between @xmath23 in our sample . this could slightly bias the average colour of massive galaxies towards redder colours within this redshift range . we see slight evidence for a mass segregation emerging at @xmath186 , where more massive galaxies tend to be located preferentially in high density areas ( see figure [ fig9 ] ) . this tentative result is consistent with what is found at lower and intermediate redshifts , where more massive galaxies tend to be located in high density environments ( see e.g. * ? ? ? recent studies at intermediate redshift ( @xmath10 , see e.g. @xcite ) have suggested that the observed colour - density relation is mainly caused by the strong correlation between rest - frame colour and stellar mass . this also requires the presence of a stellar mass - density relation , such that higher mass galaxies are preferentially located in regions of higher overdensity . we indeed find a weak trend for this behaviour , emerging at @xmath187 , at a significance of @xmath188 ( see figure [ fig9 ] ) . this is roughly consistent with the extrapolation of a similar weak positive correlation between stellar mass and local density found at @xmath7 by @xcite , which seems to get steeper and more significant with decreasing redshift . another question is if the higher fraction of blue galaxies in high overdensities ( see section [ colour - mass - density ] ) is due to a trend in stellar mass . to answer this question we investigate the colour - stellar mass relation and the colour - density relation in quartiles of local density and stellar mass respectively . figure [ fig10 ] , left panel , shows the colour - stellar mass relation in high and low density quartiles . the right panel of figure [ fig10 ] shows the colour - density relation in high and low stellar mass quartiles . the same high and low quartiles of local density and stellar mass are used as described above ( section [ extreme ] ) . as in figures [ fig8 ] and [ fig9 ] we plot the results of each monte carlo run as well as the average and rms of all runs instead of the measured data . the whole redshift range of @xmath67 is shown in figure [ fig10 ] . to compare our result with the colour - density and colour - stellar mass relations at lower redshift we use the data of ( * g10 hereafter ) . this sample is based on a deep near - infrared survey ( the powir survey , @xcite ) and spectroscopic redshifts from the deep2 redshift survey @xcite . the local densities and colours are measured in a similar way as in the present study . we split the g10 sample in high and low quartiles of local density and stellar mass as described above . the data covers the redshift range @xmath189 . the median @xmath6 colours of this sample are overplotted as big symbols : dark red boxes are used for the high quartile and dark blue pentagons for the low quartile of the powir sample data - points respectively . the left panel of figure [ fig10 ] shows that the strong correlation between @xmath6 and @xmath125 is present in both , high ( red ) and low ( blue ) density quartiles . the relation is very similar in both density quartiles . the colour - stellar mass relation at lower redshifts of @xmath190 ( squares and pentagons in figure [ fig10 ] ) is remarkably similar to the colour - stellar mass relation in the gns data ( triangles and circles ) , with a similar slope and a slightly larger colour difference between low and high local density quartiles ( @xmath191 mag ) . at the high mass end low @xmath13 galaxies have redder average colours than galaxies of the same stellar mass at high @xmath13 . the colours of @xmath192 galaxies at @xmath193 are indistinguishable from the colours of similar mass galaxies at @xmath189 . the right panel of figure [ fig10 ] shows the correlation between colour and local density for galaxies in the low and high stellar mass quartile . a clear colour offset between low- and high - mass galaxies of @xmath194 mag is present at all densities . interestingly , there is a trend that mean colours of galaxies in the high - mass quartile are bluer at higher overdensities ( @xmath195 ) than at low and average local densities . for galaxies in the low - mass quartile we do not see a strong correlation between colour and local density . combined with the results of the colour - density relation in figure [ fig7 ] , this would point towards high - mass galaxies being responsible for the higher fraction of blue galaxies at the highest overdensities . note however that the rms scatter between the single monte carlo simulations is larger than the decrease in colour . this large spread is due to the low numbers of objects at the highest overdensities ( 33 galaxies at @xmath196 . the colour difference between the gns data - points and the @xmath7 data - points from g10 is mainly due to the differences in the stellar mass distribution in the two surveys , leading to different limits of the low and high quartiles . the gns reaches much lower stellar masses down to @xmath197 , whereas the completeness limit of the powir survey is @xmath198 . additionally , the g10 sample has a larger number of high mass galaxies with @xmath199 than the gns sample , leading to redder average colours , as expected from the colour - mass relation . if the colour - density relation we see for high - mass galaxies is real , then it is reversed with respect to what is found at lower and intermediate redshifts up to @xmath200 , where galaxies in higher local densities tend to be redder ( see e.g .. * ? ? ? * ; * ? ? ? * ; * ? ? ? figure [ fig10 ] shows that the high and low mass quartiles of the g10 sample ( up to @xmath10 ) show a weak correlation between colour and local density , such that the average colour increases with higher local density . on the other hand , it was argued by some studies that the colour - density relation and colour - sfr relation at @xmath10 might be reversed @xcite . note , however , that @xcite argue that the reversed sfr - density relation ( were galaxies in denser environments have higher sfrs ) is mainly driven by starforming _ low_-mass galaxies , whereas our data indicate that the reversed colour - density relation is due to on average bluer _ high_-mass galaxies . in other worlds , we see a lack of red high - mass galaxies in regions of high relative overdensities . the on average bluer high - mass galaxies , however , are on average still redder than low - mass galaxies at comparable densities , but bluer than their high - mass counterparts at average and low local densities . note that the bluer colour of high mass galaxies does not necessarily imply that there is more ongoing star formation in these galaxies , but that there is possibly _ less dust - attenuated star formation _ at highest overdensities . massive galaxies in our sample show an overall very high dust content relative to low mass galaxies ( bauer et al . submitted ) . the behaviour of the sfr - density relation using dust corrected star formation rates from bauer et al . ( submitted ) will be investigated in a forthcoming paper . recently , a study of the colour - density relation at redshifts up to @xmath201 was performed by chuter et al . ( submitted ) using the ukidss ( ukirt infrared deep sky survey ) ultra deep survey ( uds ) data . they find that the local colour - density relation , with redder galaxies located in regions of higher local density , is present up to a redshift of @xmath202 . above this redshift the distinction between the environments of red and blue galaxies can not be confirmed at a statistically significant level . the authors also report a possible reversal of the colour - density relation at even higher redshift , however , the currently available uds data release ( dr3 ) does not allow for reliable conclusions at high @xmath13 . the results we present in this study are consistent with extrapolating the results of chuter et al . ( submitted ) , suggesting a gradual disappearance of the colour density relation with redshift and a possible reversal of the colour - density relation at the most extreme overdensities at @xmath141 . in the following we investigate how , and if , the environments of the most massive galaxies ( @xmath148 ) differ from the rest of the galaxy population and if there is a correlation between local density and galaxy size . the subsample of massive galaxies for which a size measurement is available comprises 57 galaxies from the selection of massive galaxies in the goods fields on which the gns pointings were centred @xcite . the measured local densities of those galaxies are very reliable since they are in the centre of their respective pointing and should not be affected by survey edges , as discussed in section [ density ] . the left panel of figure [ fig11 ] plots the local densities of the massive galaxy sample ( red dots ) and the rest of the sample ( blue circles ) against redshift . a k - s test between the two subsamples shows that they are not statistically different . to examine a possible environmental effect on the sizes of massive galaxies in our sample , we use the galaxies effective radii measured by @xcite . they argue that the measured effective radii of these massive galaxies are consistently smaller than the typical effective radii of galaxies of comparable stellar mass in the local universe . different scenarios have been proposed to account for this size evolution , one of them being dry merging . in this scenario repeated minor merging of gas poor galaxies would not trigger the formation of new stars , but could possibly increase the size of a galaxy by dynamical friction and the injection of angular momentum @xcite . this scenario would then suggest a connection between galaxy sizes and local density , since it requires the presence of numerous companions for galaxies to grow in size . the right panel of figure [ fig11 ] shows the effective radii @xmath203 of massive galaxies as a function of their local density @xmath124 . a spearman rank correlation test finds no significant correlation between @xmath203 and local density , although all galaxies in the most underdense environments ( @xmath204 ) have small @xmath203 ( @xmath205 3 kpc ) . however , due to the small number of objects in our sample this effect probably arises by chance . the lack of a correlation between galaxy size and local density is probably due to the different effects that the environment might have on galaxies . high local densities may not only increase the size of a galaxy via minor mergers as suggested by e.g. @xcite . high density environments might as well tidally truncate galaxies ( see e.g. * ? ? ? * ) , although tidal truncation is most effective on low - mass galaxies . another possibility is that the size evolution , does not occur through frequent minor merging of satellite galaxies , but through internal processes like agn feedback @xcite .

we compare the average rest - frame colour and fraction of blue galaxies in different local densities and at different stellar masses . we find a strong correlation between colour and stellar mass at all redshifts up to . we do not find a strong correlation between colour and local density , however , there may be evidence that the highest overdensities are populated by a higher fraction of blue galaxies than average or underdense areas . this could indicating that the colour - density relation at high redshift is reversed with respect to lower redshifts ( ) , where higher densities are found to have lower blue fractions . galaxies : evolution galaxies : high - redshift

we study the relationship between galaxy colour , stellar mass , and local galaxy density in a deep near - infrared imaging survey up to a redshift of using the goods nicmos survey ( gns ) . the gns is a deep near - infrared hubble space telescope survey imaging a total of 45 arcmin of the goods fields , reaching a stellar mass completeness limit of at . using this data we measure galaxy local densities based on galaxy counts within a fixed aperture , as well as the distance to the 3 , 5 and 7 nearest neighbour . we compare the average rest - frame colour and fraction of blue galaxies in different local densities and at different stellar masses . we find a strong correlation between colour and stellar mass at all redshifts up to . massive red galaxies are already in place at at the expected location of the red - sequence in the colour - magnitude diagram , although they are star forming . we do not find a strong correlation between colour and local density , however , there may be evidence that the highest overdensities are populated by a higher fraction of blue galaxies than average or underdense areas . this could indicating that the colour - density relation at high redshift is reversed with respect to lower redshifts ( ) , where higher densities are found to have lower blue fractions . our data suggests that the possible higher blue fraction at extreme overdensities might be due to a lack of _ massive _ red galaxies at the highest local densities . galaxies : evolution galaxies : high - redshift

1011.4846

i

in this study we investigate the influence of stellar mass and local density on galaxy rest - frame colour and the fraction of blue galaxies at redshifts between @xmath206 based on observational data from a deep hst @xmath25-band survey of unprecedented depth , the goods nicmos survey ( gns ) , reaching a stellar mass completeness limit of @xmath207 at @xmath3 . we find the following results : 1 . galaxy colour depends strongly on galaxy stellar mass at all redshifts up to @xmath0 . the colour - stellar mass relation does not evolve with redshift below @xmath0 . the stellar mass where the blue and red fractions cross over is roughly constant at @xmath208 in the redshift range between @xmath55 , which is remarkably similar to the cross - over mass found at lower redshifts between @xmath190 . the strong colour - stellar mass relation is very similar across all local environments and does not evolve strongly with redshift . the colour - stellar mass relation at @xmath67 has a slope similar to the relation at lower redshift ( @xmath190 ) , which also has a larger offset in colour between low and high local densities . at the same stellar mass , massive galaxies at high redshifts ( @xmath67 ) are bluer than at low redshifts ( @xmath190 ) , whereas the average colour of lower mass galaxies ( @xmath192 ) does not vary strongly with redshift . we do not find a strong influence of local environment on galaxy colours . if the colour - density relation persists at @xmath141 it must be very weak . we determine an upper limit to the possible change in the average @xmath6 colour between high and low relative densities of @xmath209 magnitudes . however , the most overdense regions ( @xmath210 times overdense ) may be populated by a higher fraction of blue galaxies than average and underdense regions . the difference in @xmath211 is @xmath212 . we find possible evidence that this higher blue fractions at the most extreme overdensities could be caused by a lack of massive red galaxies at the highest local densities . + 4 . we do not find a significant correlation between galaxy sizes ( effective radii ) and relative overdensity , although we do not find any galaxies with large effective radii ( @xmath213kpc ) at very low densities ( @xmath214 . however , this might be due to the small number of objects we find in low density environments and is probably a chance effect . + to summarise , our data suggests that stellar mass is the most important factor in determining the colours of galaxies in the early universe up to @xmath0 . local density might have a small additional effect , but only at the most extreme overdensities , which are populated by a higher fraction of blue galaxies . these results are consistent with studies at lower and intermediate redshift that suggest a gradual weakening of the environmental influence with higher redshift . a possible interpretation for this is that the environmental processes that alter the properties of galaxies are proceeding slowly over cosmic time . some of the most influential high density environments like galaxy clusters are still in the process of being build - up at @xmath141 and yet can not change galaxy colours via e.g. , ram pressure stripping or strangulation . if the trend for higher blue fractions at the highest local densities is real , it would suggest that we are witnessing the epoch of high star formation in more massive galaxies and that the local environment contributes to this epoch by triggering sf through galaxy interactions . note however , that the bluer colours at high local densities could as well be due to lower dust attenuation in these environments . the star formation rates of galaxies in the gns are currently investigated by bauer et al . ( submitted ) and will be the focus of a subsequent study of the relation between sfr , stellar mass and local density ( grtzbauch et al . , in preparation ) . future deep and wide surveys such as the ukidss uds and vista will be better able to address the environment vs. stellar mass issue in more detail in the coming years .

we study the relationship between galaxy colour , stellar mass , and local galaxy density in a deep near - infrared imaging survey up to a redshift of using the goods nicmos survey ( gns ) . the gns is a deep near - infrared hubble space telescope survey imaging a total of 45 arcmin of the goods fields , reaching a stellar mass completeness limit of at . our data suggests that the possible higher blue fraction at extreme overdensities might be due to a lack of _ massive _ red galaxies at the highest local densities .

we study the relationship between galaxy colour , stellar mass , and local galaxy density in a deep near - infrared imaging survey up to a redshift of using the goods nicmos survey ( gns ) . the gns is a deep near - infrared hubble space telescope survey imaging a total of 45 arcmin of the goods fields , reaching a stellar mass completeness limit of at . using this data we measure galaxy local densities based on galaxy counts within a fixed aperture , as well as the distance to the 3 , 5 and 7 nearest neighbour . we compare the average rest - frame colour and fraction of blue galaxies in different local densities and at different stellar masses . we find a strong correlation between colour and stellar mass at all redshifts up to . massive red galaxies are already in place at at the expected location of the red - sequence in the colour - magnitude diagram , although they are star forming . we do not find a strong correlation between colour and local density , however , there may be evidence that the highest overdensities are populated by a higher fraction of blue galaxies than average or underdense areas . this could indicating that the colour - density relation at high redshift is reversed with respect to lower redshifts ( ) , where higher densities are found to have lower blue fractions . our data suggests that the possible higher blue fraction at extreme overdensities might be due to a lack of _ massive _ red galaxies at the highest local densities . galaxies : evolution galaxies : high - redshift

astro-ph0402617

i

deep x - ray images of a patch of the sky show numerous x - ray sources , which mainly consist of a mixture of absorbed and unabsorbed active galactic nuclei ( agns ) . it is now recognized that these agns make up the bulk of what has been called the `` x - ray background '' . while normal galaxies , whose x - ray emission is probably dominated by the integration of x - ray binaries , start to emerge @xcite at the faintest fluxes , the dominant x - ray source population in the deep chandra and xmm - newton surveys comes from agn activities . thus multiwavelength studies of these x - ray sources are key to understanding the detailed history and physical conditions of the formation and the growth of the supermassive blackholes ( smbhs ) , which are now known to reside in the centers of almost all galaxies with a bulge @xcite . the region known as the `` groth - westphal strip '' ( gws ) , consists of hubble space telescope ( hst ) wide - field planetary camera 2 ( wfpc2 ) medium - deep images of a strip of 28 contiguous fields@xcite . it is a particularly useful field for extensive multiwavelength studies . numerous on - going and future followup projects have been/ are being conducted on and around this field . existing morphological information from the original wfpc2 observations , combined with the deep extragalactic evolutionary probe ( deep ) , canada - france redshift survey ( cfrs)lilly / cfrs/ ] and the ongoing deep 2 redshift surveys , is providing us with the first clues to the nature of the x - ray source counterparts . because of the contamination from starlight in the host galaxy , optical searches for faint agns in deep survey fields such as gws need elaborate efforts . such attempts have been made by searching for an unresolved component at the centers of galaxies , searching for variable nuclei , and by selecting those with ultraviolet - excess cores @xcite . these surveys reveal up to 10% of galaxies as agn candidates with nuclei extending as faint as m@xmath7@xmath8 15 . optical searches , however , are less sensitive to agns obscured by dust around the active nucleus . on the other hand , x - ray surveys for agns are not hindered by the luminosity of the underlying host galaxy . in particular , x - ray surveys with hard band ( @xmath9 kev ) sensitivity are also sensitive to the obscured agns . in view of this , we have obtained an 80 ks exposure the northeast part of the gws with xmm - newton . this field also has the advantage of a low column density of neutral gas in our galaxy , corresponding to @xmath10 @xmath11 @xcite . a quick look view and the preliminary log n - log s relations from these data have been presented in @xcite and @xcite . in this paper , we present the nature of the 23 x - ray sources in the gws , where morphological properties from the wfpc2 images and some redshifts are available from the deep / cfrs redshift surveys . we further make supplemental near infrared spectroscopic observation for some of these x - ray sources for which we did not observe agn signatures in the optical spectra . @xmath2 band photometry of the x - ray sources are also presented . the scope of this paper is as follows . in section [ sec : xobs ] , we describe the x - ray data and analysis , including source detection and spectral analysis . in section [ sec : opt_ir ] , we explain the source of the optical and near infrared ( nir ) data . the optical and nir nature of the xmm - newton sources and related statistics are presented . in [ sec : disc ] , we discuss the overall results on these x - ray sources and black hole mass and the relationship with the bulge luminosity . we also comment on selected individual sources . a summary is given in [ sec : sum ] . throughout this paper , we use @xmath12 , @xmath13 , and @xmath14 . unless otherwise noted , @xmath15 is the 2 - 10 kev rest - frame luminosity in units of @xmath16 calculated using the cosmological parameters shown above .

, 23 are within the wfpc2 fields . ten spectroscopic redshifts are available from the deep extragalactic evolutionary probe ( deep ) and canada - france redshift survey ( cfrs ) projects . is seen , suggestive of agn activity . the optical counterparts for the majority of the x - ray sources are bulge - dominated .

we summarize the multiwavelength properties of x - ray sources detected in the 80 ks xmm - newton observation of the groth - westphal strip , a contiguous strip of 28 hst wide - field planetary camera 2 ( wfpc2 ) images . among the x - ray sources detected in the xmm - newton field of view , 23 are within the wfpc2 fields . ten spectroscopic redshifts are available from the deep extragalactic evolutionary probe ( deep ) and canada - france redshift survey ( cfrs ) projects . four of these show broad mg ii emission and can be classified as type 1 agns . two of those without any broad lines , nevertheless , have [ nev ] emission which is an unambiguous signature of agn activity . one is a narrow - line seyfert 1 and the other a type 2 agn . as a followup , we have made near - infrared ( nir ) spectroscopic observations using the ohs / cisco spectrometer for five of the x - ray sources for which we found no indication of an agn activity in the optical spectrum . we have detected h+[nii ] emission in four of them . a broad h component and/or a large [ nii]/h ratio is seen , suggestive of agn activity . nineteen sources have been detected in the band and four of these are extremely red objects ( eros ; ) . the optical counterparts for the majority of the x - ray sources are bulge - dominated . the color of these bulge - dominated hosts are indeed consistent with evolving elliptical galaxies , while contaminations from star formation / agn seems to be present in their color . assuming that the known local relations among the bulge luminosity , central velocity dispersion , and the mass of the central blackhole still hold at , we compare the agn luminosity with the eddington luminosity of the central blackhole mass . the agn bolometric luminosity to eddington luminosity ratio ranges from 0.3 to 10% .

astro-ph0402617

r

the 23 sources detected in our 80 ks xmm - newton observation of the gws are representative of the x - ray sources that contribute most to the `` cosmic x - ray background '' and many of them represent the regime which marks the peak of accretion onto smbhs in centers of galaxies . a dominant population in this field consists of agns with @xmath72 44 at @xmath6 . only a few of them show signs of agn activity in their optical spectra . subaru ohs nir spectroscopy of four of the x - ray sources with no previous optical signature of agns revealed h@xmath1+[nii ] emission lines showing hints of broad h@xmath1 and/or stronger narrow [ nii ] lines indicative of agn activity . the host galaxies of the x - ray sources tend to be bulge - dominated and four are extremely - red objects ( eros ) ( or very red objects ; vros ) ( @xmath73 ) . also one object ( x130 ) has an upper limit @xmath74 , which is consistent with being an ero . [ fig : col ] shows @xmath5 and @xmath75 colors of the x - ray sources in our sample as a function of redshift . we have excluded x33 ( no @xmath2 and @xmath58 photometry available),x46 ( x - ray source is off - nucleus , see below ) , and x83 ( galactic star ) from the plot . those without redshift information are plotted left of z=0 . for reference , we plot k- and evolution - corrected galaxy colors for elliptical ( labeled as e1 in fig . [ fig : col ] ) , sa and sc galaxies from @xcite . model e1 corresponds to poggianti s model `` e '' , which has a star - formation rate with e - folding time of 1 gyr . we have neglected the difference of cosmological parameters used by us and@xcite , which corresponds to a @xmath76 difference in the age of the universe . in plotting these color tracks , we have converted the @xmath77 and @xmath78 magnitudes to @xmath57 and @xmath58 using the formulae given by @xcite . we also plot the colors of an elliptical galaxy model , which we have calculated for our filters and cosmology from the evolving seds by @xcite ( labeled as e2 ) . the plotted model is for a passively evolving galaxy after a short burst at the formation epoch of @xmath79 and @xmath80 at @xmath81 . the difference between @xmath82 and @xmath2 magnitudes have been neglected , following @xcite . [ fig : col ] shows that the @xmath75 color of the x - ray sources with bulge - dominated hosts indeed traces that of elliptical galaxies and , in particular , those of eros with redshifts are roughly consistent with the passively evolving elliptical model ( e2 ) . the @xmath83 color , which is more sensitive to the contaminations from star formation and agn activities , shows a scatter towards bluer colors from the elliptical regime . the reddest one ( x20 ) , with @xmath84 may be contributed by a dust enshrouded agn or a starburst . point - like sources tend to be distributed towards bluer ( qso ) colors , although the scatter is large . the scatter may be contributed to by unresolved host galaxies , intrinsic scatter in qso colors and/or reddening by intrinsic dust absorption . the hst imaging of this field has allowed us to find a significant population of x - ray sources at @xmath6 whose counterparts have a resolved bulge component , either as part of a disk+bulge structure or a pure bulge . in view of the relationship found between bulge mass and the central blackhole mass in nearby galaxies @xcite , it is interesting to make a first - order estimation of blackhole mass ( @xmath85 ) from the bulge - component of the host galaxy and compare it with the x - ray luminosity . in the rough estimation below , we take the approach of @xcite by first converting the bulge luminosity to the central velocity dispersion ( @xmath36 ) of the bulge stellar component using an empirical relation . then we use the tight @xmath86 @xcite correlation to obtain the estimated blackhole mass . we use the f814w k - correction for the e galaxy in fig . 18(d ) of @xcite to calculated the f814w absolute magnitude ( @xmath87 ) . we also assume an early - type galaxy color of @xmath88 @xcite . we then use the relations , @xmath89 @xcite to obtain the estimated blackhole mass . because the f814w band corresponds to the @xmath90 band at the source rest frame of @xmath6 , the combination of the k - correction and the magnitude conversion to @xmath91 is insensitive to the assumed galaxy spectral energy distribution . [ fig : mbhvslx ] shows the estimated @xmath92 versus @xmath15 ( absorption corrected , see sect . [ sec : z_and_l ] ) for 10 x - ray sources in the sample which have a resolved bulge component in the hst wfpc2 f814w image ( mds ) . it is interesting to estimate the eddington ratio @xmath93 for these x - ray sources , where @xmath94 is the bolometric luminosity of the agn and @xmath95 is the eddington luminosity corresponding to the blackhole mass . writing @xmath96 , where @xmath97 @xcite , we overplot three lines showing @xmath98 and @xmath99 in fig . [ fig : mbhvslx ] . fig . [ fig : mbhvslx ] shows that the estimated blackhole masses for the 10 agns range from @xmath100 @xmath101 and the eddington ratios from 0.3%-10% . these results have interesting implications on how agn evolve and the current stage of evolution for the agn represented here ( @xmath6 , @xmath102 ) . this is indeed a characteristic redshift and luminosity marking the peak of the accretion history of the universe . the result that these agn are typically radiating at a few percent may have important implications on the accretion history and formation of smbhs . if this is a typical eddington ratio throughout the agn phase of these objects , the growth of the blackhole occurs on a timescale of @xmath103 a few @xmath104 yrs , where @xmath105 yrs is the salpeter timescale , that is the timescale at which the mass of an object accreting at the eddington luminosity grows by a factor of @xmath106 ( for a radiative efficiency @xmath107 of a standard accretion disk model ) . this scenario has difficulty in that the timescale of a few @xmath108 yrs may be too long , while the number density of agn at @xmath109 decreases beyond @xmath6 @xcite . alternatively , it is possible that these agn have gone through a brief luminous phase in the past with near - eddington accretion rates . these may have been observed as more luminous qsos ( @xmath110 ) at @xmath111 . yet another more exotic possibility is that they are just accreting with a low radiative efficiency ( @xmath112 ) , allowing much less time for the smbh to grow . we note , however , that there are a number of caveats in interpreting these results and drawing conclusions relating the x - ray agn evolution and growth of the smbh . firstly , the current mds database shows the analysis for stellar ( point - like ) images or galaxies ( pure bulge , pure disk or bulge+disk decomposition ) , but only limited analysis @xcite has been completed for decomposing point - like ( stellar ) nuclei from the host galaxy ( stellar+bulge+disk , stellar+bulge or stellar+disk ) . thus we select against those with strong agn components ( or with large @xmath113 ) , which are likely to be listed as `` stellar '' in the mds database or the bulge luminosity in the database may be contaminated by the central agn component . this situation should be improved in the future , where the hst images are analyzed with point - like nucleus+host galaxy decomposition . extending this study to other deep fields with x - ray and hst ( wfpc2 as well as acs ) data , including the extended chandra deep field - south ( e - cdfs ) and the cosmos field , will be a next logical step . secondly , a much more fundamental limitation is that we have assumed the local relations in eq . [ eq : mass ] are still valid at @xmath6 . this assumption is not guaranteed to be valid . x8 : : : this is a typical type 1 qso at z=1.22 with a broad mg ii line . x10 : : : the deep optical spectrum shows many narrow emission lines including high - excitation lines like [ nev]@xmath114 , which are unambiguous indicators of agn activity . permitted lines ( mg ii , h@xmath64 ) are also narrow . since h@xmath115/[oiii]@xmath116 , these lines are not dominated by a seyfert 2 . it is either a seyfert 2 whose emission lines are heavily contaminated by starburst activity or a narrow - line seyfert 1 galaxy ( nls1 ) @xcite , where h@xmath64 is contributed to from the ( narrow end of the ) broad line region . because our x - ray spectral analysis shows no x - ray absorption ( @xmath117 ; see table [ tab : spec ] ) , the nls1 interpretation is more plausible . x11 : : : the optical counterpart has a very bright stellar ( point - like ) morphology and there is no optical spectrum available for this source to discriminate between a galactic star and a qso . however , its x - ray spectrum is inconsistent with a thermal plasma , having a significant residual in the soft part . also its x - ray to optical flux ratio @xmath118 ( @xmath119 is measured in 2 - 10 kev ) is well within the agn regime ( roughly between -1 and 1 ; see e.g. @xcite ) . thus it is most likely to be a qso . x20 : : : thanks to the chandra position , we can identify the x - ray source with the brightest bulge - dominated galaxy at @xmath120 , among four candidates apparently interacting with one another indicated by tidal bridges ( see fig . [ fig : poststamp ] ) . it is an interesting case where galaxy interactions are possibly feeding the agn activity at this early stage of the universe . it has a qso luminosity ( @xmath121 ) , but the optical image is dominated by bulge component of the host galaxy . the deep spectrum shows a broad mg ii line . the x - ray spectrum shows an absorption of @xmath122 . this is an example of optical type-1 x - ray type 2 agn . this is also an ero ( @xmath84 ) and a sub - mm source detected in a deep scuba survey @xcite . x22 : : : no previous optical / ir spectroscopic observations existed for this source . our subaru ohs / cisco observation detected h@xmath1 and @xmath123\lambda\lambda$ ] 6548,6583 emission lines , giving z=0.983 . based on the sign of broad h@xmath1 and strong @xmath124 , high luminosity @xmath125 . while we mark it as an agn - ir , it may well be a type 1 agn . x28 : : : this source is the most conspicuous hard x - ray source in the field with an intrinsic absorption of @xmath126 [ @xmath11 ] . it is a bulge - dominated galaxy with no optical / ir spectroscopy and a photometric redshift of @xmath128 @xcite based on its v i color alone . this is most likely a seyfert 2 based on the x - ray properties . x46 : : : the position of the source has been determined with chandra and the relative alignment of the wfpc2 image and x - ray sources has been achieved the three other cxo sources in the field . the x - ray source counterpart is identified with a hot spot just off the patchy irregular starforming galaxy deep gss 074_2638 ( mds u2ay1:0019 ) at z=0.432 . if we assume that the x - ray source is at the same redshift as this irregular galaxy , the luminosity would be @xmath129 . this is too luminous for an ultraluminous x - ray source ( ulx ) . we also note that there is a nearby edge - on disk galaxy ( deep gss 074_2237 , z=0.156 ) . the x - ray source is 4@xmath18 away ( projected distance of 10 kpc ) from its nucleus and located towards the direction perpendicular to the disk . therefore the x - ray source could be a ulx associated with the halo of the galaxy . however , even if the x - ray source was at the redshift of this disk galaxy , its luminosity would still be @xmath130 , again well above the ulx regime . one possibility is that this irregular galaxy is undergoing a merging process and the x - ray source is at the nucleus of one of the merging galaxies , or it may simply be a background qso . x52 : : : the deep spectrum show no broad lines and the location of mgii shows only absorption . other features include [ oii]@xmath131 and [ neiii]@xmath132 . the presence of [ nev]@xmath133 is suggested but uncertain . we observed this object with subaru ohs and found a moderately broad h@xmath1 ( fwhm @xmath67 ) and a strong [ nii ] doublet . [ fig : ohs ] ) . the fact that there is no broad mgii line but a moderately broad h@xmath1 suggests that the agn is obscured by a dust cloud . this is consistent with the hard color of this object , with the second largest hr(2 - 4.5 kev/0.5 - 2 kev ) in the sample . [ fig : hr ] . this is an ero ( @xmath134 ) . x66 : : : we find no indication of an agn in the deep spectrum . like x52 , our subaru ohs observation revealed possible agn activity through the detection of a moderately broad @xmath135 ( fwhm @xmath67 ) line and a strong [ nii ] doublet . this is an obscured agn similar to x52 and has a hardest hr(2 - 4.5 kev/0.5 - 2 kev ) . there is also a hint of [ neiii]@xmath132 , a line which is often stronger in agn than starforming galaxies . x69 : : : a spectroscopic redshift of @xmath136 has been determined by our subaru observation in close agreement with the photometric redshift determined by @xcite of @xmath137 . the subaru ohs spectrum seems to indicate either strong [ nii]@xmath138 or broad h@xmath1 suggestive of agn activity . this is an ero ( @xmath139 ) . x83 : : : because of the low x - ray to optical flux ratio ( @xmath140 ) for this bright optical object ( f606w=14.8 ) , this is certainly a galactic star . x125 : : : although the mds database shows that it is a point source , its color is consistent with an elliptical galaxy at the photometric redshift of @xmath141 @xcite . the optical counterpart is probably dominated by the host galaxy . x146 : : : this object is detected only in the hard ( 2 - 8 kev ) x - ray band . the deep optical spectrum clearly shows [ nev]@xmath133 emission and strong [ neiii]@xmath132 . this is a typical seyfert 2 galaxy with absorbed x - ray spectrum

we summarize the multiwavelength properties of x - ray sources detected in the 80 ks xmm - newton observation of the groth - westphal strip , a contiguous strip of 28 hst wide - field planetary camera 2 ( wfpc2 ) images . among the x - ray sources detected in the xmm - newton field of view nineteen sources have been detected in the band and four of these are extremely red objects ( eros ; ) . the color of these bulge - dominated hosts are indeed consistent with evolving elliptical galaxies , while contaminations from star formation / agn seems to be present in their color . assuming that the known local relations among the bulge luminosity , central velocity dispersion , and the mass of the central blackhole still hold at

we summarize the multiwavelength properties of x - ray sources detected in the 80 ks xmm - newton observation of the groth - westphal strip , a contiguous strip of 28 hst wide - field planetary camera 2 ( wfpc2 ) images . among the x - ray sources detected in the xmm - newton field of view , 23 are within the wfpc2 fields . ten spectroscopic redshifts are available from the deep extragalactic evolutionary probe ( deep ) and canada - france redshift survey ( cfrs ) projects . four of these show broad mg ii emission and can be classified as type 1 agns . two of those without any broad lines , nevertheless , have [ nev ] emission which is an unambiguous signature of agn activity . one is a narrow - line seyfert 1 and the other a type 2 agn . as a followup , we have made near - infrared ( nir ) spectroscopic observations using the ohs / cisco spectrometer for five of the x - ray sources for which we found no indication of an agn activity in the optical spectrum . we have detected h+[nii ] emission in four of them . a broad h component and/or a large [ nii]/h ratio is seen , suggestive of agn activity . nineteen sources have been detected in the band and four of these are extremely red objects ( eros ; ) . the optical counterparts for the majority of the x - ray sources are bulge - dominated . the color of these bulge - dominated hosts are indeed consistent with evolving elliptical galaxies , while contaminations from star formation / agn seems to be present in their color . assuming that the known local relations among the bulge luminosity , central velocity dispersion , and the mass of the central blackhole still hold at , we compare the agn luminosity with the eddington luminosity of the central blackhole mass . the agn bolometric luminosity to eddington luminosity ratio ranges from 0.3 to 10% .

0912.1345

c

we have used a monte - carlo radiative transfer code to model the spatial and frequency distribution of the @xmath0emission due to star formation in ( proto-)galaxies at the centre of dm halos with masses of @xmath12 to @xmath162 for a range of assumptions for the spatial distribution and the dynamical state of neutral hydrogen . dm halos in this mass range had been previously identified as the likely hosts of dlas and the recently detected population of faint spatially extended @xmath0emitters . our main results are the following : * as previously found by other authors , the spectral shape of the @xmath0emission from star formation in galaxies for which the dynamics of neutral hydrogen is dominated by infall / outflow is characterized by a strong blue / red peak , occasionally accompanied by a weaker red / blue peak . the spectral shape is very sensitive to the spatial distribution , velocity structure and ( to a smaller extent ) the temperature structure of the gas . the larger central column densities in the more massive galaxies / halos make escape of the @xmath0photons more difficult . the photons must then scatter further in frequency and space and thus emerge with a larger frequency shift and the emission extends to larger radii . larger bulk motions lead to more energy per scattering being transferred between the photons and the gas . this results in a larger frequency shift of the dominant spectral peak and a larger contrast between the strong and weak spectral peak . * the surface brightness profiles for photons emitted at the centre of the halos show a central peak with wings extending as far as our assumed neutral hydrogen distribution as long as the column density of neutral hydrogen exceeds about @xmath163 . the spatial profile of the emission is likewise sensitive to the spatial distribution , velocity and temperature structure of the gas . the spatial distribution is significantly more centrally peaked when the amplitude of the bulk motions increase toward the centre of the halo . * expanding shells of neutral hydrogen similar to those invoked to explain the @xmath0emission from lbgs produce spectra with one or more prominent red peaks . the surface brightness profiles are very flat , remaining essentially constant for 75% of the radius of the shell . this appears at odds with the observed profiles of the emitters , almost all of which show a central peak . * our modelling simultaneously reproduces the column density distribution of the neutral hydrogen and the velocity width of the associated low ionisation metal absorption of dlas , as well as the size distribution and the luminosity function of the rauch et al . emitters if we assume i ) that absorbers and emitters are hosted by dm halos that retain about 20% of the cosmic baryon fraction in the form of neutral hydrogen , with a spatial distribution which follows a nfw profile with concentration parameter @xmath164 times larger than that of the dark matter , ii ) that absorbers and emitters are hosted by dm halos with virial velocities @xmath165 , and iii ) that the central @xmath0emission due to star formation has a duty cycle of @xmath166 and the luminosity is proportional to the mass of neutral hydrogen in the dm halos . * the dm halos that contribute most to the incidence rate of dlas have masses in the range @xmath167 - @xmath168 and virial velocities in the range of 35 to 230 @xmath90 . the lower cut - off is mainly determined by the rather sharp decrease in the velocity width distribution of the associated low - ionization metal absorption in dlas at velocity width @xmath169 but may also be reflected in the turn - over of the @xmath0luminosity function at the faintest fluxes . the dm host halo masses are significantly smaller than those inferred for @xmath170 lbgs , consistent with the much higher space density of the faint emitters . the success of our detailed @xmath0radiative transfer modelling in explaining the observed properties of both dlas and the faint rauch et al emitters with a consistent set of assumptions further strengthens the suggestion that the faint emitters are indeed the long - searched for host galaxies of dla / lls . together with our modelling , the observed properties of the faint emitters should thus provide robust estimates not only of the space density , @xmath0luminosity and extent of the gas distribution but also of the masses of the dm halos , the duty cycle of star formation and the spatial profile and kinematics of the gas distribution of a statistically representative sample of dla host galaxies . the current ultra - deep spectroscopic surveys in the hudf and hdf should soon provide important additional information on the stellar content and possibly also dust content of these objects which will allow to further test the nature of what are almost certainly the building blocks of typical present - day galaxies like our own .

we investigate the spatial and spectral distribution ofemission due to star - formation at the centre of dlas , and its dependence on the spatial and velocity structure of the gas . our model simultaneously reproduces the observed properties of dlas and the faintemitters , including the velocity width and column density distribution of dlas and the large spatial extent of the emission of the faint emitters . our modelling confirms previous suggestions that dlas are predominately hosted by dark matter ( dm ) halos in the mass range , and are thus of significantly lower mass than those inferred for lyman break galaxies ( lbgs ) . our modelling suggests that dm halos hosting dlas retain up to 20% of the cosmic baryon fraction in the form of neutral hydrogen , and that star formation at the centre of the halos is responsible for the faintemission . the scattering of a significant fraction of theemission to the observed radii , which can be as large as 50kpc or more , requires the amplitude of the bulk motions of the gas at the centre of the halos to be moderate . the observed space density and size distribution of the emitters together with the incidence rate of dlas suggests that theemission due to star formation has a duty cycle of .

we use detailedradiative transfer calculations to further test the claim of rauch et al . ( 2008 ) that they have detected spatially extended faintemission from the elusive host population of dampedabsorption systems ( dlas ) in their recent ultra - deep spectroscopic survey . we investigate the spatial and spectral distribution ofemission due to star - formation at the centre of dlas , and its dependence on the spatial and velocity structure of the gas . our model simultaneously reproduces the observed properties of dlas and the faintemitters , including the velocity width and column density distribution of dlas and the large spatial extent of the emission of the faint emitters . our modelling confirms previous suggestions that dlas are predominately hosted by dark matter ( dm ) halos in the mass range , and are thus of significantly lower mass than those inferred for lyman break galaxies ( lbgs ) . our modelling suggests that dm halos hosting dlas retain up to 20% of the cosmic baryon fraction in the form of neutral hydrogen , and that star formation at the centre of the halos is responsible for the faintemission . the scattering of a significant fraction of theemission to the observed radii , which can be as large as 50kpc or more , requires the amplitude of the bulk motions of the gas at the centre of the halos to be moderate . the observed space density and size distribution of the emitters together with the incidence rate of dlas suggests that theemission due to star formation has a duty cycle of . [ firstpage ] quasars : absorption lines galaxies : formation

0706.0519

i

in the local universe , most galactic nuclei harbor a supermassive black hole ( e.g. , * ? ? ? * ) . the mass of the black hole correlates with global properties of the host , such as the velocity dispersion and luminosity of the spheroidal ( or bulge ) component , indicating a connection between nuclear activity and galaxy formation and evolution @xcite . understanding the origin of this relation is a major challenge for cosmological models and is believed to hold the key to solving several astrophysical problems such as the role of feedback from nuclear activity in suppressing star formation in massive galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in the standard cosmological scenario , spheroids grow by mergers of smaller galaxies while black holes grow by accreting surrounding matter . depending on the relative timing of the two processes , the scaling relations between black hole mass and spheroid luminosity and velocity dispersion ( hereafter m@xmath1-l or m@xmath1-l@xmath2 to specify the blue band and m@xmath1-@xmath3 relations , respectively ) could also evolve with cosmic time . for example if the spheroid evolved passively due to aging of stellar evolutions , changing l but not @xmath3 , while the black hole grows by accretion we would expect evolution in both the m - l and the m-@xmath3 relations , with the latter evolving more slowly than the former . by contrast , if black holes completed their growth first and the dominant mode of growth now is the transformation of stellar disks into spheroids , the two relations would evolve in the opposite sense @xcite . the tightness of the local relationships has been interpreted as evidence for feedback that synchronizes the relative growth . in this context , the tight relationships would be naturally reproduced if galaxies and black holes moved up the m-@xmath3 relation during merging events , so that the correlation would appear not to evolve with redshift @xcite . detailed theoretical predictions are extremely difficult due to the daunting range of scales ranging from the mpc scale halo to the pc scale dynamical sphere of influence of the black hole , to the @xmath13pc scale of the accretion disk and physical processes involved radiative transfer , heating and cooling , accretion , just to name a few . in spite of the challenge , numerous groups have been able to develop models that are increasingly more successful at reproducing a variety of observations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? however , to this date , the evolution of scaling laws remains very uncertain and sensitive to the schemes and approximations adopted to deal with the complex physics ( compare for example the recent works by @xcite and @xcite ) . accurate empirical measurements are needed to discriminate between scenarios , and provide input on the relative importance of various physical phenomena as well as on the accuracy of approximations . with this goal in mind , a number of groups have started observational programs to trace the evolution of scaling laws over cosmic time @xcite . however , observers face two fundamental limitations . on the one hand , since the sphere of influence of supermassive black holes is too small to be resolved at cosmological distances with present technology black hole mass estimates can only be obtained for active galaxies . typically , this involves broad line agn and the dynamics of the broad line region , with consequent loss of information about the host galaxy which is swamped by nuclear light . on the other hand at a deeper level the evolution of the scaling laws , depends on the interplay of at least four physical processes : i ) black hole accretion ; ii ) evolution of the stellar populations ; iii ) dynamical evolution of the spheroid , e.g. through mergers ; iv ) black hole feedback on star formation . for this reason , even when a scaling law can be measured as a function of redshift , the interpretation is often times ambiguous . for example , as discussed by @xcite , how much of the evolution of the m - l relation is due to evolution in the spheroid mass and how much is due to evolution of the stellar populations ? in this paper we address the two fundamental limitations by adopting the following strategy . first , as in our pilot study @xcite and in the first paper of this series ( * ? ? ? * hereafter paper i ) , we focus on relatively moderate redshift ( @xmath14 ) and luminosity ( monochromatic luminosity at 5100 @xmath15 erg s@xmath16 ) agn . although the lookback time is considerably smaller than that of the most distant quasars studied by other groups , this choice allows us to determine the host galaxy properties with considerably smaller uncertainties . second , we concentrate on a relatively small sample and measure several independent properties of the host galaxies . paper i reported stellar velocity dispersion measurements based on keck spectroscopy . this paper presents host spheroid luminosity and size measurements based on hst - acs imaging . we use this combined dataset to study at the same time and for the same sample the m@xmath1-l and m-@xmath3 relations and the fundamental plane of host spheroids . the combination of these diagnostics which can be thought as projections of a more fundamental manifold ( e.g. , * ? ? ? * ) allows us to disentangle stellar mass growth , stellar population evolution and black hole growth , and helps to identify the processes at work ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? the paper is organized as follows . in [ sec : data ] , we summarize the properties of the sample , describe the hst - acs observations , and present our surface photometry . we also derive black hole masses using nuclear luminosities as measured from hst images and the new calibration of the broad line region size - nuclear luminosity relation @xcite , together with h@xmath17 line widths from paper i. to construct a suitable local comparison sample , we use sloan digital sky survey images to derive new measurements of the spheroid luminosity of a sample of local seyferts with m@xmath1 available from reverberation mapping @xcite . [ sec : results ] describes our main results , i.e. the fundamental plane , m@xmath1-l@xmath18 , and m@xmath1-@xmath3 relation of the distant seyferts . detailed estimates of systematic errors and selection effects are given in [ sec : sys ] . [ sec : mani ] analyzes the three scaling relations under the assumption that the distant seyferts will evolve to match the local relations and derives constraints on the evolution of stellar mass , size and stellar populations of the host spheroids as a function of black hole growth . the results are discussed and compared with the literature in [ sec : disc ] , and summarized in [ sec : sum ] . throughout this paper magnitudes are given in the ab scale . we assume a concordance cosmology with matter and dark energy density @xmath19 , @xmath20 , and hubble constant h@xmath21=70 kms@xmath16mpc@xmath16 .

we use high resolution images obtained with the advanced camera for surveys on board the hubble space telescope to determine morphology , nuclear luminosity and structural parameters of the spheroidal component for a sample of 20 seyfert galaxies at . the offsets correspond to ( ) and ( ) , respectively for the m-l and m- relations ( the double error bars indicate random and systematic uncertainties ) . based on the disturbed morphologies of a fraction of the sample ( 6/20 ) we suggest collisional mergers with disk - dominated systems as the physical mechanism driving the evolution .

we use high resolution images obtained with the advanced camera for surveys on board the hubble space telescope to determine morphology , nuclear luminosity and structural parameters of the spheroidal component for a sample of 20 seyfert galaxies at . we combine these measurements with spectroscopic information from the keck telescope ( paper i ) to determine the black hole mass - spheroid luminosity relation ( m-l ) , the fundamental plane ( fp ) of the host galaxies and the black hole mass - spheroid velocity dispersion relation ( m- ) . the fp is consistent with that of inactive spheroids at comparable redshifts . assuming pure luminosity evolution , we find that the host spheroids had smaller luminosity and stellar velocity dispersion than today for a fixed m . the offsets correspond to ( ) and ( ) , respectively for the m-l and m- relations ( the double error bars indicate random and systematic uncertainties ) . a detailed analysis of known systematic errors and selection effects shows that they can not account for the observed offset . we conclude that the data are inconsistent with pure luminosity evolution and the existence of universal and tight scaling relations . in order to obey the three local scaling relations by assuming no significant black hole growth the distant spheroids have to grow their stellar mass by approximately 60% ( ) in the next 4 billion years , while preserving their size and holding their stellar mass to light ratio approximately constant . the measured evolution can be expressed as , consistent with black holes of a few m completing their growth before their host galaxies . based on the disturbed morphologies of a fraction of the sample ( 6/20 ) we suggest collisional mergers with disk - dominated systems as the physical mechanism driving the evolution .

0706.0519

r

this section presents the main results of this paper . first in [ ssec : fp ] we discuss the fundamental plane of the host galaxies in comparison with that of normal quiescent galaxies , for the subsample of objects that have both @xmath3 and structural parameters . in [ ssec : ml ] we present the m@xmath1-l@xmath2 relation for distant seyfert galaxies . having established that the fundamental plane of the host galaxies is indistinguishable from that of quiescent galaxies , we adopt the luminosity evolution inferred from fp analysis @xcite to compare with the local m@xmath1-l@xmath2 relation . in [ ssec : ms ] we revisit the m@xmath1-@xmath3 relation derived in paper i , using the new improved black hole mass estimates based on nuclear luminosities determined from hst imaging . in the local universe early - type galaxies obey the fundamental plane , i.e. an empirical correlation between effective radius , central velocity dispersion and effective surface brightness of the form : @xmath37 with @xmath38 , @xmath39 and @xmath40 for the coma cluster in the b(ab ) band . the evolution of the fp out to redshift @xmath41 is well established for quiescent early - type galaxies , for agn hosts @xcite , and for the spheroidal component of spiral galaxies with bulge - to - total luminosity ratio greater than 0.2 ( macarthur et al . 2007 , in preparation ) . in figure [ fig : fpb ] we plot the fp parameters of the subset of distant seyferts for which structural parameters and stellar velocity dispersion is available , together with a comparable sample of quiescent galaxies taken from @xcite . the good agreement between the fp of quiescent and active galaxies gives us confidence that our surface photometry is not systematically biased by the presence of a nuclear point source . the offset with respect to the local relation ( solid line ) is normally interpreted as evolution of the stellar populations . under the assumption of pure luminosity evolution , luminosity evolves with redshift such that the expected value at @xmath8 is given by @xmath42 @xcite . applying the same assumption to the sample of distant seyferts at @xmath0 implies that : @xmath43 , where random and systematic errors have been added in quadrature for simplicity . in order to compare with the local relations we need to account for the fact that the luminosity of a stellar population decreases as it ages . as our first working hypothesis , in this section we will present our results assuming that stellar populations evolved as inferred from the fp studies under a pure evolution scenario , and use the variable l@xmath44 obtained using equation [ eq : lbev ] . a more general discussion will be given in [ sec : mani ] . the relation between black hole mass and host spheroid luminosity for our points as well as for local comparison samples is shown in figure [ fig : bhl ] . the main result is that the seyfert galaxies at @xmath0 and those at @xmath8 cover approximately the same range in spheroid luminosity , but the average black hole mass is higher for the distant seyferts . the mismatch is exacerbated if one considers that five of the distant seyferts measurements are upper limits ( while only one of the local seyferts is an upper limit ) . conservatively we will generally consider the measured offset as the best estimate of the offset although it should be kept in mind that it is most likely a lower limit . quantitatively , the offset with respect to the fiducial local relationship ( solid line ) corresponds to @xmath45 ( @xmath46 ) , considering the intrinsic scatter of the relation to be a free parameter and then marginalizing over it . listed systematic errors are derived as discussed in section [ sec : sys ] . if measured with respect to the local seyferts ( magenta line ) , the best estimate of the offset changes to @xmath47 this is visualized in figure [ fig : bhlhisto ] where we plot the distribution of residuals with respect to the local fiducial relation for the distant and local samples . we conclude that pure luminosity evolution is inconsistent with the observations , if we required that at @xmath8 all galaxies obey the m@xmath1-l@xmath2 relation . we can not solve this inconsistency by invoking different luminosity evolution . the stellar populations would be required to become brighter with time in order to reconcile the data with the local relationship . this can be ruled out on physical grounds . therefore , taking this result at face value , we have to conclude that either not all spheroids obey the m - l relations , or that a significant amount of new stars have been added to the spheroids since @xmath0 . the interpretation of this result will be discussed in sections [ sec : mani ] and [ sec : disc ] , after we conclude presenting the evidence and discussing systematic errors and selection effects in the remainder of this section . figure [ fig : ms ] shows the m@xmath1-@xmath3 relation for the distant seyferts as well as the local comparison samples . the samples and symbols are the same as in figure [ fig : bhl ] with few minor exceptions : i ) only the 14 distant seyferts with available stellar velocity dispersion ( from paper i ) are plotted , including s28 and s99 for which hst photometry is not available . ii ) local relations are from @xcite and @xcite ; iii ) local seyferts obey the same relation as quiescent galaxies by construction , as this is the constraint used to derive the virial coefficient @xcite , so there is no need to show a separate local relation for seyferts . the only substantial difference with respect to figure 8 in paper i is that black hole masses have been recalculated based on hst photometry . the m@xmath1-@xmath3 relation shows the same basic result as the m@xmath1-l@xmath2 relation . at fixed host galaxy properties , distant seyferts appear to host larger black hole mass than local ones . quantitatively , the offset corresponds to @xmath6 ( i.e. @xmath48 ) . note that offset is slightly reduced ( 0.08 in @xmath49 ) with respect to paper i and the systematic error is smaller due to the improved estimate of black hole masses that avoid stellar contamination . as shown in figure [ fig : ms ] and discussed in paper i , adopting the local relation from @xcite or @xcite changes the offset by much less than the error bars because the two local relations are very well matched in the range of black hole mass and stellar velocity dispersion covered by our sample .

we combine these measurements with spectroscopic information from the keck telescope ( paper i ) to determine the black hole mass - spheroid luminosity relation ( m-l ) , the fundamental plane ( fp ) of the host galaxies and the black hole mass - spheroid velocity dispersion relation ( m- ) .

we use high resolution images obtained with the advanced camera for surveys on board the hubble space telescope to determine morphology , nuclear luminosity and structural parameters of the spheroidal component for a sample of 20 seyfert galaxies at . we combine these measurements with spectroscopic information from the keck telescope ( paper i ) to determine the black hole mass - spheroid luminosity relation ( m-l ) , the fundamental plane ( fp ) of the host galaxies and the black hole mass - spheroid velocity dispersion relation ( m- ) . the fp is consistent with that of inactive spheroids at comparable redshifts . assuming pure luminosity evolution , we find that the host spheroids had smaller luminosity and stellar velocity dispersion than today for a fixed m . the offsets correspond to ( ) and ( ) , respectively for the m-l and m- relations ( the double error bars indicate random and systematic uncertainties ) . a detailed analysis of known systematic errors and selection effects shows that they can not account for the observed offset . we conclude that the data are inconsistent with pure luminosity evolution and the existence of universal and tight scaling relations . in order to obey the three local scaling relations by assuming no significant black hole growth the distant spheroids have to grow their stellar mass by approximately 60% ( ) in the next 4 billion years , while preserving their size and holding their stellar mass to light ratio approximately constant . the measured evolution can be expressed as , consistent with black holes of a few m completing their growth before their host galaxies . based on the disturbed morphologies of a fraction of the sample ( 6/20 ) we suggest collisional mergers with disk - dominated systems as the physical mechanism driving the evolution .

0706.0519

i

this paper is devoted to the study of the cosmic evolution of black holes and their host galaxies . to this aim we have performed a detailed analysis of a sample of 22 seyfert 1 galaxies at @xmath14 . the choice of this particular redshift and moderate luminosity agns allows us to derive precision measurements of the host galaxy properties , as well as to obtain an estimate of the black hole mass from the dynamics of the broad line region . using high resolution images taken with acs we derived luminosity , effective radius and effective surface brightness of the host spheroid as well as nuclear luminosity . we combined this information with emission line widths and stellar velocity dispersion based on high signal to noise keck spectroscopy ( paper i ) to construct the m@xmath1-l , m@xmath1-@xmath3 and fundamental plane relations of distant seyferts . we compared the @xmath14 scaling relations with those followed by local samples of quiescent and active galaxies to determine evolutionary trends . the main results can be summarized as follows : 1 . the m@xmath1-l@xmath2 relation at @xmath14 is inconsistent with the local relation and the assumption of pure luminosity evolution of the host galaxy . adopting pure luminosity evolution consistent with fundamental plane studies , the offset from the local relation corresponds to an offset in present day b - band luminosity of @xmath4 , i.e. @xmath86 , in the sense that black holes lived in smaller bulges at @xmath14 than today . the m@xmath1-@xmath3 relation at @xmath14 is inconsistent with the local relation and the assumption of pure luminosity evolution . the offset with respect to the local relation corresponds to @xmath87 , i.e. @xmath88 , in the sense that black holes lived in smaller bulges at @xmath14 than today . monte carlo simulations show that the offset is not the result of selection effects , which are negligible for the m@xmath1-@xmath3 relation , and can account for at most 0.1 dex of the observed offset of the m@xmath1-l relation . 4 . in order to satisfy the local m@xmath1-@xmath3 , m@xmath1-l and fp relations by @xmath8 assuming no black hole growth our distant spheroids have to grow their stellar mass by approximately 60% ( @xmath89 ) in the next 4 billion years , while preserving their size and holding their stellar mass to light ratio approximately constant . this corresponds to an evolution of the black hole to spheroid mass ratio of the form @xmath90 . assuming that our results are not due to unknown systematic errors or unknown selection effects , the observed evolution can be qualitatively explained if our seyferts undergo a single collisional merger with a disk - dominated system between z=0.36 and today this is consistent with the observed merging / interacting fraction and a timescale for merging visibility of @xmath291 gyr . a single merger could increase the spheroid mass by transporting stellar mass from the progenitors disks , without the corresponding growth of the central black holes due to the lack of black hole in the disk dominated system . at the same time , this process would add younger stars to the spheroid ( either from the merging disks or from newly formed stars ) thus counteracting the fading of the old stellar populations and producing an approximately constant stellar mass to light ratio in the spheroid . numerical simulations including realistic prescriptions for star formation , agn activity and mass loss will be needed to see if these mergers do , indeed , preserve r@xmath31 and m@xmath91/l@xmath2 . if these indications are supported by future studies , then they will confirm that black holes completed their growth before their host galaxies and are perhaps to be seen less as a by - product of galaxy formation than as an orchestrator @xcite . we thank david hogg and the sdss project for providing calibrated images of the local comparison sample . we thank aaron barth , brad peterson , gregory shields , and risa wechsler for discussions . we thank chien peng for useful discussions and advice on using galfit and the anonymous referee for useful suggestions and constructive criticism . we are grateful to kevin bundy for providing the catalog of galaxies in the goods fields with photometric and spectroscopic redshift used to find the control sample described in [ sec : disc ] . this work is based on data obtained with the hubble space telescope and the 10 m w.m . keck telescope . we acknowledge financial support from nasa through hst grant go-10216 . tt acknowledges support from the nsf through career award nsf-0642621 , and from the sloan foundation through a sloan research fellowship . , m. c. , denney , k. d. , cackett , e. m. , dietrich , m. , fogel , j. k. j. , ghosh , h. , horne , k. , kuehn , c. , minezaki , t. , onken , c. a. , peterson , b. m. , pogge , r. w. , pronik , v. i. , richstone , d. o. , sergeev , s. g. , vestergaard , m. , walker , m. g. , & yoshii , y. 2006 , , 651 , 775 , x. , strauss , m. a. , richards , g. t. , hennawi , j. f. , becker , r. h. , white , r. l. , diamond - stanic , a. m. , donley , j. l. , jiang , l. , kim , j. s. , vestergaard , m. , young , j. e. , gunn , j. e. , lupton , r. h. , knapp , g. r. , schneider , d. p. , brandt , w. n. , bahcall , n. a. , barentine , j. c. , brinkmann , j. , brewington , h. j. , fukugita , m. , harvanek , m. , kleinman , s. j. , krzesinski , j. , long , d. , neilsen , jr . , e. h. , nitta , a. , snedden , s. a. , & voges , w. 2006 , , 131 , 1203 , k. , bender , r. , bower , g. , dressler , a. , faber , s. m. , filippenko , a. v. , green , r. , grillmair , c. , ho , l. c. , kormendy , j. , lauer , t. r. , magorrian , j. , pinkney , j. , richstone , d. , & tremaine , s. 2000 , , 539 , l13 , j. m. , davis , m. , faber , s. m. , guhathakurta , p. , gwyn , s. , huang , j. , koo , d. c. , le floch , e. , lin , l. , newman , j. , noeske , k. , papovich , c. , willmer , c. n. a. , coil , a. , conselice , c. j. , cooper , m. , hopkins , a. m. , metevier , a. , primack , j. , rieke , g. , & weiner , b. j. 2006 , arxiv astrophysics e - prints , r. k. , bernardi , m. , schechter , p. l. , burles , s. , eisenstein , d. j. , finkbeiner , d. p. , frieman , j. , lupton , r. h. , schlegel , d. j. , subbarao , m. , shimasaku , k. , bahcall , n. a. , brinkmann , j. , & ivezi , . 2003 , , 594 , 225 , s. , gebhardt , k. , bender , r. , bower , g. , dressler , a. , faber , s. m. , filippenko , a. v. , green , r. , grillmair , c. , ho , l. c. , kormendy , j. , lauer , t. r. , magorrian , j. , pinkney , j. , & richstone , d. 2002 , , 574 , 740 lrrcrrr s01 & 15 39 16.23 & + 03 23 22.06 & 0.3596 & 18.74 & @xmath92 + s02 & 16 11 11.67 & + 51 31 31.12 & 0.3544 & 18.94 & - + s03 & 17 32 03.11 & + 61 17 51.96 & 0.3583 & 18.20 & - + s04 & 21 02 11.51 & -06 46 45.03 & 0.3580 & 18.41 & 186@xmath93 8 + s05 & 21 04 51.85 & -07 12 09.45 & 0.3531 & 18.35 & 132@xmath93 5 + s06 & 21 20 34.19 & -06 41 22.24 & 0.3689 & 18.41 & 169@xmath9314 + s07 & 23 09 46.14 & + 00 00 48.91 & 0.3520 & 18.11 & 145@xmath9313 + s08 & 23 59 53.44 & -09 36 55.53 & 0.3591 & 18.42 & 187@xmath9311 + s09 & 00 59 16.11 & + 15 38 16.08 & 0.3548 & 18.16 & 187@xmath9315 + s10 & 01 01 12.07 & -09 45 00.76 & 0.3506 & 17.92 & - + s11 & 01 07 15.97 & -08 34 29.40 & 0.3562 & 18.34 & 127@xmath93 9 + s12 & 02 13 40.60 & + 13 47 56.06 & 0.3575 & 18.12 & 173@xmath9322 + s16 & 11 19 37.58 & + 00 56 20.42 & 0.3702 & 19.22 & - + s21 & 11 05 56.18 & + 03 12 43.26 & 0.3534 & 17.21 & - + s23 & 14 00 16.66 & -01 08 22.19 & 0.3515 & 18.08 & 172@xmath93 8 + s24 & 14 00 34.71 & + 00 47 33.48 & 0.3621 & 18.21 & 214@xmath9310 + s26 & 15 29 22.26 & + 59 28 54.56 & 0.3691 & 18.88 & 128@xmath93 8 + s27 & 15 36 51.28 & + 54 14 42.71 & 0.3667 & 18.80 & - s28 & 16 11 56.30 & + 45 16 11.04 & 0.3682 & 18.59 & 210@xmath9310 s29 & 21 58 41.93 & -01 15 00.33 & 0.3575 & 18.77 & - s31 & 10 15 27.26 & + 62 59 11.51 & 0.3504 & 18.14 & - s99 & 16 00 02.80 & + 41 30 27.00 & 0.3690 & 18.33 & 224@xmath9312 [ tab : sample ] lrrcrrrrc s01 & 18.50 & 19.92 & 10.28 & 21.85 & 5.29 & 0.74 & 0.29 & 8.21 + s02 & 19.03 & 19.85 & 10.31 & 20.27 & 2.63 & 0.36 & 0.22 & 7.99 + s03 & 17.94 & 20.23 & 10.16 & 17.04 & 0.50 & 1.69 & 0.39 & 8.29 + s04 & 18.06 & 20.12 & 10.20 & 18.36 & 0.96 & 1.42 & 0.36 & 8.45 + s05 & 17.93 & 20.45 & 10.07 & 18.84 & 1.03 & 2.04 & 0.47 & 8.77 + s06 & 18.35 & 20.48 & 10.06 & 18.81 & 1.01 & 0.54 & 0.18 & 8.17 + s07 & 17.79 & 20.35 & 10.11 & 18.69 & 1.01 & 2.26 & 0.45 & 8.55 + s08 & 18.31 & 21.75 & 9.55 & 20.50 & 1.23 & 1.25 & 0.40 & 8.10 + s09 & 18.17 & 19.00 & 10.65 & 19.87 & 3.24 & 0.78 & 0.22 & 8.15 + s10 & 18.01 & 19.30 & 10.53 & 16.08 & 0.49 & 1.11 & 0.27 & 8.27 + s12 & 18.12 & 21.16 & 9.78 & 18.14 & 0.54 & 1.05 & 0.28 & 8.69 + s16 & 19.14 & 22.26 & 9.34 & 19.97 & 0.76 & 0.70 & 0.48 & 8.26 + s21 & 17.45 & 18.95 & 10.67 & 15.82 & 0.51 & 2.30 & 0.34 & 8.81 s23 & 17.99 & 20.85 & 9.91 & 17.93 & 0.57 & 1.20 & 0.29 & 8.72 s24 & 18.06 & 18.59 & 10.81 & 22.41 & 12.6 & 0.44 & 0.11 & 8.33 s26 & 18.87 & 20.06 & 10.23 & 17.73 & 0.75 & 0.50 & 0.27 & 8.01 s27 & 18.51 & 19.46 & 10.46 & 21.17 & 4.78 & 0.92 & 0.36 & 8.10 [ tab : meas ] lrcc ark120 & 0.032 & 10.82 & 8.18 + mrk79 & 0.022 & 9.79 & 7.72 + mrk110 & 0.035 & 9.85 & 7.40 + mrk590 & 0.026 & 10.40 & 7.68 + mrk817 & 0.031 & 10.49 & 7.69 + ngc3227 & 0.004 & 8.85 & 7.62 + ngc4051 & 0.002 & 8.43 & 6.28 + ngc4151 & 0.003 & 9.49 & 7.66 + ngc5548 & 0.017 & 10.53 & 7.83 + [ tab : local ]

a detailed analysis of known systematic errors and selection effects shows that they can not account for the observed offset . we conclude that the data are inconsistent with pure luminosity evolution and the existence of universal and tight scaling relations . in order to obey the three local scaling relations by assuming no significant black hole growth the distant spheroids have to grow their stellar mass by approximately 60% ( ) in the next 4 billion years , while preserving their size and holding their stellar mass to light ratio approximately constant .

we use high resolution images obtained with the advanced camera for surveys on board the hubble space telescope to determine morphology , nuclear luminosity and structural parameters of the spheroidal component for a sample of 20 seyfert galaxies at . we combine these measurements with spectroscopic information from the keck telescope ( paper i ) to determine the black hole mass - spheroid luminosity relation ( m-l ) , the fundamental plane ( fp ) of the host galaxies and the black hole mass - spheroid velocity dispersion relation ( m- ) . the fp is consistent with that of inactive spheroids at comparable redshifts . assuming pure luminosity evolution , we find that the host spheroids had smaller luminosity and stellar velocity dispersion than today for a fixed m . the offsets correspond to ( ) and ( ) , respectively for the m-l and m- relations ( the double error bars indicate random and systematic uncertainties ) . a detailed analysis of known systematic errors and selection effects shows that they can not account for the observed offset . we conclude that the data are inconsistent with pure luminosity evolution and the existence of universal and tight scaling relations . in order to obey the three local scaling relations by assuming no significant black hole growth the distant spheroids have to grow their stellar mass by approximately 60% ( ) in the next 4 billion years , while preserving their size and holding their stellar mass to light ratio approximately constant . the measured evolution can be expressed as , consistent with black holes of a few m completing their growth before their host galaxies . based on the disturbed morphologies of a fraction of the sample ( 6/20 ) we suggest collisional mergers with disk - dominated systems as the physical mechanism driving the evolution .

astro-ph9708252

i

a key part of measuring the hubble constant , @xmath9 is to look out far enough so that the bulk velocities of galaxies are trivial compared to the hubble flow itself . due to the virgo cluster infall pattern , observation of the unbiased hubble flow can only be contemplated at distances in excess of @xmath10 km s@xmath4 . furthermore , bulk flows on even larger scales , such as those associated with the great attractor , may bias measurement of @xmath11 turner , cen , & ostriker ( 1992 ) and shi , widrow , & dursi ( 1996 ) , for example , show that under standard theories of structure formation , measurements of @xmath6 can depart significantly from its true `` global '' value due to the inhomogeneous distribution of matter in the universe , unless care is taken to sample deeply with large angular coverage . indeed , a common concern with many recent @xmath6 determinations is that they are not truly sampling the distant hubble flow ( bartlett et al . 1995 ) . characterizing the far - field requires observing large numbers of objects at large distances so that the hubble diagrams are insensitive to random peculiar velocities or bulk flows . hubble diagrams at present are largely based on the tully - fisher or @xmath12 relationships , the luminosities of supernovae ( sn ia or sn ii ) , and brightest cluster galaxies ( bcg ) . tully - fisher distances are available out to @xmath39,000 km s@xmath0 and have been recently used to measure a far - field @xmath6 ( giovanelli et al , 1997 ) , while @xmath12 have full - sky coverage out to only @xmath36,000 km s@xmath13 only a few sn ii have been observed in sufficient detail at large distances ( schmidt et al . 1994 ) , but the snia hubble diagram is becoming richer with time and provides some sampling of the hubble flow out to @xmath330,000 km s@xmath4 ( riess , press , & kirshner 1996 ; hamuy et al . 1996 ) . at present , however , calibration of the snia distance scale remains controversial ( see sandage et al . 1996 ) , and the sn ia diagrams remain relatively sparse at large distances . in this work we focus on calibrating the bcg hubble diagram , which is based on a recent characterization of bcg as relative distance estimators ( postman & lauer 1995 ) . in the classic work of sandage ( 1972 ) and sandage & hardy ( 1973 ) , bcg were used to show that the hubble flow was linear over a large range in redshift . lauer & postman ( 1994 ) observed bcg to define a frame for measuring the peculiar velocity of the local group , but as this work was in progress they realized that they could test for @xmath6 variations with distance with greater precision than was previously available in response to the concerns of turner , cen , & ostriker ( 1992 ) . lauer & postman ( 1992 ) presented a hubble diagram based on the 114 bcg that defined the volume - limited full - sky sample of abell clusters within 15,000 km s@xmath0 which is shown again here in figure [ bcg_hub ] . in brief , the absolute magnitudes of bcg , @xmath14 measured in apertures of fixed metric size , @xmath15 can be predicted from @xmath16 ( hoessel 1980 ) . figure [ bcg_hub ] shows the metric luminosities as apparent fluxes , corrected by the @xmath17 relationship to a standard value of @xmath18 the bcg hubble diagram slope is @xmath19 of the expected value , consistent with a uniform hubble flow over @xmath20 lauer & postman ( 1992 ) limit any variation in the _ apparent _ or local @xmath6 ( the hubble constant measured over a limited depth ) as compared to @xmath6 measured globally over the entire volume , to @xmath21 the snia hubble diagram also shows no evidence for @xmath6 variations with distance ; riess , press , & kirshner ( 1996 ) show its slope ( relative to euclidean ) to be @xmath22 the full - sky coverage of the abell cluster sample is crucial , as any dipole pattern caused by large bulk flows ( such at that advanced by lauer & postman 1994 ) will integrate out of the hubble diagram to first order . the linearity of the bcg hubble diagram shows that an excellent estimate of the far - field @xmath6 can be obtained once the zero point of the diagram is calibrated . we note that bcg presently provide the only volume - limited sample that explores the hubble flow at these distances . a hubble constant can be obtained from the bcg hubble diagram once an absolute distance is known to a subset of the galaxies . in essence , one transfers the full sample to a common distance , and finds the average absolute luminosity of the bcg on the assumption that the calibrating set is typical . random velocities and bulk flows of the bcg contribute to the `` cosmic scatter '' in their luminosity distribution , but cause no systematic offset ( with the caveats discussed in @xmath23[far_enough ] ) . we contrast this approach to others that use the apparent distance ratio between the virgo and coma clusters , or any other near and far aggregate of galaxies , to reach the far - field . instead , we are using the bcg as complete probes of the hubble flow over a large volume . we chose to calibrate the bcg hubble diagram with surface brightness fluctuation ( sbf ) distance estimates to four of the nearest bcg . the sbf method ( tonry & schneider 1988 ) uses the ratio of the second to first moments of the stellar luminosity function within early - type stellar systems as a distance estimator . the ratio of moments corresponds to an apparent magnitude , , that in the near - ir corresponds to the brightness of a typical red giant star . when the images are deep enough such that a star of apparent luminosity contributes more than a single photon to an observation , the random spatial point - to - point surface brightness fluctuations in a galaxy image are dominated by the finite number of stars it comprises , rather than photon shot noise . a power spectrum of the sbf pattern provides . use of the sbf method on galaxies with distances known from other methods ( see jacoby et al . 1992 for additional details ) provides the zero point , allowing absolute distances to be computed from . the most recent calibration of the sbf method is presented by tonry et al . major components of this work are : 1 ) understanding how varies with stellar population , 2 ) determining the zero point of the method , and 3 ) establishing the universality of the calibration . tonry et al . observe in the @xmath1 band , which minimizes variations in with stellar population _ ab initio . _ they also show that variations in are fully characterized by the ( @xmath24 ) colors of the stellar systems . based on 149 nearby galaxies they find @xmath25.\ ] ] this relationship has scatter of only 0.05 mag and agrees well with the theoretical calculations of worthey ( 1993a , 1993b ) both in slope _ and _ zero point . tammann ( 1992 ) was concerned that an earlier sbf calibration based on @xmath26 was incomplete and that additionally depended on the galaxies @xmath27 indices . in response , tonry et al . use their extensive sample to show that there is no correlation between the residuals of equation ( [ eqmibar ] ) and @xmath28 the zero point of equation ( [ eqmibar ] ) is based on cepheid distances to seven spiral galaxies with bulge sbf observations . tonry et al . present numerous comparisons of sbf to pnlf , tully - fisher , @xmath29 , snia , and sn ii distances , finding no evidence for any systematic offset between sbf bulge and elliptical galaxy measurements , nor any other systematic effect that challenges the calibration . although the nearest bcg are too far away for the sbf method to work from the ground , the high spatial resolution of _ hst _ allows sbf to be used beyond the 15,000 km s@xmath4 depth of the lauer & postman ( 1994 ) sample . an important caveat is that there is no direct match to the @xmath1 filter among the wfpc2 filter set . the f814w filter is a close analogue to @xmath1 ( see holtzman et al . 1995a ) , but requires additional calibration to tie it to the tonry et al . ( 1997 ) zero point . ajhar et al . ( 1997 ) accomplished this task in preparation for the present work , by comparing _ f814w sbf observations to the @xmath1 results for 16 galaxies in the tonry et al . sample . for the wfpc2 ccds and f814w filter , ajhar et al . find @xmath30,\ ] ] with scatter similar to that about equation ( [ eqmibar ] ) . a key difference between equation ( [ eqmibar ] ) and ( [ eqm8bar ] ) is the steeper relationship between 8bar and @xmath31 which ajhar et al . show is consistent with the differences between the f814w and @xmath1 filters . calibration of _ hst _ for sbf work is thus crucial for the present work .

( 1997 ) . the bcg globular cluster luminosity functions give distances essentially identical to the sbf results . using the velocities and sbf distances of the concordance of the present results with other recent determinations , and a review of theoretical treatments on perturbations in the near - field hubble flow , argue that going to the far - field removes an important source of uncertainty , but that there is not a large systematic error to be corrected for to begin with .

we used _ hst _ to obtain surface brightness fluctuation ( sbf ) observations of four nearby brightest cluster galaxies ( bcg ) to calibrate the bcg hubble diagram of lauer & postman ( 1992 ) . this bcg hubble diagram contains 114 galaxies covering the full celestial sphere and is volume limited to 15,000 km s providing excellent sampling of the far - field hubble flow . the sbf zero point is based on the cepheid calibration of the ground method ( tonry et al . 1997 ) as extended to the wfpc2 f814w filter by ajhar et al . ( 1997 ) . the bcg globular cluster luminosity functions give distances essentially identical to the sbf results . using the velocities and sbf distances of the four bcg alone gives in the cmb frame , valid on,500 km s scales . use of bcg as photometric redshift estimators allows the bcg hubble diagram to be calibrated independently of recession velocities , yielding a far - field with an effective depth of,000 km s . the error in this case is dominated by the photometric cosmic scatter in using bcg as distance estimators . the concordance of the present results with other recent determinations , and a review of theoretical treatments on perturbations in the near - field hubble flow , argue that going to the far - field removes an important source of uncertainty , but that there is not a large systematic error to be corrected for to begin with . further improvements in depend more on understanding nearby calibrators than on improved sampling of the distant flow . 8bar_814 8bar_i_814 .+ .1em

astro-ph9708252

c

we have used _ hst _ to obtain sbf distances to four bcg beyond 4,000 km s@xmath4 to calibrate the lauer & postman ( 1992 ) bcg hubble diagram , producing an estimate of the global value of @xmath6 valid on @xmath311,000 km s@xmath4 scales . this method gives @xmath180 and is based on the full lauer & postman ( 1994 ) 15,000 km s@xmath4 volume limited bcg sample . as such , the result is independent of virgo or coma cluster distances and membership issues , as well as the recession velocities of the four bcg studied . the large error reflects the photometric scatter about the @xmath17 ridge line , which was used to transfer the bcg hubble diagram to the sbf distance scale . as more bcg are observed with _ hst , _ the formal errors in this far - field @xmath6 should decrease . our review of the present understanding of the formation of large scale structure argues that we are likely to have fairly sampled the far - field . even theories with enough power on large spatial scales to generate bulk flows as large as those observed by lauer & postman ( 1994 ) are unlikely to have deviations outside of @xmath181 for the volume sampled by the bcg hubble diagram . in contrast , the compatibility of our results with those based on more nearby objects argues that there is little effect on @xmath6 and the depth of the measurements . going to the far - field most likely removes a source of uncertainty , rather than correcting for a systematic error . indeed we find @xmath2 just from hubble ratios based on the sbf distances and observed recession velocities to the four sbf - calibrated bcg at @xmath34,000 km s@xmath4 alone , a result consistent with our far - field result . the present @xmath6 rests on calibration of the sbf method and an understanding of its systematic effects . at the fundamental level , we are tied to the nearby cepheid calibrators . changes in the cepheid scale will propagate to the present results through the tonry et al . and ajhar et al . calibrations . as noted in the introduction , tonry et al . ( 1997 ) sbf calibration is tied to seven spiral galaxies with cepheid distances . further , tonry et al . have observed enough galaxies to perform an exhaustive series of tests , finding no systematic offsets between sbf observations of bulges and elliptical galaxies . a weaker link is transferring the ground @xmath1 method to the wfpc2 f814w filter , a task accomplished by ajhar et al . ( 1997 ) ; we will attempt to refine this calibration as more nearby systems are observed with _ hst . _ we conclude that the major uncertainties in the distance scale are those close to home rather than far away . we thank guy worthey and barbara ryden for helpful discussions , and john blakeslee for the photometry of a262 . this research was supported in part by _ hst _ go analysis funds provided through stsci grant go-05910.03 - 94a . ajhar , e. a. , lauer , t. r. , tonry , j. l. , blakeslee , j. b. , dressler , a. , holtzman , j. a. , & postman , m. 1997 , , 114 , 626 bartlett , j. g. , blanchard , a. , silk , j. , & turner , m. s. 1995 , science , 267 , 980 baum , w. a , hammergren , m. , thomsen , b. , groth , e. j. , faber , s. m. , grillmair , c. j. , & ajhar , e. a. 1997 , , 113 , 1483 bertschinger , e. 1984 , , 58 , 1 blakeslee , j. p. , & tonry , j. l. 1996 , , 465 , l19 burstein , d. , & heiles , c. 1984 , , 54 , 33 feast , m. w. , & whitelock , p. a. 1997 , preprint , astro - ph/9706097 feldman , h. a. , & watkins , r. 1994 , , 430 , l17 freedman , w. l. et al . 1994 , , 371 , 757 freedman , w. l. 1997 , in @xmath182 texas symposium , eds . olinto , a. , frieman , j. , & schramm , d. 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we used _ hst _ to obtain surface brightness fluctuation ( sbf ) observations of four nearby brightest cluster galaxies ( bcg ) to calibrate the bcg hubble diagram of lauer & postman ( 1992 ) . 1997 ) as extended to the wfpc2 f814w filter by ajhar et al .

we used _ hst _ to obtain surface brightness fluctuation ( sbf ) observations of four nearby brightest cluster galaxies ( bcg ) to calibrate the bcg hubble diagram of lauer & postman ( 1992 ) . this bcg hubble diagram contains 114 galaxies covering the full celestial sphere and is volume limited to 15,000 km s providing excellent sampling of the far - field hubble flow . the sbf zero point is based on the cepheid calibration of the ground method ( tonry et al . 1997 ) as extended to the wfpc2 f814w filter by ajhar et al . ( 1997 ) . the bcg globular cluster luminosity functions give distances essentially identical to the sbf results . using the velocities and sbf distances of the four bcg alone gives in the cmb frame , valid on,500 km s scales . use of bcg as photometric redshift estimators allows the bcg hubble diagram to be calibrated independently of recession velocities , yielding a far - field with an effective depth of,000 km s . the error in this case is dominated by the photometric cosmic scatter in using bcg as distance estimators . the concordance of the present results with other recent determinations , and a review of theoretical treatments on perturbations in the near - field hubble flow , argue that going to the far - field removes an important source of uncertainty , but that there is not a large systematic error to be corrected for to begin with . further improvements in depend more on understanding nearby calibrators than on improved sampling of the distant flow . 8bar_814 8bar_i_814 .+ .1em

1009.3927

m

our approach is based on a variant of the impulse approximation for studying gravitational perturbations on systems . in some respects , our formalism has similarities to that of @xcite , who considered tidal interactions between stars as a means for forming close binaries . @xcite calculated the response of gas spheres to external gravitational perturbations and the energy deposited into non - radial oscillations . later , similar analytic estimates of the energy and angular momentum exchange between a circumstellar disk and a passing star on a near - parabolic orbit were inferred by @xcite in the context of accretion disks . consider a flat , rotationally supported disk of stars , perturbed gravitationally by a passing object . in the usual impulse approximation @xcite , it is assumed that the stars in the perturbed system remain strictly stationary during the course of the encounter . the tidal force from the perturber relative to the center of mass of the perturbed body is calculated at each location within it from each point along the relative orbit of the interaction . the total velocity impulse delivered to each star in the perturbed object is then calculated by integrating the force over the entire orbit . in the simplest application of this method , the perturber follows a straight - line trajectory , as for a high - speed encounter , although as we show in what follows , it is possible to generalize the technique also to parabolic collisions , following @xcite . the analytic expressions that result from the impulse approximation @xcite give reasonably accurate results for the energy deposited in objects during tidal encounters for systems that are dominated by internal random motions @xcite . however , this method is not appropriate for capturing the essentials of responses like those in figures 1 because , by construction , it does not distinguish between prograde and retrograde interactions , since the stars in the perturbed body are held fixed during the encounter . to qualitatively capture the influence of resonances during tidal interactions , we employ the following variant of the impulse approximation . during the course of the encounter , stars in the perturbed system are allowed to move along unperturbed orbits within their host . for simplicity , we assume that the unperturbed orbits are strictly circular , although modest departures from these paths could , in principle , be handled using epicyclic theory . in this manner , the response of a given star will depend not only on its spatial location within the perturbed system , but also its velocity . as we demonstrate explicitly below , this approach makes it possible to characterize the resonant aspects of tidal interactions that distinguish between prograde and retrograde collisions , as in figure 1 . if the orbit of the encounter is non - circular , as in the examples that follow , the orbital angular frequency varies with time and , so , a given star within the perturbed system will be in precise resonance with the motion of the perturber for only a limited time . for this reason , we will refer to the formalism herein as describing _ quasi - resonant _ behavior , meaning that the response only resembles that characteristic of a true resonant interaction . this meaning should be taken to be equivalent to tt72 s description of tidal interactions between spinning objects as displaying `` near - resonant '' qualities . to be specific , consider a disk of stars on circular orbits comprising the _ victim _ interacting with an object which we will refer to as the _ perturber_. employ a coordinate system with origin at the center of mass of the victim and assume that the disk is razor thin and orient the coordinate system so that the disk is in the @xmath6 plane . then , the coordinate vector to any star within the victim is given by @xmath7 where @xmath2 is constant , because we assume that the unperturbed orbits internal to the victim are circular , and the position vector to the perturber will be denoted by @xmath8 in the sections below , we will consider various choices for the trajectory @xmath9 , which will fix the time - dependence of the components @xmath10 . we will adopt the convention that the unperturbed disk always lies in the @xmath6 plane . thus , for non - coplanar encounters , we will incline the orbit plane defined by the trajectory @xmath9 so that @xmath11 will be non - zero . the acceleration of each star relative to that on the center of mass of the perturbed body is @xmath12 \ , , \ ] ] where @xmath13 is the interaction potential between the perturber and the victim , @xmath14 is the mass of the victim , and the integral is over the density profile of this object . expand @xmath15 about the origin in a taylor series using @xmath16 after algebra , taking into account that the origin is located at the center of mass of the victim , the @xmath17-th component of the acceleration becomes @xmath18 \ , + \ , \ldots \ , \biggr \rbrace \ , , \ ] ] where @xmath19 and @xmath20 is the moment of inertia tensor @xcite : @xmath21 for simplicity , treat the force on each star in the disk from the perturber as that from a point mass . then , the interaction potential is @xmath22 performing the derivatives required in the above expression , we obtain the acceleration of a particular star at a given time . the velocity impulse delivered by the encounter can then be obtained by integrating over time . thus , the leading term in the series is @xcite @xmath23 dt \ , .\ ] ] likewise , the next order correction term can be written @xmath24 \biggr \rbrace dt \ , . \label{correction}\ ] ] in principle , this procedure can be extended to even higher order terms in the series . note that the terms in this last equation are all @xmath25 since the elements in the matrix @xmath26 involve integrals over squares of the internal coordinates of the victim , while the terms in eq . ( [ impulse ] ) are @xmath27 . in what follows , we will employ eq . ( [ impulse ] ) as the starting point for our analysis . unlike as in the usual impulse approximation we will allow both @xmath9 _ and _ @xmath28 to vary in time . we will , however , assume that the trajectory of the interaction , specified by @xmath9 , is prescribed ( i.e. orbital decay is not accounted for ) , and that the orbital motion within the victim , set by @xmath28 , is such that the stars follow their unperturbed motions throughout the course of the interaction .

such encounters are responsible for the formation of long tails and bridges of stars during galaxy collisions . for high - speed encounters , the traditional impulse approximation , however , does not distinguish between prograde and retrograde encounters , and therefore completely misses the resonant response . here , using perturbation theory , we compute the effects of quasi - resonant phenomena on stars orbiting within a disk .

when a spinning system experiences a transient gravitational encounter with an external perturber , a _ quasi - resonance _ occurs if the spin frequency of the victim matches the peak orbital frequency of the perturber . such encounters are responsible for the formation of long tails and bridges of stars during galaxy collisions . for high - speed encounters , the resulting velocity perturbations can be described within the impulse approximation . the traditional impulse approximation , however , does not distinguish between prograde and retrograde encounters , and therefore completely misses the resonant response . here , using perturbation theory , we compute the effects of quasi - resonant phenomena on stars orbiting within a disk . explicit expressions are derived for the velocity and energy change to the stars induced by tidal forces from an external gravitational perturber passing either on a straight line or parabolic orbit . comparisons with numerical restricted three - body calculations illustrate the applicability of our analysis .

1508.02993

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a _ compression body _ is a compact , orientable , irreducible @xmath3-manifold @xmath4 with a distinguished ` exterior ' boundary component @xmath5 , such that the inclusion @xmath6 is a @xmath7-surjective . fixing a closed , orientable surface @xmath8 , an _ @xmath0-compression body _ is a pair @xmath9 where @xmath4 is a compression body and @xmath10 is a homeomorphism . any @xmath0-compression body can be constructed as follows , see lemma [ compressdiscs ] . starting with @xmath11 $ ] , attach @xmath12-handles along a collection of disjoint essential annuli in @xmath13 and then glue a 3-ball onto every resulting spherical boundary component . here , the exterior boundary is @xmath14 , which clearly @xmath7-surjects , and has a natural identification with @xmath8 . two extreme examples of this construction occur when the collection of annuli is empty , in which case we obtain the _ trivial compression body _ @xmath15 $ ] , and when the collection is large enough so that after attaching the two - handles , _ every _ interior boundary component is a sphere , in which case @xmath16 and @xmath4 is a _ handlebody_. two @xmath0-compression bodies @xmath9 and @xmath17 are _ isomorphic _ if there is a homeomorphism @xmath18 such that @xmath19 . we also say that @xmath9 _ is contained in _ @xmath17 if there is an embedding @xmath18 such that @xmath19 . it follows ( see [ csec ] ) that @xmath9 and @xmath17 are isomorphic if and only if each is contained in the other . the _ compression body graph _ , written @xmath20 , is the graph whose vertices are isomorphism classes of nontrivial @xmath0-compression bodies , and where @xmath21 are adjacent if either @xmath22 the _ mapping class group _ of @xmath8 , written @xmath23 , is the group of isotopy classes of self - homeomorphisms @xmath24 of @xmath0 . it acts on @xmath25 by precomposing the markings : @xmath26 [ main ] when @xmath27 , the natural map @xmath28 is a surjection . here @xmath29 is the genus of the surface @xmath0 . note that when @xmath0 is a torus the theorem is false , since then @xmath20 is an infinite graph with no edges . the action of @xmath23 is faithful except when @xmath0 has genus two , in which case the kernel is generated by the hyperelliptic involution . this follows from the analogous statement about the action of the mapping class group on the complex of curves , since any simple closed curve @xmath30 on @xmath0 gives a _ small compression body _ @xmath31 $ ] obtained by attaching a two - handle along an annulus framing @xmath30 on @xmath32 , and @xmath23 acts on these small compression bodies via the defining curves , see [ csec ] . metrically , the compression body graph is @xmath33-hyperbolic and has infinite diameter . this follows from as yet unpublished work of maher - schleimer , who study a _ handlebody graph _ that is quasi - isometric to @xmath20 . we find the fine structure of @xmath20 more natural , but maher - schleimer should be credited as the first to study the notion of distance between handlebodies or compression bodies defined by such graphs . the compression body graph is an example of a _ comparability graph _ , where an edge joins vertices that are comparable in a partial order . as such , it is _ perfect , _ i.e. the chromatic and clique numbers of all subgraphs agree . such graph invariants come up briefly below ; for instance , lemma [ lem : chromatic ] implies that the chromatic and clique numbers of @xmath2 are @xmath34 . the inspiration for theorem [ main ] is the celebrated theorem of ivanov @xcite , see also luo @xcite , that the automorphism group of the curve graph is @xmath35 . here , the _ curve graph _ is the graph @xmath36 whose vertices are isotopy classes of simple closed curves on @xmath0 , and edges connect isotopy classes that admit disjoint representatives . ivanov used his theorem to conclude that the isometry group of teichmller space , regarded with the teichmller metric , is also @xmath35 , and that the outer automorphism group of the mapping class group is trivial . since then , there have been a number of papers proving similar rigidity results for complexes associated to a surface @xmath0 , e.g. the complex of non - separating curves @xcite , and the pants complex @xcite . the action of the mapping class group on @xmath20 encodes a wealth of information about the interaction of mapping classes and @xmath3-manifolds . for instance , an element @xmath37 fixes an @xmath0-compression body @xmath9 if and only if the homeomorphism @xmath38 of @xmath39 extends to a homeomorphism of @xmath4 . extension into compression bodies has been previously studied by casson - long @xcite , long @xcite , biringer - johnson - minsky @xcite and ackermann @xcite , among others . in studying the cobordism group of surface automorphisms , bonahon ( * prop 5.1 ) shows that when a homeomorphism of a surface @xmath8 extends to a @xmath3-manifold @xmath40 with @xmath41 , it also extends to a @xmath3-manifold in which all the non - periodic action happens on the union of a compression body and an interval bundle . for the proof of theorem [ main ] , we introduce an auxiliary simplicial complex , which is of independent interest . the _ torus complex _ , denoted @xmath42 , is the simplicial complex whose vertices are isotopy classes of non - separating simple closed curves , and where a collection of vertices @xmath43 spans a @xmath44-simplex if there exists a punctured torus @xmath45 such that @xmath46 can be isotoped to be contained in @xmath47 for all @xmath48 . [ thm : torus - aut ] for @xmath27 , the natural map @xmath49 is a surjection . in other words , every bijection of the set of non - separating simple closed curves on @xmath0 that preserves when curves lie in a punctured torus is given by a mapping class . as in theorem [ main ] , this map is an isomorphism except when @xmath0 has genus two , in which case the kernel is generated by the hyperelliptic involution . the relationship between @xmath42 and @xmath2 is described in the following proof sketch . we will outline here the proof of the main theorem , modulo results to be proved later . a full proof will be given at the end of the paper in section [ sec : proof ] . suppose that @xmath50 is an automorphism . in proposition [ prop : small - invariant ] , we show that @xmath51 preserves the set of small compression bodies @xmath31 $ ] , those that are obtained from @xmath0 by compressing a single curve @xmath52 . moreover , @xmath51 preserves whether the compressing curve is non - separating or separating . briefly , the idea is that small compression bodies are ( among ) those with small _ height _ , a notion of complexity introduced in [ sec : height ] , and that the height of a compression body @xmath4 is encoded in the chromatic number of certain subsets of the link of @xmath53 . this is the subject of section [ small ] . in particular , @xmath51 acts on the set of non - separating simple closed curves on @xmath0 . this action has the property that it preserves when a set of non - separating curves comes from a single punctured torus @xmath45 . when @xmath54 , this is because two non - separating curves @xmath55 lie in a punctured torus if and only if the compression bodies @xmath31 $ ] and @xmath56 $ ] contain a common sub - compression body , while @xmath57 requires an additional argument this leads us to consider the _ torus complex _ @xmath42 . section [ torus ] is dedicated to proving theorem [ thm : torus - aut ] and is entirely separate from the rest of the paper . consequently , the action of @xmath51 on the set of non - separating small compression bodies agrees with the action of mapping class @xmath58 . we then show that the actions of @xmath51 and @xmath24 agree on all of @xmath2 , using that a compression body is determined by the small compression bodies it contains . the authors would like to thank joseph maher and saul schleimer for helpful conversations . the first author was partially supported by nsf grant dms-1308678 .

when is a closed , orientable surface with genus , we show that the automorphism group of the compression body graph is the mapping class group . here , vertices are compression bodies with exterior boundary , and edges connect pairs of compression bodies where one contains the other . = 1

when is a closed , orientable surface with genus , we show that the automorphism group of the compression body graph is the mapping class group . here , vertices are compression bodies with exterior boundary , and edges connect pairs of compression bodies where one contains the other . = 1

1703.07940

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most commonly used reinforcement learning ( rl ) algorithms store an estimate of what s known as the value function ( vf ) . the vf corresponds to a particular policy , and is a mapping from each state - action pair to a real value which reflects the amount of reward the agent will obtain starting from that state - action pair and following the policy in question ( sutton and barto 1998 ) . in order for an rl algorithm to perform well ( i.e. to achieve a high reward ) , it is important that the vf estimate is as accurate as possible , since it is this estimate which governs how the algorithm will update its policy . traditional rl algorithms such as td(@xmath4 ) or @xmath5-learning can generate exact vf estimates when dealing with small state and action spaces . however , when environments are complex ( with large state or action spaces ) , applying such algorithms directly becomes too computationally demanding . as a result it is common to introduce some form of architecture with which to approximate the vf , for example a parametrised set of functions ( sutton and barto 1998 ; bertsekas and tsitsiklis 1996 ) . one issue when introducing vf approximation , however , is that the accuracy of the algorithm s vf estimate is highly dependent upon the exact form of the architecture chosen ( it may be , for example , that no element of the chosen set of parametrised functions closely fits the vf ) . accordingly , a number of authors have explored the possibility of allowing the approximation architecture to be _ learned _ by the agent , rather than pre - set manually by the designer see buoniu et al ( 2009 ) for an overview . what we might hope to achieve by employing such an approach is to create an rl algorithm which still has relatively low computational demands , but at the same time has increased flexibility , allowing us to apply the algorithm to a wider set of problems without needing to invest time to suitably adapt it in each case . if we assume that the approximation architecture being adapted is linear ( so that the vf is represented as a weighted sum of basis functions ) such methods are known as _ basis function adaptation_. a simple and perhaps , as yet , under - explored method of basis function adaptation involves using an estimate of the frequency with which an agent has visited certain states to determine which states to more accurately represent . such methods are `` unsupervised '' in the sense that no direct reference to the reward or to any estimate of the vf is made . the concept of using visit frequencies in an unsupervised manner is not completely new ( menache et al 2005 ; bernstein and shimkin 2010 ) however it remains relatively unexplored compared to methods which seek to measure the error in the vf estimate explicitly and to then use this error as feedback ( munos and moore 2002 ; bertsekas and yu 2009 ; di castro and mannor 2010 ; mahadevan et al 2013 ) . as we will demonstrate , however , unsupervised methods have some distinct advantages : ( a ) estimates of visit frequencies are cheap to calculate and to store , ( b ) accurate estimates of visit frequencies can be generated with fewer samples than accurate estimates of , for example , temporal differences ( which are a common form of feedback used to adapt basis functions ) , and ( c ) under suitable conditions , and applying an appropriate scoring function , such methods can in fact generate very accurate vf estimates , guaranteeing in certain cases scores arbitrarily close to zero . our overarching objective in this article is to more closely examine unsupervised methods and seek to quantify , where possible , these advantages . it is point ( c ) which is perhaps the most surprising , and it forms the substance of the article s main result . for any fixed policy you will have a stationary distribution describing the probability of being in each state . suppose ( i ) the policy and transition function for a given problem are close to deterministic , and ( ii ) the prior for the transition function is uniformly distributed ( this will be more precisely described below ) . we will show that , under these conditions , an agent which follows an arbitrary policy will , on average , tend to spend almost all of its time in a small subset of the state space . indeed , if the state space is of size @xmath0 , there is a theoretical upper bound on the average size of this subset : @xmath6 . provided we have enough basis functions to individually represent the states in this subset , unsupervised basis function adaptation methods can ensure that the vf is arbitrarily well estimated over this subset . if the scoring function we apply is weighted by the probability of visiting each state , we can then guarantee an arbitrarily low score . the implication of this is that , under these circumstances , unsupervised methods will perform _ at least as well _ as other more complex methods , but , compared to these other methods , will do so _ more cheaply _ ( in the sense of sampling required and also computational demands ) . whilst conditions ( i ) and ( ii ) encompass many important and general problems , we will also explore the potential to generalise condition ( ii ) to encompass a larger set of possible priors . we also explore these ideas experimentally . our experimental results suggest that our techniques provide a powerful advantage in many real world settings . over a set of realistic parameter settings the techniques ( when compared to fixed state aggregation ) can reduce vf error by an amount in the range of @xmath7-@xmath8% . in some cases the experimental results also suggest that the assumptions required by the theory can be relaxed . as noted above , unsupervised techniques at present are relatively unexplored . menache et al ( 2005 ) provided a brief evaluation of an unsupervised algorithm ( to provide a comparison with two more complex adaptation algorithms ) in the setting of policy evaluation . berstein and shimkin ( 2009 ) examined an algorithm where a set of kernels are progressively split ( `` once - and - for - all '' ) based on the visit frequency for each kernel . their algorithm includes policy updates which incorporate knowledge of uncertainty in the vf estimate . the algorithm we propose below works in conjunction with a state aggregation approximation architecture , employing a form of `` cell - splitting '' to give state space regions more or less resolution . this bears similarities to a number of approaches examined in the literature ( the main difference in our approach is the rules under which cells are split or joined ) . moore and atkeson ( 1995 ) provide an early algorithm based on updating a state aggregation architecture , whilst whiteson et al ( 2007 ) examined a basis function construction method involving cell splitting . our analysis is new both in terms of the details of the unsupervised algorithm we outline ( it is designed so as to minimise memory requirements , in particular to ensure that space complexity is roughly of the order of the number of basis functions , whilst still permitting the approximation architecture to be continuously adapted on - line ) and in terms of the theoretical concepts we derive . in the remainder of this section we outline the formal framework we will be using . in section [ unsupervised ] we set out the details of our algorithm ( pasa , short for `` probabilistic adaptive state aggregation '' ) which performs unsupervised basis function adaptation based on state aggregation . in section [ theoretic ] we outline our main theoretical results . finally , in section [ simulation ] we set out some empirical results designed to both support and extend the results in section [ theoretic ] . we assume that we have an agent which interacts with an environment over a sequence of iterations @xmath9 . for each @xmath10 the agent will be in a particular state to hold in the case of a continuous state space , additional assumptions would need to be introduced . ] @xmath11 ( @xmath12 ) and will take a particular action @xmath13 ( @xmath14 ) . each action is taken according to a _ policy _ @xmath15 whereby the probability the agent takes action @xmath13 in state @xmath11 is denoted as @xmath16 . we are considering the problem of policy evaluation , so we will always assume that the agent s policy @xmath15 is fixed ( i.e. does not change as a function of @xmath10 ) . the _ reward function _ @xmath17 is a mapping from each state - action pair @xmath18 to a real number , such that if the agent is in state @xmath11 and takes action @xmath13 , then it will receive a _ reward _ @xmath19 . the reward function is assumed to be deterministic and bounded , i.e. @xmath20 for all @xmath21 . the _ transition function _ @xmath22 defines how the agent s state evolves over time . if the agent is in state @xmath11 and takes an action @xmath13 in iteration @xmath10 , then the probability it will transition to the state @xmath23 in iteration @xmath24 is given by @xmath25 . both @xmath22 and @xmath17 are taken as unknown , however we assume we are given a prior distribution for both . the _ value function _ @xmath26 , which maps each of the @xmath27 state - action pairs to a real value , is defined as follows : @xmath28 where the expectation is taken over the distributions of @xmath22 and @xmath15 ( i.e. for a particular instance of @xmath22 , not over its prior distribution ) and where @xmath29 is known as a _ discount factor_. we have used superscript brackets to indicate dependency on the iteration @xmath10 . initially the vf is unknown , our objective , given some @xmath15 , is to learn the vf for a particular instance of @xmath22 . assuming we are able to store an explicit real value for each state - action pair , traditional rl algorithms provide a means of estimating @xmath26 . these estimates will converge to the correct value as @xmath10 becomes large ( sutton and barto 1998 ) . in cases where @xmath0 or @xmath30 are large , though , it may be impossible to store @xmath27 real values . hence , when dealing with such cases , it is common to employ vf approximation . once we approximate the vf , however , even if the underlying rl algorithm still converges to generate an estimate of the vf ( which is not always guaranteed ) , we can no longer rely on the estimate being arbitrarily close to the true value @xmath26 . one form of vf approximation , _ parametrised value function approximation _ , involves generating an approximation of the vf using a parametrised set of functions . the goal of the rl algorithm then becomes to find a value for the parameters so that the vf estimate is as near to the true value as possible . the approximate vf is denoted as @xmath31 , and , assuming we are approximating over the state space only and not the action space , this value is parametrised by a matrix @xmath32 of dimension @xmath33 ( where @xmath34 ) . such an approximation architecture is _ linear _ if @xmath31 can be expressed in the form @xmath35 , where @xmath36 is the @xmath37th column of @xmath32 and @xmath38 is a fixed vector of dimension @xmath1 for each pair @xmath18 . the @xmath39 distinct vectors of dimension @xmath0 given by @xmath40 are called _ basis functions_. it is common to assume that @xmath41 for all @xmath37 , in which case we have only @xmath1 distinct basis functions , and @xmath42 . a _ state aggregation _ approximation architecture see , for example , singh et al ( 1995 ) and whiteson et al ( 2007 ) is a simple linear approximation architecture which we can define as being a mapping @xmath43 from each state @xmath11 to a _ cell _ @xmath44 ( @xmath45 ) . defining the architecture as a `` mapping '' implies that every state corresponds to exactly one cell . we will denote as @xmath46 the set of states in the @xmath47th cell . given a state aggregation approximation architecture , the underlying rl algorithm can not distinguish states in the same cell , and hence @xmath48 will be the same for all states which are in the same cell ( @xmath32 in this context can be interpreted as a set of weights , one given to each cell - action pair ) . if we want to design an algorithm to adapt an approximation architecture , we need a means to assess how well it is doing this . a _ scoring function _ is used to assess the accuracy of a vf estimate ( and can also therefore be used to evaluate an algorithm designed to generate a vf estimate ) . many basis function adaptation algorithms use a scoring function as a form of feedback to help guide how the basis functions should be updated . in such cases it is important that the score is something which can be measured computationally . one commonly used score is the squared error in the vf estimate for each state - action , weighted by the probability of each state - action occurring ( menache et al 2005 ; bertsekas and yu 2009 ; di castro and mannor 2010 ) . we will refer to this as the _ mean squared error _ ( mse ) : @xmath49 this is where @xmath50 is a vector of the probability of each state given the stationary distribution associated with @xmath15 ( given some fixed policy @xmath15 , the transition matrix obtained from @xmath15 and @xmath22 has a corresponding stationary distribution , provided the transition matrix is irreducible and aperiodic ) . note that the true vf @xmath26 appears in ( [ mseexact ] ) . this value , however , is unknown . therefore , another commonly used scoring function ( which , unlike mse , can be estimated empirically ) uses @xmath51 , the _ bellman operator _ , to obtain an approximation of the mse . this scoring function we denote as @xmath52 ( this is a weighted sum of what is sometimes known as the _ bellman error _ at each state - action ) : @xmath53 where : @xmath54 our results in section [ theoretic ] will be stated in relation to mse and @xmath52 . it will be crucial to all of our results that the scoring function is weighted by @xmath50 . two important comments should be made in relation to this . the first is that , whilst applying such a weighting appears natural , a scoring function does not necessarily need to be weighted by @xmath50 ( or an approximation of @xmath50 ) . there may be circumstances under which a more appropriate measure of the accuracy of a vf estimate would , for example , weight every state equally ( the most appropriate measure to use in each situation would depend on a number of complex factors ) . we acknowledge this as a limitation of the analysis in section [ theoretic ] . the second is that , in investigating unsupervised basis function adaptation methods , we are implicitly making a comparison with methods of basis function adaptation which use explicit scores as a source of feedback ( these could be called `` supervised '' methods ) . if an algorithm uses a scoring function as feedback , then ( irrespective of which scoring function is most appropriate ) it is best evaluated in terms of how well it minimises _ that particular scoring function_. the scoring function @xmath52 is an attractive choice to provide feedback for supervised methods since , by weighting the error by the probability of visiting a state , it is possible to generate an estimate of the score without knowing the probability of visiting each state . in fact , any feedback based on a scoring function which is _ not _ weighted by @xmath50 would implicitly require some way of normalising the score for each state . this in turn would require an estimate for @xmath50 , which implies that @xmath55 distinct values need to be recorded . hence , if unsupervised methods can perform comparatively well in terms of minimising probability weighted scoring functions , this is of great importance when comparing such methods to supervised alternatives . in the definitions above both mse and @xmath52 are weighted by the probability of each action occurring . we could redefine mse and @xmath52 to weight each action equally when sampling for @xmath52 this would not be an issue computationally since @xmath15 is known to the algorithm , i.e. we can simply divide each sample by @xmath16 ( acknowledging that samples from rarely chosen actions would contribute more significantly to the variance of the estimate ) . our results in section [ theoretic ] will extend to @xmath52 under such an alternative definition .

when using reinforcement learning ( rl ) algorithms to evaluate a policy it is common , given a large state space , to introduce some form of approximation architecture for the value function ( vf ) . the exact form of this architecture can have a significant effect on the accuracy of the vf estimate , however , and determining a suitable approximation architecture can often be a highly complex task . consequently there is a large amount of interest in the potential for allowing rl algorithms to adaptively generate ( i.e. to learn ) approximation architectures . we investigate a method of adapting approximation architectures which uses feedback regarding the frequency with which an agent has visited certain states to guide which areas of the state space to approximate with greater detail . our algorithm can guarantee , assuming we use an appropriate scoring function to measure vf error , error which is arbitrarily close to zero as becomes large . it is able to do this despite having only space complexity ( and negligible time complexity ) .

when using reinforcement learning ( rl ) algorithms to evaluate a policy it is common , given a large state space , to introduce some form of approximation architecture for the value function ( vf ) . the exact form of this architecture can have a significant effect on the accuracy of the vf estimate , however , and determining a suitable approximation architecture can often be a highly complex task . consequently there is a large amount of interest in the potential for allowing rl algorithms to adaptively generate ( i.e. to learn ) approximation architectures . we investigate a method of adapting approximation architectures which uses feedback regarding the frequency with which an agent has visited certain states to guide which areas of the state space to approximate with greater detail . we introduce an algorithm based upon this idea which adapts a state aggregation approximation architecture on - line . assuming states , we demonstrate theoretically that provided the following relatively non - restrictive assumptions are satisfied : ( a ) the number of cells in the state aggregation architecture is of order or greater , ( b ) the policy and transition function are close to deterministic , and ( c ) the prior for the transition function is uniformly distributed our algorithm can guarantee , assuming we use an appropriate scoring function to measure vf error , error which is arbitrarily close to zero as becomes large . it is able to do this despite having only space complexity ( and negligible time complexity ) . we conclude by generating a set of empirical results which support the theoretical results . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

cond-mat9807401

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study of the critical behaviour of the ising model has several attractions . on the one hand , the ising - like models are simple enough , which is of a special advantage in the statistical physics . on the other hand , in spite of their simplicity , such models show rich and interesting behaviour at the critical point . also , the existence of the exact solution for the two - dimensional ising model often makes it an object for verifying different approximation schemes . all the stated above yielded the high interest devoted to the problem . in particular a great deal of generalization of the model appeared . among different ways of generalization , much attention has been devoted to the affect of the impurities on the critical behaviour of the ising - like models as well as to the investigation of critical regimes of the models on the lattices of a non - integer dimension ( @xmath3 ) . there have been devised different realizations of the last stated generalization . for example , one can approach the concept of non - integer dimensionality either by explicit construction of the non - integer dimensional object , which leads to the concept of a fractal @xcite , or by formal carrying out an analytic continuation of the function , which by definition depends on a natural value of dimension . within the theory of critical phenomena the latter ambiguity was reflected in examining the critical behaviour of the many - particle systems on fractal @xcite or on abstract hypercubic lattices of the non - integer @xmath3 . there arosed a question whether a model on a fractal lattice ( being scale invariant ) possesses universality as well as a system on a hypercubic lattice ( having translation invariance ) . the problem has been widely studied but still remains open @xcite . today s point of view states that the usual demand for strong universality ( in sense of critical properties depending only on symmetry of the order parameter , interaction range and space dimension ) seems not to be obeyed by fractal lattice systems , and for them the concept of universality itself should be revised @xcite . speaking about the study of ising - like models on analytically continued hypercubic lattices of non - integer @xmath3 , one should note a great variety of theoretical approaches devised for these problems . these include : the wilson - fisher @xmath9-expansion @xcite improved by the summation method @xcite ; kadanoff lower - bound renormalization applied to some special non - integer dimensions @xcite ; high - temperature expansion improved by a variation technique @xcite ; finite - size scaling method applied to numerical transfer - matrices data @xcite ; new perturbation theory based on the physical branch of the solution of the renormalization group equation @xcite ; fixed dimension renormalization group technique @xcite applied directly to arbitrary non - integer @xmath3 @xcite . perhaps the first paper devoted to the study of the ising model in different , however not non - integer dimension , was @xcite where non - universal properties of the model were discussed . all these approaches , as well as the computer simulations , confirm the correctness of the universality hypothesis also for non - integer @xmath3 hypercubic lattices and allow to obtain the critical exponents as functions of @xmath3 with high accuracy . in spite of the variety of approaches to treat the general non - integer @xmath3 case @xcite the results for the ising model critical exponents obtained on their basis lay close to each other ; the above mentioned analytic continuations may appear actually equivalent . note , however , that the analytic continuation in @xmath10 at general non - integer dimension leads to the fail of the yang - lee theorem @xcite . on the other hand , the study of ising - like spin systems on non - integer dimension hypercubic lattices can not be reduced to the fractal lattice systems @xcite except for the case of vanishing lacunarity limit @xcite and thus is the task of individual interest . returning to the study of the critical behaviour at integer @xmath3 , one should note that the problem becomes more complicated when studying spin systems with a structural disorder . whereas the case of the annealed disorder is of less interest from the point of view of determining asymptotical values of critical exponents @xcite , the weak * quenched * disorder has been a subject of intensive study . here the harris criterion @xcite has been devised . it states that if the heat capacity exponent @xmath11 of a pure model is negative , that is the heat capacity has no divergence at the critical point , impurities do not affect the critical behaviour of the model in the sense that critical exponents remain unchanged under dilution . only in the case @xmath12 , the critical behaviour of the disordered model is governed by a _ new set of critical exponents_. as far as for a @xmath13 @xmath7-vector spin model only the @xmath13 ising model ( @xmath4 ) is characterized by @xmath14 , it is the ising model which is of special interest . and because of the triviality of the annealed disorder in the sense mentioned above , the most interesting object for study is just the quenched ising model . the appearance of a set of new critical exponents for that model at @xmath15 is confirmed by the experiments @xcite , renormalization group @xmath16 calculations @xcite , monte - carlo @xmath17 @xcite and @xmath18 @xcite simulations . the situation is not so simple for the @xmath19 ising model . onsager exact solution of the pure model proves the logarithmic divergence of heat capacity , which yields @xmath20 , and allows one , in accordance with the harris criterion , to clasify this case as a marginal one . most of the theoretical works suggest that the @xmath19 ising model with a quenched disorder has the same critical behaviour as the @xmath19 pure ising model ( except for logarithmic corrections ) @xcite ( see also review @xcite ) . this result is corroborated by @xmath21-simulations on two - dimensional lattices @xcite and experiments @xcite . deviations from the expected critical exponents , which sometimes are observed during such computations , are explained by a system being not in the asymptotic region ( see @xcite for recent study ) . nevertheless , some authors assert that for the @xmath19 ising model with a quenched disorder a new critical behaviour appears @xcite while the undiluted ising model at non - integer @xmath3 was a subject of intensive study @xcite , it is not the case for the diluted ising model . only the work @xcite can be mentioned here , where the model was studied within the golner - riedel scaling field @xcite approach . it is worthwhile to note that the @xmath22-expansion technique applied to this model , due to the fact that @xmath23-equations appear to be degenerated on the one loop level , results in @xmath24-expansion for the critical exponents @xcite . the latter is known up to the three - loop order @xcite . the equations of the massive field theory at fixed integer @xmath3 @xcite first applied to the diluted ising model at @xmath25 in @xcite were found to be the most effective method for investigating this problem . in order to consider an arbitrary non - integer @xmath3 the parisi approach @xcite was generalized in @xcite where critical behaviour of the model was studied in a two - loop approximation . the aim of the present work , based on the massive field theoretical approach , is to make a more detailed investigation of the critical behaviour of the diluted @xmath26-vector model at arbitrary @xmath3 . though it is the case @xmath4 in which we are interested most of all , we consider the @xmath23-equations for any @xmath7 , which also allow us to study the crossover in the model at any @xmath3 . we will obtain the @xmath23-equations within the 3-loop approximation and apply to their analysis different resummation procedures in order to find the most reliable one . the set - up of the article is as follows . in the next section we introduce the model and the notation . then we describe the @xmath23-procedure adopted here and give the series for the @xmath23-functions of the weakly diluted quenched @xmath7-vector model in the three - loop approximation . being asymptotic , these series are to be resummed . this is done in section 2 where different ways of resummation are used . section 3 concludes our study giving results for the quantitative characteristics of the critical behaviour and discussing them . in the conclusions we give some general comments to the present work . in the appendix we list some lengthy expressions for the coefficients of the @xmath23-functions in the three - loop approximation

within the massive field theoretical renormalization group approach the expressions for the- and- functions of the anisotropic-vector model are obtained for general space dimension in three - loop approximation . * key words : * critical phenomena , diluted spin systems , ising model , renormalization group . * pacs numbers : * 64.60.ak , 61.43.-j , 11.10.gh _ to appear in j.stat.phys .

within the massive field theoretical renormalization group approach the expressions for the- and- functions of the anisotropic-vector model are obtained for general space dimension in three - loop approximation . resumming corresponding asymptotic series , critical exponents for the case of the weakly diluted quenched ising model ( , ) , as well as estimates for the marginal order parameter component number of the weakly diluted quenched-vector model are calculated as functions of in the region . conclusions concerning the effectiveness of different resummation techniques are drawn . * key words : * critical phenomena , diluted spin systems , ising model , renormalization group . * pacs numbers : * 64.60.ak , 61.43.-j , 11.10.gh _ to appear in j.stat.phys . vol . 92 , nos 5/6 _

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now we are going to apply the mathematical framework which was discussed in previous sections in order to obtain numerical characteristics of the critical behaviour of the weakly - diluted ising model in general dimensions . it was noted in the section 1 that the critical behaviour of the quenched weakly - diluted ising model is described by the effective lagrangian ( [ lagrangian ] ) in the case @xmath4 and zero replica limit @xmath5 . namely , the task in the end comes to obtaining fixed points which are defined by simultaneous zero of the both @xmath0-functions . among all the possible fixed points one is interested only in those in the ranges @xmath98 and only in stable ones where the stability means that two eigenvalues @xmath99 of the stability matrix @xmath100 , @xmath101 are positive or possess positive real parts . the structure of the @xmath0-functions ( [ beta_u])-([beta_v ] ) yields the possibility of four solutions for the fixed points . the first two @xmath102 and @xmath103 in our case at @xmath104 are out of physical interest , while the second pair which consists of pure @xmath105 and mixed @xmath106 points , are responsible for two possible critical regimes . the critical behaviour of the diluted model coincides with that of the pure model when the pure fixed point appears to be stable . if the mixed point is stable , the _ new _ ( diluted ) critical behaviour of the system takes place . the type of the critical behaviour depends on the number @xmath7 of the order parameter components and on the dimensionality @xmath3 : at any @xmath107 a system with large enough @xmath7 is not sensitive to the weak dilution in the sense that asymptotic values of critical exponents do not change ; only starting from some marginal value @xmath6 , at @xmath108 a mixed fixed point becomes stable and the crossover to the random critical behaviour occurs . the problem of determining @xmath6 as a function of @xmath3 will be discussed later . now we would like to state that @xmath109 for any @xmath110 , and thus just the mixed fixed point governs the asymptotic critical behaviour of the diluted ising model . if one attempts to find the fixed points from the @xmath0-functions ( [ beta_u])-([beta_v ] ) without resummation , there always appears only the gaussian @xmath102 trivial solution ; the existence of the rest possible three fixed points depends on the concrete details of the @xmath0-functions portions in the braces in expressions ( [ beta_u])-([beta_v ] ) . in a @xmath13 case it appears that without a resummation the non - trivial mixed fixed point does not exist in one- , two- and four - loop approximations @xcite . it is only the three - loop approximation where all the four solutions of the set of equations ( [ fixedpoint ] ) exist @xcite . in figure [ fig1 ] we show the behaviour of the non - resummed @xmath0-functions of the three - dimensional weakly diluted ising model in the three - loop approximation . resummed functions are shown in the same approximation in figure [ fig2 ] . note that in this approximation the shape of the functions remains alike in the region of small couplings @xmath44 and @xmath46 . fixed points correspond to the crossing of the lines @xmath111 as it is demonstrated in figures [ fig3 ] , [ fig4 ] . the left - hand column in figures [ fig3 ] , [ fig4 ] shows the lines of zeros of non - resummed @xmath0-functions in three - dimensions in one- , two- , three- and four - loop ( results of @xcite ) approximations . one can see in the figures that without resummation all non - trivial solutions are obtained only within the three - loop level of the perturbation theory . in the next order all fixed points disappear which is a strong evidence of their accidental origin . at any arbitrary @xmath3 , @xmath8 the qualitative behaviour of the functions is very similar to that shown in figures [ fig3 ] and [ fig4 ] . as it has already been mentioned , in order to reestablish the lost pure and mixed points one applies the resummation procedure to @xmath0-functions . in the three - dimensional space the result of resummation is illustrated by the right - hand column in figures [ fig3 ] and [ fig4 ] . here we have used the chisholm - borel resummation technique choosing chisholm approximant in the form discussed in the previous section with @xmath75 in successive approximation in the number of loops . the icons in the figures which correspond to a one - loop level are the visual proof of the degeneracy of the @xmath0-functions in this order of the perturbation theory : the plots of root - lines are parallel independently of resummation . the rest three images in the right - hand columns are a good graphic demonstration of the reliability of the chisholm - borel resummational method : two- , three- and four - loop pictures are quantitatively similar , the coordinates of the pure and mixed point are close . the numerical results of our study are given in table [ table1 ] . here , the coordinates of the stable mixed fixed point and the values of the critical exponents of the quenched weakly diluted ising model are listed as functions of @xmath3 between @xmath112 and @xmath113 . the eigenvalues @xmath114 and @xmath115 of the stability matrix are given as well . it was already noted that the values of @xmath1-functions in a stable point yield the numerical characteristics of the critical behaviour of the model . for example , given the resummed functions @xmath116 and @xmath117 , the pair of equations @xmath118 allows us to find the exponents @xmath54 and @xmath56 . all other exponents can be obtained from the familiar scaling laws . however , one can proceed in a different way . that is , by means of the scaling laws it is possible to reconstitute the expansion in coupling constants of any exponent of interest or of any combination of exponents , and only after that to apply the resummation procedure . if exact calculation were performed the answer would not depend on the sequence of operations . however , this is not the case for the present approximate calculations . we have chosen the scheme of computing where the resummation procedure was applied to the combination @xmath119 and @xmath120 . the exponents @xmath121 , @xmath0 and @xmath54 have been calculated on the basis of numerical values of the exponents @xmath1 and @xmath56 . the resummation scheme appears to be quite insensitive to the choice of the parameter @xmath73 given by ( [ leroy ] ) , ( [ p ] ) . however note , that computations have been performed here , as well as in @xcite , with @xmath75 . comparing our data from table [ table1 ] for the critical exponents at @xmath112 with the results for the pure ising model one can see that the exponent @xmath1 differs from the exact value @xmath122 by the order of @xmath123 , the exponent @xmath56 is smaller from the exact value @xmath124 less than by @xmath125 . this confirm the conjecture that the critical behaviour of the weakly diluted quenched ising model at @xmath112 within logarithmic correction coincide with that of the pure model ( see @xcite for review ) . it is also interesting to compare numbers given in table [ table1 ] with those obtained for general @xmath3 within the 2-loop approximation @xcite : all the exponents of the three - loop level lie slightly farther from the expected exact values of onsager than those of the two - loop approximation . this may be explained by the oscillatory nature of approaching to the exact values depending on the order of the perturbation theory . it is also interesting to note that the two - loop approximation yields better estimates for the heat capacity critical exponent @xmath121 for all @xmath3 in the range under consideration . namely , in accordance with the harris criterion , the exponent @xmath121 for the diluted ising system should remain negative . this picture is confirmed much better by the two - loop approximation where @xmath121 is negative in the whole range of @xmath3 , unlike the three - loop level of the perturbation theory , the results of which yield @xmath126 for @xmath127 . however , table [ table1 ] shows that the next ( third ) order does improve our understanding of the critical behaviour of the model in general dimensions . the results of the two - loop calculations @xcite show that starting from some marginal space dimension the approach to the stable point becomes oscillatory : the eigenvalues @xmath114 and @xmath115 turn to be complex possessing positive real parts . this is an artifact of the calculation scheme and therefore it was expected @xcite that by increasing the accuracy of calculations one decreases the region of @xmath3 which corresponds to the complex eigenvalues . it is really the case . in the three - loop approximation the region of complex @xmath128 is bounded from below by @xmath129 , whereas in the two - loop approximation @xcite the corresponding value is lower and is equal to @xmath130 . thus , the region of @xmath3 characterized by the oscillatory approach to the stable fixed point shrinks with the increase of the order of the perturbation theory . the comparison of the three - dimensional value of @xmath56 with the four - loop result @xcite @xmath131 gives the accuracy of @xmath132 for our computations ( compare with @xmath133 for two - loops , where the value @xmath134 was obtained ) . thus , it may be stated that the general accuracy of calculations decreases when passing from @xmath135 to @xmath112 which , in particular , results from the fact that our approach is asymptotically exact at upper critical dimension @xmath135 . the comparison of the present results with the other data available is provided by figure [ fig5 ] . here , the behaviour of the correlation length critical exponent @xmath56 obtained by different methods is demonstrated in general dimensions . the results of the massive field - theoretical scheme are plotted by solid ( three - loop approximation ; the present paper ) and dashed ( two - loop approximation ; ref . @xcite ) lines . one can see that the two lines practically coincide far enough from @xmath112 , in particular , both lie very close to the most accurate result for @xmath15 @xcite which is shown by the box . the application of the scaling - field method @xcite yields numbers shown in figure [ fig5 ] by stars . the limit from below ( @xmath136 ) of the method applicability is caused by the truncation of the set of scaling - field equations , which was considered in @xcite . one can also attempt to obtain some results by resumming the @xmath24-expansion which is known for the diluted ising model up to three - loop order @xcite and for the exponents @xmath56 and @xmath54 reads : @xmath137 where @xmath138 is rieman s zeta function . the corresponding results are shown by open diamonds . they were obtained by applying the pad - borel resummation scheme to the series of @xmath24- expansion ( [ nu_sqrteps ] ) @xcite . the value of @xmath56 obtained in such a way is of physical interest only very close to @xmath135 . even in the next orders of the expansions the values of critical exponents are not improved @xcite ; this is an evidence of the @xmath24-expansion unreliability in tasks like the one under consideration . to compare , one can state that the situation with the applied in the present paper theoretical scheme is contrary to the @xmath24-expansion . while the two - loop approximation is valid in ranges @xmath139 , the next order of the perturbation theory enlarges the upper bound up to @xmath113 . one can expect that the next steps within the perturbation theory will allow one to obtain the description of the critical behaviour of the model with enough accuracy for any @xmath3 , @xmath8 . let us recall now that expressions ( [ beta_u])-([gamma ] ) for the @xmath23-functions , as well as their three - loop parts listed in the appendix , allow us to study asymptotic critical properties of the @xmath2-vector model with arbitrary @xmath7 and @xmath59 in arbitrary @xmath3 not only for the case @xmath4 , @xmath5 . in particular , by keeping @xmath7 as an arbitrary number and putting @xmath5 one can obtain the numerical estimates for the marginal order parameter component number @xmath6 which divides the diluted ( governed by the mixed fixed point ) asymptotic critical behaviour from the pure one , when the @xmath26-symmetric fixed point remains stable . in accordance with the harris criterion the case @xmath140 corresponds to zero of the heat capacity critical exponent @xmath121 of the model . one may extract the value of @xmath6 from this condition . however , the above discussed results of the three - loop approximation do not yield enough accuracy for @xmath121 . alternatively , the fixed mixed point should coincide with the pure fixed point at @xmath140 , which in particular means that @xmath141 . the last condition was chosen as a basis of our calculation . the appropriate numbers of the present three - loop approximation ( thick solid line ) together with the data of the two - loop approximation ( dashed line ) @xcite are shown in figure [ fig6 ] . the result of @xmath22-expansion @xmath142 is depicted by the thin solid line . in the three - loop approximation we obtain @xmath143 and @xmath144 . these values are to be compared with the exact results of onsager which yield @xmath145 at @xmath112 , and the theoretical estimate @xmath146 @xcite . one can see that the two - loop results are closer to the expected values for both @xmath112 and @xmath15 . for a two - dimensional case the two - loop value @xmath147 @xcite differs from the exact one by @xmath148 , while the three - loop number decreases the accuracy to @xmath149 . the case @xmath150 contradicts the suggestion that the @xmath151-model asymptotic critical behaviour should not change under dilution in three - dimensions . the reason for decreasing the calculation accuracy with increasing the order of the perturbation theory may lie in oscillatory approach to the exact result . one can expect that already the four - loop case will improve the estimates for @xmath6 for all @xmath152 . let us also note that the determination of @xmath6 may serve as a test for improving the resummation scheme .

resumming corresponding asymptotic series , critical exponents for the case of the weakly diluted quenched ising model ( , ) , as well as estimates for the marginal order parameter component number of the weakly diluted quenched-vector model are calculated as functions of in the region . conclusions concerning the effectiveness of different resummation techniques are drawn .

within the massive field theoretical renormalization group approach the expressions for the- and- functions of the anisotropic-vector model are obtained for general space dimension in three - loop approximation . resumming corresponding asymptotic series , critical exponents for the case of the weakly diluted quenched ising model ( , ) , as well as estimates for the marginal order parameter component number of the weakly diluted quenched-vector model are calculated as functions of in the region . conclusions concerning the effectiveness of different resummation techniques are drawn . * key words : * critical phenomena , diluted spin systems , ising model , renormalization group . * pacs numbers : * 64.60.ak , 61.43.-j , 11.10.gh _ to appear in j.stat.phys . vol . 92 , nos 5/6 _

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cosmic rays ( crs ) up to @xmath5ev are most likely accelerated in galactic supernova remnant ( snr ) shocks via the diffusive shock acceleration ( dsa ) mechanism @xcite . this mechanism is believed to be highly non - linear , due to the expected coupling between the evolution of the thermal plasma , the crs , and the magnetic turbulence in the shock vicinity . indeed , there is now observational evidence suggesting that electrons are being accelerated in the non - relativistic shocks of snrs , and that significant magnetic turbulence is being produced as part of the process ( see , e.g. * ? ? ? * ; * ? ? ? the evidence comes from x - ray observations of snrs that show the existence of thin , non - thermal rims , which are interpreted as synchrotron emission by tev electrons accelerated at the shocks . the rapid variability and thinness of the rims ( which depend on the synchrotron cooling time of the electrons ) have allowed to estimate the strength of the field , suggesting downstream amplitudes @xmath0 times larger than typically expected in the ism of the galaxy . this implies a significant amplification even accounting for the compression of the field at the shock , which would contribute a factor of @xmath6 to the growth of the field . the origin of this strong amplification is an open question . on the one hand , using mhd shock simulations , @xcite showed that the presence of density and magnetic fluctuations in the upstream medium of non - relativistic shocks may introduce vorticity into the flow and produce field amplification at the shock itself ( see , also , * ? ? ? this mechanism would produce a magnetic enhancement larger than expected from the simple shock compression of the upstream field . on the other hand , it has been proposed that the magnetic field may be amplified by plasma instabilities driven by the crs themselves , as they propagate through the upstream medium of shocks @xcite . this idea is interesting because , besides helping to explain the field amplification , the implied magnetic turbulence would increase the cr confinement to the shock vicinity , enhancing the efficiency of dsa . due to this , understanding the extent to which magnetic fields are amplified by crs , as well as characterizing the corresponding magnetic turbulence , is essential for any realistic model of dsa . the cosmic ray current - driven ( crcd ) instability proposed by @xcite has gathered considerable attention recently . the crcd instability consists of circularly polarized alfvn - type waves , driven by the electric current of crs propagating along the magnetic field lines . it requires the cr larmor radii , @xmath7 , to be much larger than the wavelength of the fastest growing mode , @xmath8 , where @xmath9 , @xmath10 , and @xmath11 are the magnitude of the initial magnetic field , the cr current , and the speed of light , respectively . this feature makes this instability different from the previously proposed resonant instability , in which the waves grow at wavelengths comparable to @xmath7 @xcite . the growth rate of the crcd instability is given by @xmath12 @xcite , where @xmath13 is the mass density of the background plasma . for the typical conditions of cr - modified snr shocks ( where the energy densities of crs , @xmath14 , downstream thermal plasma , @xmath15 , and magnetic field,@xmath16 , satisfy @xmath17 ) , this rate is expected to be significantly larger than that of the resonant instability . the non - linear evolution of the crcd instability has been studied using both mhd @xcite and particle - in - cell ( pic ) @xcite simulations . both kinds of studies showed that the crcd instability has the potential of growing to very non - linear amplitudes as long as the cr current is kept constant , i.e. , if the back - reaction on the cr trajectories is neglected . in particular , @xcite found that , at constant cr current , the field growth stops when the alfvn velocity of the background plasma , @xmath18 , gets close to the cr drift velocity , @xmath19 . however , pic studies show that if the cr back - reaction is considered , the field can also saturate due to the trapping of the crs in the amplified field . when @xmath7 becomes comparable to the dominant length scale of the magnetic turbulence , the crs get strongly deflected , which significantly reduces their current and quenches the magnetic growth . this is the most likely saturation mechanism in the case of snrs , which implies a _ maximum _ amplification factor of @xmath1 in the upstream medium of shocks , and confirms the crcd instability as a viable mechanism for magnetic turbulence generation in snrs @xcite . when the field compression at the shock is considered , this amplification may increase by an extra factor of @xmath6 . however , since the upstream amplification factor of @xmath20 constitutes an upper limit , the crcd instability alone would not be enough to account for the factor of @xmath0 inferred from the x - ray observations . in this paper we study the possibility of magnetic amplification beyond the saturation of the crcd instability . the situation we explore is one where crs propagate through a plasma where previous crcd magnetic turbulence has already been produced on scales larger than the typical cr larmor radius , @xmath7 . thus , our analysis would be applicable to the lower energy crs , which are more confined to the shock vicinity . this is motivated by the fact that the crcd instability is probably driven first by the highest energy crs , in regions far upstream from the shock . this instability saturates when the larmor radius of these high energy particles is about the length scale of the pre - amplified magnetic fluctuations , @xmath21 . thus , as the shock approaches , a large fraction of the cr energy will be carried by magnetized " crs , i.e. , crs with @xmath7 smaller than @xmath21 . then , near the shock , crs will find regions of pre - amplified , quasi - transverse field , which can be considered homogeneous on scales @xmath22 . if @xmath23 , then crs will not easily diffuse through the regions of pre - amplified field . instead , they will protrude into these regions only by a distance of @xmath22 . this situation will produce a cr current , @xmath24 , perpendicular to the initial , pre - amplified field , @xmath25 , due to the coherent deflection experienced by crs in the homogeneous " ( on scales of @xmath22 ) magnetic field . we propose that , under these conditions , an extra magnetic amplification is possible due to a new instability : the _ perpendicular current - driven instability _ ( pcdi ) , which consists of purely growing , compressional waves that arise when @xmath24 is perpendicular to @xmath25 . as we show below , the pcdi would produce larger magnetic amplifications compared to the crcd instability acting alone . in addition , this instability can amplify magnetic fluctuations on scales comparable to the larmor radii of the lowest energy crs , which would improve their diffusion and increase the efficiency of their acceleration at the shock . if this did not happen , the large - scale , transverse fields generated by crcd instability would hamper the low energy cr diffusion , which would probably shut off the acceleration of the crs that cause the crcd amplification in the first place . in [ sec : physics ] , we explain the physics of the pcdi . first , we show how the penetration of crs into the regions of pre - amplified field can give rise to a current , @xmath24 , perpendicular to the pre - amplified field , @xmath26 , and why we expect that situation to happen in the upstream medium of snr shocks . then , we show how the presence of a @xmath24 perpendicular to @xmath26 can produce the pcdi , and derive its dispersion relation . in [ sec : simulations ] , we show the results of our study of the pcdi using pic simulations . first , we model the non - linear evolution of the instability assuming a constant cr current , i.e. , ignoring the back - reaction on the crs , and provide a simple analytical model for the non - linear behavior of the pcdi modes . second , we show the results of a series of simulations that model the non - linear evolution of the pcdi including the full cr dynamics . the main focus is to show the role of the cr back - reaction on the final saturation of the instability . in [ sec : discussion ] , we apply our results to the case of snr shocks . finally , in [ sec : conclusions ] we summarize our results and present our conclusions .

. this amplification may be due to plasma instabilities driven by shock - accelerated particles , or cosmic rays ( crs ) , as they propagate ahead of the shocks . one candidate process is the cosmic ray current - driven ( crcd ) instability ( bell 2004 ) , caused by the electric current of we find that additional amplification can occur due to a new instability , driven by the cr current perpendicular to the field , which we term the _ perpendicular current - driven instability _ ( pcdi ) . we derive the growth rate of this instability , and , using pic simulations , study its non - linear evolution . we show that the maximum amplification of pcdi is determined by the disruption of cr current , which happens when cr larmor radii in the amplified field become comparable to the length scale of the instability .

x - ray observations of synchrotron rims in supernova remnant ( snr ) shocks show evidence of efficient electron acceleration and strong magnetic field amplification ( a factor of between the upstream and downstream medium ) . this amplification may be due to plasma instabilities driven by shock - accelerated particles , or cosmic rays ( crs ) , as they propagate ahead of the shocks . one candidate process is the cosmic ray current - driven ( crcd ) instability ( bell 2004 ) , caused by the electric current of unmagnetized " crs ( i.e. , crs whose larmor radii are much larger than the length scale of the crcd modes ) propagating parallel to the upstream magnetic field . particle - in - cell ( pic ) simulations have shown that the back - reaction of the amplified field on crs would limit the amplification factor of this instability to less than in galactic snrs ( not including the additional field compression at the shock ) . in this paper , we study the possibility of further amplification driven near shocks by magnetized " crs , whose larmor radii are smaller than the length scale of the field that was previously amplified by the crcd instability . we find that additional amplification can occur due to a new instability , driven by the cr current perpendicular to the field , which we term the _ perpendicular current - driven instability _ ( pcdi ) . we derive the growth rate of this instability , and , using pic simulations , study its non - linear evolution . we show that the maximum amplification of pcdi is determined by the disruption of cr current , which happens when cr larmor radii in the amplified field become comparable to the length scale of the instability . we find that , in regions close to the shock , pcdi grows on scales smaller than the scales of the crcd instability , and , therefore , it results in larger amplification of the field ( amplification factor up to ) . one possible observational signature of pcdi is the characteristic dependence of the amplified field on the shock velocity , , which contrasts with the one corresponding to the crcd instability acting alone , . our results strengthen the idea of crs driving a significant part of the magnetic field amplification observed in snr shocks .

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in this work we proposed a new plasma instability , the perpendicular current - driven instability ( pcdi ) , as a candidate to amplify magnetic fields due to crs diffusing in front of snr shocks . the pcdi consists of purely growing , compressional waves produced by the cr current , @xmath24 , perpendicular to the initial magnetic field , @xmath25 . the time and length scale of growth of the pcdi are similar to the ones of the crcd instability , i.e. , @xmath211 and @xmath212 . however , whereas the crcd instability is driven by a current _ parallel _ to @xmath25 , the pdci is produced by a current _ perpendicular _ to the initial field . thus , the fastest growing instability will be determined by whether @xmath24 is quasi - perpendicular or quasi - parallel to the @xmath25 . we show that , in the upstream medium of snr shocks , the required perpendicular current can be due to crs with larmor radii , @xmath7 , smaller than the length scale of a previously amplified magnetic turbulence , @xmath213 . this scenario is motivated by earlier pic studies showing that , far from the shock , the crcd instability can produce non - linear magnetic amplification , driven by the highest energy crs . this amplification , although limited to a factor of less than @xmath1 for the expected energy carried by crs , would be characterized by non - linear fluctuations in the plasma density and magnetic field strength @xcite . the typical length scale of these fluctuations would be close to the larmor radius of the highest energy crs ( which is the saturation criterion that implies a maximum amplification factor of @xmath1 ) , producing a situation where most crs would have a @xmath7 significantly smaller than the typical size of the pre - amplified fluctuations . we show that , under these conditions , the current perpendicular to @xmath25 can be produced by lower energy crs protruding into the regions of pre - amplified field by a distance @xmath173 , which would give rise to a mean velocity of magnitude @xmath30 perpendicular to the field . due to this , in regions close to the shock , @xmath24 would be quasi - perpendicular to the field , making the pcdi grow faster and on length scales smaller than the scales of the crcd instability . we used the two - dimensional pic simulations to study the evolution of the pcdi . we showed that the instability exists and confirmed its theoretical growth rate . we also studied its possible saturation mechanisms , and found that the strong deflection of crs in the amplified field ultimately stops the magnetic growth , which happens when the the larmor radius of the crs , @xmath7 , is close to the size of the magnetic fluctuations , @xmath122 . this saturation mechanism is qualitatively the same as the one found for the crcd instability @xcite . however , since the perpendicular cr current is due to a cr mean velocity of magnitude @xmath30 , then the maximum magnetic field amplification would be @xmath194 times below energy equipartition with the crs . this would imply a maximum amplification factor in the upstream medium of the snr shocks of @xmath2 . the maximum downstream amplification could increase to @xmath214 , including the compression at the shock . the pcdi would also contribute to the efficiency of the acceleration of low energy particles at the shock , by providing magnetic fluctuation on scales comparable to their larmor radii , which allows them to diffuse . given the geometry of the pcdi ( see figure [ fig : figure1 ] ) , where the fluctuations in the fields and particle properties happen in a plane perpendicular to @xmath24 , we believe that our two - dimensional simulations ( with @xmath24 pointing out of the plane of the simulation ) are already capturing the essence of the instability . however , future three - dimensional simulations will be important to investigate possible extra effects that may appear by including the additional dimension . one interesting signature of the pcdi is that it predicts the amplified field , @xmath48 , that satisfies @xmath3 , assuming a weak dependence of @xmath215 ( @xmath216 ) on @xmath202 . this relationship contrasts with the one obtained for the crcd instability acting alone , @xmath4 @xcite , and constitutes a possible observational test to shed light on the nature of the magnetic amplification in snr shocks ( see observational results of * ? ? ? although we have focused on the case of non - relativistic shocks in snrs , the pcdi may also be relevant for the case of upstream magnetic amplification in the relativistic shocks of jets and gamma ray bursts . in that case , as seen from the reference frame of the upstream medium , the crs will only experience a small deflection before being advected into the downstream medium of the shock . thus , crs will provide an electric current parallel to the shock normal that may also amplify pcdi modes . the amplification of magnetic field due to the expansion of magnetic loops ( as in the non - linear regime of the pcdi ) in the upstream medium of grb shocks was already discussed by @xcite . they suggest that the growth of the field would saturate when neighboring loops collide . our simulations show that these collisions do not stop the growth . instead , they make neighboring loops merge and grow in size . we also found that under certain conditions , electrostatic forces due to the charge separation involved in the expansion of the loops may contribute to the quenching of the nonlinear growth . this possibility requires a dedicated study , which will be presented elsewhere . in conclusion , we have shown that the pcdi constitutes a viable amplification mechanism that , in combination with the crcd instability , strengthens the idea of crs being responsible for the significant fraction of magnetic amplification inferred from snr shock observations . axford , w. i. , leer , e. , & skadron , g. 1977 , 15th int . cosmic ray conf . , 11 , 132 ballet , j. 2006 , adv . in space res . , 37 , 1902 bell , a. r. 1978 , , 182 , 147 bell , a. r. 2004 , , 353 , 550 bell , a. r. 2005 , , 358 , 181 blandford , r. d. , & ostriker , j. p. 1978 , , 221 , l29 buneman , o. 1993 , `` computer space plasma physics '' , terra scientific , tokyo , 67 giacalone , j. & jokipii , j.r . 2007 , , 663 , 41 krymsky , g. f. 1977 , sov . dokl . , 23 , 327 kulsrud , r. , & pearce , w. p. 1969 , , 156 , 445 lyutikov , m. 2009 , arxiv:0912.1784 milosavljevic , m. , & nakar , e. 2006 , , 651 , 979 niemiec , j. , pohl , m. , stroman , t. , & nishikawa , k. 2008 , , 684 , 1189 riquelme , m. a. , & spitkovsky , a. 2009 , , 694 , 626 sironi , l. , & goodman , j. 2007 , , 671 , 1858 spitkovsky , a. 2005 , aip conf . proc , 801 , 345 , astro - ph/0603211 stroman , t. , pohl , m. , niemiec , j. 2009 , , 706 , 38 uchiyama , y. , aharonian , f. a. , tanaka , t. , takahashi , t. , & maeda , t. 2007 , nature , 449 vlk , h. j. , berezhko , e. g. , & ksenofontov , l. t. 2005 , , 433 , 229 zirakashvili , v. n. , ptuskin , v. s. , & volk , h. j. 2008 , , 678 , 255

x - ray observations of synchrotron rims in supernova remnant ( snr ) shocks show evidence of efficient electron acceleration and strong magnetic field amplification ( a factor of between the upstream and downstream medium ) we find that , in regions close to the shock , pcdi grows on scales smaller than the scales of the crcd instability , and , therefore , it results in larger amplification of the field ( amplification factor up to ) . our results strengthen the idea of crs driving a significant part of the magnetic field amplification observed in snr shocks .

x - ray observations of synchrotron rims in supernova remnant ( snr ) shocks show evidence of efficient electron acceleration and strong magnetic field amplification ( a factor of between the upstream and downstream medium ) . this amplification may be due to plasma instabilities driven by shock - accelerated particles , or cosmic rays ( crs ) , as they propagate ahead of the shocks . one candidate process is the cosmic ray current - driven ( crcd ) instability ( bell 2004 ) , caused by the electric current of unmagnetized " crs ( i.e. , crs whose larmor radii are much larger than the length scale of the crcd modes ) propagating parallel to the upstream magnetic field . particle - in - cell ( pic ) simulations have shown that the back - reaction of the amplified field on crs would limit the amplification factor of this instability to less than in galactic snrs ( not including the additional field compression at the shock ) . in this paper , we study the possibility of further amplification driven near shocks by magnetized " crs , whose larmor radii are smaller than the length scale of the field that was previously amplified by the crcd instability . we find that additional amplification can occur due to a new instability , driven by the cr current perpendicular to the field , which we term the _ perpendicular current - driven instability _ ( pcdi ) . we derive the growth rate of this instability , and , using pic simulations , study its non - linear evolution . we show that the maximum amplification of pcdi is determined by the disruption of cr current , which happens when cr larmor radii in the amplified field become comparable to the length scale of the instability . we find that , in regions close to the shock , pcdi grows on scales smaller than the scales of the crcd instability , and , therefore , it results in larger amplification of the field ( amplification factor up to ) . one possible observational signature of pcdi is the characteristic dependence of the amplified field on the shock velocity , , which contrasts with the one corresponding to the crcd instability acting alone , . our results strengthen the idea of crs driving a significant part of the magnetic field amplification observed in snr shocks .

1006.0972

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in this section we discuss two important experimental issues . first , the scintillation factor in xenon @xmath1 is extremely important in interpreting results and yet is not well known . second , the channeling effect in dama / libra , again not well known , may change the location of the regions in wimp parameter space that are compatible with the data . the interpretation of the xenon10 and xenon100 results requires the ability to reliably reconstruct the nuclear recoil energy from the observed signal . this reconstruction depends on the scintillation efficiency factor @xmath1 for which there is considerable uncertainty at low energies . here we discuss this factor and present three models for @xmath1 at low energy . interactions in the liquid xenon comprising the xenon10 and xenon100 detectors give rise to a prompt scintillation signal , @xmath4 , followed by a delayed secondary scintillation signal , @xmath5 . the @xmath4 signal arises from a rapid relaxation of excited xenon states produced as a result of the interaction . the @xmath5 signal arises from ionized electrons also produced in the interaction ; these drift through the liquid xenon under an applied electric field , but once they reach the liquid surface they are extracted into a xenon gas phase where they emit proportional scintillation light . the drift time of the electrons causes this secondary scintillation ( the @xmath5 signal ) to be observed later than the @xmath4 signal , allowing both scintillation signals to be measured separately . the @xmath4 signal can be used to determine the energy of the interaction , while the combination of both signals allows discrimination between nuclear recoil events ( possibly wimp interactions ) and electron recoil events ( necessarily background interactions ) . the ratio of @xmath5 to @xmath4 is much higher in the case of electron recoils than in the case of nuclear recoils . interpretation of the xenon results requires the ability to reliably reconstruct the nuclear recoil energy @xmath12 from the observed @xmath4 signal . calibration of the nuclear recoil energy dependence of @xmath4 often involves gauging the detector s response to electron recoils at higher energies ; parts of the detector s response ( _ e.g. _ the fraction of scintillation photons that yield photoelectrons ( pe ) in the photodetectors ) are more easily determined in this case than with nuclear recoils at lower energies . taking @xmath4 to be normalized to the number of pe , @xmath4 and @xmath12 are related by an equation involving the higher energy electron recoil calibrations : @xmath13 here , @xmath14 is the light yield in pe / kevee for 122 kevee @xmath15-rays . @xmath1(@xmath12 ) is the scintillation efficiency of nuclear recoils relative to 122 kevee @xmath15-rays in zero electric field ; this factor is a function of the nuclear recoil energy . since there is an applied electric field in the experiment , which reduces the scintillation yield by quickly removing charged particles from the original interaction region , two additional factors must be taken into account : @xmath16 and @xmath17 are the suppression in the scintillation yield for electronic and nuclear recoils , respectively , due to the presence of the electric field in the detector volume . the quantities @xmath16 , @xmath17 , and @xmath14 are detector dependent ; @xmath1 is not . recent comments have drawn attention to the role that @xmath1determinations play in setting experimental constraints for xenon - based detectors @xcite . a variety of @xmath1 measurements have been made over the years @xcite , but limited statistics and systematics issues have so far prevented a clear picture from emerging as to the behavior of @xmath1 at low recoil energies . there are two primary issues in debate : ( 1 ) which of the @xmath1 measurements should be used as a basis for analyzing direct detection results ? and ( 2 ) measurements of @xmath1 have only been made at energies above some minimum ; what is the behavior of @xmath1 at low energies , where no measurements have as yet been made ? for the first issue , the xenon100 collaboration has chosen to use a global fit to multiple @xmath1 measurements in their analysis , whereas ref . @xcite suggests that the recent measurements by manzur _ et al . _ @xcite should be used ; in both cases , @xmath1 measurements are based upon fixed energy neutron scatters . we do not contribute to the debate as to which @xmath1 data sets are most appropriate ; however , in the interest of examining the most conservative xenon constraints , we use the manzur _ et al . _ data alone in our analyses . the choice of @xmath1 measurements to use in the xenon analyses has a significant impact on the resulting constraints for low wimp masses . the manzur _ et al . _ data yield the lowest values for @xmath1 among the fixed - energy neutron scatter measurements , implying the highest recoil energy thresholds and therefore the lowest sensitivity for the xenon detectors to low mass wimps ( which generate only low energy recoils ) . the manzur _ et al . _ data is shown in figure [ fig : leff ] . a comment is in order about the lower zeplin - iii @xmath1 measurement @xcite represented as a band in fig . 1 of @xcite . zeplin fits a nonlinear @xmath1 model to their broad spectrum nuclear recoil calibration data to obtain @xmath1 curves that were used in their analysis . these fits suggest a constant @xmath1 at recoil energies above @xmath030 kevnr , with @xmath1 sharply falling at energies below @xmath020 kevnr and approaching zero at @xmath07 - 8 kevnr ; see figure 15 of ref . @xcite and the accompanying text . thus the suggestion has been made by nonmembers of the zeplin team @xcite that @xmath1 should be taken to be zero below @xmath08 kevnr as a conservative model of @xmath1 . this @xmath1 model would yield significantly weaker xenon constraints relative to what we have referred to as conservative models based on the manzur _ _ measurements of @xmath1 @xcite . however , the members of the zeplin experiment themselves do not advocate their fits as being an indicator of @xmath1 behavior at recoil energies below @xmath0 8 kevnr @xcite . in addition , the dependence of these curves on statistical and systematic uncertainties has not been fully determined , where these uncertainties can significantly impact the lowest recoil energy portion of their fits . the zeplin - iii dark matter analysis is , in fact , mainly insensitive to the low recoil energy portion of their @xmath1 curves . further discussion of the zeplin data can be found in the appendix . moreover , as explained in detail in the appendix , below the recoil energies of 7 kevnr , the manzur _ et al . _ measurements are incompatible with @xmath18 at far more than the 3@xmath2 level . we consider the manzur _ _ measurements more reliable than the zeplin - iii estimate of @xmath1 at low energies . the second issue in debate is how @xmath1 behaves at energies below where measurements have been made . most @xmath1 measurements are at recoil energies above 5 kevnr ; manzur _ et al . _ have a measurement at @xmath19 kevnr . the @xmath1 behavior below these energies is unclear from an experimental and theoretical standpoint , at least at the precision necessary for use in a wimp constraint analysis . the xenon collaboration has suggested that @xmath1 measurements are consistent with @xmath1 being effectively constant at low recoil energies , at least at energies where recoils may contribute to their signal @xcite . various @xmath1 measurements are also consistent with an @xmath1 that decreases as one goes to lower recoil energies ; see _ e.g. _ sect . v of ref . @xcite which provides a theoretically motivated empirical model of such a decreasing @xmath1 . furthermore , ref . @xcite states that `` the mechanisms behind the generation of _ any _ significant amount of scintillation are still unknown and may simply be absent at the few kevnr level . '' given this uncertainty we use three different extrapolations of @xmath1 at low energies : constant , decreasing as one goes to lower recoil energies , or just zero . we choose as our fiducial @xmath1 model a piecewise linear interpolation between the central manzur _ _ values at their measured energies , shown in figure [ fig : leff ] . in addition , we will also examine similarly constructed @xmath1 models using the 1@xmath2 uncertainties in the manzur _ _ measurements are added in quadrature with the upper and lower uncertainties averaged ; uncertainties in the corresponding recoil energies for those measurements have been neglected . ] . the choice of linear interpolation vs. a quadratic interpolation or spline fit to the @xmath1 points has a negligle impact on the generated constraints compared to that from the 1@xmath2 variations in the @xmath1 points themselves . below recoil energies of 3.9 kevnr , the lowest manzur _ et al . _ measurement at 3.9 kevnr , where the two errors in the first case are the statistical and systematic uncertainties , respectively , and the second case is the combined uncertainty as described in the previous footnote . ] , we examine three behaviors for @xmath1 , also shown in figure [ fig : leff ] : ( 1 ) a constant @xmath1 , ( 2 ) an @xmath1 that goes linearly to zero at zero recoil energy , and ( 3 ) an @xmath1 that is strictly zero . even if the scintillation goes to zero at some low but finite recoil energy , there is no reason to expect this to occur above @xmath02 - 3 kevnr ; the measurements of @xmath1 provide no indication of an abrupt ( rather than gradual ) falling of @xmath1 at energies just below where the measurements exist . as such , the third case is perhaps unrealistically conservative , but never - the - less provides the most conservative case . in addition , the use of this case will allow us to examine the contribution of low energy recoils in generating constraints . the average @xmath4 signals as a function of the nuclear recoil energy @xmath12 that correspond to these @xmath1 models are shown in figure [ fig : s1enr ] for xenon10 and xenon100 . in the interest of examining the most conservative xenon constraints , we base all three cases on the data from manzur _ et al . _ @xcite . of the existing data sets , the manzur _ et al . _ data yield the lowest values for @xmath1 , implying higher recoil energy thresholds for the xenon experiments , and thereby reducing the sensitivity of xenon to low mass wimps . the channeling effect is of crucial importance when considering the compatibility of dama with other experimental results as this effect has the potential to significantly alter the wimp masses and cross - sections which are compatible with the dama modulation signal . channeling and blocking effects in crystals refer to the orientation dependence of charged ion penetration in crystals . in the `` channeling effect , '' ions incident upon a crystal along symmetry axes and planes suffer a series of small - angle scattering that maintain them in the open``channels '' in between the rows or planes of lattice atoms and thus penetrate much further into the crystal than in other directions . channeled incident ions do not get close to lattice sites , where they would be deflected at large angles , and they lose energy almost exclusively into electrons . the `` blocking effect '' consists in a reduction of the flux of ions originating in lattice sites along symmetry axes and planes , creating what is called a `` blocking dip '' in the flux of ions exiting from a thin enough crystal as a function of the exit angle with respect to a particular symmetry axis or plane . the potential importance of the channeling effect for direct dark matter detection was first pointed out by h. sekiya _ et al . _ @xcite and subsequently for nai(tl ) by drobyshevski @xcite and by the dama collaboration @xcite . when na or i ions recoiling after a collision with a dark matter wimp are channeled , their quenching factor is the ratio of ionization or scintillation produced by a nuclear recoil event in a crystal relative to that produced in an electron recoil event of the same energy . this is analogous to the @xmath1 factor in liquid xenon and is likewise used to reconstruct the nuclear recoil energy from the observed ionization / scintillation of an event . ] is approximately @xmath20 instead of @xmath21 and @xmath22 , since they give their energy to electrons . the dama collaboration @xcite estimated the fraction of channeled recoils and found it to be large for low recoiling energies in the kev range . using this evaluation of the channeling fraction , the regions in cross - section versus mass of acceptable wimp models in agreement with the dama data were found to be considerably shifted towards lower wimp masses and cross - sections . however , the dama calculation of the channeling fraction did not take into account that the recoiling lattice ions start initially from lattice sites ( or very close to them ) and , therefore , blocking effects are important . in fact , as argued originally by lindhard @xcite , in a perfect lattice and in the absence of energy - loss processes , the probability of a particle starting from a lattice site to be channeled would be zero . the argument uses statistical mechanics in which the probability of particle paths related by time - reversal is the same . in a perfectly rigid lattice , the fraction of channeled recoils would , in fact , be zero . however , the atoms in a crystal are actually vibrating about their equilibrium positions in the lattice . it is this displacement from equilibrium that allows for a non - zero channeling probability of recoiling ions . the vibration amplitude increases with the temperature , thus the effect is temperature dependent : in general the channeling fraction increases with temperature . upper bounds to the recoiling channeling fractions in nai(tl ) crystals at 20@xmath23c were obtained in ref . @xcite , using analytic models of channeling developed since the 1960 s , when channeling was discovered ( see for example refs . @xcite and references therein ) . these upper bounds on the channeling fractions were obtained with temperature effects taken into account not only through the vibrations of the colliding nucleus but also in the lattice . the latter depend on the parameter @xmath24 ( see ref . @xcite for details ) which in the relevant literature is found to be a number between 1 and 2 , with 1 giving the largest channeling fractions ( see figure [ fig : frac - roomt ] , reproduced from ref . @xcite ) . the fractions shown in figure [ fig : frac - roomt ] are also an upper bound in that no dechanneling mechanism has been taken into account to compute them . the collisions with tl impurities would take channeled ions out of their channel , and this process is not included ( see ref . @xcite for further explanations ) .

* abstract * we consider the compatibility of dama / libra , cogent , xenon10 and xenon100 results for spin - independent ( si ) dark matter weakly interacting massive particles ( wimps ) , particularly at low masses ( gev ) , assuming a standard dark matter halo . xenon100 results are found to be insensitive to the low energy extrapolation .

* abstract * we consider the compatibility of dama / libra , cogent , xenon10 and xenon100 results for spin - independent ( si ) dark matter weakly interacting massive particles ( wimps ) , particularly at low masses ( gev ) , assuming a standard dark matter halo . the xenon bounds depend on the scintillation efficiency factor for which there is considerable uncertainty . thus we consider various extrapolations for at low energy . with the measurements we consider , xenon100 results are found to be insensitive to the low energy extrapolation . we find the strongest bounds are from xenon10 , rather than xenon100 , due to the lower energy threshold . for reasonable choices of and for the case of si elastic scattering , xenon10 is incompatible with the dama / libra 3 region and severely constrains the 7 - 12 gev wimp mass region of interest published by the cogent collaboration .

1006.0972

r

in figure [ fig : dama ] , we show the wimp masses and si cross - sections compatible with the dama modulation signal both with and without channeling included ; contours are shown for regions compatible at the 7@xmath2 , 5@xmath2 , 3@xmath2 , and 90% level ( in order from larger to smaller regions ) . for the channeling , we use the largest channeling fractions shown in figure [ fig : frac - roomt ] as they provide the largest potential effect on the dama constraints . figure [ fig : dama ] shows that even in this case there is negligible difference between the channeling and non - channeling scenarios except for regions incompatible with dama at greater than the 5@xmath2 level . even in these cases , the difference lies only at wimp masses below 4 gev and at relatively high si cross - sections . as channeling is a negligible effect , we do not further include it . compared to our previous analysis in @xcite , the current study takes advantage of additional recently released dama data . the effect of the additional data has been to sharpen the regions in parameter space that match the data . for example , at @xmath25 , there are now two completely separate regions ( peaked at different wimp masses ) that were previously joined . in our current work we also display a @xmath26 contour in which the two regions are again connected . we remind the reader that we are using the goodness - of - fit statistic described in detail in ref . @xcite . our main results are shown in figs . ( [ fig : constantleff])-([fig : zeroleff ] ) , corresponding to the three cases for the behavior of @xmath1 at low recoil energies . the solid gray contours indicate the wimp parameters compatible with the dama modulation within the 5@xmath2 , 3@xmath2 , and 90% level ; the 5@xmath2 dama region is also shaded light gray . the ( filled ) pink contour corresponds to the 7 - 12 gev wimp mass region suggested by cogent ( we reiterate that we have not reanalyzed their data and simply display their published region here ) . cdms , dama ( total events ) , xenon10 , and xenon100 curves indicate regions for which the wimp parameters are excluded at the 90% level ( the parameters above these curves are excluded ) . the solid green region for xenon10 and solid purple region for xenon100 do _ not _ indicate regions compatible within a given level ( as opposed to the dama and cogent regions ) ; they instead indicate how the 90% exclusion constraints vary with the 1@xmath2 level uncertainties in the @xmath1 measurements . overlapping xenon10 and xenon100 1@xmath2 regions are shown in blue . for the fiducial ( central value ) @xmath1 model in the case where it is constant below 3.9 kevnr , shown in figure [ fig : constantleff ] , the xenon100 constraint excludes all of the dama 3@xmath2 region , but only the portion of the cogent region with wimp masses above 9 gev . we note that , because we use only the manzur _ et al . _ @xmath1 data @xcite , this constraint is weaker than that presented by xenon100 @xcite . if the 1@xmath2 uncertainties in @xmath1 are included , xenon100 could exclude nearly all of the dama 5@xmath2 region and the entire cogent region , if the largest value of @xmath1 in the 1@xmath2 region is taken . on the other hand , it might exclude only the cogent region above 11 gev and not even all of the dama 90% region , if the lowest value of @xmath1 in the 1@xmath2 region is used . however , the cdms constraint , unaffected by the issues with @xmath1 , constrains the same cogent region as the fiducial xenon100 case here , with a slighter weaker constraint on the dama region ( incompatible with the dama 2@xmath2 region , not shown ) . for the fiducial ( central value ) @xmath1 model in the case where it falls linearly to zero at zero recoil energy , shown in figure [ fig : fallingleff ] , the xenon100 constraint again excludes nearly all of the dama 3@xmath2 region and the portion of the cogent region with wimp masses above 9 gev . the 1@xmath2 variations in the @xmath1 measurements also yield a similar variation in the xenon100 constraint as they did in the constant @xmath1 case . the most extreme case , taking @xmath1 to be zero below 3.9 kevnr , yields similar xenon100 constraints as the other two cases , as seen in figure [ fig : zeroleff ] , although the constraint using the 1@xmath2 upper values of @xmath1 does not quite exclude the full cogent region , leaving a narrow window at wimp masses of 7 - 8 gev . it should be emphasized , however , that the linearly falling @xmath1 case is already conservative and taking @xmath1 to be zero below 3.9 kevnr is perhaps unrealistically conservative . the xenon100 constraints are nearly identical in the dama and cogent regions for all three cases of low energy @xmath1 behavior . in fact , the constraints based on the central and 1@xmath2 lower values of @xmath1 _ are _ identical ; only when using the upper 1@xmath2 @xmath1 values do the constraints differ . there are two main reasons for the similarity among the constraints : ( 1 ) the imposed @xmath9 pe cutoff and ( 2 ) the small potential contribution from recoil events with energies below 3.9 kevnr where the @xmath1 models differ . as can be seen in figure [ fig : s1enr ] , a recoil energy of 3.9 kevnr yields an average @xmath4 signal of 1.0 pe in xenon100 when using any of the three fiducial @xmath1 models . with the @xmath8 cutoff , there is no contribution from recoils at energies below 3.9 kevnr where the fiducial @xmath1 models differ ; thus , these constraints are identical . when using the 1@xmath2 lower values of @xmath1 , no recoils below 5.9 kevnr are included , so the lesser constraining portion of the 1@xmath2 xenon100 constraint bands shown in the figures are likewise identical . on the other hand , when using the 1@xmath2 upper values of @xmath1 , the @xmath9 pe cutoff corresponds to recoil energies of 2.5 , 3.1 , and 3.9 kevnr for the constant , linearly falling , and zero low energy @xmath1 models , respectively . in this case , low energy recoils contribute to the constraints . however , these low energy recoils can make only a small contribution to the observed signal , as will be discussed below . as the potential effect of the low energy @xmath1 behavior on the xenon100 constraints is masked by the @xmath9 pe cutoff , we show in figure [ fig : extended ] the xenon100 constraints for the three fiducial @xmath1 models when this cutoff is relaxed . in this figure , we have arbitrarily assumed the nuclear recoil band cut efficiency is constant at low recoil energies . in reality , this efficiency should fall at very low recoil energies and this approximation becomes inappropriate at recoil energies that yield @xmath8 somewhere below 1 pe . for this reason , these constraints should not be taken to be valid constraints ; we show them only to illustrate the potential effect of low energy recoils and the low energy @xmath1 behavior . with all cut efficiencies properly taken into account , the true constraints would lie somewhere between the constraints shown in this figure and those shown in the previous figures . with the relaxing of the @xmath8 cutoff , the xenon100 constraints are still nearly identical in the dama and cogent regions for all three cases of low energy @xmath1 behavior . these constraints are very similar to the ones found in the previous figures , when a @xmath8 cutoff was included , and are actually identical for the zero @xmath1 model as this model has no contributions from recoils with @xmath27 pe anyways . the three cases only begin to differ significantly in the low mass , high cross - section parameter space located around and above the dama regions in this figure . this can be explained by the xenon100 s1 analysis threshold of 4 pe s ( the full analysis range is 4 - 20 pe s ) . in the absence of a finite energy resolution , this corresponds to a nuclear recoil energy of 9.5 kevnr in our fiducial @xmath1 models , well into the energy range where the @xmath1 behavior is known . with a poisson fluctuation in the number of observed pe s , recoils at lower energies have a finite chance of producing 4 or more pe s and falling into the analysis range , even if the average number of pe s for events at those energies is below 4 . however , at 3.9 kevnr , the average expected number of pe s is 1.0 ; only 1.9% of such events yield 4 or more pe s . recoils of 3 kevnr yield an average number of expected pe s of 0.79 and 0.61 for the constant and falling @xmath1 cases , respectively , with corresponding probabilities of being observed ( 4 + pe s ) of 0.87% and 0.36% ( the third case , zero @xmath1 , produces no pe s at these energies ) . the small fraction of recoil events with energies below 3.9 kevnr that will be observed in the analysis range means that their contribution is only significant when there are essentially no events at higher energies ( due to low wimp masses and a finite escape velocity in the halo ) , but to produce a sufficient number of events to fall into the analysis range requires a very large number of wimp scatters in the @xmath01 - 4 kevnr range , which requires a high wimp cross - section . thus , even when using an overly optimistic nuclear recoil band efficiency , the three @xmath1 cases can only result in different constraints in the low mass , high cross - section region . this is not necessarily the case for @xmath1 curves based on measurements that yield values higher than manzur _ et al . _ , as this would push the analysis range corresponding to 4 - 20 pe s to lower recoil energies ; such cases , however , inevitably move the xenon100 constraints to the left . in any case , the most significant issue in the xenon100 analysis is the choice of @xmath1 measurements used to determine the @xmath1 dependence , not the @xmath1 behavior at low energies . we now turn to the xenon10 bounds . we have reanalyzed the xenon10 results in terms of the same @xmath1 models as used for xenon100 and discussed in the previous section ; our results differ from those shown by the xenon collaboration due to the difference in @xmath1 used in their analyses and ours . the xenon10 results are important because of the lower @xmath4 threshold of about 2 pe s used in that analysis , which corresponds to 4.6 kevnr nuclear recoil energies in our fiducial @xmath1 models ( neglecting poisson fluctuations ) , much lower than the 9.5 kevnr of the xenon100 4 pe threshold . because of the lower threshold , the behavior of @xmath1 at low recoil energies is relevant in producing the xenon10 constraints as poisson fluctuations allow for a non - trivial probability of seeing 2 + pe s for recoil energies below 3.9 kevnr . for the constant @xmath1 case shown in figure [ fig : constantleff ] , the lower threshold allows for a stronger sensitivity to lower wimp masses for xenon10 relative to xenon100 . the fiducial case excludes at the 90% c.l . all of the cogent region and dama to the 5@xmath2 contour . when the 1@xmath2 uncertainties in the @xmath1 measurements are taken into account , the constraints relax : dama is excluded to only the 3@xmath2 contour and the some of cogent region at wimp masses below 9 gev survive . the xenon10 constraints mildly weaken if @xmath1 is taken to fall linearly to zero below 3.9 kevnr , as seen in figure [ fig : fallingleff ] . the fiducial case still excludes all of the cogent region and dama to about the 4@xmath2 contour ( not shown ) . the @xmath1 1@xmath2 band here allows the same dama and cogent regions to survive as with the constant @xmath1 case . for the case where @xmath1 is zero below 3.9 kevnr , shown in figure [ fig : zeroleff ] , the xenon10 constraints further weaken and approach the xenon100 constraints as the low energy events are essentially turned off and the lower xenon10 threshold becomes less relevant . again , we note that this last case ( zero @xmath1 at low recoil energies ) is an extremely conservative case . as with xenon100 , the potential effect of the low energy @xmath1 behavior on the xenon10 constraints is limited by the imposed @xmath9 pe cutoff . we also show in figure [ fig : extended ] the xenon10 constraints for the three fiducial @xmath1 models when this cutoff is relaxed . the same caveats apply : the nuclear recoil band cut efficiency that is used is not appropriate for the full recoil energy range that it is applied over , so these do not represent valid constraints . again , these constraints are only used to illustrate the potential impact of the low energy @xmath1 behavior on xenon10 constraints . the actual constraints when all efficiencies are accounted for properly would fall somewhere between the constraints shown in figure [ fig : extended ] and those shown in figs . ( [ fig : constantleff])-([fig : zeroleff ] ) . with the @xmath8 cutoff relaxed , figure [ fig : extended ] shows how the low threshold allows for a strong xenon10 sensitivity to lower wimp masses . this is particularly evident with the constant @xmath1 case where , as can be seen in figure [ fig : s1enr ] , recoils of energy 1 kevnr yield an average @xmath4 signal of 0.4 pe ; @xmath06% of such recoils will produce the necessary 2 + pe . for the falling @xmath1 case , that same average @xmath4 signal of 0.4 pe occurs at a higher recoil energy of 2 kevnr , but this energy is still sufficiently low to provide sensitivity to low mass wimps . the presence of these non - trivial poisson fluctuations at low recoil energies leads to a very strong dependence of the xenon10 constraints on the low energy @xmath1 behavior . this should remain the case even when the various efficiencies are handled properly , though not quite to the degree shown in figure [ fig : extended ] . in particular , when the proper efficiencies are included , the xenon10 constraints in the constant and falling @xmath1 cases should gain an upward curve at low wimp masses , as seen with the other constraints , rather than the current linear appearance . these linear portions of the constraints at low wimp masses ( as they appear with the logarithmic scaling of the figure ) continue to arbitrarily low wimp masses ; however , they arise from the poisson tails of increasingly smaller energy events that would be suppressed when using the proper efficiencies . though we have not included it in this work , cdms silicon data may provide further constraints on the dama and cogent regions and should be considered in a full discussion of compatibility between the various experimental results . the cdms silicon results will be considered in future work . in summary , we have examined a number of subtleties relevant to direct detection studies of low mass wimps . in the interest of examining the most conservative xenon constraints , we have used the manzur _ et al . _ @xcite data alone in our analyses of the existing data sets , the manzur _ et al . _ data yield the lowest values for @xmath1 , implying higher recoil energy thresholds for the xenon experiments , and thereby reducing the sensitivity of xenon to low mass wimps . we find that , when basing the @xmath1 curves on these manzur _ et al . _ measurements , the behavior of @xmath1 at low energies ( less than 3.9 kevnr ) has negligible effect on the xenon100 constraints in the regions of interest for dama and/or cogent . for xenon100 , the choice of data sets upon which the @xmath1 dependence is based is more important than the extrapolated behavior of @xmath1 at low recoil energies . the strongest bounds are from xenon10 , rather than xenon100 , due to the lower energy threshold . for reasonable choices of @xmath1 and for the case of spin independent elastic scattering , we find that xenon10 is incompatible with the dama / libra 3@xmath2 region and severely constrains the cogent 7 - 12 gev wimp mass region . is grateful for financial support from the swedish research council ( vr ) through the oskar klein centre . g.g . was supported in part by the us department of energy grant de - fg03 - 91er40662 , task c. p.g . was supported in part by the nfs grant phy-0456825 at the university of utah . k.f . acknowledges the support of the doe and the michigan center for theoretical physics via the university of michgian . , p.g . , and c.s . thank the galileo galilei institute for theoretical physics for the hospitality and the infn for partial support during the completion of this work . we thank also e. aprile , k. arisaka , d. hooper , and k. zurek for helpful conversations ; p. sorensen for bringing to our attention the xenon10 @xmath4 peak finding efficiency factor that was missing in the first version of this paper ; l. baudis , a. manalaysay , g. plante , and p. sorensen for discussions regarding the xenon detectors and analysis ; and b. edwards and t. sumner for discussions regarding the zeplin - iii @xmath1 estimates .

we find the strongest bounds are from xenon10 , rather than xenon100 , due to the lower energy threshold . for reasonable choices of and for the case of si elastic scattering , xenon10 is incompatible with the dama / libra 3 region and severely constrains the 7 - 12 gev wimp mass region of interest published by the cogent collaboration .

* abstract * we consider the compatibility of dama / libra , cogent , xenon10 and xenon100 results for spin - independent ( si ) dark matter weakly interacting massive particles ( wimps ) , particularly at low masses ( gev ) , assuming a standard dark matter halo . the xenon bounds depend on the scintillation efficiency factor for which there is considerable uncertainty . thus we consider various extrapolations for at low energy . with the measurements we consider , xenon100 results are found to be insensitive to the low energy extrapolation . we find the strongest bounds are from xenon10 , rather than xenon100 , due to the lower energy threshold . for reasonable choices of and for the case of si elastic scattering , xenon10 is incompatible with the dama / libra 3 region and severely constrains the 7 - 12 gev wimp mass region of interest published by the cogent collaboration .

1207.0660

i

_ no - regret strategies _ are simple adaptive learning rules that recently received a lot of attention in the literature . in a repeated game , a player has a _ regret _ for an action if , loosely speaking , she could have obtained a greater average payoff had she played that action more often in the past . in the course of the game , the player reinforces actions that she regrets not having played enough , for instance , by choosing next action with probability proportional to the regret for that action , as in hart and mas - colell s @xcite _ regret matching _ rule . existence of _ no - regret strategies _ ( i.e. , strategies that guarantee no regrets almost surely in the long run ) is known since @xcite ; wide classes of no - regret strategies are identified by @xcite and @xcite . a _ no - regret dynamics _ is a stochastic process that describes trajectories of the average correlated play of players and that emerges when every player follows a no - regret strategy ( different players may play different strategies ) . by definition , it converges to the hannan set ( the set of all correlated actions that satisfy the no - regret condition first stated by @xcite).the hannan set of a game is also known as the set of _ weak correlated equilibria _ @xcite or _ coarse correlated equilibria _ * ch.3 ) . ] this set is typically large . it contains the set of correlated equilibria of the game and we show that it may even contain correlated actions that put positive weight _ only _ on strictly dominated actions . thus convergence of the average play to the hannan set often provides very little information about what the players will actually play , as it does not even imply exclusion of strictly dominated actions . in this paper we show that no - regret dynamics are intimately linked to the classical fictitious play process @xcite . drawing on @xcite , we first show that contrary to the standard , discrete - time version , continuous fictitious play leads to no regret . we then show that , for a large class of no - regret dynamics , if a player s maximal regret is @xmath1 , then she plays an @xmath0-best reply to the average correlated play of the others . since in this class the maximal regret vanishes ( see corollary [ cor:1 ] below ) , it follows that , for a good choice of behavior when all regrets are negative , the dynamics is a vanishingly perturbed version of fictitious play . for two - player finite games , this observation and the theory of perturbed differential inclusions @xcite allow us to relate formally the asymptotic behavior of no - regret dynamics and of continuous fictitious play ( or its time - rescaled version , the best - reply dynamics @xcite ) . in classes of games in which the behavior of continuous fictitious play is well known , this provides substantial information on the asymptotic behavior of no - regret dynamics . in particular , we recover most known convergence properties of no - regret dynamics . our results do not just allow us to find new and sometimes much shorter proofs of convergence of no - regret dynamics towards the set of nash equilibria in some classes of games , such as dominance solvable game or potential games . they also allow us to relate the asymptotic behavior of no - regret dynamics and continuous fictitious play in case of divergence , as in the famous shapley game @xcite . these results extend only partially to @xmath2-player games ( though they fully extend to @xmath2-player games with linear incentives @xcite ) . the issue is that in @xmath2-player games no - regret dynamics turn out to be related to the correlated version of continuous fictitious play , in which the players play a best - reply to the _ correlated _ past play of the others . this version of fictitious play is defined through a correspondence which is not convex valued . this creates technical difficulties , because the theory of perturbed differential inclusions is not developed for non convex valued correspondences . a different way to analyze no - regret dynamics is to show that some sets attract nearby solution trajectories . we show that strict nash equilibria and , more generally , the intersection of the hannan set and the sets that are _ _ closed under rational behavior ( curb ) _ _ are attracting for no - regret dynamics , in a sense to be defined in section [ sec : curb ] . the remainder of the note is organized as follows . the next section introduces no - regret dynamics . section [ sec : main ] studies the links between no - regret dynamics and fictitious play . section [ sec : curb ] shows that the intersection of the hannan set and curb sets is attracting for no - regret dynamics . section [ sec : cont ] studies the continuous - time version and the expected version of no - regret dynamics . finally , the appendix contains the proofs of the main results , as well as counterexamples illustrating the complexity of the relationship between ict and limit sets .

1.2 potential based no - regret dynamics are shown to be related to fictitious play . roughly , these are-best reply dynamics where is the maximal regret , which vanishes with time . this allows for alternative and sometimes much shorter proofs of known results on convergence of no - regret dynamics to the set of nash equilibria .

1.2 potential based no - regret dynamics are shown to be related to fictitious play . roughly , these are-best reply dynamics where is the maximal regret , which vanishes with time . this allows for alternative and sometimes much shorter proofs of known results on convergence of no - regret dynamics to the set of nash equilibria . _ keywords : _ regret minimization , no - regret strategy , fictitious play , best reply dynamics , nash equilibrium , hannan set , curb set _ jel classification numbers : _ c73 , d81 ,

cond-mat0501519

i

the thermoelectric power , @xmath5 , of intermetallic compounds with cerium and ytterbium ions exhibits some characteristic features which allow the classification of these compounds . into several distinct groups.@xcite in the case of cerium ions , the thermopower of the compounds belonging to the first group ( type ( a ) systems ) has a deep negative minimum at low temperatures @xcite and a high - temperature maximum , typically between 100 k and 300 k. at the maximum , @xmath5 could be either positive or negative , as shown in fig . [ fig : tepall ] . at very low temperatures , the type ( a ) systems order magnetically or become superconducting . the compounds of the second group ( type ( b ) systems ) have a negative low - temperature minimum and a positive high - temperature maximum but , in addition , the thermopower shows a smaller positive peak at lowest temperatures.@xcite this second peak is sometimes concealed by a low - temperature phase transition ; for example , in cecu@xmath4si@xmath4 it becomes visible only in an external magnetic field which suppresses the superconducting transition,@xcite and in ceru@xmath3ge@xmath4 it shows up when the external pressure suppresses the magnetic transition.@xcite the experimental evidence is now accumulating that the initial slope of the thermopower @xmath6 is positive for this class of ( heavy fermion ) materials , provided the measurements are performed at low enough temperature and with sufficient accuracy.@xcite in the third group ( type ( c ) systems ) , the low - temperature peak is well pronounced and shifted towards the high - temperature peak . the main difference with respect to the type ( b ) systems is that the sign - change of @xmath5 does not occur.@xcite finally , in some cases ( type ( d ) systems ) the thermopower grows monotonically towards the high - temperature maximum , and the low - temperature structure appears only as a shoulder on a broad peak , or is not resolved at all . @xcite the clue to these various types of behavior comes from the high - pressure@xcite and doping studies , @xcite which show that the thermopower of cerium compounds changes continuously from type ( a ) to type ( d ) . a typical example is provided by the @xmath5 of ceru@xmath3ge@xmath4 , which is plotted in fig.[fig : tepall ] as a function of temperature , for various pressures.@xcite at ambient pressure , ceru@xmath3ge@xmath4 is a type ( a ) system with a magnetic ground state and negative thermopower below 300 k. an increase of pressure leads to a thermopower with a small positive peak at low temperatures and an enhanced peak at high temperatures . a further increase of pressure enhances both peaks , shifts the low - temperature peak towards the high - temperature one , and makes the thermopower at intermediate temperatures less negative . for large enough pressure , the sign - change does not occur at all and for very high pressure the low - temperature peak merges with the high - temperature one , and transforms into a shoulder ( see inset to fig . [ fig : tepall ] ) . the high - temperature peak grows continuously but its position remains more or less constant , as @xmath5 changes from type ( a ) to ( c ) . eventually , for pressures above 10 gpa , the @xmath5 assumes the ( d ) shape . here , the initial slope of @xmath5 decreases and the position of the maximum shifts to higher temperatures , but its magnitude does not change as pressure increases . similar behavior is also seen in the high - pressure data of , cecu@xmath3si@xmath4,@xcite cecu@xmath4ge@xmath4,@xcite or cepd@xmath4si@xmath4.@xcite as regards doping , the substitutions which reduce the volume and make ce ions less magnetic , transform @xmath5 from type ( a ) to type ( b),@xcite from ( b ) to ( c),@xcite or from ( a ) to(c),@xcite while the substitutions which expand the volume and make the ce more magnetic , transform the thermopower from , say , type ( d ) to type ( c ) or from type ( c ) to type ( b).@xcite this variation of shape is an indication that the local environment plays an important role in determining the magnetic character of ce and yb ions . even at high temperatures , where each 4_f _ ion is an independent scatterer , the thermopower of a sample with a high concentration of 4_f _ ions can not be obtained by rescaling the low - concentration data . the ytterbium intermetallics can be classified using the mirror - image analogy with cerium systems . this holds because the yb ions fluctuate between 4_f_@xmath7 and 4_f_@xmath8 , while the ce ions fluctuate between 4_f_@xmath9 and 4 _ f_@xmath10 configurations , and the dynamics of a single _ f _ hole and a single _ f _ electron is the same . a well - defined local moment leads in yb systems to the type ( a ) behavior , such that the thermopower has a negative minimum at high temperatures and a positive maximum at low temperatures;@xcite the size of the minimum is about the same as the size of the maximum . the thermopower of ( b)-type yb systems@xcite mirrors the ( b)-type ce systems . here , one finds two negative minima separated by a small positive maximum . the type ( c ) yb systems have a nonmonotonic thermopower with a large ( negative ) minimum at high temperatures and a smaller one at low temperatures , but there is no sign - change.@xcite finally , the thermopower with a single negative peak centered around 100 k @xcite mirrors the type ( d ) behavior of ce systems . the reduction of volume by pressure or doping@xcite stabilizes the magnetic @xmath11 configuration of yb ions , and transforms @xmath5 from , say , type ( b ) to type ( a ) , from ( c ) to ( b ) , or from ( c ) to ( a ) . the experimental results show that 4_f _ systems with similar thermopowers exhibit similarities in other thermodynamic@xcite and transport@xcite properties , and there is an obvious correlation between the shape of @xmath5 and the magnetic character of the 4_f _ ions . the thermopower measurements provide a simple and sensitive tool for characterizing the magnetic state of a 4_f _ ion in a given metallic matrix : the shape of @xmath5 changes from the ( a)-type in the case of magnetic ce ( yb ) ions with stable f@xmath12 ( 4_f_@xmath7 ) configuration to the ( d)-type for non - magnetic ce ( yb ) ions which fluctuate between the 4_f_@xmath12 ( 4_f_@xmath7 ) and 4_f_@xmath13 ( 4_f_@xmath8 ) configurations . we explain the thermoelectric properties of ce and yb ions in terms of a single - impurity anderson model which takes into account the splitting of the 4_f _ states by the crystalline electric field ( cf ) , and assumes an infinitely large _ f f _ coulomb repulsion , which restricts the number of _ f _ electrons or _ f _ holes to @xmath0 for ce and @xmath1 for yb . we assume that pressure changes the coupling and the relative occupation of the _ f _ and conduction states , and impose the charge - neutrality constraint on the local scattering problem at each temperature and pressure . the total charge conservation provides a minimal self - consistency condition for a poor - man s treatment of pressure effects in stoichiometric compounds . the excitation spectrum of such a model in the vicinity of various fixed points , the crossovers induced by temperature and pressure , and the corresponding effects on @xmath5 , the number of _ f _ particles , @xmath14 , and the electrical resistance , @xmath15 , are calculated by the non - crossing approximation ( nca ) . the description of the stoichiometric compounds in terms of an impurity model is certainly inadequate at low temperatures where the _ f _ electrons become coherent . the errors due to such an approximation and the low - temperature errors inherent in the nca calculations are discussed in detail at the end of sec . [ theoretical description ] . our paper extends the long - standing theory of coqblin , @xcite which described the high - temperature properties of ce and yb intermetallics by the coqblin - schrieffer ( cs ) model with cf splitting , and its more recent version@xcite which improved the low - temperature calculations by rescaling the coupling constants . these previous theories explained the main features of the temperature dependence of the thermopower@xcite and the magnetic susceptibility@xcite but could not describe the pressure effects , because the cs model neglects charge fluctuations . furthermore , the approximations used to solve the effective high- and low - temperature models cease to be valid at temperatures at which @xmath5 changes sign,@xcite such that the shape of @xmath5 between the two maxima ( minima ) in ce ( yb ) systems could only be inferred from an interpolation . here , we consider both the local _ spin _ and _ charge _ fluctuations , and provide the full description of the impurity problem at various pressures and temperatures , from above the cf temperature to below the kondo temperature , including the intermediate regime where @xmath5 changes sign . our results explain the shapes ( a ) to ( d ) of the thermopower , which are found in the systems like ceal@xmath16,@xcite ceru@xmath3ge@xmath4 , @xcite cecu@xmath3si@xmath4,@xcite cecu@xmath4ge@xmath4,@xcite or cepd@xmath4si@xmath4 , @xcite and the mirror - image shapes found in systems like ybnisn , yninau@xmath4 , ybsi or ybcu@xmath4si@xmath4.@xcite we also explain the pressure data like on ceru@xmath3ge@xmath4@xcite or cecu@xmath3si@xmath4,@xcite and the chemical pressure data on ce@xmath17la@xmath18pdsn @xcite and ce@xmath17la@xmath18ru@xmath3si@xmath4@xcite or ybcu@xmath4si@xmath4.@xcite the paper is organized as follows . in sec . [ theoretical description ] we introduce the model , discuss its limitations , and describe the method of solution . in sec . [ results ] we provide the results for the transport coefficients of ce- and yb - based intermetallics . in sec . [ discussion ] we discuss the effects of temperature and pressure on the spectral function , analyze the fixed - point behavior , and relate the shapes of the thermopower to the properties of elementary excitations . [ conclusions ] , gives the summary and the conclusions .

2ex the thermoelectric properties of intermetallic compounds with ce or yb ions are explained by the single - impurity anderson model which takes into account the crystal - field splitting of the 4_f _ ground - state multiplet , and assumes a strong coulomb repulsion which restricts the number of _ f _ electrons or _ f _ holes to for ce and for yb ions . using the non - crossing approximation and imposing the charge neutrality constraint on the local scattering problem at each temperature and pressure , the excitation spectrum and the transport coefficients of the model are obtained .

2ex the thermoelectric properties of intermetallic compounds with ce or yb ions are explained by the single - impurity anderson model which takes into account the crystal - field splitting of the 4_f _ ground - state multiplet , and assumes a strong coulomb repulsion which restricts the number of _ f _ electrons or _ f _ holes to for ce and for yb ions . using the non - crossing approximation and imposing the charge neutrality constraint on the local scattering problem at each temperature and pressure , the excitation spectrum and the transport coefficients of the model are obtained . the thermopower calculated in such a way exhibits all the characteristic features observed in ce and yb intermetallics . calculating the effect of pressure on various characteristic energy scales of the model , we obtain the phase diagram which agrees with the experimental data on cerusi , cecusi , cepdsi , and similar compounds . the evolution of the thermopower and the electrical resistance as a function of temperature , pressure or doping is explained in terms of the crossovers between various fixed points of the model and the redistribution of the single - particle spectral weight within the fermi window .

cond-mat0501519

c

we have applied the single - impurity anderson model to the investigation of the temperature and pressure dependence of the thermopower of ce and yb intermetallics , and found that the crossovers between various fixed points explain the seemingly complicated temperature dependence of @xmath5 . the basic assumption of our approach is that for a given concentration of rare - earth ions , and above some coherence temperature , the system is in an `` effective impurity '' regime . in that `` impurity limit '' , we treat the rare - earth ions as independent scattering centers and solve the ensuing single - impurity model by the nca . our calculations impose the charge neutrality constraint on the local scattering problem , which provides a minimal self - consistency condition for describing the pressure effects . the excitation spectrum obtained in such a way is very sensitive to the changes in the coupling constant @xmath203 , and an increase of the hybridization or a shift of the _ f _ state , which modifies the magnetic state of the _ f _ ion , has a huge effect on the spectral function . since the excitation spectrum is related to the transport coefficients by kubo formulas , the thermopower changes rapidly as a function of temperature , pressure or doping . the shapes ( a ) to ( d ) assumed by @xmath5 in various regions of the parameter space follow straightforwardly from the redistribution of the single - particle spectral weight within the fermi window . the nca solution of the single - impurity anderson model breaks down for @xmath204 . however , the excitations above the ground state are determined by the general fl laws , which can be used to find the initial slope of @xmath5 . estimating the kondo scale and the number of _ f _ electrons by the nca calculations , we find that an increase of pressure reduces ( enhances ) the low - temperature value of @xmath6 in ce ( yb ) compounds . combining the fl and the nca results , we can obtain @xmath5 in the full temperature range at any pressure . our results explain the thermopower of most intermetallic ce compounds mentioned in section [ introduction ] . the multi - peaked @xmath5 , which characterizes the type ( a ) and ( b ) systems , is obtained for kondo ions with small @xmath49 and well - defined cf resonances . a type ( c ) thermopower , which has weakly resolved peaks or just a broad hump , is obtained for kondo ions with large @xmath49 and partially overlapping cf resonances . a single - peaked @xmath5 of the ( d)-type is obtained for the vf ions which do not show any cf splitting of the single - particle excitations . if we assume that pressure increases @xmath60 , and reduces @xmath61 , our results account for the changes of @xmath49 , @xmath121 , @xmath6 , and @xmath117 , observed in pressure experiments on ce compounds . @xcite the strong doping dependance@xcite of @xmath5 is explained as a chemical pressure effect , which changes the _ f _ occupation . in our local model the `` effective concentration '' of _ f _ electrons is determined self - consistently , and the thermopower of concentrated and dilute systems can not be related by simple scaling . ( just like the high pressure data can not be described in terms of rescaled ambient pressure data . ) the relevant energy scales obtained for different values of @xmath60 agree with the @xmath2 phase diagram of ceru@xmath3ge@xmath4 and cecu@xmath3ge@xmath4 , inferred from the high - pressure transport and thermodynamic data.@xcite for yb compounds , we argue that pressure or chemical pressure mainly affect the position of the crystal field levels relative to the band center , while leaving the hybridization width unchanged . by shifting @xmath64 , so as to increase the number of holes , we obtain the thermopower of the type ( a ) to ( d ) , in agreement with the experimental data . the qualitative features seen in yb intermetallics at various pressures or chemical pressures are captured as well,@xcite but different compounds require different initial parameters , and a detailed analysis is yet to be done . in summary , the normal - state properties of stoichiometric compounds with ce and yb ions seem to be very well described by the local model which takes into account spin and charge fluctuations . the classification of the thermopower data follows straightforwardly from the fixed point analysis of the single - impurity anderson model with the cf splitting . a rich variety of shapes assumed by @xmath5 at various pressures or doping dramatically illustrates the effect of the local environment on the response of the single rare earth ion . the nature of the ground state , and the fact that the ground state of many ce and yb systems can be changed with pressure or doping , do not seem to affect the thermopower in the normal state . we take this as an indication that the normal state properties of ce and yb compounds are dominated by the local dynamics . the main problem with our poor man s treatment of ordered compounds is that it neglects the coherent scattering which sets in at low enough temperatures , and reduces the thermopower below the values predicted by the local fermi liquid theory . we can argue that these effects do not change the qualitative features of the thermopower but the proper answer can not be obtained without solving the lattice model . * acknowledgements * + we acknowledge useful comments and suggestions from b. coqblin , j. freericks , c. geibel , a. hewson , b. horvati , and h. wilhelm . this work has been supported by the ministry of science of croatia ( cro - us joint projects , grant number 1/2003 , by the national science foundation under grant number dmr-0210717 , and the swiss national science foundation under grant number 7krpj065554 - 01/1 . j. sakurai , h. takagi , s. taniguchi , t. kuwal , y. isikawa , and j .- l . tholance , j. phys . japan * 65 * , suppl . b , 49 ( 1996 ) . p. link , d. jaccard , and p. lejay , physica b * 225 * , 207 ( 1996 ) . v. zlati et al , phys . * b * 68 , 104432 ( 2003 ) . g. sparn , w. lieka , u. gottwick , f. steglich , and n. grewe , j. magn . mater . * 47 & 48 * , 521 ( 1985 ) . d. jaccard , j. m. mignot , b. bellarbi , a. benoit , h. f. braun , and j. sierro , j. magn . * 47 & 48 * , 23 ( 1985 ) . d. huo , t. kuwai , t. mizushima , y. isikawa , and j. sakurai , physica b * 312 & 313 * , 232 ( 2002 ) . d. huo , k. mori , t. kuwai , s. fukuda , y. isikawa , and j. sakurai , physica b * 281 & 282 * , 101 ( 2000 ) . j. sakurai , d. huo , d. kato , t. kuwai , y. isikawa , and k. mori , physica b * 281 & 282 * , 98 ( 2000 ) . p. b. van aken , h. j. van daal , and k. h. j. buschow , phys . a * 49 * , 201 ( 1974 ) . r. cibin , d. jaccard , and j. sierro , j. magn . magn . mater . * 108 * , 107 ( 1992 ) . h. wilhelm and d. jaccard , phys . b * 69 * , 214408 ( 2004 ) k. behnia , d. jaccard , and j. flouquet , j. phys . : cond matt . , * 16 * , 5187 ( 2004 ) f. steglich , festkrperprobleme xvii , 319 ( 1977 ) . j. sakurai , j. c. gomez sal , and j. rodriguez fernandez , j. magn . * 140 * - * 144 * , 1223 ( 1995 ) . a. amato , d. jaccard , j. sierro , p.haen , p. lejay , and j. flouquet , j. low . phys . * 77 * , 195 ( 1989 ) . y. nuki and t. komatsubara , j. magn . * 63 & 64 * , 281 ( 1987 ) . j. sakurai , t. ohyama , and y. komura , j. magn . mater . * 47 & 48 * , 320 ( 1985 ) . e. bauer , adv . * 40 * , 417 ( 1991 ) . c. fierz , d. jaccard , and j. sierro , j. appl . phys . * 63 * , 3899 ( 1988 ) . d. jaccard , k. behnia and j. sierro , phys . a * 163 * , 475 ( 1992 ) . d. jaccard , j. m. mignot , b. bellarbi , a. benoit , h. f. braun , and j. sierro , j. magn . mater . * 47&48 * , 23 ( 1985 ) . y. bando , j. sakurai , and e. v. sampathkumaran , physica b * 186 * - * 188 * , 525 ( 1993 ) . e. gratz , e. bauer , r. hauser , n. pillmayr , g. hilscher , h. mller , and b. barbara , j. magn . mater . * 76 & 77 * , 275 ( 1988 ) . j. sakurai , h. kamimura , and y. komura , j. magn . mater . * 76 & 77 * , 287 ( 1988 ) . d. huo , k. mori , t. kuwai , h. kondo y. isikawa , and j. sakurai , j. phys . japan * 68 * , 3377 ( 1999 ) . vol.68 no.10 , october , 1999 pp.3377 - 3382 m. oko , c. geibel , and f. steglich , phys . b * 64 * , 195107 - 1 ( 2001 ) . g. nakamoto , t. nobata , s. ueda , y. nakajima , t. fujioka , and m. kurisu , physica b * 259 * - * 261 * , 154 ( 1999 ) . k. alami - yadri , d. jaccard , and d. andreica , j. low temp . phys . * 114 * , 135 ( 1999 ) . r. casanova , d. jaccard , c. marcenat , n. hamdaoui , and m. j. besnus , j. magn . mater . * 90 & 91*,587 ( 1990 ) . o. trovarelli , c. geibel , b. buschinger , r. borth , s. mederle , m. grosche , g. sparn , and f. steglich , phys . b * 60 * , 1136 ( 1999 ) . d. andreica , k. alami - yadri , d. jaccard , a. amato , and a. schenk , physica b * 259 * - * 261 * , 144 ( 1999 ) . h. j. van daal , p. b. van aken , and k. h. j. buschow , phys . lett . a * 49 * , 246 ( 1974 ) . i. aviani , m. miljak , v. zlatic , k .- schotte , c. geibel , and f. steglich phys . rev . * b 64 * , 184438 ( 2001 ) h. wilhelm and d. jaccard , phys . rev . * b 66 * , 064428 ( 2002 ) a. demuer , a. t. holmes , and d. jaccard , j. phys . : condens . matter * 14 * l529-l535 ( 2002 ) h. wilhelm et al , science and technology at high pressure ( proc . airapt-17 ) m h manghnani , w j nellis and m f nicol ( hyderabad : universities press ) p 697 ( 2000 ) ( preprint cond - mat/9908442 ) h. wilhelm et al , preprint , cond - mat/0408280 for not too large values of @xmath60 , the thermopower at the minimum is negative ( see @xmath60=90 mev curve in fig . [ fig : theo_tep_low ] ) but if @xmath60 continues to increase the minimum of @xmath5 becomes more shallow and does not extend to negative values ( see curves in fig . [ fig : theo_tep_low ] obtained for @xmath60=100 - 120 mev ) .

, we obtain the phase diagram which agrees with the experimental data on cerusi , cecusi , cepdsi , and similar compounds . the evolution of the thermopower and the electrical resistance as a function of temperature , pressure or doping is explained in terms of the crossovers between various fixed points of the model and the redistribution of the single - particle spectral weight within the fermi window .

2ex the thermoelectric properties of intermetallic compounds with ce or yb ions are explained by the single - impurity anderson model which takes into account the crystal - field splitting of the 4_f _ ground - state multiplet , and assumes a strong coulomb repulsion which restricts the number of _ f _ electrons or _ f _ holes to for ce and for yb ions . using the non - crossing approximation and imposing the charge neutrality constraint on the local scattering problem at each temperature and pressure , the excitation spectrum and the transport coefficients of the model are obtained . the thermopower calculated in such a way exhibits all the characteristic features observed in ce and yb intermetallics . calculating the effect of pressure on various characteristic energy scales of the model , we obtain the phase diagram which agrees with the experimental data on cerusi , cecusi , cepdsi , and similar compounds . the evolution of the thermopower and the electrical resistance as a function of temperature , pressure or doping is explained in terms of the crossovers between various fixed points of the model and the redistribution of the single - particle spectral weight within the fermi window .

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table 3 summarizes the mips photometric results for the twa . several stars in the association are known optical variables and we give the epoch of the start of the observations in the second column of the table . the 24 @xmath9 m , 70 @xmath9 m , and 160 @xmath9 m flux densities are given in units of milli - janskys ( mjy ; where 1 mjy = @xmath27 erg @xmath28 s@xmath14 hz@xmath14 ) . uncertainties in the flux densities are the square root of the quadratic sum of the measurement and calibration uncertainties , noting that most relative uncertainties are much lower . also listed in table 3 is the s / n of the detections in each mips band . although some of the s / n values are extremely high , the uncertainties quoted for the photometry in all three bandpasses are dominated by uncertainties in the absolute flux calibration of the instrument . these are estimated to be @xmath610% for the 24 @xmath9 m band and @xmath620% for the 70 @xmath9 m and 160 @xmath9 m bandpasses . upper limits assigned in table 3 to non - detections at 70 @xmath9 m are at the level of 3@xmath19 over the noise of the background . our primary goal for this observational program is to detect and measure ir excesses in the twa . this requires that good estimates of @xmath10 be made for the twa stellar photospheres at the effective wavelengths of the mips bandpasses . for all of stars in the sample , stellar photospheres were derived using a grid of kurucz @xcite and `` nextgen '' @xcite photospheric models and fitting available optical photometry combined with near - ir flux densities compiled from the two - micron all sky survey ( 2mass ) point source catalog . temperature is a free parameter in the fitting , but in all cases solar metallicity and @xmath29 are assumed . the nextgen models are known to yield better fits to late - type main sequence stars than kurucz models , and were used for all twa members except for hr 4796a and twa 19a , which have much higher effective temperatures than the rest of the sample . the best - fitting model temperatures ( @xmath30 ) of the twa are listed in table 1 . comparison of the 24 @xmath9 m data for the twa with the 2mass @xmath31-band flux densities of these stars shows that the association can essentially be divided into two populations . figure 1 plots the 24-to-2.17 @xmath9 m flux density ratio against the flux density in the @xmath31-band . in all cases , the 2mass photometry is consistent with the stellar photospheres emitting the near - ir light . the four stars with ir excesses discovered by _ iras _ are about a factor of 100 brighter at 24 @xmath9 m relative to @xmath31 than the other stars in the sample . in fact , for the stars with flux ratios @xmath320.02 , the data are consistent with the 24 @xmath9 m flux being solely from the photosphere . as a guide , a dashed line in figure 1 marks the limit of @xmath33(24 @xmath9m)/@xmath34 if both bandpasses fall within the rayleigh - jeans regime of the stellar continuum . since the twa members are typically spectral type k and m , the @xmath31 band falls close to the emission peak of the photosphere . as a result , the stars typically lie above the rayleigh - jeans limit in figure 1 . figure 2 further explores the empirical relation between the 24 @xmath9 m flux density with the near - ir . the stars with previously known ir excesses or @xmath35 k are omitted from figure 2 , and the flux ratio shown in figure 1 is now plotted against the temperature of the model stellar photosphere . the majority of the 19 stars plotted form a locus that is offset from the @xmath33(24 @xmath9m)/@xmath34 ratios expected from blackbodies . spectra derived from the nextgen models generally give a good approximation to the observed flux ratios , although the twa members have not reached the main sequence . the unweighted average flux ratio @xmath36 with an rms of only 0.004 . the concentration of the points close to the expected values from the nextgen models in figure 2 suggests that we are seeing no ir excess at 24 @xmath9 m for most of these late - type , young stars . the mips photometry is consistent with the 24 @xmath9 m flux emanating from the photosphere for most of the members of the twa . one example is twa 6 , where the mips 24 @xmath9 m measurement supports the contention by @xcite that the 520 @xmath9 m spectrum of this star taken with _ spitzer _ and the infrared spectrograph ( irs ; * ? ? ? * ) is indeed the spectrum of the photosphere . although the nextgen models yield a much better brightness estimate of the photosphere at 24 @xmath9 m than blackbodies in this temperature range , figure 2 shows that the flux ratio is possibly more dependent on the model temperature than is actually observed . note , twa 12 , 13b , and 17 fall well below the nextgen curve . these deviations and the intrinsic scatter of the data are intriguing , but the limited number of objects in the sample complicate a detailed investigation of their possible causes , especially considering that only temperature was varied in constructing the models and that the twa stars are younger than the nominal zero - age main sequence stars described by the nextgen models . in the case of twa 17 , the 24 @xmath9 m flux density is measured to be only @xmath37 mjy and the source is detected at a @xmath38 with mips . therefore , we do not confirm the possible excess at 12 and 18 @xmath9 m reported from ground - based observations by @xcite . the measurement of @xmath33(24 @xmath9m)/@xmath34 for twa 7 suggests that it possesses a 24 @xmath9 m excess that contributes @xmath640% to the total brightness of this system at this wavelength . except for the four _ iras _ detections , twa 7 has a higher flux ratio in figures 1 and 2 than all of the other twa members . the next highest ratio belongs to twa 9b , but its deviation from the expected flux of the photosphere is less than half of that shown by twa 7 , and is no larger than the flux deficits at 24 @xmath9 m measured for twa 12 , 13b , and 17 . since the 2mass and mips measurements are not simultaneous , an alternate explanation for the apparent ir excess in twa 7 could be the variability of the star which is not uncommon for t tauri stars , although there are no published data suggesting that this star is variable . also , the clustering of most measurements around @xmath39(24 @xmath9m)/@xmath40 is a clear demonstration that most stars in the twa do not , in fact , exhibit significant variability . regardless of the strength of a possible 24 @xmath9 m excess in the observed continuum of twa 7 , this object is detected at 70 @xmath9 m at a flux level @xmath640@xmath1 brighter than the photospheric emission estimated for the star at this wavelength . figure 3 presents the ratio between the observed and predicted 70 @xmath9 m flux densities . only six of the 20 systems ( twa 19 is resolvable at 70 @xmath9 m ) are detected with mips at 70 @xmath9 m . twa 13 joins twa 7 and the four _ iras _ sources in having a detected 70 @xmath9 m excess . twa 13 can not be resolved with _ spitzer _ at 70 @xmath9 m , so it is unknown which of the two components produces the excess , or if both components of the binary contribute to the observed flux . figure 3 shows the same basic division in the twa sample as is found at 24 @xmath9 m . the 70 @xmath9 m excesses for twa 7 and 13 are @xmath1710@xmath1 fainter than the other detections . one - sigma upper limits are also shown in figure 3 for the remainder of the sample . as discussed in 2 , the sensitivity limits of the 70 @xmath9 m array render detection of the photospheres of the twa sample impractical . excesses similar to those of twa 7 and 13 can not be ruled out for many members of the association , and it is clear from the data that it is not necessary for an object to show an excess at 24 @xmath9 m to find one at 70 @xmath9 m . for instance , there is no hint from the 24 @xmath9 m measurement of twa 13 of an excess at longer wavelengths . there are three stars where a 70 @xmath9 m excess at @xmath1810@xmath1 the flux density of the photosphere can be ruled out at the 3@xmath19 confidence level : twa 2 , 5a , and 8a . therefore , the minimum range in strength for 70 @xmath9 m excesses in the twa is greater than a factor of 300 . the seds of the six systems in the twa with confirmed ir excesses are shown in figure 4 . it is readily apparent that this small sample of young stars exhibits a rich variety of ir properties . the t tauri stars tw hya and hen 3 - 600 show no hint of their seds turning over even out to 160 @xmath9 m . in fact , the mips 160 @xmath9 m measurement for tw hya reveals that the spectrum of the presumed optically thick accretion disk continues to rise into the infrared . similar to tw hya , the mips data for hen 3 - 600 are consistent with the earlier _ iras _ results and show that the 70 and 160 @xmath9 m flux densities are roughly equivalent . in contrast , hd 98800a and b do not show the extreme activity associated with t tauri stars . however , hd 98800b generates a huge ir excess that is well fit by a single blackbody with @xmath41 - 170 k @xcite , whereas component a lacks an easily measured excess even though the total luminosities of the two companions are virtually identical . the mips photometry is consistent with earlier results . likewise , the ir excess of hr 4796a produces an ir sed that can be fit by a single blackbody , but it is significantly cooler than found for hd 98800b ( @xmath42 k ; * ? ? ? * ) . with the addition of the _ spitzer _ observations , we fit this excess with a @xmath43 k blackbody . given that hr 4796a is an a0v star , it is not surprising that it has an ir excess because of the finding that younger a stars have a higher probability of possessing a 24 @xmath9 m excess and having stronger thermal excess emission than older a stars @xcite . it is of note that hr 4796a has by far ( by @xmath610@xmath1 ) the largest ratio of 24 @xmath9 m excess emission - to - photospheric emission of the 265 a and b stars examined by @xcite . figure 5 presents the mips sed - mode observations of tw hya and hd 98800b . these low - resolution spectra do not show any spectral features of high equivalent width in either object . arcturus was used to calibrate the spectra and they are consistent with the 70 @xmath9 m flux densities derived from the photometry . the ir spectral slopes of tw hya and hd 98800b are quite different , with the continuum of tw hya being much redder than that of hd 98800b . a power - law having a spectral index , @xmath44 , where @xmath45 , is adequate to describe these data . for tw hya , @xmath46 , and is consistent with the finding that the 160 @xmath9 m flux density is higher than the 70 @xmath9 m measurement . the slope of a single power - law fit to the continuum of hd 98800b between 52 and 97 @xmath9 m yields @xmath47 . the blackbody fit with @xmath48 k to the pds of hd 98800b is also shown in figure 5 , and its slope within this spectral region is in good agreement with the sed - mode data . our primary reason for calculating the stellar and ir excess luminosity is to measure the fractional luminosities of those stars that show direct evidence of pds formation and to provide well defined upper limits for those stars that fail to show an excess . table 4 lists the stellar luminosity , @xmath49 , derived by numerical integration , and the fractional luminosity , @xmath50 , where @xmath51 is the luminosity of the infrared excess that is the result of numerically integrating the flux density in excess of the predicted level of the photosphere . direct measurements of the distance to twa members are limited to only five systems ( table 1 ) . we have assigned a distance of 55 pc , the distance corresponding to the unweighted average of the parallaxes measured by _ hipparcos _ excluding twa 19 , to the other stars in the sample . in general , @xmath49 is higher than expected for the twa given their spectral types because these young , rapidly evolving stars have higher luminosities , lower temperatures , and larger radii than when they reach the main sequence . conservative upper limits for @xmath50 have been assigned to objects listed in table 4 that show no evidence for a 24 @xmath9 m excess by assuming that the 1@xmath19 upper limits estimated for the 70 @xmath9 m flux densities represent the brightness of a possible ir excess plus photosphere at this wavelength . it is also assumed that any possible ir excess is well approximated by a blackbody with temperature , @xmath52 . the upper limit on the temperature of a possible cold pds is given in table 4 and is set so that @xmath52 and the assumed value for @xmath33(70 @xmath9 m ) raise @xmath33(24 @xmath9 m ) by no more than 10% ; the adopted uncertainty in the absolute flux calibration of the mips measurements at 24 @xmath9 m . these upper limits on temperature do not preclude small amounts of warmer dust within systems that are still consistent with the 24 @xmath9 m measurements , but they do constrain the properties of circumstellar material able to produce substantial excesses at 70 @xmath9 m and be undetected by _ the mass of circumstellar dust responsible for the luminosity of ir excesses observed in the twa , or that could produce the upper limits found for @xmath52 and @xmath50 , can be deduced following the inferences of @xcite and @xcite . that is , the minimum mass in dust can be estimated by @xmath53 @xcite , where @xmath54 is the average radius of a dust grain , @xmath55 is the minimum distance from the star where the grains are in radiative equilibrium , and @xmath56 is the mass density of the grains . the equation above assumes that the dust is radiating from a thin shell at a distance @xmath55 from the illuminating star and that the debris disk is optically thin . also , it is assumed that the dust grains are spherical and have cross sections equal to their geometric cross sections . in table 4 , we tabulate @xmath57 using the values for average grain size and density adopted by @xcite ( @xmath58 @xmath0 m ; @xmath59 g @xmath60 ) . the minimum dust mass responsible for detected ir excesses range from @xmath61 g for hr 4796a to @xmath62 g for twa 13 . for hd 98800b , the assumption that the debris disk is optically thin is not valid , accounting for the much smaller mass estimate than that determined by @xcite . the mass estimates in table 4 for the twa are conservative lower bounds for the total circumstellar dust mass in these systems since the mips observations are not sensitive to colder material located further from a star and emission from larger particles . for example , there is evidence for material around twa 7 colder than the @xmath680 k dust detected by _ spitzer_. observations at 850 @xmath9 m by @xcite detected twa 7 with @xmath63 mjy . this flux density is about a factor of seven higher than the extrapolation to 850 @xmath9 m of the @xmath680 k blackbody determined by the 24 and 70 @xmath9 m excesses . @xcite and @xcite interpret the sub - millimeter emission as coming from 20 k dust with grain sizes on the order of a few hundred microns . as a consequence , the mass estimate for the dust disk around twa 7 derived by the sub - millimeter measurement is @xmath64 greater than that estimated from the ir excess .

high signal - to - noise 24 m photometry is presented for all of these stars , including 20 stars that were not detected by _ twa 7 also exhibits a strong 70 m excess that is a factor of 40 brighter than the stellar photosphere at this wavelength . at 70 m , an excess of similar magnitude is detected for twa 13 , though no 24 m excess was detected for this binary . measurements of two t tauri stars , tw hya and hen 6 - 300 , confirm that their spectacular ir spectral energy distributions ( seds ) do not turn over even by 160 m , consistent with the expectation for their active accretion disks . data for the luminous planetary debris systems in the twa , hd 98800b and hr 4796a , are consistent with single - temperature blackbody seds and agree with previous ir , sub - millimeter , and millimeter measurements . this bimodal distribution is especially striking given that the four stars in the association with strong ir excesses are brighter at 24 m than their photospheres .

_ spitzer space telescope _ infrared measurements are presented for 24 members of the tw hydrae association ( twa ) . high signal - to - noise 24 m photometry is presented for all of these stars , including 20 stars that were not detected by _ iras_. among these 20 stars , only a single object , twa 7 , shows excess emission at 24 m and at the level of only 40% above the star s photosphere . twa 7 also exhibits a strong 70 m excess that is a factor of 40 brighter than the stellar photosphere at this wavelength . at 70 m , an excess of similar magnitude is detected for twa 13 , though no 24 m excess was detected for this binary . for the 18 stars that failed to show measurable ir excesses , the sensitivity of the current 70 m observations does not rule out substantial cool excesses at levels 1040 above their stellar continua . measurements of two t tauri stars , tw hya and hen 6 - 300 , confirm that their spectacular ir spectral energy distributions ( seds ) do not turn over even by 160 m , consistent with the expectation for their active accretion disks . in contrast , the _ spitzer _ data for the luminous planetary debris systems in the twa , hd 98800b and hr 4796a , are consistent with single - temperature blackbody seds and agree with previous ir , sub - millimeter , and millimeter measurements . the major new result of this study is the dramatic bimodal distribution found for the association in the form of excess emission at a wavelength of 24 m , indicating negligible amounts of warm ( k ) dust and debris around 20 of 24 stars in this group of very young stars . this bimodal distribution is especially striking given that the four stars in the association with strong ir excesses are brighter at 24 m than their photospheres . clearly , two terrestrial planetary systems , hd 98800b and hr 4796a , exist in some form . in addition , there are at least two active accreting objects , tw hya and hen 6 - 300 , that may still be forming planetesimals . the remaining stars may possess significant amounts of cold dust , as in twa 7 and twa 13 , that have yet to be found . 0.2 in 0.1 in 0.1 in 0.1 in 0.1 in 0.2 in

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the main result of the _ spitzer_-mips observations of the twa is to show that most stars in the association exhibit no evidence for circumstellar dust and that the 24 @xmath9 m data place severe limits on the presence of warm ( @xmath65 k ) dust within these systems . although the twa includes four remarkable ir - excess systems , there are no other objects that come close to their 24 @xmath9 m output relative to the observed near - ir photospheric emission . the bimodal distribution of warm dust in the twa , identified by @xcite at shorter wavelengths , is confirmed at 24 @xmath9 m for a larger sample of objects ( see figure 1 ) . the bimodal nature of 70 @xmath9 m excesses is not as pronounced as at shorter wavelengths , but there is still a gap of about a factor of 10 between the strengths of the 70 @xmath9 m excess of hen 3 - 600 and the _ spitzer _ detections of twa 7 and 13 . there is also a range of at least @xmath66 between the brightest and faintest of the 70 @xmath9 m excesses in the twa relative to their photospheres at this wavelength . the luminosity of the observed ir excesses range from @xmath67% ( tw hya and hd 98800b ) to @xmath68% ( twa 13 ) of @xmath49 . it is difficult to fully characterize the ir excesses of twa 7 and 13 given that they only begin to appear at @xmath624 @xmath9 m . in the case of twa 13 , there is also the complicating factor that the system is a binary and the distribution of the material responsible for the excess is unknown . however , calculating a color temperature for the two objects yields similar results : @xmath6980 k. assuming that the excesses are well fit by blackbodies , both systems have a fractional ir luminosity of @xmath61% of that measured for hd 98800b ; @xmath70 and @xmath71 , for twa 7 and 13 , respectively . although the lack of observed excess 24 @xmath9 m emission constrains the temperatures of possible pdss for most of the 70 @xmath9 m non - detections to be @xmath72 k , the mips observational upper limits can not rule out ir excesses with fractional luminosity in the range of @xmath73@xmath74 . even at the estimated young age of the association it may already be more likely to detect cooler material , further away from the stars , than warmer material that results in an excess at 24 @xmath9 m or shorter wavelengths . clearly , at 70 @xmath9 m wavelength , large amounts of additional _ spitzer _ time will be needed to detect and measure the cool dust and debris around these stars . the variety of the ir properties in the twa is remarkable given the assumption that its members have similar ages . at 810 myr after the formation of the twa , there are still two systems ( tw hya and hen 3 - 600 ) accreting presumably primordial dust and they have enough circumstellar material to reprocess a large fraction ( 1030% ) of the stellar luminosity into the infrared . also in the association are two multiple - star systems , hd 98800 and hr 4796 , that have a prominent pds around only one of the stellar components and the debris is relatively warm ( @xmath75170 k ) . twa 7 shows evidence for a weak 24 @xmath9 m excess with the detected material being cooler ( @xmath76 k ) and located in orbits @xmath77 au from the star . the remaining 19 stars , including twa 7 and 13 , have apparently been cleansed to a high degree of dust with @xmath78 k. this variety of properties suggests that dust is swept from regions within several au ( see table 4 ) of the star very early in the system s evolution . the fact that stars in the association show no signature of warm dust while other members exhibit strong t tauri activity implies that the transition period from the t tauri stage to the more quiescent state observed for most of the twa k- and m - type stars , is very short . an efficient mechanism for the removal of dust is thought to be the formation of planets that sweep up dust and larger debris in the regions that they orbit . @xcite suggest that planetary formation was rapidly completed in the twa at least in the region where terrestrial planets would be expected to form . this led to the rapid disappearance of dust in the inner several au of these systems , leaving only the stellar photosphere to be detected at wavelengths of 24 @xmath9 m and shorter . strong stellar winds during the t tauri stage and the poynting - robertson drag are also mechanisms that can decrease the ir emission from a system by ridding the environment of small dust grains . of course , in most twa systems , and within 10 myr of their formation , dust destruction mechanisms must more than compensate for the dust production mechanism of collisions between larger bodies to clear out the terrestrial planet region . hd 98800b and hr 4796a are likely cases where their debris systems indicate that collisions between bodies are still important and produce dust close enough to the stars to result in large excesses at 24 @xmath9 m . nearly all members of the observed sample are x - ray emitters , supporting the assertion that stellar winds in these young , low - mass stars may be an important dust destruction mechanism ( see e.g. , * ? ? ? we list the x - ray to stellar luminosity ratios , @xmath79 , for twa stars in the last column of table 4 . the x - ray data are drawn from the _ rosat _ all sky survey catalog and @xmath80 is calculated in the manner described by @xcite . @xcite find an apparent correlation between ir and x - ray luminosity for their sample of f- and g - type stars with ages spanning 520 myr in the scorpius - centaurus ob association . this possible correlation is in the sense of brighter 24 @xmath81 m excesses tending to be associated with fainter stars in x - ray flux , and @xcite suggest that the stronger stellar wind implied by the chromospheric activity may help explain the general lack of young systems with 24 @xmath81 m excesses . given that only three stars in the twa sample have confirmed pdss that produce measurable excesses at 24 @xmath81 m , it is not possible to test the validity of the x - ray ir flux correlation . however , hd 98800b , hr 4796a , and twa 7 , are all underluminous in x - rays compared to the average observed x - ray emission for the twa . we can compare the _ spitzer _ observations of young stars with models for the early solar system . following the discussions in @xcite and @xcite , we assume that the rate of dust production directly scales as the rate of lunar cratering during the late heavy bombardment . the rate of dust production , @xmath82 , is given by : @xmath83 where @xmath84 is the look - back time in 10@xmath85 yr ( gyr ) , @xmath86 is the current rate of dust production and @xmath87 and @xmath88 are fitting constants such that @xmath89 and @xmath90 = 0.144 @xcite . in this model , the dust production rate has been approximately constant during the past 3.3 gyr , but was as high as @xmath91 the current value when @xmath92 . we set @xmath93 g s@xmath14 based on the zodiacal light in the solar system @xcite , implying that the early solar system may have had a dust production rate of @xmath94 g s@xmath14 . in a model where this quantity of dust is produced far from the star and then loses angular momentum under the action of the poynting - robertson effect , it is straightforward to show ( e.g. , * ? ? ? * ) that the luminosity of the dust , @xmath95 , is given by the expression : @xmath96 for the twa , young m - type stars would have luminosities at 24 @xmath81 m of @xmath97 erg s@xmath14 hz@xmath14 and , for distances of @xmath650 pc , we expect f@xmath98(24 @xmath81 m ) @xmath99 700 mjy , vastly greater than what is observed . this result suggests the absence of terrestrial planet - forming environments around these stars . however , in m - type stars where the luminosity is relatively low and the stellar wind rate is relatively large , dust grains mainly lose angular momentum by stellar wind drag rather than through poynting - robertson drag ( see * ? ? ? * ; * ? ? ? * ) . in this case , and if @xmath100 denotes the stellar wind loss rate , then : @xmath101 although we do not know @xmath100 for young m - type stars , we can extrapolate from their x - ray emission since the winds are likely to be driven by the same hot corona which produces the x - rays . it is plausible that young m - type stars have mass loss rates 10@xmath102 greater than the current solar wind loss rate of @xmath103 g s@xmath14 , and we estimate that @xmath104 g s@xmath14 . for main sequence early m - type stars , we may adopt @xmath105 . therefore , we expect that at 24 @xmath81 m , @xmath106 erg s@xmath14 hz@xmath14 and a predicted flux at 50 pc of only @xmath60.7 mjy . a 24 @xmath81 m excess this small is beyond the sensitivity of our current measurements , and it is possible that planet forming activity may still be occurring around the young m - type stars in the twa even though we do not detect an infrared excess . the twa gives us an important example of the rapid evolution of the circumstellar material around generally low - mass stars with ages of @xmath107 myr that is in line with time scales of terrestrial planet formation inferred for our solar system from radiochemistry of meteorites @xcite . the diverse ir properties of the association also suggest that the evolutionary processes relevant to planetary formation and accretion disk dispersal may occur at different rates even for stars with similar spectral types . for most of the systems observed , the lack of emission from dust within a few au of the stars leads to two possible conclusions . either , ( 1 ) the early conditions around pre - main sequence m and late k stars prevent the formation of terrestrial planets in most cases , or that ( 2 ) terrestrial planet building has already progressed to the point where the mass is in the form of planetesimals . this work is based on observations made with the _ spitzer space telescope _ , which is operated by the jet propulsion laboratory ( jpl ) , california institute of technology ( cit ) , under national aeronautics and space administration ( nasa ) contract 1407 . we thank nasa , jpl , and the _ spitzer _ science center for support through _ spitzer _ , mips , and science working group contracts 960785 , 959969 , and 1256424 to the university of arizona . we thank m. blaylock , c. engelbracht , k. gordon , k. misselt , j. muzerolle , g. neugebauer , j. stansberry , k. stapelfeldt , k. su , b. zuckerman , and an anonymous referee for useful comments and discussions . v. krause acknowledges a summer undergraduate research fellowship at jpl . this publication makes use of data products from the two - 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600 & 38.268 & 1650 @xmath108 170 & @xmath18 10@xmath113 & 700 @xmath108 140 & 140 & 740 @xmath108 190 & 6 + hd 98800ab & 177.665 & 8500 @xmath108 350 & 1000 & 6260 @xmath108 1250 & 200 & 2100 @xmath108 420 & 67 + twa 5a & 38.255 & 21.1 @xmath108 2.1 & 220 & @xmath32 9 & & & + & & & & & & & + twa 6 & 134.825 & 5.7 @xmath108 0.6 & 240 & @xmath32 8 & & & + twa 7 & 35.398 & 30.2 @xmath108 3.0 & 260 & 85 @xmath108 17 & 22 & & + twa 8 & 35.905 & 14.5 @xmath108 1.5 & 160 & @xmath32 11 & & & + a & & 11.1 @xmath108 1.5 & & & & & + b & & 3.4 @xmath108 0.4 & & & & & + twa 9 & 37.870 & 9.3 @xmath108 1.1 & 160 & @xmath32 34 & & & + a & & 6.0 @xmath108 0.6 & & & & & + b & & 3.3 @xmath108 0.3 & & & & & + twa 10 & 55.726 & 5.1 @xmath108 0.5 & 190 & @xmath32 8 & & & + & & & & & & & + hr 4796a & 35.928 & 3030 @xmath108 303 & @xmath18 10@xmath113 & 5160 @xmath108 1100 & 240 & 1800 @xmath108 360 & 55 + twa 12 & 177.907 & 5.7 @xmath108 0.6 & 50 & @xmath32 29 & & & + twa 13 & 177.680 & 17.6 @xmath108 1.8 & 150 & 27.6 @xmath108 5.9 & 13 & & + a & & 8.8 @xmath108 1.3 & & & & & + b & & 8.8 @xmath108 1.3 & & & & & + twa 14 & 55.677 & 4.1 @xmath108 0.4 & 27 & @xmath32 25 & & & + twa 15 & 55.701 & 2.9 @xmath108 0.3 & 72 & @xmath32 12 & & & + a & & 1.4 @xmath108 0.2 & & & & & + b & & 1.5 @xmath108 0.2 & & & & & + & & & & & & & + twa 16 & 55.714 & 6.6 @xmath108 0.6 & 45 & @xmath32 18 & & & + twa 17 & 55.743 & 1.5 @xmath108 0.2 & 13 & @xmath32 13 & & & + twa 18 & 55.762 & 2.3 @xmath108 0.3 & 20 & @xmath32 9 & & & + twa 19a & 55.689 & 10.4 @xmath108 1.1 & 100 & @xmath32 27 & & & + twa 19b & 55.689 & 4.6 @xmath108 0.5 & 44 & @xmath32 27 & & & + tw hya & & & & 0.24 & @xmath114 & @xmath115 + twa 2ab & @xmath116 & @xmath117 & 0.27 & 0.39 & @xmath118 & @xmath119 + hen 3 - 600 & & & & 0.35 & @xmath120 & @xmath121 + hd 98800b & 160 & 2.2 & @xmath122 & 0.53 & @xmath123 & @xmath124 + & & & & + twa 5a & @xmath125 & @xmath126 & 0.01 & 0.36 & @xmath127 & @xmath128 + twa 6 & @xmath129 & @xmath130 & 0.02 & 0.14 & @xmath131 & @xmath132 + twa 7 & @xmath133 & 6.8 & 2.4 & 0.31 & @xmath134 & @xmath135 + twa 8a & @xmath136 & @xmath137 & 0.04 & 0.19 & @xmath138 & @xmath139 + twa 8b & @xmath140 & @xmath141 & 0.19 & 0.04 & @xmath142 & + & & & & + twa 9a & @xmath143 & @xmath144 & 1.3 & 0.15 & @xmath145 & @xmath139 + twa 9b & @xmath143 & @xmath146 & 1.5 & 0.03 & @xmath147 & + twa 10 & @xmath148 & @xmath149 & 0.09 & 0.09 & @xmath150 & @xmath128 + hr 4796a & @xmath151 & 30 & 110 & 19.7 & @xmath152 & + twa 12 & @xmath153 & @xmath154 & 0.94 & 0.09 & @xmath155 & @xmath156 + & & & & + twa 13a & @xmath157 & 7.8 & 1.4 & 0.18 & @xmath158 & @xmath159 + twa 13b & @xmath157 & 7.7 & 1.4 & 0.17 & @xmath160 & + twa 14 & @xmath153 & @xmath161 & 0.59 & 0.07 & @xmath162 & @xmath132 + twa 15a & @xmath143 & @xmath163 & 0.27 & 0.03 & @xmath164 & @xmath165 + twa 15b & @xmath153 & @xmath166 & 0.20 & 0.03 & @xmath167 & + & & & & + twa 16 & @xmath148 & @xmath168 & 0.15 & 0.12 & @xmath169 & @xmath170 + twa 17 & @xmath143 & @xmath161 & 0.54 & 0.06 & @xmath171 & @xmath172 + twa 18 & @xmath148 & @xmath166 & 0.06 & 0.06 & @xmath150 & @xmath172 + twa 19a & @xmath173 & @xmath174 & 1.0 & 2.10 & @xmath175 & @xmath124 + twa 19b & @xmath140 & @xmath176 & 2.7 & 0.38 & @xmath164 & +

for the 18 stars that failed to show measurable ir excesses , the sensitivity of the current 70 m observations does not rule out substantial cool excesses at levels 1040 above their stellar continua . the major new result of this study is the dramatic bimodal distribution found for the association in the form of excess emission at a wavelength of 24 m , indicating negligible amounts of warm ( k ) dust and debris around 20 of 24 stars in this group of very young stars . clearly , two terrestrial planetary systems , hd 98800b and hr 4796a , exist in some form . in addition , there are at least two active accreting objects , tw hya and hen 6 - 300 , that may still be forming planetesimals . the remaining stars may possess significant amounts of cold dust , as in twa 7 and twa 13 , that have yet to be found . 0.2 in 0.1 in 0.1 in 0.1 in 0.1 in 0.2 in

_ spitzer space telescope _ infrared measurements are presented for 24 members of the tw hydrae association ( twa ) . high signal - to - noise 24 m photometry is presented for all of these stars , including 20 stars that were not detected by _ iras_. among these 20 stars , only a single object , twa 7 , shows excess emission at 24 m and at the level of only 40% above the star s photosphere . twa 7 also exhibits a strong 70 m excess that is a factor of 40 brighter than the stellar photosphere at this wavelength . at 70 m , an excess of similar magnitude is detected for twa 13 , though no 24 m excess was detected for this binary . for the 18 stars that failed to show measurable ir excesses , the sensitivity of the current 70 m observations does not rule out substantial cool excesses at levels 1040 above their stellar continua . measurements of two t tauri stars , tw hya and hen 6 - 300 , confirm that their spectacular ir spectral energy distributions ( seds ) do not turn over even by 160 m , consistent with the expectation for their active accretion disks . in contrast , the _ spitzer _ data for the luminous planetary debris systems in the twa , hd 98800b and hr 4796a , are consistent with single - temperature blackbody seds and agree with previous ir , sub - millimeter , and millimeter measurements . the major new result of this study is the dramatic bimodal distribution found for the association in the form of excess emission at a wavelength of 24 m , indicating negligible amounts of warm ( k ) dust and debris around 20 of 24 stars in this group of very young stars . this bimodal distribution is especially striking given that the four stars in the association with strong ir excesses are brighter at 24 m than their photospheres . clearly , two terrestrial planetary systems , hd 98800b and hr 4796a , exist in some form . in addition , there are at least two active accreting objects , tw hya and hen 6 - 300 , that may still be forming planetesimals . the remaining stars may possess significant amounts of cold dust , as in twa 7 and twa 13 , that have yet to be found . 0.2 in 0.1 in 0.1 in 0.1 in 0.1 in 0.2 in

1409.1189

c

we have analysed spectra of the low metallicity starforming galaxy _ phl 293b _ corresponding to four epochs obtained in four different combinations of telescopes and spectrographs , the sdss , vlt - uves , vlt-_x - shooter _ and wht - isis . we find moderate narrow absorption components in the balmer series blueshifted by 800km / s . we detected also the ir caii triplet lines at the galaxy velocity rest frame , i.e. the rest frame defined by the ionised gas narrow emission lines . we also find narrow absorptions at @xmath45 4911 at @xmath45 5004 ( partially filled up by [ oiii ] @xmath3 5007 ) and a previously unidentified absorption at @xmath455183 . we interpret these narrow absorptions as the feii multiplet ( 42 ) @xmath2 4923.93,5018.44,5169.03 , similar to those detected in a variety of transient luminous objects like the lbv candidate ngc 2366 v1 or sn type iin 1995 g , 1999el or 1999eb , blueshifted by the same amount as the balmer absorption features i.e. @xmath13800 km / s to @xmath2 4911,5005,5155 . the analysis of the photometric data provided by the css puts a strong upper limit to the possible variability of _ phl 293b_. basically any optical yearly variability allowed by the data should be smaller than 0.02 magnitudes at the 3 sigma level in the 8.5 years between april 2005 and september 2013 . the possibility of any secular trend in the luminosity of _ phl 293b _ in the last 15 years ( considering only ccd data ) is also limited to at most 0.02 magnitudes at the 3 sigma level . this lack of variability and the observed strength of the balmer and feii absorptions rule out any transient of the type of an lbv or sn type iin as the origin of the blue shifted absorptions of h and feii . the evidence points to either a young and dense expanding supershell or a stationary cooling wind , both driven by the young cluster wind . we suggest that the observed absorptions and broad balmer emissions are originated in one of these scenarios which seem capable of explaining the observed spectral features , the constant ( within errors ) photometric history and the rarity of the phenomenon . many starbursts , both nearby and at high z , show blueshifted far uv ism narrow absorption lines . on that basis , coupled with the observational evidence , we expect that the far uv spectrum of _ phl 293b _ will show blue shifted ism lines and moderate ly@xmath8 emission with perhaps a p cygni - like profile . we have to bear in mind that there are not many hii galaxies known to show prominent broad wings in their emission lines and none with the quality of the data presented here for _ phl 293b_. this leaves open the possibility that we are witnessing an event not detected in other systems due to low s / n data . even if it is true that we havent been actively looking for them , and that data of the quality and variety discussed here is not widely available , it is still puzzling that fe absorptions have not been detected in other star forming hii galaxies . a search should be performed in high dispersion , high signal - to - noise spectra of hii galaxies to investigate the presence of supershells in starbursts with or without strong broad components in the balmer lines . until such data is gathered and analysed , the fact that we do not see many hii galaxies showing spectra similar to _ phl 293b _ means that this may be a relatively short duration stage in the evolution of compact and massive stellar clusters , lasting perhaps only a few thousand years .

the lack of variability rules out transient phenomena like luminous blue variables or sn iin as the origin of the blue shifted absorptions of hi and feii . the evidence points to either a young and dense expanding supershell or a stationary cooling wind , in both cases driven by the young cluster wind .

_ x - shooter _ and isis wht spectra of the starforming galaxy _ phl 293b _ also known as _ a2228 - 00 _ and _ sdss j223036.79 - 000636.9 _ are presented in this paper . we find broad ( fwhm = 1000km / s ) and very broad ( fwzi = 4000km / s ) components in the balmer lines , narrow absorption components in the balmer series blueshifted by 800km / s , previously undetected feii multiplet ( 42 ) absorptions also blueshifted by 800km / s , ir caii triplet stellar absorptions consistent with [ fe / h ] and no broad components or blushifted absorptions in the hei lines . based on historical records , we found no optical variability at the 5 level of 0.02 mag between 2005 and 2013 and no optical variability at the level of 0.1mag for the past 24 years . the lack of variability rules out transient phenomena like luminous blue variables or sn iin as the origin of the blue shifted absorptions of hi and feii . the evidence points to either a young and dense expanding supershell or a stationary cooling wind , in both cases driven by the young cluster wind . [ firstpage ] galaxies : abundances galaxies : dwarfs

gr-qc9603027

i

three decades after the first exploratory steps were made @xcite canonical quantum gravity continues as a vigorous program of fundamental research . new life has been breathed into this field about a decade ago by ashtekar s discovery @xcite of a representation of general relativity in terms of new variables , which render the hamiltonian and diffeomorphism constraints more tractable . the developments in nonperturbative canonical quantum gravity which followed this advance @xcite justify a reasonable hope that a mathematically consistent quantum gravity might be attainable . still , the program is far from completed and many facets of the theory remain to be explored . one such facet is the relation between the metric representation and ashtekar s representation . this question is far from trivial : ashtekar s formulation starts out with complexified general relativity and suitable reality conditions on the new variables have to be imposed at the end . the metric representation , on the other hand , stays within the domain of the real theory all along . thus it is not clear , a priori , whether there is a unique one to one relation between the complexified theory and the real theory . can , e.g. , a single solution of the wheeler - dewitt equation in ashtekar s variables before imposing reality conditions give rise to several mathematically and physically distinct solutions in metric variables ? in the present paper we wish to examine this question in the framework of the minisuperspace model of diagonal bianchi type ix with a non - vanishing cosmological constant . kodama @xcite and brencowe @xcite have found a simple solution of the basic constraints of quantum gravity with cosmological term in ashtekar s variables in the form of an exponential of the chern - simons functional . by projecting to bianchi type ix geometries one also obtains a solution for the minisuperspace model @xcite . in the present paper we shall start from the wheeler - dewitt equation for the minisuperspace model in the metric representation and a specific choice of operator ordering ( which is gleaned from the special operator ordering appearing naturally if supergravity is used as a starting point @xcite ) . the ashtekar representation is then introduced only on the quantum level as a mathematical device , like a laplace - transform , to simplify the equations . in fact , the representation is introduced as a kind of complexified momentum - representation , in which ashtekar s variables are the complexified canonically conjugate momenta of the inverse triad corresponding to the bianchi type ix 3-metric . the integration contour in the complex manifold spanned by these momentum variables may be chosen quite freely within the requirements of convergence and the vanishing of boundary terms in partial integrations . integration contours which can be deformed into each other while satisfying these requirements are topologically equivalent . however , a given solution in ashtekar variables may admit topologically inequivalent choices of integration contours . such a solution in ashtekar variables may then correspond to several mathematically and physically distinct solutions in the metric representation . in fact , we shall show that this happens for the chern - simons topological solution in the diagonal bianchi type ix minisuperspace model . we find that five topologically inequivalent integration contours over the ashtekar variables exist , which are organized by five distinct saddle - points of the reduced chern - simons functional and the accompanying paths of steepest ascent and descent . these findings raise the interesting question , whether similar results may also be obtained in the full theory . the answer to this question is not obvious , because the enlargement of the configuration space , in principle , could render integration contours topologically equivalent , which appear as topologically inequivalent when projected on the minisuperspace under investigation . while this general question transcends our minisuperspace framework and must be left open here , our results for the minisuperspace model yield several new exact solutions in metric variables with non - vanishing cosmological constant . these solutions turn out to be of interest in their own right . to simplify their discussion we restrict ourselves to the physically more interesting case @xmath0 throughout this paper and postpone the examination of the case @xmath1 to a future work . we discuss the asymptotic limits of the solutions for @xmath2 and @xmath3 and show that , at least semi - classically , two of them satisfy the cosmological boundary conditions proposed by vilenkin @xcite and by hartle and hawking @xcite , respectively . furthermore , we show that it is just the no - boundary state which additionally fulfills a physically well - motivated normalizability condition . the remainder of this paper is organized as follows : in section [ 1 ] we establish our notation , put down the wheeler - dewitt equation in the adopted operator ordering , and briefly list the five exact solutions for vanishing cosmological constant which are known from recent work on bianchi type ix supergravity . in section [ 2 ] the ashtekar representation is introduced as a complexified momentum - representation , and the resulting chern - simons solution of the wheeler - dewitt operator is given . in section [ 3 ] that solution is transformed to the metric representation along five topologically distinct integration contours , which establishes a basis of five linearly independent solutions which are all generated by the chern - simons solution . their asymptotic behavior for @xmath2 , @xmath3 , or @xmath4 ( where @xmath5 is the scale parameter and @xmath6 the cosmological constant ) is studied in section [ 4 ] . here , in addition , we establish the relation of two of these solutions to those picked out by the boundary or no - boundary conditions of vilenkin , and hartle and hawking , respectively . in the last section we draw some conclusions and indicate how our results may also be used to establish certain limiting forms of bianchi type ix models coupled to a scalar matter field with very small mass .

this class consists of all the `` topological solutions '' which are associated with the bianchi type ix reduction of the chern - simons functional in ashtekar variables . we show how the saddle - points of the reduced chern - simons functional generate a complete basis of such integration contours and the associated solutions . among the solutions we identify two , which , semi - classically , satisfy the boundary conditions proposed by vilenkin and by hartle and hawking , respectively . in the limit of vanishing cosmological constant our solutions reduce to a class found earlier in special fermion sectors of supersymmetric bianchi type ix models .

a class of exact solutions of the wheeler - dewitt equation for diagonal bianchi type ix cosmologies with cosmological constant is derived in the metric representation . this class consists of all the `` topological solutions '' which are associated with the bianchi type ix reduction of the chern - simons functional in ashtekar variables . the different solutions within the class arise from the topologically inequivalent choices of the integration contours in the transformation from the ashtekar representation to the metric representation . we show how the saddle - points of the reduced chern - simons functional generate a complete basis of such integration contours and the associated solutions . among the solutions we identify two , which , semi - classically , satisfy the boundary conditions proposed by vilenkin and by hartle and hawking , respectively . in the limit of vanishing cosmological constant our solutions reduce to a class found earlier in special fermion sectors of supersymmetric bianchi type ix models .

hep-ph0304223

i

recently much interest is given for high - density qcd , especially for quark cooper - pair condensation phenomena at high - density quark matter ( called as color superconductivity ( csc ) ) , in connection with , e.g. , physics of heavy ion collisions and neutron stars @xcite . its mechanism is similar to the bcs theory for the electron - phonon system @xcite , in which the attractive interaction of electrons is provided by phonon exchange and causes the cooper instability near the fermi surface . as for quark matter , the quark - quark interaction is mediated by colored gluons , and is often approximated by some effective interactions , e.g. , the one - gluon - exchange ( oge ) or the instanton - induced interaction , both of which give rise to the attractive quark - quark interaction in the color anti - symmetric @xmath0 channel . csc leads to spontaneous symmetry breaking of color @xmath1 into @xmath2 as a result of condensation of quark cooper pairs @xcite . in this paper we would like to address another phenomenon expected in quark matter : spin polarization or ferromagnetism of quark matter . we examine the possibility of the spin - polarized phase with csc in quark matter . as far as we know , interplay between the color superconducting phase and other phases characterized by the non - vanishing mean fields of the spinor bilinears @xmath3 has not been explored except for the case of chiral symmetry breaking @xcite . our main concern here is to investigate the possibility of the quark cooper instability under the axial - vector mean - field , @xmath4 which is responsible for spin polarization of quark matter . it would be worth mentioning in this context that ferromagnetism ( or spin polarization ) and superconductivity are fundamental concepts in condensed matter physics , and their coexistent phase has been discussed for a long time @xcite . as a recent progress , a superconducting phase have been discovered in ferromagnetic materials and many efforts have been made to understand the coexisting mechanism @xcite . besides being interesting in its own right , the coexistence problem may be related to some physical phenomena . recently , a new type of neutron stars , called as `` magnetars '' , with a super strong magnetic field of @xmath5 g ) has been discovered @xcite . they may raise an interesting question for the origin of the magnetic field in compact stars , since its strength is too large to regard it as a successor from progenitor stars , unlike canonical neutron stars @xcite . since hadronic matter spreads over inside neutron stars beyond the nuclear density ( @xmath6@xmath7@xmath8@xmath9 ) , it should be interesting to consider the microscopic origin of the magnetic field in magnetars . in this context , a possibility of ferromagnetism in quark matter due to the oge interaction has been suggested by one of the authors ( t.t . ) within a variational framework @xcite ; a competition between the kinetic and the fock exchange energies gives rise to spin polarization , similarly to bloch s idea for itinerant electrons . salient features of spin polarization in the relativistic system are also discussed in ref . thus , it might be also interesting to examine the possibility of the spin - polarized phase with csc in quark matter , in connection with magnetars . we investigate spin polarization in the color superconducting phase by a self - consistent framework , in which quark cooper pairs are formed under the axial - vector mean - field . we shall see that this phenomenon is a manifestation of spontaneous breaking of both color @xmath1 and rotation symmetries . we adopt here the oge interaction as an effective quark - quark interaction . since the fermi momentum is very large at high density , asymptotic freedom of qcd implies that the interaction between quarks is very weak @xcite . so it may be reasonable to think that the oge interaction has a dominant contribution for the quark - quark interaction . in the framework of relativistic mean - field theories , the axial - vector and tensor mean - fields , which stem from the fock exchange terms , @xmath10 and @xmath11 , may have a central role to split the degenerate single - particle energies of the two spin states , and then leads to spin polarization , e.g. , see @xcite for discussion in nuclear matter . as for quark matter , several types of the color singlet mean - fields appear after the fierz transformation in the fock exchange terms , but we retain only the axial - vector mean - field as the origin of spin polarization , because the oge interaction by no means holds the tensor mean - field due to chiral symmetry in qcd , unlike nuclear matter @xcite . presence of the axial - vector mean - field deforms the quark fermi seas according to their spin degrees of freedom , and thereby the gap function should be no more isotropic in the momentum space . we assume here an anisotropic gap function @xmath12 on the fermi surface by a physical consideration and solve the coupled schwinger - dyson equations self - consistently by way of the nambu formalism to find the axial - vector mean - field @xmath13 and the superconducting gap function @xmath12 . thus we discuss the interplay between spin polarization and superconductivity in quark matter . in section 2 we give a framework to deal with the present subject . the explicit structure of the anisotropic gap function @xmath12 in the color , flavor , and dirac spaces is carefully discussed there and in the appendix b and appendix c. numerical results about @xmath13 and @xmath12 are given in section 3 , where phase diagram of spin polarization and color superconductivity is given in the mass - baryon number density plane . section 4 is devoted to summary and concluding remarks .

a coexistent phase of spin polarization and color superconductivity in high - density qcd is investigated using a self - consistent mean - field method at zero temperature . the axial - vector self - energy stemming from the fock exchange term of the one - gluon - exchange interaction has a central role to cause spin polarization . the magnitude of spin polarization is determined by the coupled schwinger - dyson equations with a superconducting gap function . as a significant feature , the fermi surface is deformed by the axial - vector self - energy and then rotation symmetry is spontaneously broken down . the gap function results in being anisotropic in the momentum space in accordance with the deformation . as a result of numerical calculations

a coexistent phase of spin polarization and color superconductivity in high - density qcd is investigated using a self - consistent mean - field method at zero temperature . the axial - vector self - energy stemming from the fock exchange term of the one - gluon - exchange interaction has a central role to cause spin polarization . the magnitude of spin polarization is determined by the coupled schwinger - dyson equations with a superconducting gap function . as a significant feature , the fermi surface is deformed by the axial - vector self - energy and then rotation symmetry is spontaneously broken down . the gap function results in being anisotropic in the momentum space in accordance with the deformation . as a result of numerical calculations , it is found that spin polarization barely conflicts with color superconductivity , but almost coexists with it . = -2.0 cm = 1.5em

1604.00873

i

directed graphs ( digraphs ) are widely used to describe interactions in technological , biological , and social complex systems @xcite . a digraph is composed of vertices and arcs ( directed edges ) which link between vertices . for instance , the gene regulation system of a biological cell can be modeled as a digraph of genes , in which an arc points from gene @xmath0 to gene @xmath1 if @xmath0 regulates the expression of @xmath1 @xcite . real - world complex systems are full of feedback interactions and adaptation mechanisms , and the digraphs of these systems usually contain an abundant number of directed cycles , which make the system s dynamical properties difficult to predict and to externally control @xcite . not all vertices and arcs are equally important in feedback interactions . some vertices and arcs may participate in a much greater number of directed cycles than other vertices and arcs . a minimum feedback vertex set ( fvs ) contains a smallest number of vertices whose deletion from the digraph destroys all the directed cycles . similarly , a minimum feedback arc set ( fas ) is an arc set of smallest cardinality such that every directed cycle of the digraph has at least one arc in this set . in terms of collective effect , the vertices in a fvs and the arcs in a fas may be most significant to the dynamical complexity of a complex networked system @xcite , and these vertices and arcs may also be optimal targets of distributed network attack processes @xcite . the directed feedback problems , namely constructing a minimum fvs and a minimum fas for a generic digraph , are combinatorial optimization problems in the nondeterministic polynomial - hard ( np - hard ) class and therefore are intrinsically very difficult @xcite . some progresses have been achieved by computer scientists and applied mathematicians in understanding this classic hard problem since the 1990s @xcite . approximate algorithms with provable bounds have been designed ( see , for example @xcite ) and efficient heuristic algorithms such as greedy local search @xcite and simulated annealing @xcite have been implemented and tested on benchmark small problem instances . yet unlike the fvs problem on an undirected graph @xcite , it is still very difficult to give tight bounds on the minimal cardinality of the directed fvs and fas problems . in this paper we study the directed fvs problem using statistical physics methods . our method is also applicable to the fas problem since it is essentially equivalent to the fvs problem @xcite . we construct a spin glass model for the directed fvs problem and derive the replica - symmetric ( rs ) mean field theory for this model . the mean field theory enables us to estimate the minimum directed fvs cardinality for random digraphs . based on this mean field theory we implement a belief propagation - guided decimation ( bpd ) algorithm and apply this message - passing algorithm to large random digraph instances . the bpd algorithm slightly outperforms the simulated annealing algorithm @xcite in terms of the fvs cardinality and the arc density of the remaining directed acyclic graph ( dag ) , while the computing times of the two algorithms are comparable to each other . our work will be helpful for future investigations on the dynamical complexity of various real - world networked systems and for further studies of targeted attacks on directed networks . in this paper we also point out a major difficulty of the rs mean field theory in treating directed cycle - caused long range correlations . directed and undirected cycles cause long - range correlations and frustrations in dynamical systems and spin glass models . they are very important network structural properties , but theoretical efforts directly treating them as constraints are quite lacking . directed cycles are global properties of a digraph ( each of which may involve a lot of vertices and arcs ) . compared with problems with local constraints ( such as the @xmath2-satisfiability problem @xcite ) , optimization problems constrained by directed cycles are much more difficult to tackle theoretically . the present paper is a continuation of our earlier report @xcite which treated the undirected fvs problem successfully . we realized that the directness of the cycle constraints makes the directed fvs problem much harder than its undirected counterpart . it is clear that further efforts are needed to overcome the gap between the bpd results and the rs predictions in fig . [ fig : rdfvs ] . the next section defines the directed fvs and fas problems and explains their essential equivalence . we then introduce a fvs spin glass model in sec . [ sec : model ] and study it by rs mean field theory in sec . [ sec : rs ] . in sec . [ sec : bpd ] we describe the bpd message - passing algorithm and compare its performance with the simulated annealing algorithm on random digraphs . we conclude this paper in sec . [ sec : conclusion ] . the two appendices contain some additional technical discussions .

a directed graph ( digraph ) is formed by vertices and arcs ( directed edges ) from one vertex to another . the directed feedback vertex set problem aims at constructing a fvs of minimum cardinality . this is a fundamental cycle - constrained hard combinatorial optimization problem with wide practical applications . in this paper the bpd algorithm slightly outperforms the simulated annealing algorithm on large random graph instances . the predictions of the rs mean field theory are noticeably lower than the bpd results , possibly due to its neglect of cycle - caused long range correlations .

a directed graph ( digraph ) is formed by vertices and arcs ( directed edges ) from one vertex to another . a feedback vertex set ( fvs ) is a set of vertices that contains at least one vertex of every directed cycle in this digraph . the directed feedback vertex set problem aims at constructing a fvs of minimum cardinality . this is a fundamental cycle - constrained hard combinatorial optimization problem with wide practical applications . in this paper we construct a spin glass model for the directed fvs problem by converting the global cycle constraints into local arc constraints , and study this model through the replica - symmetric ( rs ) mean field theory of statistical physics . we then implement a belief propagation - guided decimation ( bpd ) algorithm for single digraph instances . the bpd algorithm slightly outperforms the simulated annealing algorithm on large random graph instances . the predictions of the rs mean field theory are noticeably lower than the bpd results , possibly due to its neglect of cycle - caused long range correlations . janary 17 , 2016 ( first version ) ; april 04 , 2016 ( revised version )

1307.0005

i

new abelian gauge symmetries are arguably the simplest extensions of the standard model ( sm ) ( for a recent review , see @xcite ) . if sm fermions are charged under a new abelian @xmath7 , its couplings are strongly constrained by direct searches and especially by fcnc processes . the simplest and widely studied possibility in the literature is when sm fermions have flavor - independent charges . most popular examples in this class are @xmath8 or linear combinations @xmath9 . they are actually the only family - independent , anomaly - free gauged symmetries commuting with the sm gauge group in case where there are no new fermions beyond the ones of the sm . family - dependent anomaly - free models with no extra fermions were also extensively studied . in all such cases , the @xmath0 should be heavy enough to escape detection , at least in the multi - tev range . there is also a large literature on light @xmath10 s of string or field theory origin with anomaly cancellation a la green - schwarz @xcite , with low - energy anomalies canceled by axionic couplings and generalized chern - simons terms , or in other models with stueckelberg realization of @xmath0 @xcite . a radically different option is to have no sm fermions charged under @xmath0 . this is a relatively natural framework in string theory with d - branes . but it is also natural from a field theory viewpoint , with additional heavy fermions @xmath11 , called mediators " in what follows , which mediate effective interactions , described by the dimension - four kinetic mixing and higher - dimensional operators between the @xmath0 and the sm sector @xcite . if one wants mediators parametrically heavier than the electroweak scale ( say in the tev range ) , we need , in addition to possible sm higgs contributions , an additional source to their mass . a purely dirac mass is of course a simple viable option . however as argued in @xcite , because of the furry theorem , the only low - dimensional induced effective operator is the kinetic mixing , whereas the next higher - dimensional ones are of dimension eight . throughout our paper , we consider the kinetic mixing to be small enough . if we are interested in @xmath0 couplings to gluons , this can be achieved for example by having colored mediators with no hypercharge . in this case , the main couplings between the hidden " @xmath0 and the sm are generated by higher - dimensional effective operators ( hdo s ) , the lowest relevant ones being of dimension six . however , we will show that in the parameter space allowed by the planck / wmap data , the phenomenological consequences induced by the presence of a kinetic mixing allowed by various constraints are negligible . the simplest and natural option to obtain dimension - six effective operators is to generate the mediator masses by the vev of the scalar field @xmath12 breaking spontaneously the @xmath0 gauge symmetry . the corresponding induced mediator masses , called generically @xmath13 in what follows , determine the mass scale of the hdo s and also the uv cutoff of the effective theory . there could also be contributions to their mass from the sm higgs field @xmath14 , which are considered to be smaller , such that we can expand in powers of @xmath15 and obtain operators invariant under the sm gauge group . such a framework was already investigated in @xcite from the viewpoint of the effective couplings of @xmath0 to electroweak gauge bosons . the potential implications to dark matter , considered to be the lightest fermion in the dark sector was also investigated , with the outcome that a monochromatic gamma ray line from the dark matter annihilation is potentially observable . the potential existence of a signal in the fermi data was largely discussed in the recent literature @xcite and will not be discussed further here . in this paper we extend the previous works by allowing the mediators to be colored and therefore the @xmath0 to couple to gluons . we restrict ourselves throughout the paper to cp even couplings for simplicity . these couplings are more restricted by symmetries than the ones to the electroweak gauge bosons and their presence change significantly the phenomenology of such models . whereas at dimension - six order four such operators are possible , only two of them are induced by heavy fermion mediators loops . moreover , only one operator contributes to amplitudes in which at least one of the gluons is on - shell , as will be the case throughout our paper . we analyze in detail the corresponding phenomenology from the viewpoint of the dark matter relic abundance , direct and indirect dark matter detection and lhc constraints . allowing couplings to gluons and at the same time to electroweak gauge bosons does not change significantly the phenomenology of the @xmath0 compared to the case where only couplings to gluons are allowed . one interesting conceptual difference is that , whereas the @xmath0 couplings to gluons and photons _ vanish _ for an on - shell @xmath0 due to the landau - yang theorem @xcite , the couplings to the electroweak gauge bosons @xmath16,@xmath17 do not vanish ; they lead on the contrary to an _ enhancement _ close to the @xmath0 pole . another interesting result is that , unlike the case of kinetic mixing , the dark matter annihilation into gluons induced by virtual @xmath0 exchange can give correct relic density for heavy dark matter and @xmath0 masses , well above the electroweak scale . since our interest here is to have complementary constraints from dark matter searches and lhc , we nonetheless confine our analysis to masses below than or of the order tev in what follows . the paper is organized as follows . section 2 introduces the basic formalism we will use , which is stueckelberg realization of @xmath0 symmetry . it contains the list of the lowest dimensional effective operators generated by integrating - out heavy fermionic mediators , their classification depending on the nature of messenger masses and charges and the explicit loop computation of the @xmath0 couplings to gluons . section 3 deals with the consequences of the model for dark matter generation in the early universe , focusing on the annihilation to a gluon pair . section 4 contains the various phenomenological constraints coming from the unique @xmath0 coupling to gluons generated at one - loop by heavy colored mediators . section 5 contains the re - analysis of the various constraints when @xmath0 couplings to electroweak gauge bosons are also added . appendices contain more details about the gauge independence of the @xmath0 mediated hidden - sector - sm couplings , the effective operator couplings @xmath0 to gluons induced by heavy mediator loops and the complete cross - sections of the s- and t - channel annihilation of the dark matter .

these are fermions charged under both and the sm , while all sm fermions are neutral under . we prove that only one operator contribute to the couplings between charged matter and on - shell gluons . we then make a complete phenomenological analysis of the scenario where the lightest fermion charged under is the dark matter candidate . combining results from wmap / planck data , mono - jet searches at lhc , and direct / indirect dark matter detections restrict considerably the allowed parameter space .

a general analysis is performed on the dimension - six operators mixing an almost hidden to the standard model ( sm ) , when the communicates with the sm via heavy mediators . these are fermions charged under both and the sm , while all sm fermions are neutral under . we classify the operators as a function of the gauge anomalies behaviour of mediators and explicitly compute the dimension - six operators coupling to gluons , generated at one - loop by chiral but anomaly - free , sets of fermion mediators . we prove that only one operator contribute to the couplings between charged matter and on - shell gluons . we then make a complete phenomenological analysis of the scenario where the lightest fermion charged under is the dark matter candidate . combining results from wmap / planck data , mono - jet searches at lhc , and direct / indirect dark matter detections restrict considerably the allowed parameter space . lpt orsay-13 - 49 , cpht - rr054.0613 , ift - uam / csic-13 - 76 = 20pt * emilian dudas , lucien heurtier , yann mambrini and bryan zaldivar * + : _ cpht , ecole polytechnique , 91128 palaiseau cedex , france _ + : _ laboratoire de physique thorique , universit paris - sud , f-91405 orsay , france _ + : _ instituto de fisica teorica , ift - uam / csic , 28049 madrid , spain _

nlin0602033

c

besides its biological motivation , the model presented in this work exhibits interesting generic properties concerning pattern formation that are for the first time discussed within the scope of a specific model system . the homogeneous ion channel density distribution on the biomembrane may become unstable with respect to either a stationary or an oscillatory bifurcation , whereas we focused exclusively on analyzing the latter bifurcation type . as the total ion channel density is a conserved field , the supercritical hopf - bifurcation occuring at finite wave number shows nonlinear properties largely differing from those emerging in systems lacking conserved order parameters . in presence of a global conservation law , such as the one encountered in our model , it can be expected that the asymptotic description of pattern formation by means of amplitude equations is altered through the coupling of known forms of envelope equations to long - wavelength modes . this allegation has been confirmed by the perturbation expansion of the initial model equations that yielded a set of coupled amplitude equations in case of traveling ion channel density waves rather than a single complex ginzburg - landau equation . the validity range of the latter reduced dynamics has been checked by simulations of the inital model equations . this coupling to stationary , long - wavelength excitations has however been completely neglected during the discussion of the stationary bifurcation scenario in ref . @xcite which gives consequently a distorted picture of the nonlinear bifurcation behavior . detailed phase diagrams highlight in which parameter space hopf - bifurcations at finite wavelengths take place . neither the threshold value of the control parameter nor the supercriticality of the oscillatory bifurcation are modified by implicating the long - wavelength mode evoked by the conserved ion channel density field into the asymptotic description near onset of instability . the stability of traveling ion channel density waves is however strongly affected by the latter real mode for infinitely extended systems . it turns out that the long - wavelength mode , reflecting the conserved density field , triggers an instability at finite perturbation wave number whereas plane wave solutions would be long - wavelength unstable in the absence of the large - scale mode . if compared to a case without a real mode , stable traveling wave solutions are generally shifted towards strongly negative ratios of opened and closed ion channel charges respectively and thus the domain , wherein spatiotemporal chaos is likely to be seen , significantly broadens . if finally all model parameters are fixed the observation of stable traveling ion channel density waves becomes less probable the more the ion channels contribute to the total conductance of the considered membrane layer . the dynamics of traveling waves in finite geometries and consequently their stability properties naturally differ from those in infinitely extended systems @xcite . how the finite size of the system further influences the studied traveling ion channel density waves at hand , already affected by a large - scale mode , is postponed to future work . the formation of dissipative patterns of ion channels on a membrane that were discussed in the present work is most likely to be observed in in vitro systems as the one proposed in ref . @xcite where a linear array of 48 field - effect transistors in silicon was coated with a bimolecular layer of lipid and gramicidin . nevertheless the investigated electrodiffusive mechanism seems to be also relevant for in vivo systems as shown by experiments on the effect of electric fields on clustering of acetylcholine receptors as cited in ref . @xcite . couplings between a long - wavelength mode and a traveling wave are expected in other models from cell biology as well , e.g. in mixtures of cytoskeletal filaments interacting with molecular motors @xcite . the investigation of an oscillatory instability occuring at finite wave number coupling to a stationary , long - wavelength mode , that was motivated by the biological model at hand , will be extended within the scope of a reaction - diffusion system in a forthcoming work to oscillatory , long - wavelength excitations influencing on oscillatory instabilities at finite wave number @xcite . * acknowledgments * fruitful discussions with m. hilt and f. ziebert were very much appreciated .

it is shown that the homogeneous distribution of ion channels may become unstable to either a stationary or an oscillatory instability . the nonlinear behavior immediately above threshold of an oscillatory bifurcation occuring at finite wave number is analyzed in terms of amplitude equations . due to the conservation law imposed on ion channels large - scale modes couple to the finite wave number instability and

a model of mobile , charged ion channels embedded in a biomembrane is investigated . the ion channels fluctuate between an opened and a closed state according to a simple two state reaction scheme whereas the total number of ion channels is a conserved quantity . local transport mechanisms suggest that the ion channel densities are governed by electrodiffusion - like equations that have to be supplemented by a cable type equation describing the dynamics of the transmembrane voltage . it is shown that the homogeneous distribution of ion channels may become unstable to either a stationary or an oscillatory instability . the nonlinear behavior immediately above threshold of an oscillatory bifurcation occuring at finite wave number is analyzed in terms of amplitude equations . due to the conservation law imposed on ion channels large - scale modes couple to the finite wave number instability and have thus to be included in the asymptotic analysis near onset of pattern formation . a modified ginzburg landau equation extended by long - wavelength stationary excitations is established and it is highlighted how the global conservation law affects the stability of traveling ion channel density waves .

astro-ph9803086

i

one of the most promising source of gravitational waves is the coalescence of inspiralling compact binaries . the recent development of interferometric gravitational waves detectors ( _ e.g . geo600 , ligo , tama _ and _ virgo _ ) gives an important motivation for studying this problem . such a study requires a relativistic formalism to derive the equations of motion and then an accurate and tricky method to solve the resulting system of partial differential equations . we have recently @xcite proposed a relativistic formalism able to tackle the problem of co - rotating _ as well as _ counter - rotating binaries system , these latter being more relevant from the astrophysical point of view . we present now a very accurate approach based on multi - domain spectral method that circumvents the gibbs phenomenon to numerically solve this problem and which can be applied to a wide class of other astrophysical situations . various astrophysical applications of spectral methods have been developed in our group ( for a review , see @xcite ) , including 3-d gravitational collapse of stellar core @xcite , neutron star collapse into a black hole @xcite , tidal disruption of a star near a massive black hole @xcite , rapidly rotating neutron stars @xcite , magnetized neutron stars @xcite and their resulting gravitational radiation @xcite , spontaneous symmetry breaking of rapidly rotating neutron stars @xcite , proto - neutron stars evolution @xcite . in computational fluid dynamics , spectral methods are known for their very high accuracy @xcite ; indeed for a @xmath1 function , the numerical error decreases as @xmath2 ( _ evanescent error _ ) , where @xmath3 is the number of coefficients involved in the spectral expansion , or equivalently the number of grid points in the physical domain . this is much faster than the error decay of finite - difference methods , which behaves as @xmath4 , with @xmath5 generally not larger than @xmath6 . for this reason , spectral methods are particularly interesting for treating 3-d problems such as binary configurations a situation in which the number of grid points is still severely limited by the capability of present and next generation computers . spectral methods lose much of their accuracy when non - smooth functions are treated because of the so - called _ gibbs phenomenon_. this phenomenon is well known from the most familiar spectral method , namely the theory of fourier series : the fourier coefficients @xmath7 of a function @xmath8 which is of class @xmath9 but not @xmath10 decrease as @xmath11 only . in particular , if the function has some discontinuity , its approximation by a fourier series does not converge towards @xmath8 at the discontinuity point : there remains a gap which is of the order 10% . the multi - domain spectral method described in this paper circumvents the gibbs phenomenon . the basic idea is to divide the space into domains chosen so that the physical discontinuities are located onto the boundaries between the domains ( sect . [ s : mapping ] ) . the simplest example is the case of a perfect fluid star , where two domains may be distinguished : the interior and the exterior of the star . the boundary is then simply the surface of the star . the second ingredient of the technique is a mapping between the domains defined in this way and some simple mathematical domains , which are cross products of intervals : @xmath12 \times [ b_1,b_2 ] \times [ c_1,c_2]$ ] . the spectral expansion is then performed with respect to functions of the coordinates spanning these intervals ( sect . [ s : multi ] ) . the method of resolution of a basic equation , namely the poisson equation , is exposed in sect . [ s : resol_poisson ] . for stiff equations of state , the above procedure is not sufficient to ensure the smoothness of all the functions . indeed , for a polytrope with an adiabatic index greater than 2 , the density field has an infinite derivative on the surface of the star . we present in sect . [ s : regul ] a method for regularizing the density and recover the spectral precision . the power of the multi - domain spectral method is illustrated in sect . [ s : illustr ] , where comparisons are performed between numerical solutions obtained by an implementation of the method and analytical solutions ( ellipsoidal configurations of incompressible fluids ) . finally sect . [ s : conclu ] concludes the article by discussing the great advantages of the multi - domain spectral method for dealing with relativistic binary neutron stars .

a multi - domain spectral method for computing very high precision 3-d stellar models is presented . the relative numerical error reveals to be of the order of . it may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too .

a multi - domain spectral method for computing very high precision 3-d stellar models is presented . the boundary of each domain is chosen in order to coincide with a physical discontinuity ( e.g. the star s surface ) . in addition , a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used . consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any gibbs phenomenon , which yields to a very high precision . the power of this method is demonstrated by direct comparison with analytical solutions such as maclaurin spheroids and roche ellipsoids . the relative numerical error reveals to be of the order of . this approach has been developed for the study of relativistic inspiralling binaries . it may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too . # 1#2 # 1#2 ^ 2#1 ^ 2 # 1to 0pt#1

0805.3577

i

the @xmath14 reaction is one of the critical links in the @xmath15 and @xmath16 branches of the @xmath17chain of solar hydrogen burning [ 13 ] . the total capture rate determined by processes of this chain is sensitive to the cross section @xmath18 ( or the astrophysical @xmath0-factor @xmath3 ) for the @xmath19 reaction and predicted neutrino rate varies as @xmath20^{0.8}$ ] @xcite . despite the impressive improvements in our understanding of the @xmath14 reaction made in the past decades ( see refs [ 410 ] and references therein ) , however , some ambiguities connected with both the extrapolation of the measured cross sections for the aforesaid reaction to the solar energy region and the theoretical predictions for @xmath18 ( or @xmath3 ) still exist and they may influence the predictions of the standard solar model @xcite . experimentally , there are two types of data for the @xmath19 reaction at extremely low energies : i ) six measurements based on detecting of @xmath21-rays capture ( see @xcite and references therein ) from which the astrophysical @xmath0-factor @xmath22 extracted by the authors of those works changes within the range 0.47@xmath230.58 @xmath24 , which yield a weighted mean of @xmath22=0.507@xmath25 0.016 @xmath26 @xcite , and ii ) five measurements based on detecting of @xmath15 ( see @xcite references therein as well as [ 6 - 10 ] ) from which @xmath22 extracted by the authors of these works changes within the range 0.53@xmath270.63 @xmath28 , which yield weighted means of @xmath22=0.572@xmath25 0.026 @xmath29 @xcite , @xmath22=0.53 @xmath28 @xcite , @xmath22=0.547@xmath25 0.017 @xmath28 @xcite , and @xmath22=0.560@xmath25 0.017 @xmath29 @xcite and @xmath300.595@xmath25 0.018 and 0.596@xmath25 0.021 @xmath28 @xcite . all of these measured data have a similar energy dependence for the astrophysical @xmath0-factors @xmath3 but the extrapolation of each of the measured data from the observed energy ranges to low experimentally inaccessible energy regions , including @xmath11=0 , gives a value of @xmath22 with an uncertainty exceeding noticeably the experimental one . the recent aforesaid values of @xmath22 recommended in refs.[6 - 9 ] and @xcite have nevertheless been obtained from the analysis of the precisely measured data for @xmath31 by means of the artificial renormalization of the energy dependence of the r - matrix calculation @xcite and of the resonating - group method calculation @xcite for @xmath3 to the corresponding experimental data , respectively . the theoretical calculations of @xmath22 performed within different methods also show considerable spread [ 11 - 14 ] . the aforesaid resonating - group method calculations of @xmath22 performed in ref.@xcite show considerable sensitivity to the form of the effective nn interaction used and the estimates have been obtained within the range of 0.312@xmath23 0.841 @xmath28 . calculations performed in microscopic single - channel ( ( @xmath5 ) ) and two - channel ( ( @xmath32 ) and ( @xmath33 ) ) cluster models gave the values of @xmath22= 0.56 @xmath28 @xcite ( @xmath22= 0.52 @xmath28 @xcite ) and of @xmath22=0.83 @xmath28 @xcite , respectively , that is , the estimate of the value of the @xmath22 strongly changes when the model space is expanded . the calculations performed by the authors of refs.@xcite and @xcite in the two - body potential model with different forms of the two - body potential gave the values of @xmath22=0.516 and about of 0.5 @xmath28 , respectively , although different values of 1.174 in @xcite and 1.0 in @xcite have been used for the spectroscopic factor for the ( @xmath34)-configuration in @xmath35 . calculations performed in the variational monte - carlo technique ( vmct ) with seven - particle wave functions derived from realistic nn interaction gave @xmath36 @xmath29 @xcite . but , as it was emphasized in paper @xcite , serious problems occur with the normalization for the calculated astrophysical @xmath0-factor @xmath37 in respect to the experimental data . the estimation of @xmath22=0.52@xmath25 0.03 @xmath38 @xcite also should be noted . the latter has been obtained within the framework of the asymptotic method developed in @xcite based on the idea proposed in paper @xcite . this idea is based on the assumption about the fact that low - energy direct radiative captures in light nuclei ( @xmath39 ) proceed mainly in regions well outside the range of the internuclear interactions . but in ref . @xcite the contribution from the nuclear interior ( @xmath40 4 fm ) to the amplitude was assumed to be negligibly small . in this assumption from the analysis of the experimental astrophysical @xmath0-factors for the direct capture @xmath19(g.s . ) and @xmath19(0.429 mev ) reactions in the energy range 180@xmath41 500 kev @xcite the values of the nuclear vertex constants ( nvc ) for the virtual decays @xmath42 and @xmath43 @xcite ( or the respective asymptotic normalization coefficients ( anc ) for @xmath44(g.s . ) and @xmath44(0.429 mev ) ) obtained were then used for calculations of the astrophysical @xmath0-factors for the same reactions at @xmath45180 kev , including @xmath11=0 . however , the experimental astrophysical @xmath0-factors for the direct capture @xmath14 reactions @xcite used in @xcite for the analysis have considerable spread . consequently , the values of the anc s @xmath44 and the @xmath22 obtained in @xcite may not be enough accurate . therefore , determination of precise experimental values of the anc s for @xmath44(g.s . ) and @xmath44(0.429 mev ) is highly desirable since it has direct effects in the correct extrapolation of the @xmath19 astrophysical @xmath0-factor at solar energies @xcite . in this work new analysis of the highly precise experimental astrophysical @xmath0-factors for the direct capture @xmath19 reaction at extremely low energies ( @xmath46 90 kev ) [ 6 - 10 ] is performed within the modified two - body potential approach @xcite to obtain @xmath7indirectly measured values both of the anc s ( the nvc s ) for @xmath8 and @xmath47 , and of @xmath3 at @xmath48 90 kev , including @xmath11=0 . in the present work we show that one can extract anc s for @xmath49 directly from the @xmath19 reaction where the ambiguities inherent for the standard two -body potential model calculation of the @xmath14 reaction being connected with the choice of the geometric parameters ( the radius @xmath50 and the diffuseness @xmath51 ) for the woods saxon potential and the spectroscopic factors , can be reduced in the physically acceptable limit , being within the experimental errors for the @xmath3 . the contents of this paper are as follows . in section 2 basic formulae of the modified two - body potential approach to the direct radiative capture @xmath14 reaction are given . there the analysis of the precise measured astrophysical @xmath0-factors for the direct radiative capture @xmath19 reaction is performed ( subsections 2.22.4 ) . the conclusion is given in section 3 .

a new analysis of the precise experimental astrophysical-factors for the direct capture reaction [ b.s . the woods new estimates are obtained for theindirectly measured values of the asymptotic normalization constants ( the nuclear vertex constants ) for and as well as the astrophysical-factors at e 90 kev , including=0 .

a new analysis of the precise experimental astrophysical-factors for the direct capture reaction [ b.s . nara singh et al . , phys.rev.lett . * 93 * ( 2004 ) 262503 ; d. bemmerer et al . , phys.rev.lett . * 97 * ( 2006 ) 122502 ; f.confortola et al . , phys.rev . * c 75 * ( 2007 ) 065803 and t.a.d.brown et al . , phys.rev . * c 76 * ( 2007 ) 055801 ] populating to the ground and first excited states of is carried out based on the modified two - body potential approach in which the direct astrophysical-factor , , is expressed in terms of the asymptotic normalization constants for and two additional conditions are involved to verify the peripheral character of the reaction under consideration . the woods saxon potential form is used for the bound ()- state and the- scattering wave functions . new estimates are obtained for theindirectly measured values of the asymptotic normalization constants ( the nuclear vertex constants ) for and as well as the astrophysical-factors at e 90 kev , including=0 . the values of asymptotic normalization constants have been used for getting information about the-particle spectroscopic factors for the mirror ()-pair . pacs : 25.40.lw;26.35.+c +

0805.3577

c

the analysis of the experimental astrophysical @xmath0-factors , @xmath110 , for the @xmath19 reaction , which were precisely measured at energies @xmath11=92.9 - 1235 kev [ 610 ] , has been performed within the modified two - body potential approach proposed recently in ref.@xcite . the scrupulous quantitative analysis shows that the @xmath14 reaction within the considered energy ranges is peripheral and the parameterization of the direct astrophysical @xmath0-factors in terms of anc s for the @xmath211 is adequate to the physics of the peripheral reaction under consideration . it is demonstrated that the experimental astrophysical @xmath0-factors of the reaction under consideration measured in the aforesaid energy region can be used as an independent source of getting the information about the anc s ( or nvc s ) for @xmath188 . the weighted means of the anc s ( nvc s ) for @xmath211 are obtained . they have to be @xmath174=23.19@xmath25 1.37 @xmath189 and @xmath175=15.73@xmath25 1.02 @xmath189 for @xmath211(g.s ) and @xmath211(0.429 mev ) , respectively . the corresponding values of the nvc s are @xmath255= 1.11@xmath25 0.07 fm and @xmath197= 0.75@xmath25 0.05 fm . the uncertainty in the anc ( nvc ) -values includes the experimental errors for the experimental astrophysical @xmath0-factors , @xmath110 , and that of the used approach . besides , the values of anc s were used for getting the information about the @xmath12-particle spectroscopic factors for the mirror ( @xmath13)-pair . the obtained values of the anc s were also used for obtaining the experimental @xmath14 astrophysical @xmath0-factors for capture to the ground and first excited states , the branching ratio at the six experimental points of energy @xmath11 ( @xmath236 126.5 kev ) [ 69 ] and for their extrapolation at energies less than 90 kev , including @xmath11=0 . in particular , for the weighted mean of the branching ratio @xmath253 and the total astrophysical @xmath0-factor @xmath22 the values of @xmath253=0.41@xmath25 0.01 and @xmath256 kev b have been obtained , respectively . the latter is noticeably larger than the result of @xmath22=0.507@xmath25 0.016 kev b , deduced in ref.@xcite from the measurements of capture @xmath21 ray , and is in an agreement with those of @xmath22=0.572@xmath25 0.026 kev b @xcite , deduced in ref.@xcite from the measurements of @xmath15 activity , and @xmath22=0.56 kev @xcite obtained within the microscopical ( @xmath34)-cluster model . the authors thank d.bemmerer for providing the experimental results of the updated data analysis . the work has been supported by the academy of science of the republic of uzbekistan ( grant no.fa-f2-f077 ) . * j. n. bahcall , a. m. serenelli , and s. basu , astrophys . j. * 621 * , l85 ( 2005 ) . j. n. bahcall , w.f . huebner , s. h. lubow , p. d. parker , and r. k. ulrich , rev.mod.phys . * 54 * , 767 ( 1982 ) . j. n. bahcall , and m. h. pinsonneault , rev.mod.phys . * 64 * , 781 ( 1992 ) . e.g. adelberger , s.m.austin , j.n . bahcall , a.b.balantekin , g.bogaert , l.s.brown , l.buchmann , f.e.cecil , a.e.champagne , l. de braeckeleer , ch.a . duba , s.r . elliott , s.j . freedman , m. gai , g.goldring , ch . r. gould , a. gruzinov , w.c . haxton , k.m . heeger , and e.henley , rev . phys . * 70 * , 1265 ( 1998 ) . c.angulo , m.arnould , m.rayet , p.descouvemont , d.baye , c.leclercq-willain , a.coc , s.barhoumi , p.aguer , c.rolfs , r.kunz , j.w . hammer , a.mayer , t. paradellis , s.kossionides , c.chronidou , k.spyrou , s.deglinnocenti , g. fiorentini , b.ricci , s.zavatarelli , c.providencia , h.wolters , j.soares , c.grama , j.rahighi , a.shotter , m.l.rachti , nucl . a * 656 * , 3 ( 1999 ) . b. s. nara singh , m. hass , y. nir - el , and g. haquin , phys.rev.lett . * 93 * , 262503 ( 2004 ) . d. bemmerer , f. confortola , h. costantini , a. formicola , gy . gyrky , r. bonetti , c. broggini , p. corvisiero , z. elekes , zs . flp , g. gervino , a. guglielmetti , c. gustavino , g. imbriani , m. junker , m. laubenstein , a. lemut , b. limata , v.lozza , m. marta , r. menegazzo , p. prati , v. roca , c. rolfs , c. rossi alvarez , e. somorjai , o. straniero , f. strieder , f. terrasi , and h.p . trautvetter ( the luna collaboration ) , phys.rev.lett . * 97 * , 122502 ( 2006 ) . gy . gyrky , f. confortola , h. costantini , a. formicola , d. bemmerer , r. bonetti , c. broggini , p. corvisiero , z. elekes , zs . flp , g. gervino , a. guglielmetti , c. gustavino , g. imbriani , m. junker , m. laubenstein , a. lemut , b. limata , v.lozza , m. marta , r. menegazzo , p. prati , v. roca , c. rolfs , c. rossi alvarez , e. somorjai , o. straniero , f. strieder , f. terrasi , and h.p . trautvetter ( the luna collaboration ) , phys.rev . c * 75 * , 035805 ( 2007 ) . f. confortola , d. bemmerer , h. costantini , a. formicola , gy . gyrky , p. bezzon , r. bonetti , c. broggini , p. corvisiero , z. elekes , zs . flp , g. gervino , a. guglielmetti , c. gustavino , g. imbriani , m. junker , m. laubenstein , a. lemut , b. limata , v.lozza , m. marta , r. menegazzo , p. prati , v. roca , c. rolfs , c. rossi alvarez , e. somorjai , o. straniero , f. strieder , f. terrasi , and h.p . trautvetter ( the luna collaboration ) , phys.rev . c * 75 * , 065803 ( 2007 ) . brown , c. bordeanu , r.f . snover , d.w . storm , d. melconian , a.l . sallaska , s.k.l . sjue , s. triambak , phys.rev . c * 76 * , 055801 ( 2007 ) . p.descouvement , a. adahchour , c. angulo , a. coc , e. vangioni - 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th ] 1 apr 2008 ; phys.atomic nucl . to be published ( 2008 ) . neudatchin , v.i . kukulin , a.n . boyarkina and v.d . korennoy , lett.nuovo cim.*5 * , 834 ( 1972 ) . kukulin , v.g . neudatchin , and yu . f. smirnov , nucl.phys . a * 245 * ( 1975 ) . kukulin , v.g . neudatchin , i.t . obukhovsky and yu.f . `` clusters as subsystems in light nuclei '' . in clustering phenomena in nuclei , vol.3 , eds . k. wildermuth and p. kramer ( vieweg , braunschweig , 1983)p.1 . barnard , c. m. jones , and g.c . phillips , nucl.phys . * 50 * , 629 ( 1964 ) . c. rolfs , a * 217 * , 29(1973 ) . h. walliser , h. kanada , and y.c . tang , nucl.phys . a * 419 * , 133 ( 1984 ) . timofeyuk , r.c . johnson , a.m. timofeyuk , phys.rev.lett.*91 * , 232501 ( 2003 ) . timofeyuk , p. descouvemont , r.c . johnson , phys.rev . c * 75 * , 034302 ( 2007 ) . timofeyuk , p. descouvemont , phys.rev . c * 71 * , 064305 ( 2005 ) . h.krwinkel , h.w . becker , l. buchmann , j. grres , k.u . kettner , w.e . kieser , r. santo , p. schmalbrock , h.p . trautvetter , a. vlieks , c. rolfs , j.w . hammer , r.e . azuma , w.s . rodney , z.phys . a * 304 * , 307 ( 1982 ) . t. altmeyer , e. kolbe , t. warmann , k. langanke , h.j . assenbaum , z.phys . a * 330 * , 277 ( 1988 ) . u. schrder , a. redder , c. rolfs , r.e . azuma , l. buchmann , c. campbell , j.d . king , t.r . donoghue , phys.lett . b * 192 * , 55 ( 1987 ) .

nara singh et al . , phys.rev.lett . , phys.rev.lett . , phys.rev . , phys.rev . * c 76 * ( 2007 ) 055801 ] populating to the ground and first excited states of is carried out based on the modified two - body potential approach in which the direct astrophysical-factor , , is expressed in terms of the asymptotic normalization constants for and two additional conditions are involved to verify the peripheral character of the reaction under consideration . the values of asymptotic normalization constants have been used for getting information about the-particle spectroscopic factors for the mirror ()-pair .

a new analysis of the precise experimental astrophysical-factors for the direct capture reaction [ b.s . nara singh et al . , phys.rev.lett . * 93 * ( 2004 ) 262503 ; d. bemmerer et al . , phys.rev.lett . * 97 * ( 2006 ) 122502 ; f.confortola et al . , phys.rev . * c 75 * ( 2007 ) 065803 and t.a.d.brown et al . , phys.rev . * c 76 * ( 2007 ) 055801 ] populating to the ground and first excited states of is carried out based on the modified two - body potential approach in which the direct astrophysical-factor , , is expressed in terms of the asymptotic normalization constants for and two additional conditions are involved to verify the peripheral character of the reaction under consideration . the woods saxon potential form is used for the bound ()- state and the- scattering wave functions . new estimates are obtained for theindirectly measured values of the asymptotic normalization constants ( the nuclear vertex constants ) for and as well as the astrophysical-factors at e 90 kev , including=0 . the values of asymptotic normalization constants have been used for getting information about the-particle spectroscopic factors for the mirror ()-pair . pacs : 25.40.lw;26.35.+c +

0911.2373

i

the diffeomorphism invariance of einstein s theory of gravity is in an intimate relation with the fact that there is a significant redundancy in the representation of the true physical degrees of freedom . it can therefore be a great challenge to carry out a faithful investigation of dynamical processes even in case of spherically symmetric spacetimes , in spite of the simplifications offered by the symmetries . correspondingly , the selection of the most appropriate variables , done by applying a suitable gauge fixing , i.e. , the most effective framework to carry out the study of a given dynamical system , is considered to be a sort of art . in the numerical investigations of spherically symmetric dynamical systems , the method of choptuik that had been applied first by him in @xcite while exploring the critical phenomenon in the gravitational collapse of various gravity - matter systems turned to be the most successful in the sense that it is still widely used . however , choptuik s choice has both advantages and disadvantages . perhaps the most important advantage is that one has to solve only two first order partial differential equations ( pdes ) for the basic metric variables , and @xmath1 in terms of which the spacetime metric can be given as @xmath2 ] which , along with the matter field equations , determine the full evolution of the associated gravity matter system . on the other hand , the following objections may also be raised . first of all , the radial coordinate @xmath3 is chosen so that the area @xmath4 of the @xmath5-invariant @xmath6-spheres are given as @xmath7 . as it is well - known , coordinate systems of this type are not suitable to follow evolution in regions where `` trapped surfaces '' are formed because a coordinate singularity also develops ( for a short discussion see , e.g. , the last paragraph of @xcite ) . another objection is that one of the first order pdes is hyperbolic while the other is elliptic . this means that one of the metric equations which is a constraint equation has to be integrated on succeeding time level surfaces repeatedly . this process slows down time integration and makes it hard to apply the powerful tool of adaptive mesh refinement ( amr ) which ensures high numerical accuracy in strongly dynamical processes @xcite . there are two side - remarks in order . first of all , although it is possible to implement a variant of amr for the numerical integration of mixed hyperbolic and elliptic equations @xcite , the precision is partly lost because the applicability of amr necessitates the extrapolation of some variables in time , something which is better to be avoided in a time integration process . thereby , the use of a fully hyperbolic system is preferable in case of numerical integration of the field equations based on a finite difference schema . secondly , it was shown by one of the present authors in @xcite that by making use of the kodama vector field as the time evolutions vector field , the mixed elliptic - hyperbolic system can be replaced by a fully hyperbolic one . however , we have found the inevitable formation of a coordinate singularity in numerical simulations , the appearance of which was anticipated in the discussion below equation ( 4.15 ) of @xcite . the above findings motivate the search for a better analytic set - up with a more appropriate choice of the basic variables . before proceeding and presenting our proposal for such a choice we would like to mention that several attempts have also been made to use reduced versions of the adm and bssn @xcite formalisms in spherical symmetry , see @xcite . these models have been yielded by the reduction of a more complicated evolutionary system , therefore they do not optimally fit the spherically symmetric setup . either they apply coordinates that are not suitable to cover regions with trapped surfaces , as it happens , e.g. , in @xcite , or they are simply too complicated see , e.g. , the basic set of field equations ( 9a)(9f ) and ( 10a)(10c ) in @xcite . they may also suffer from numerical instabilities at the origin because negative powers of @xmath3 appear in the evolutionary equations . thereby , it is of considerable interest to single out a simple and general enough framework within which time evolution can be investigated on the largest possible part of the physical spacetime up to the appearance of true geometrical singularities . to match this requirement , we shall start by choosing a fully hyperbolic evolutionary system that is automatically applicable to describe the evolution in trapped region(s ) . this choice should be such that the equations are free from the numerical instabilities that used to appear in the origin in spherically symmetric spacetimes . an analytic framework fitting the above outlined expectations may be chosen as follows . based on the results of earlier investigations in spherically symmetric ( see , e.g. , @xcite ) and also in generic ( see , e.g. , @xcite ) dynamical spacetimes , the metric of the four dimensional spherically symmetric spacetime @xmath8 will be assumed to possess the form @xmath9 where the coordinates @xmath10 and @xmath11 label the points of the two - dimensional timelike surfaces transverse to the transitivity surfaces of the rotation group , and @xmath12 , @xmath13 , @xmath3 are smooth functions of ( @xmath10 , @xmath11 ) . note that @xmath11 generally differs from the area - radial coordinate . this condition , as we have already mentioned , is necessary to extend the domain of time evolution to include trapped surfaces when they exist . by making use of this geometrical framework , gravitational collapse have been investigated in some simple gravity - matter systems . in the simplest possible case of asymptotically flat configurations , the associated time evolution of the system is qualitatively expected @xcite to be as indicated on fig.[coll ] where the event horizon$ ] . ] , and the apparent horizon are also shown . the latter is foliated by marginally trapped surfaces and it is represented by a curve connecting the two ends of the zigzag line depicting the singularity . a portion of matter either falls into the singularity or reaches future timelike or null infinity , @xmath14 or @xmath15 . the asymptotic structure of the spacetime is expected to approach that of the schwarzschild solution as we get closer to @xmath14 along the null generators of @xmath15 @xcite . if the collapsing matter has no considerable radiative degrees of freedom , the mass of the developing black hole is expected to be close to the total mass on the initial data surface . note that spherical symmetry makes it possible to define mass and energy inside an invariant metric sphere ( see section[trap ] ) . if the mass inside the marginally outer trapped surface is found to approach the total mass while moving outwards along the apparent horizon , then we have a strong indication that our spacetime grid covers the truly dynamical part of the collapse . moreover , as it will be demonstrated in section[dyn ] , the lapse function @xmath13 may always be chosen such that the cauchy surfaces can get arbitrarily close to the singularity . we were also interested in investigating the time evolution of more exotic initial data specifications . likewise in the standard friedman - robertson - walker cosmological models these are known to be spherically symmetric around any of their spacetime events there is a freedom in choosing the topology of the initial data surfaces . the base manifold @xmath16 of the investigated spacetimes coincides with the future cauchy development of some three - dimensional achronal hypersurface @xmath17 . thereby , @xmath18 $ ] and it possesses the product space structure @xmath19 @xcite . since the spacetime is spherically symmetric , the @xmath20 time level surfaces these are diffeomorphic to @xmath17can also be foliated by the transitivity surfaces of the rotation group . in virtue of the particular form of the applied line element ( [ the_metric.eq ] ) the metric induced on the transitivity surfaces of the rotation group is given as @xmath21 . thereby , the vanishing of @xmath3 , which is , in fact , the area - radius function , is directly related to the existence of an origin . to see how many origins we might have , let us consider some simple choices for the topology of the initial data surface @xmath17 . whenever @xmath17 is a connected geodesically complete spacelike hypersurface possessing a trivial product bundle structure , its topology is either @xmath22 , @xmath23\times\mathbb{s}^2 $ ] , @xmath24 or @xmath25 ( see as an illustration the bottom line of fig.[top ] ) . accordingly , there may be one origin , two origins or no origin at all on our initial hypersurface . = 4.3 cm = 4.3 cm = 4.3 cm = 4.3 cm during time evolution , the geometrical properties of the time level surfaces may change such that new origins are produced , possibly indicating a change in the topology , as illustrated on fig.[top ] . at this point it is important to clear up the some of the related notions and potential misconceptions . while in the above sentences the terminology of topology change have been used , it should be kept in mind that it is the topology of the limit of time level surfaces comprising the future boundary of the pertinent `` domain of dependence''what may differ from that of the time level surfaces . a careful approach is needed in applying notions such as _ domain of dependence , cauchy development _ and _ cauchy surface _ which were introduced in @xcite by geroch . we would like to emphasise first that there is a significant distinction between the notions `` initial data surface '' and `` cauchy surface '' . we may chose an arbitrary achronal hypersurface @xmath17 as an initial data surface . the initial data together with the field equations can be used to determine the solution everywhere in the domain of dependence @xmath26 $ ] . as opposed to this , the use of the notion of `` cauchy surface '' tacitly requires additional knowledge about the global properties of the underlying spacetime . in particular , see theorem 11 of @xcite , a spacetime is known to be globally hyperbolic if and only if it possesses a cauchy surface . the confusion might arise and , in fact , apparently it does arise in many circumstances in consequence of the fact that the domain of dependence @xmath26 $ ] of any initial data surface @xmath17 , is a globally hyperbolic spacetime itself on its own right , i.e. , @xmath17 is a cauchy surface for @xmath26 $ ] . in many cases it is obvious to recognise that there exists a globally hyperbolic global extension @xmath27 of @xmath28,g_{ab})$ ] such that the boundary of @xmath26 $ ] is not empty in @xmath29 , while the cauchy horizon , @xmath30=h^+[\sigma ] \cup h^-[\sigma]$ ] of @xmath26 $ ] is obviously empty with respect to @xmath26 $ ] . however , a generic method that could be applied in all the possible cases does not exist . although the concept of `` maximal cauchy development '' was introduced in @xcite , it is based on zorn s lemma , which makes its use difficult in practice . as a simple example , consider the maximal analytic extension of the schwarzschild spacetime . in kruskal coordinates @xmath31 the line element is given by @xmath32 where the schwarzschild coordinates @xmath3 and @xmath33 are determined by the following implicit relations ( see , e.g. , @xcite ) : @xmath34 by introducing suitable new coordinates @xmath35 and @xmath36 , the line element of the schwarzschild spacetime preserves the form ( [ the_metric.eq ] ) . the time slicings two of which are indicated on fig.[sch]and the corresponding lapse functions vary accordingly . in the first case ( left panel ) , two points on the @xmath37 hypersurface hit the @xmath38 schwarzschild singularity . the appearance of these points can be interpreted as the formation of two origins , since @xmath39 in all other points of @xmath37 . correspondingly , the topology @xmath24 of @xmath40 is replaced by the disjoint union of @xmath41 , @xmath42 and @xmath43 at @xmath44 ( see the third column of fig . [ top ] ) . it is not hard to modify @xmath40 by inserting suitably located further `` steps '' such that the number of @xmath42 components of the pertinent @xmath45 may take an arbitrary integer value . although the time level surfaces on the left panel do not cover the future domain of dependence , @xmath46 $ ] , of @xmath40 , it is worthwhile to keep in mind that @xmath40 is a cauchy surface for the schwarzschild spacetime . as it is indicated on the right panel of fig.[sch ] , the entire of @xmath46 $ ] can be covered by time level surfaces if the new coordinates @xmath10 and @xmath11 , and in turn , the lapse @xmath13 are chosen properly . there is no topology change and the section of the cauchy surfaces within the black hole region uniformly converge to the @xmath38 singularity . in section[dyn ] , the application of this type of dynamically determined @xmath13 will be demonstrated via various examples . we would like to mention that the type of topology changes indicated by the left panel of fig.[sch ] showed up in many of our numerical simulations . we have found that , in consequence of the developing inhomogeneities , certain parts of the time level surfaces may get closer to the singularity much faster than others . nevertheless , as shown by the above example , the change of the topology refers to the limit of the applied time level surfaces rather than the underlying spacetimes . as it will be demonstrated in the succeeding sections , the @xmath13 function can be chosen such that the time evolution is slowed down in spacetime regions close to the singularity . this way we were able to enlarge the domain of dependences significantly and to get arbitrarily close to the developing spacetime singularities in our simulations . as a consequence , we were able to investigate the rate of blowing up of the curvature while approaching the singularity . the structure of this paper is the following . in section[intr ] , with the help of a simple - minded approach , we demonstrate the main technical issues in solving the einstein - scalar field equations numerically . these difficulties are resolved in section[intr2 ] , where the misner - sharp mass is introduced as an auxiliary variable to stabilise the applied numerical representation near the origin . here we also describe the `` trick '' which makes our framework capable to follow the time evolution within the trapped region . section[stabor ] outlines the analytic procedure that guarantees the required stability of the time evolution in the neighbourhood of an origin . in section[energybal ] , a method is presented which provides the opportunity to monitor the energy transfer processes . trapped surfaces , trapped regions and apparent horizons are defined in section[trap ] . dynamical investigations of gravitational collapse are presented in simple and in certain less obvious circumstances are presented in section[dyn ] . the results of the convergence and accuracy tests are also presented in this section . the paper is closed by summarising our results and by providing a short discussions concerning the interpretation and some of the immediate consequences of our findings .

the analytic setup is chosen such that our numerical method is capable to follow the time evolution even after the appearance of trapped surfaces , more importantly , until the true physical singularities are reached . using this framework , the gravitational collapse of various gravity - matter systems are investigated , with distinguished attention to the evolution in trapped regions .

a new numerical framework , based on the use of a simple first order strongly hyperbolic evolution equations , is introduced and tested in case of-dimensional spherically symmetric gravitating systems . the analytic setup is chosen such that our numerical method is capable to follow the time evolution even after the appearance of trapped surfaces , more importantly , until the true physical singularities are reached . using this framework , the gravitational collapse of various gravity - matter systems are investigated , with distinguished attention to the evolution in trapped regions . it is justified that in advance to the formation of these curvature singularities , trapped regions develop in all cases , thereby supporting the validity of the weak cosmic censor hypothesis of penrose . various upper bounds on the rate of blow - up of the ricci and kretschmann scalars and the misner - sharp mass are provided . in spite of the unboundedness of the ricci scalar , the einstein - hilbert action was found to remain finite in all the investigated cases . in addition , important conceptual issues related to the phenomenon of topology changes are also discussed .

1101.0604

c

we have proposed a novel scheme to probe the edge vortex excitations of chiral majorana fermion edge states realized in superconducting systems utilizing a flux qubit . to analyze the coupling we mapped the hamiltonian of the majorana edge states on the transverse - field ising model , so that the coupling between the qubit and the majorana edge modes becomes a local operator . in the weak coupling regime @xmath212 we have found that the ground state expectation values of the qubit spin are given by @xmath213 additionally , the susceptibility tensor of the qubit spin in the basis @xmath214 is given by @xmath215^{1- 2 \delta_\mu } \lambda^{2\delta_\mu}},\end{gathered}\ ] ] with the real part @xmath179 and the imaginary part @xmath216 of the self - energy given by @xmath217 we see that all of these quantities acquire additional anomalous scaling @xmath218 due to the fact that each spin flip of the qubit spin couples to a disorder field @xmath76 . similar scaling with temperature appears in interferometric setups,@xcite but using a flux qubit allows to attribute its origin to the dynamics of vortices much more easily and also gives additional tunability of the strength of the coupling . another effect of the vortex tunneling being present is the phase change @xmath219 of the susceptibility around the resonance.@xcite this phase shift occurs due to the anomalous scaling and the presence of the abelian statistical angle of the disorder field , in view of the fact that @xmath187 is just a correlator of two disorder fields in the frequency domain . the long wavelength theory which we used is only applicable when all of the energy scales are much smaller than the cutoff energy of the majorana modes this is an important constraint for the flux qubit coupled to the majorana edge states . in systems where the time - reversal symmetry is broken in the bulk ( unlike for topological insulator - based proposals @xcite ) , the velocity of the majorana edge states can be estimated to be @xmath220 and the dispersion stays approximately linear all the way up to @xmath5 . the cutoff of the majorana modes is related to the energy scale of the ising model @xmath221 . equating @xmath222 and @xmath223 , we obtain the lattice constant of the ising model @xmath224 , with @xmath225 the fermi wavelength . the fermi wavelength is typically smaller than any other length scale , and so the long wavelength approximation we have used is well - justified . for a typical flux qubit the tunneling strength @xmath12 is indeed much smaller than the superconducting gap , the level splitting @xmath9 may vary from zero to quantities much larger than the superconducting gap . our proposal provides a way to measure properties of the non - abelian edge vortex excitations different from the conventional detection scheme that requires fusing vortices into fermion excitations . however , none of our results for the single flux qubit can be directly connected to the non - abelian statistics of the quasiparticles , even after including higher - order corrections . thus , it is of interest for future research to investigate a system where the edge vortex excitations are coupled to two qubits such that braiding of vortex excitations can be probed . @xcite another feature of systems with several qubits worth to investigate is the ability of the majorana edge modes to mediate entanglement between different flux qubits .

we show how a superconducting flux qubit attached to such a system couples to the two chiral edge modes via the disorder field of the ising model . due to this coupling , measuring the back - action of the edge states on the qubit allows to probe the properties of majorana edge modes .

a pair of counter - propagating majorana edge modes appears in chiral _ p_-wave superconductors and in other superconducting systems belonging to the same universality class . these modes can be described by an ising conformal field theory . we show how a superconducting flux qubit attached to such a system couples to the two chiral edge modes via the disorder field of the ising model . due to this coupling , measuring the back - action of the edge states on the qubit allows to probe the properties of majorana edge modes .

0709.3625

i

in the presence of a perpendicular magnetic field , the quasi - free charge carriers of a two - dimensional electron system ( 2des ) condense in equidistant and numerously degenerated landau levels @xcite . variations of the electrostatic potential locally shift the degeneracy and , therefore , cause the formation of landau bands . the bending of the landau dispersion at the edge of a 2des is discussed thoroughly in the literature @xcite as it is the key for the understanding of the quantum hall effect @xcite . if the lateral extension of a 2des is limited electrostatically or by the physical edge of the underlying ( lithographically defined ) structure , the landau bands rise on a length scale which substantially exceeds the magnetic length . however , if the confining barrier is fabricated by means of epitaxy , namely , by the technique of cleaved - edge overgrowth @xcite , the realization of a sharp edge potential becomes possible . the corresponding edge channels are then located at distances on the order of the magnetic length @xcite . in this paper , we report on the magnetotunneling spectroscopy between two quantum hall systems which are separated by an atomically precise potential barrier within a gaas / algaas heterostructure . the width of the barrier amounts to , i.e. it falls always below the magnetic length . in the vicinity of the barrier , a complex landau band structure exists which can be described in the case of weak coupling as a superposition of the mirror - inverted dispersions of both subsystems . the degeneracy at the crossings is lifted by small landau band gaps @xcite . the tunneling current through the structure becomes maximum when the fermi level coincides with one of these anticrossings @xcite . the conductance is additionally determined by random tunneling centers in the barrier which are responsible for quantum interferences between opposite edge channels @xcite . while the electron systems of our structure are field - induced by means of a gate electrode , cf . [ fig : intro]a , a former experiment by kang . is based on modulation - doped electron films @xcite . a fixed electron density implies that a certain landau band gap coincides with the fermi level only for a small range of the magnetic field . in contrast , a sample design with a gate electrode allows to investigate a particular band gap at different magnetic fields provided that the fermi level is adjusted in a suitable way . in order to probe the same anticrossing for different barrier widths , it is , therefore , not necessary to prepare several samples as the effective shape of the barrier ( in units of the magnetic length @xmath0 and the cyclotron energy @xmath1 ) can simply be varied by the magnetic field . carrying out measurements for different electron densities with the same sample is also indispensable if quantum interferences are investigated which depend on the random configuration of tunneling centers within the barrier . another effect can be observed just with a single sample , namely , the small magnetic shift of the landau band gaps on the scale of the cyclotron energy which would otherwise be perturbed by the unavoidable fluctuations between successive growth processes . all effects discussed in this paper depend basically on the shape of the landau band structure at the tunneling barrier ( fig . [ fig : intro]b ) . for weakly coupled electron systems , ho has calculated the energy dispersion by using an approximation approach @xcite . though the result reflects the actual dispersion very well , the gap positions differ noticeably from the findings of a complete quantum mechanical calculation if a fine energy resolution is relevant as for our experiment @xcite . instead of combining the dispersions of both subsystems , takagaki and ploog have developed a tight - binding model which is not only applicable for weakly , but also for strongly coupled electron systems @xcite . the tunneling barrier is thereby represented by a reduced hopping amplitude between two simulation grid lines . since the effective shape of the barrier is not explicitly considered in this model , the latter is inappropriate to make accurate predictions on the gap position in dependence of the magnetic field . the landau dispersion which is necessary for the interpretation of the obtained experimental data has been calculated exactly by solving the single - electron schrdinger equation . since the potential term in the hamiltonian is given by a superposition of the parabolic magnetic confinement potential and the piecewise constant conduction band offset of the intrinsic semiconductor heterostructure , the problem is generally closely related to the linear quantum harmonic oscillator . the analytic solution becomes possible with an ansatz for the wave function which is composed of parabolic cylinder functions . for calculating the energy eigenstates , we have developed a dedicated algorithm which numerically solves the continuity conditions at the heterojunctions . it is generally applicable to all systems which consist of up to three regions of constant potential . hence , this method yields the landau dispersion for systems with either a rectangular barrier ( biased or not ) or a potential well ( quantum wire ) @xcite . this article is organized as follows : the sample structure and the corresponding landau dispersion are introduced in the next two sections . the subject of sec . [ sec : tun ] consists of two different tunneling models which are the basis for the understanding of the landau oscillations and simultaneously occurring conductance fluctuations . in sec . [ sec : basic ] we discuss a method for determining the electron density from magnetotunneling measurements . the comparison of the conductance traces with the landau band structure is carried out in sec . [ sec : ll - osci ] where the focus lies on the magnetic shift of the anticrossings . section [ sec : ab ] deals with aharonov - bohm oscillations at the first conductance peak on the scale of the filling factor . conductance fluctuations which appear at low magnetic fields are finally discussed in sec . [ sec : fluct_low ] .

magnetotunneling spectroscopy is employed to investigate the small energy gaps which separate subsequent landau bands . the control on the fermi level permits to trace the anticrossings for varying magnetic fields . the band structure calculation predicts a magnetic shift of the band gaps on the scale of the cyclotron energy . tunneling centers within the barrier are responsible for quantum interferences between opposite edge channels . due to the disorder potential , the landau dispersion is obtained by a dedicated algorithm which solves the schrdinger equation exactly for a single electron residing in a quantum hall system with an arbitrary unidirectional , threefold staircase potential .

a quantum hall system which is divided into two laterally coupled subsystems by means of a tunneling barrier exhibits a complex landau level dispersion . magnetotunneling spectroscopy is employed to investigate the small energy gaps which separate subsequent landau bands . the control on the fermi level permits to trace the anticrossings for varying magnetic fields . the band structure calculation predicts a magnetic shift of the band gaps on the scale of the cyclotron energy . this effect is confirmed experimentally by a displacement of the conductance peaks on the axis of the filling factor . tunneling centers within the barrier are responsible for quantum interferences between opposite edge channels . due to the disorder potential , the corresponding aharonov - bohm interferometers generate additional long - period and irregular conductance features . in the regime of strong localization , conductance fluctuations occur at small magnetic fields before the onset of the regular landau oscillations . the landau dispersion is obtained by a dedicated algorithm which solves the schrdinger equation exactly for a single electron residing in a quantum hall system with an arbitrary unidirectional , threefold staircase potential .

0709.3625

i

we have presented a gaas / algaas heterostructure which contains two laterally adjacent , field - induced quantum hall systems which are separated by a thin , epitaxially grown barrier . the structure includes a gate electrode in order to allow a detailed analysis of the landau band structure at the line junction for different magnetic fields . for the interpretation of the experimental data , the landau dispersion has been calculated exactly for non - interacting electrons residing in a 2des with a rectangular potential wall . the conductance traces in dependence of the magnetic field are dominated by so - called landau oscillations which occur due to the periodic coincidence of the fermi level with the landau band gaps . an observed enhancement of the conductance which exceeds the predictions according to the landauer - bttiker formalism is a consequence of macroscopic defects . the latter divide the long and narrow quantum region into multiple independent sections which are connected in parallel by the extended @xmath10-contact layers . our theory predicts for weakly coupled electron systems a magnetic shift of the anticrossings on the scale of the cyclotron energy of about @xmath257 . the experiment confirms this effect semiquantitatively by a displacement of the conductance peaks on the scale of the filling factor for an increasing fermi level . the conductance peak which corresponds to the gap between the first two landau bands is cropped and distorted by short- and long - period conductance fluctuations . the short - period feature is a result of the ab interference between counterpropagating edge channels along the barrier . the interference is made possible by tunneling centers which exist accidentally within the algaas barrier . for determining the distance of the involved tunneling centers from the fourier spectrum of the conductance traces , it is necessary to know the distance of the interfering edge channels . by using the result of a band structure calculation , we obtain an average distance of the point contacts of about 2 m . the observed ab oscillations basically fulfill two coherence conditions which describe the influence of the electron temperature and the internal bias voltage , respectively . the bias results from gate leakage currents which lead to an offset between the two coupled electron systems . long - period conductance fluctuations at the first conductance peak are a consequence of the disorder potential which distorts the edge channel positions in an irregular way for a varying magnetic field . in addition to the interference effects at the cropped conductance peak , we observe conductance fluctuations which emerge at small magnetic fields and disappear at the onset of the regular landau oscillations . they occur in the regime of strong localization which is a consequence of an imperfect barrier . the latter represents a multiple slit interferometer which essentially reduces the number of transversal modes in the whole system . the phase coherence length determined from the conductance fluctuations , @xmath258 , is of the same order as @xmath246 which follows from the distance of the tunneling centers involved for the ab oscillations . this work was supported financially by the _ deutsche forschungsgemeinschaft _ ( dfg ) via the priority program _ quanten - hall - systeme_. we would like to thank m. bichler and g. abstreiter as well as for sample growths . m. h. is grateful to m. grayson for useful and motivating discussions throughout this project . 10 l. d. landau , z. phys . * 64 * , 629 ( 1930 ) . b. i. halperin , phys . b * 25 * , 2185 ( 1982 ) . a. h. macdonald and p. steda , phys . b * 29 * , 1616 ( 1984 ) . k. v. klitzing , g. dorda , and m. pepper , phys . * 45 * , 494 ( 1980 ) . l. pfeiffer , k. w. west , h. l. stormer , j. p. eisenstein , k. w. baldwin , d. gershoni , and j. spector , appl . . lett . * 56 * , 1697 ( 1990 ) . m. grayson , m. huber , m. rother , w. biberacher , w. wegscheider , m. bichler , and g. abstreiter , physica e * 25 * , 212 ( 2004 ) . + m. huber , m. grayson , m. rother , w. biberacher , w. wegscheider , and g. abstreiter , phys . 94 * , 016805 ( 2005 ) . l . ho , phys . rev . b * 50 * , 4524 ( 1994 ) . w. kang , h. l. stormer , l. n. pfeiffer , k. w. baldwin , and k. w. west , nature ( lond . ) * 403 * , 59 ( 2000 ) . kim and e. fradkin , phys . b * 67 * , 045317 ( 2003 ) ; 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a quantum hall system which is divided into two laterally coupled subsystems by means of a tunneling barrier exhibits a complex landau level dispersion . this effect is confirmed experimentally by a displacement of the conductance peaks on the axis of the filling factor . , conductance fluctuations occur at small magnetic fields before the onset of the regular landau oscillations .

a quantum hall system which is divided into two laterally coupled subsystems by means of a tunneling barrier exhibits a complex landau level dispersion . magnetotunneling spectroscopy is employed to investigate the small energy gaps which separate subsequent landau bands . the control on the fermi level permits to trace the anticrossings for varying magnetic fields . the band structure calculation predicts a magnetic shift of the band gaps on the scale of the cyclotron energy . this effect is confirmed experimentally by a displacement of the conductance peaks on the axis of the filling factor . tunneling centers within the barrier are responsible for quantum interferences between opposite edge channels . due to the disorder potential , the corresponding aharonov - bohm interferometers generate additional long - period and irregular conductance features . in the regime of strong localization , conductance fluctuations occur at small magnetic fields before the onset of the regular landau oscillations . the landau dispersion is obtained by a dedicated algorithm which solves the schrdinger equation exactly for a single electron residing in a quantum hall system with an arbitrary unidirectional , threefold staircase potential .

1411.3054

r

we numerically solve the continuum and bound state currents of an @xmath0 junction at finite magnetic fields , using the shell conduction approximation with the shell at a radius @xmath208 . temperature is set to @xmath209 in all calculations . from this point on , only @xmath31 subbands with @xmath58 are assumed to be occupied in the @xmath1-section . the andreev approximation is not used in calculating the cpr . the critical current of the junction is calculated from eq . [ eq : current - critical ] , and its behaviour versus axial magnetic flux @xmath210 is studied . note that our assumption of no barriers at the @xmath2-@xmath1 interfaces also implies full andreev reflection . , continuum current @xmath211 , and the sum @xmath212 for the subband @xmath156 vs the superconducting phase @xmath122 at zero magnetic field , @xmath177 . since the junction is long , @xmath213 , the cpr is triangular . the kinks in @xmath214 at @xmath215 are due to andreev bound states crossing the gap edge into the continuum levels , but the total subband current is a smooth function of @xmath122 . b ) total subband current @xmath216 vs the superconducting phase as a function of the normalized axial magnetic flux @xmath4 . at zero flux the maximal value occurs near @xmath217 . at finite flux , the bound state and continuum currents are phase shifted . for @xmath218 , two discontinuities can be seen in @xmath216 because of the phase shifts , and the maximal value no longer occurs near @xmath217 . at @xmath219 , the phase shifts amount to @xmath220 and the zero - field curve is recovered . the maximal current at this flux is slightly smaller than the zero field case , due to a decrease in the average momentum of the andreev quasiparticles with increasing flux . the following parameters were used in both panels : @xmath221.,width=336 ] as an illuminating example we study a 500 nm long junction with a chemical potential of @xmath222 . this value for @xmath36 is chosen because it allows @xmath223 subbands to be occupied at @xmath177 ; at @xmath64 the @xmath224 subbands depopulate . , see figure [ fig : fig2_subbands ] . in this example , as @xmath4 approaches 1 , @xmath225 go to zero , at which point andreev quasiparticles can no longer be supported by the @xmath226 subbands . ] in this section we concentrate on the cpr obtained for one subband , namely @xmath227 , and discuss how the coupling of the finite angular momentum with the axial field modifies the subband cpr . since the junction length is greater than the healing length of the populated subbands ( @xmath228 ) , the long junction limit applies . many bound states are present in the junction ( @xmath229 ) . in figure [ fig : fig4_currents]a we show the bound state current @xmath230 , continuum current @xmath211 , and their sum , for the subband @xmath156 at zero magnetic field . as expected of a long junction @xcite , @xmath230 and @xmath211 are of the same order of magnitude , and the cpr is triangular in shape . an additional group of 4 bound states ( @xmath231 ) appear in the junction at @xmath232 , and exit at @xmath233 , giving rise to discontinuities in @xmath230 , @xmath211 . however , the total subband current @xmath216 is always a smooth function of @xmath122 . it is maximal near @xmath217 , ( exactly at @xmath217 at zero temperature ) regardless of the junction length @xcite . note that the continuum current is zero at @xmath217 . + in figure [ fig : fig4_currents]b we show the subband current @xmath216 as a function of the magnetic flux . as the flux is increased from zero , two discontinuities develop in the subband current ( shown for @xmath234 ) . the bound state current is modified as the eigenenergies corresponding to states @xmath235 are shifted in phase in the opposite direction to those of states @xmath236 , similarly to figure [ fig : fig3_bs_phase_shift]b . an equivalent process happens for the continuum current , as explained in eq . [ eq : d_cont_approx ] . as a result , the subband current @xmath216 also shows two discontinuities , and is no longer necessarily maximal near @xmath217 . + the amounts of the phase shifts in @xmath230 and @xmath211 depend on the quantity @xmath237 . the wavenumbers @xmath111 are subband parameters defined in eq . [ eq : wavenumbers ] , and the length @xmath6 is device dependent . therefore , the fluxes at which phase shifts equal integer multiples of @xmath220 need not occur at integer multiples of @xmath238 or @xmath239 ; they can occur at any value of @xmath4 . an example is shown in figure [ fig : fig4_currents]b for @xmath219 , where the phase shifts equal @xmath220 and the cpr recovers its shape at @xmath177 . notice , however , that the maximal value of the subband current at @xmath219 is smaller than at @xmath177 . this can be intuitively understood as follows : as the flux increases , the effective wavenumbers of the electrons and holes change according to eq . [ eq : wavenumbers ] . it can be seen that the average momentum of the electron - hole pair and therefore the healing length @xmath240 are always smaller for higher fluxes . since the magnitude of josephson current in a long junction scales approximately linearly @xcite with @xmath241 , it is suppressed at higher fluxes . this suppression is stronger near the depopulation point of a given subband , where the average momentum decreases significantly . + in order to elucidate the mechanism of the josephson interference between subbands , we show in figure [ fig : fig5_slices_8p5]a the critical current versus axial flux of the junction studied in section [ sec:31_one_subband ] . the length @xmath242 is chosen because it allows for a relatively large amount of phase pickup , since the phase pickup is proportional to the length of the junction ( @xmath237 in eq . [ eq : quantization - rule ] ) . hence , several oscillations of the critical current occur prior to the depopulation of the @xmath226 subbands at @xmath64 . the supercurrent of each subband is shown versus the phase difference @xmath122 in figure [ fig : fig5_slices_8p5 ] panels b - f , at particular values of the magnetic flux . the @xmath176 subband current equals that of @xmath243 at all fluxes . at zero flux the current of each subband is maximal near @xmath217 ( exactly @xmath217 for zero temperature ) , as discussed in section [ sec:31_one_subband ] . this can be clearly seen in panel b. the total current of the junction is the sum of the contributions from the @xmath223 subbands , and is therefore roughly three times the contribution of each . the dotted vertical lines show the phase at which the critical current occurs . + as the flux is increased , the crp of the @xmath224 subbands are modified , similarly to figure [ fig : fig4_currents]a . the critical current of the junction decreases , since the @xmath244 subbands no longer interfere constructively ( panel c ) . at @xmath245 the maximal current switches from a phase @xmath246 to @xmath247 , as shown in panel d. this is a feature of the triangular cpr . the critical current increases until @xmath248 ( panel e ) , at which point the junction current is maximal near @xmath249 . we call this a peak a secondary peak as it occurs roughly in the middle of the main period of oscillations ( see discussion below on periodicity ) , when the magnetic phase pickup of the @xmath250 subbands equals roughly @xmath251 . the magnitude of this peak is roughly two thirds the total current as zero field , as the @xmath252 subbands contribute maximally , and the @xmath56 subband current is close to zero . the process reverses itself for @xmath253 , until at @xmath219 the phase pickup of the @xmath250 subbands equals @xmath220 and all subbands interfere constructively again ( panel f ) . we refer to the peak at @xmath219 a primary peak . other primary peaks occur at @xmath254 . as in figure [ fig : fig4_currents ] , the contribution of the @xmath250 subbands decrease as @xmath4 is increased , because the decrease in the average quasiparticle momentum . this is the mechanism behind the slow decay of the magnitude of the primary peaks as flux increases . + _ aperiodicity _ the @xmath255 subbands interfere constructively when the magnetic phase pickup of the @xmath250 subbands equals an integer multiple of @xmath220 . this corresponds to the main period of the critical current oscillations with @xmath4 , which we estimate below . in other words , we want to find @xmath4 such that @xmath256 for integer @xmath257 . the wavenumbers @xmath111 are defined in eq . [ eq : wavenumbers ] . for the general case this is not easy to do analytically , as @xmath111 themselves depend on the flux through the effective chemical potentials @xmath258 . however , we can get an estimate of the expected period by invoking the andreev approximation ( eq . [ eq : wavenum - approx ] ) , and assuming the effective fermi velocities do not depend on the flux , so can be evaluated at some fixed @xmath4 , e.g. @xmath177 . these are reasonable assumptions when the flux is much smaller than the depopulation point of a given subband ( e.g. , @xmath64 for @xmath224 subbands in the example of figure [ fig : fig5_slices_8p5 ] ) . the result for the position of the first primary peak @xmath259 is : @xmath260 where @xmath163 is defined below eq . [ eq : wavenum - approx ] . for the example of figure [ fig : fig5_slices_8p5 ] , this evaluates to @xmath261 , deviating from the numerically calculated value by only @xmath262 . however , we see that the numerical positions of the next primary peaks at @xmath263 , @xmath264 can not be accurately approximated as integer multiples of @xmath259 : the period becomes shorter as @xmath4 is increased . this is because the field dependence of @xmath163 can not be ignored at higher values of @xmath4 , and the andreev approximation breaks down . intuitively , the effective fermi velocity is noticeably lower at higher fields , resulting in more time spent in the junction by the andreev pair and more phase pickup , therefore a smaller period for @xmath3 oscillations . consequently , even in the simple case of a few subbands , the oscillations of @xmath3 versus @xmath4 are not strictly periodic . + a higher chemical potential results in the occupation of a greater number of angular momentum subbands . the rich interplay between the different @xmath66-subbands results in a complex pattern of the oscillation of @xmath3 with @xmath4 . assume subbands with @xmath265 up to @xmath266 are occupied . each @xmath265 subband s supercurrent oscillates with a flux dependent ` period ' approximated by eq . [ eq : period_andreev ] , which depends on the subband velocity @xmath163 , and is therefore generally anharmonic with other subbands . typically , a peak in @xmath3 as a function of @xmath4 occurs under one of two circumstances : ( i ) when some ( at least two ) of the subbands with different @xmath265 values interfere constructively , or ( ii ) when the critical current occurs near @xmath267 , a secondary peak is formed as described in figure [ fig : fig5_slices_8p5 ] . there are @xmath268 choices for pairs of constructively interfering subbands ( parentheses indicate the binomial coefficient ) . as each @xmath265 subband s oscillations can be anharmonic with those of all other subbands , it follows that there are @xmath268 different flux - dependant ` periods ' in the @xmath3 oscillations due to condition ( i ) , with another @xmath266 due to condition ( ii ) . the @xmath3 curves therefore can display complex , aperiodic structures . + in figure [ fig : fig6_slices_20]a we plot an example of an @xmath3 versus @xmath4 curve for a junction with the same parameters as that of figure [ fig : fig5_slices_8p5 ] , except the chemical potential is raised from 8.5 mev to 20 mev . at zero flux , subbands up to @xmath269 are occupied . the @xmath270 states depopulate at @xmath271 , and the @xmath272 states at @xmath273 . as an example of configurations that can give rise to a peak in @xmath3 , subband cprs are shown in figure [ fig : fig6_slices_20 ] panels b - f , for 5 peaks indicated in panel a with vertical dotted lines . the peak at @xmath274 ( panel b ) satisfies condition ( ii ) , while the other examples are due to constructive interference of two subbands , i.e. condition ( i ) : subbands with @xmath244 at @xmath275 ( panel c ) , @xmath276 at @xmath277 ( panel e ) , and @xmath278 at @xmath279 and @xmath280 ( panels d , f ) . , for @xmath222 ( panels a - d ) and @xmath281 ( panels e - h ) , and several values of the junction length @xmath6 . the following parameters were used : @xmath282 . in panels a - d , the vertical line at @xmath283 indicates the depopulation of the @xmath224 subbands . similarly in panels e - h the vertical lines at @xmath284 indicate the depopulation of the @xmath285 subbands , respectively.,width=336 ] we now discuss the effect of the junction length @xmath6 on the pattern of @xmath3 oscillations . the left column in figure [ fig : fig7_res ] ( panels a - d ) shows the numerically obtained @xmath3 versus @xmath4 for a junction with @xmath222 , as @xmath6 is varied . all other junction parameters are the same as in figure [ fig : fig5_slices_8p5 ] . the critical current is normalized to its value at zero magnetic flux . two processes affect the behaviour of @xmath3 : ( i ) the depopulation of the @xmath224 subbands at @xmath64 , shown by vertical dotted lines in panels a - d , and ( ii ) the josephson interference effect described above . the first of these processes results in step - like discontinuities in @xmath3 at @xmath283 , a drop to roughly one - third of the zero - field @xmath3 value as the @xmath286 subbands depopulate . since the @xmath287 subband does not couple to the axial flux , @xmath3 is almost constant above @xmath64 . the slow decay of the primary peak heights below @xmath64 , and of @xmath3 above @xmath64 , are both due to the decreasing average momentum at higher fluxes , as discussed in section [ sec:31_one_subband ] . for a short junction with @xmath288 ( panel a ) and for @xmath289 , the phase shifts in the cpr of the @xmath224 subband are small ( the phase shifts are dependent on @xmath237 ) , but become more significant close to @xmath64 , where the axial velocities of the quasiparticles are smaller and the time of flight across the junction longer . this results in the observed decrease in @xmath3 before the step - like discontinuity . as @xmath6 is increased to 50 nm , the value of this phase shift increases and modulation due to interference starts to emerge . for @xmath290 ( figure [ fig : fig7_res ] panel c ) , the first primary peak occurs at @xmath291 , and for @xmath242 ( panel d ) at @xmath219 . the decrease by a factor of @xmath292 in the position of the first primary peak is approximately equal ( within @xmath293 ) to the reciprocal ratio of lengths @xmath6 , as expected from the estimate in eq . [ eq : period_andreev ] . + the right column of figure [ fig : fig7_res ] ( panels e - h ) shows the @xmath3 versus @xmath4 curves for a junction with @xmath294 . the subbands with @xmath285 depopulate at @xmath295 respectively ( vertical dotted lines in panels e - h ) , resulting in step - like discontinuities in @xmath3 at those flux values . similarly to above , the behaviour of @xmath3 is dominated by this effect for a @xmath296 junction ( panel e ) , but as @xmath6 is increased the josephson interference becomes visible ( panels f - h ) . note that between the flux values @xmath273 and @xmath297 the @xmath3 curves in the right column of figure [ fig : fig7_res ] are qualitatively similar to their counterparts in the left column , because similarly to the @xmath222 case , subbands with @xmath298 are occupied within this flux window . note that for @xmath281 , @xmath299 is much larger than for the @xmath222 case ; the oscillation amplitude appears to be smaller in panels ( e - h ) only because the relative contribution of each subband to the total current is smaller when there are more subbands occupied . + in summary , for a short junction , the depopulation of subbands is more visible than the josephson interference effect . however , as the junction length is increased , the interference effect becomes apparent . the periods of oscillation decrease slightly as flux is increased . for a junction with a low chemical potential ( only a few transverse subbands occupied , e.g. an @xmath0 point - contact @xcite ) , the pattern of @xmath3 modulation is simpler and the period longer than the case of a high chemical potential ( many transverse subbands occupied ) . a long , low-@xmath36 junction is optimal for experimental observation of this josephson interference effect .

a similar phase shift is observed in the continuum current of the junction . these have revealed , for example , fraunhofer oscillations of the critical current with respect to an externally applied out - of - plane magnetic field . for junction widths comparable to the-section coherence length , i.e. the narrow junction limit , this becomes a quasi - gaussian , monotonic decay of the critical current . in contrast to fraunhofer interference in wide planar junctions , the flux is aligned _ with _ the current and the oscillations are _ not _ periodic in the flux quantum .

a semiconductor nanowire based superconductor - normal - superconductor ( ) junction is modeled theoretically . a magnetic field is applied along the nanowire axis , parallel to the current . the bogoliubov - de gennes equations for andreev bound states are solved while considering the electronic subbands due to radial confinement in the-section . the energy - versus - phase curves of the andreev bound states shift in phase as the-section quasiparticles with orbital angular momentum couple to the axial field . a similar phase shift is observed in the continuum current of the junction . the quantum mechanical result is shown to reduce to an intuitive , semi - classical model when the andreev approximation holds . numerical calculations of the critical current versus axial field reveal flux - aperiodic oscillations that we identify as a novel form of josephson interference due to this orbital subband effect . this behavior is studied as a function of junction length and chemical potential . finally , we discuss extensions to the model that may be useful for describing realistic devices . [ qcalc_standalone ] the josephson effect is characterized by a current - phase relationship ( cpr ) linking macroscopic current flow to the phase gradient of the superconducting order parameter . the precise form of the cpr for a superconducting weak link depends on intrinsic factors such as junction geometry , material properties , coherence lengths , etc . , in addition to extrinsic variables like temperature and magnetic field . in superconductor - normal - superconductor ( ) junctions in which the-section is long enough to suppress direct tunnelling of cooper pairs , but shorter than the-section phase coherence length , a supercurrent may be carried by quasiparticles undergoing andreev reflection at the- interfaces . planar junctions of width large compared to the-section superconducting coherence length have been studied in great detail ( width refers to the dimension perpendicular to the current ) . these have revealed , for example , fraunhofer oscillations of the critical current with respect to an externally applied out - of - plane magnetic field . for junction widths comparable to the-section coherence length , i.e. the narrow junction limit , this becomes a quasi - gaussian , monotonic decay of the critical current . recently , attention has been given to nanoscale , quasi one - dimensional ( 1d ) junctions , such as those readily engineered by contacting semiconductor nanowires with superconducting leads . gating the semiconducting-section allows for modulating the supercurrent by controlling the chemical potential . the oscillations of the magnetoresistance of a nanowire junction in the voltage - biased state ( i.e. no dc supercurrent ) versus an axial magnetic field have been studied . efforts to realize majorana fermion quasiparticles in 1d semiconductors with strong spin - orbit interaction and proximity coupling to a superconductor have further raised interest in this type of junction . theoretical results have indicated that the behaviour of the critical current in such a junction versus magnetic field and chemical potential can be used to identify topological phases . + previous theoretical descriptions of quasi-1d junctions have not fully considered the effects of nanoscale confinement on the cpr , in particular the implications of orbital angular momentum coupling to an external magnetic flux . here we provide a quantum mechanical description of an idealized junction with a flux applied along the nanowire axis ( parallel to the current ) . for a planar junction , no significant modification of the cpr with an axial flux is expected , as azimuthal motion of the carriers is absent . however , for a cylindrical geometry , azimuthal motion leads to a non - trivial effect which we identify as a previously unstudied form of josephson interference . this is due to the coupling between andreev quasiparticles ( bound states and continuum states ) with orbital angular momentum and the axial flux , which results in phase shifts of the energy - versus - phase for these current carrying states . the total current summed over all channels ( occupied orbitals ) can display interference . in contrast to fraunhofer interference in wide planar junctions , the flux is aligned _ with _ the current and the oscillations are _ not _ periodic in the flux quantum . this effect is only present in nanoscale junctions with lateral dimensions ( i.e. diameter ) smaller than the london penetration depth . this is a regime in which the general theorem of byers and yang does not apply . it is shown that the supercurrent from continuum states also contributes to this interference . for certain junction parameters , the interference effect can dominate the vs characteristics . semiclassically , the effect is intuitively understood by the pickup of a magnetic phase by andreev pairs with an azimuthal velocity component as they cross the junction ballistically . the aim of this paper is to theoretically describe this type of josephson interference in a fully quantum mechanical way . in particular , we are interested in understanding the effect in isolation from the additional complications of real devices , such as non - cylindrical contact geometry , interfacial potential barriers , etc . we consider in the discussion section how to modify the present model to better describe realistic devices . here , we consider the case where the diameter is smaller than the superconducting coherence length in the-section , so that the phase of the order parameter is uniform around the-section circumference in any magnetic field up to the critical field of the leads , . spin - orbit and zeeman effects in the-section ( e.g. relevant to iii - v semiconductor nanowires ) are neglected , and we assume no barriers at the- interfaces . furthermore , we neglect magnetic depairing effects .