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astro-ph0504168	c	by performing the 2d - rhd simulations , we , for the first time , investigate the quasi - steady structure of the super - critical accretion flows around the black hole with particular attention being paid on the photon - trapping effects . we have obtained several new findings : \(1 ) the quasi - steady structure of the super - critical flow is divided into two parts : the disk region ( with mostly inflow ) and the outflow region above the disk . the two regions are separated by a sharp density jump . the gas outflow driven by the strong radiation pressure is produced around the rotation axis . further , there exists velocity shears at the boundary , which causes k - h instability around the disk surface , producing the patchy structure as well as the circular motion within the disk region . convection may also be responsible for such inhomogeneous structure . \(2 ) the photon - trapping plays an important role in the super - critical accretion regime . the advective energy transport is substantial , and the large amount of photons generated inside the disk is swallowed by the black hole without radiated away . \(3 ) our 2d - rhd model shows some differences from the slim - disk model . the slim - disk model assumes a simple convergence flow , while our simulations revealed rather complex gas motion and structure . we also found that the mass - accretion rate is not constant in space but decreases as matter accretes , roughly as @xmath243 , as a result of wind mass loss and circular motion . the calculated luminosity of the flows agrees more with the prediction of paper i rather than that of the slim - disk model . \(4 ) the emission of the super - critical accretion flows is moderately collimated . the apparent luminosity could become more than ten times larger than the eddington luminosity . the super - critical accretion flows would be identified as high @xmath127 objects in the face - on view , but not , if the viewing angle is large , for which self - occultation tends to reduce the total luminosity and the maximum flow temperature . ( 5 ) the mass - accretion rate increases with increase of the absorption opacity ( metalicity ) of the accreting matter . it implies that the black hole tends to grow up faster in the metal rich regions as in starburst galaxies or star - forming regions . in addition , the growth of the black hole may gradually slow down , since the density as well as the absorption opacity of the super - critical accretion flows are small around the massive black hole , if the normalized mass - accretion rate is kept constant . the authors would like to thank the anonymous referee for important comments and suggestions . the calculations were carried out at department of physics in rikkyo university . this work is supported in part by research fellowships of the japan society for the promotion of science for young scientists , 02796 ( ko ) , by the grant - in - aid of the ministry of education , culture , science , and sports , 14740132 , by the promotion and mutual aid corporation for private schools of japan ( mm ) , by the grants - in - aid of the ministry of education , science , culture , and sport , ( 14079205 , 16340057 ) , and by a grant - in - aid for the 21st century coe center for diversity and universality in physics " ( sm ) . abramowicz , m. a. , czerny , b. , lasota , j. p. , & szuszkiewicz , e. 1988 , apj , 332 , 646 balbus , s. a. 2003 , ara&a , 41 , 555 becker , r. h. , white , r. l. , gregg , m. d. , brotherton , m. s. , laurent - muehleisen , s. a. , & arav , n. 2000 , apj , 538 , 72 begelman , m. c. 1978 , mnras , 184 , 53 begelman , m. c. 2002 , apj , 568 , l97 chakrabarti , s. k. 1996 , apj , 464 , 664 chen , x. , taam , r. e. , abramowicz , m. a. , & igumenshchev , i. v. 1997 , mnras , 285 , 439 colella , p. & woodward , p. 1984 , j. comput . phys . , 54 , 174 collin , s. & kawaguchi , t. 2004 , a&a , 426 , 797 eggum , g. e. , coroniti , f. v. , & katz , j. i. 1987 , apj , 323 , 634 eggum , g. e. , coroniti , f. v. , & katz , j. i. 1988 , apj , 330 , 142 fujita , m. & okuda , t. 1998 , pasj , 50 639 fukue , j. 2000 , pasj , 52 , 829 fukue , j. , umemura , m. , & mineshige , s. 1997 , pasj , 49 , 673 hawley , j. f. , balbus , s. a. & stone , j. m. 2001 , apj , 554 , l49 hayashi , c. , hoshi , r. , & sugimoto , d. 1962 , prog . suppl . , 22 , 1 igumenshchev , i. v. & abramowicz , m. a. 1999 , mnras , 303 , 309 kato , s. , fukue , j. , & mineshige , s. 1998 , black - hole accretion disks ( kyoto : kyoto univ . press ) kato , y. , mineshige , s. , & shibata , k. 2004 , apj , 605 , 307 kawaguchi , t. 2003 , apj , 593 , 69 kawakatu , n. , umemura , m. , & mori , m. 2003 , apj , 583 , 85 kley , w. 1989 , a&a , 222 , 141 kley , w. & lin , d. n. c. 1999 , apj , 518 , 833 kubota , a. & done , c. 2004 , mnras , 353 , 980 levermore , c. d. & pomraning , g. c. 1981 , apj , 248 , l321 machida , m. , hayashi , m. r. , & matsumoto , r. 2000 , apj , 532 , l67 machida , m. , matsumoto , r. , & mineshige , s. 2001 , pasj , 53 , l1 mckinney , j. c. & gammie , c. f. 2002 , apj , 573 , 728 mineshige , s. , kawaguchi , t. , takeuchi , m. , & hayashida , k. 2000 , pasj , 52 , 499 nagao , t. , murayama , t. , shioya , y. , & taniguchi , y. 2002 , apj , 575 , 721 narayan , r. , igumenshchev , i. v. , abramowicz , m. a. 2000 , apj , 539 , 798 ohsuga , k. , mineshige , s. , mori , m. , & umemura , m. 2002 , apj , 574 , 315 ohsuga , k. , mineshige , s. , & watarai , k. 2003 , apj , 596 , 429 ohsuga , k. , umemura , m. , fukue , j. , & mineshige , s. 1999 , pasj , 51 , 345 okuda , t. 2002 , pasj , 54 , 253 okuda , t. & fujita , m. 2000 , pasj , 52 , l5 okuda , t. , fujita , m. , & sakashita , s. 1997 , pasj , 49 , 679 okuda , t. , teresi , v. , toscano , e. , & molteni , d. 2005 , mnras , 357 , 295 paczynsky , b. & wiita , p. j. 1980 , a&a , 88 , 23 pounds , k. a. , king , a. r. , page , k. l. , & obrien , p. t. 2003b , mnras , 346 , 1025 pounds , k. a. , reeves , j. n. , king , a. r. , page , k. l. , obrien , p. t. , & turner , m. j. l. 2003a , mnras , 345 , 705 reeves , j. n. , obrien , p. t. , & ward , m. j. 2003 , apj , 593 , 65 rybicki , g. b. & lightman , a. p. 1979 , radiative processes in astrophysics ( new york : john wiley & sons , inc . ) shakura , n. i. & sunyaev , r. a. 1973 , a&a , 24 , 337 shemmer , o. & netzer , h. 2002 , apj , 567 , l19 shemmer o. , netzer , h. , maiolino , r. , oliva , e. , croom , s. , corbett , e. , & di fabrizio , l. 2004 , apj , 614 , 547 soltan , a. 1982 , mnras , 200 , 115 spruit , h. c. , matsuda , t. , inoue , m. , & sawada , k. 1987 , mnras , 229 , 517 stone , j. m. & pringle , j. e. 2001 , mnras , 322 , 461 stone , j. m. , pringle , j. e. , & begelman , m. c. 1999 , mnras , 310 , 1002 turner , n. j. 2004 , apj , 605 , l45 turner , n. j. & stone , j. m. 2001 , apjs , 135 , 95 turner , n. j. , stone , j. m. , krolik , j. h. , & sano , t. 2003 , apj , 593 , 992 umemura , m. 2001 , apj , 560 , l29 umemura , m. , fukue , j. , & mineshige , s. 1997 , apj , 479 , l97 yu , q. & tremaine , s. 2002 , mnras , 335 , 965 wang , j .- m . & netzer , h. 2003 , a&a , 398 , 927 watarai , k. & fukue , j. 1999 , pasj , 51 , 725 watarai , k. , fukue , j. , takeuchi , m. , & mineshige , s. 2000 , pasj , 52 , 133 watarai , k. , mizuno , t. , & mineshige , s. 2001 , apj , 549 , l77 watarai , k. , ohsuga , k. , takahashi , r. , & fukue , j. 2005 , pasj , in press weymann , r. j. , carswell , r. f. , & smith , m. g. 1981 , ara&a , 19 , 41	the super - critical flow is composed of two parts : the disk region and the outflow regions above and below the disk . within the disk region the circular motion as well as the patchy density structure this implies that the black hole tends to grow up faster in the metal rich regions as in starburst galaxies or star - forming regions .	the quasi - steady structure of super - critical accretion flows around a black hole is studied based on the two - dimensional radiation - hydrodynamical ( 2d - rhd ) simulations . the super - critical flow is composed of two parts : the disk region and the outflow regions above and below the disk . within the disk region the circular motion as well as the patchy density structure are observed , which is caused by kelvin - helmholtz instability and probably by convection . the mass - accretion rate decreases inward , roughly in proportion to the radius , and the remaining part of the disk material leaves the disk to form outflow because of strong radiation pressure force . we confirm that photon trapping plays an important role within the disk . thus , matter can fall onto the black hole at a rate exceeding the eddington rate . the emission is highly anisotropic and moderately collimated so that the apparent luminosity can exceed the eddington luminosity by a factor of a few in the face - on view . the mass - accretion rate onto the black hole increases with increase of the absorption opacity ( metalicity ) of the accreting matter . this implies that the black hole tends to grow up faster in the metal rich regions as in starburst galaxies or star - forming regions .
1702.07418	r	vla observations from 1985 @xcite show a strong asymmetry in the shell at 21 cm , perhaps indicative of an external density gradient . the mean radius of the bright x - ray ring is about 2 pc , but with the east and west ears at about 2.2 pc @xcite . we neglect any possible gradient of ambient density in surrounding ism , which leads to a complicated morphology ( see * ? ? ? * ) and seek for a global qualitative description of integrated continuum radio emission . trying to model the observed radio morphology as a consequence of hypothetical global magnetic field gradient would be tricky due to the existing disagreement between observations and theory . young snrs have a predominantly radial magnetic field structure , visible through polarization measurements @xcite . on the other hand , modern theories and simulations of mfa predict a strong turbulence of amplified field @xcite as a result of the interaction of crs with the upstream plasma and ambient field . we performed 3d hd simulations describing the expansion of the snr g1.9 + 0.3 in spherical coordinates with the pluto code , adopted according to the model described in the previous section . as the magnetic field does not play a dynamical role in the evolution of the snr , we do not use mhd modules existing in pluto . however , we calculate the magnetic field strength and its amplification by using our separate nldsa modules tied to pluto , as it is necessary for cr acceleration as well as for the radio emission . our initial conditions were chosen in order to reproduce g1.9 + 0.3 after around 100 yr of evolution in terms of shock radius , which is about 2 pc ( near 100 arcsec in diameter ) for an assumed location near the gc @xcite , and shock velocity of 14000 km s@xmath4 , deduced mainly from fe emission with a width of about 28000 km s@xmath4@xcite . in all of our simulations , the ambient magnetic field strength is set to value @xmath196 g , representative of the average galactic field . for the initial density structure of the ejecta , we used the exponential profile that has been shown to be the best approximate representation of explosion models for type ia sne @xcite , thought to represent thermonuclear disruption of a white dwarf . we add clumps in the initial ejecta as per - cell random density perturbations @xcite and they trigger rayleigh taylor instability at the contact discontinuity . we assumed an initial spherical remnant with a radius of 0.05 pc ( corresponding to an initial age of @xmath5 2.5 yr ) , ejecta mass equal to the chandrasekhar mass @xmath197 and the total explosion energy @xmath198 erg . snr expands through a homogeneous isothermal plasma with temperature @xmath199 k ( corresponding to an isothermal sound speed @xmath200 and alvn speed @xmath201 km / s and alfvnic number @xmath202 . ] for ambient density 0.02 @xmath3 ) and mass density @xmath203 , characterized by the hydrogen number density @xmath204 , where @xmath205 is the mean atomic mass ( assuming cosmic abundances ) and @xmath206 is the mass of the hydrogen atom . in order to estimate the ism density and age of snr , we performed a set of 3d hd simulations with different ambient hydrogen number densities ranging from 0.01 @xmath3 to 0.04 @xmath3 ( fig . [ fig : hydro ] ) . we simulate one octant of the remnant , for the total time of 200 yr , with a resolution of 2048 @xmath207 512 @xmath207 512 grid cells , respectively , for each of the spherical coordinates @xmath208 , @xmath209 and @xmath210 ( fig . [ fig:3d - snr ] ) . soon after the explosion , snr dynamical evolution is characterized by increasing the radius and decreasing the shock velocity . the observed shock velocity of 14000 km / s and snr radius of 2 pc have to be reached in our simulations at the same time after the explosion , which we take as the snr age . the hydrogen number density satisfying this requirement is @xmath211 0.02 @xmath3 and the corresponding snr age is 115 yr , for the epoch 2008 when observations , we used for comparison with models , are made . this implies an explosion date of about 1893 and a current age of 123 yr . as referent radio data for snr g1.9 + 0.3 we use observations made by @xcite at 1.43 and 4.86 ghz with the vla , which are respectively 0.935 @xmath212 0.047 jy and 0.437 @xmath212 0.022 jy . combining these integrated flux densities gives a steep radio emission spectral index @xmath213 ( defined so that the flux density scales with frequency as @xmath214 ) of 0.62 @xmath212 0.06 , using the assumed 5 per cent statistical uncertainties in the individual flux densities . in general , observations confirm that young snrs have radio spectral indices steeper than the expected @xmath215 @xcite , derived from tp dsa @xcite . @xcite showed that young snrs with the quasi - perpendicular orientation of the magnetic field should have steeper spectral indices . for a detailed review on radio spectra of snrs and some other possible explanations for steep spectra of young snrs , see @xcite and references therein . some properties of the time - dependent solutions ( instead of quasi - stationary solutions used in our modelling ) could also be responsible for the deviation of the observed radio index from the classical value 0.5 in some young snrs , as recently shown by @xcite . we also pose a radio light curve for g1.9 + 0.3 , observed with the molonglo observatory synthesis telescope ( most ) , spanning 20 yr from 1988 to 2007 at a frequency of 843 mhz @xcite . two most recent measurements ( closest to the time when vla observations have been made ) , 0.97 @xmath212 0.11 jy from epoch 2007.430 and 1.32 @xmath212 0.09 jy from epoch 2007.463 , will only be used for comparison with our best - fitting modelled spectra made using vla measurements @xcite , although showing evident inconsistency and large measurement errors . change in the radio flux should not be neglected for earlier most measurements as they cover around one - sixth of the estimated lifetime of the snr . @xcite also obtained radio flux density measurements but significantly smaller ( @xmath2 50 per cent ) than vla measurements . they attribute this large difference to missing short spacings and poorer @xmath216 coverage of the atca images . assuming particle distribution @xmath217 ( bottom panel ) . two representative models are shown , the most efficient nldsa in model a ( thick solid line ) and the least efficient nldsa , amongst four models from table [ tab : models ] , in model d ( thin solid line ) . ] our hydrodynamical approach does not self - consistently deal with the magnetic turbulence and belonging higher order anisotropies which , according to @xcite , steepen the spectral index at quasi - perpendicular shocks . due to this , we fit snr g1.9 + 0.3 radio spectra simply by using the described non - linear acceleration model of blasi and assuming efficient acceleration ( namely , acceleration efficiency up to @xmath218 , to which corresponds @xmath88 between 3.3 and 3.45 in our simulations ) . efficient acceleration is expected for such a young snr and consistent with previous works ( e.g. , * ? ? ? the electrons that mainly produce radiation by the synchrotron mechanism ( in the amplified magnetic field @xmath2 100 @xmath106 g ) at frequencies @xmath2 1 ghz have energy @xmath2 1 gev and momentum @xmath219 . at energies around 1 gev , our energy spectra @xmath220 of accelerated particles at cr modified shocks become softer , with the effective power - law index @xmath21 around 2.2 , giving the required spectral steepening of synchrotron spectra . [ cols="^,^,^,^,^,^,^,^,^",options="header " , ] from the fit of the synchrotron emission , we obtain value @xmath221 for the electron - to - proton ratio @xmath132 , which is slightly lower than the value observed in the local cr spectra . our value is in good agreement with values derived by other authors ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , although @xcite proposed a model in which @xmath222 is a universal value that can fit all galactic snrs . as the dynamical role of electrons is negligible in the used model for nldsa , this parameter acts as a scaling factor for the total radio emission and should not have any qualitative effects on radio evolution . two free parameters are of the utmost importance for the total radio flux in our simulations : injection parameter @xmath88 , determining a fraction of particles @xmath80 entering the acceleration process and therefore global efficiency of nldsa and mfa , and caprioli s parameter @xmath78 , controlling heating of the plasma by non - linear damping of alfvn waves and therefore being able to reduce the shock modification to some extent . as already said , efficient acceleration is necessary for the required spectral steepening of the radio spectra , but also @xmath88 values around 3.4 lead to very strong mfa and in turn can cause overestimate of the snr total radio flux . therefore , some damping is likely and a search through parameter space leads to the conclusion that , in our modelling , caprioli s parameter @xmath78 between 0.1 and 0.4 provides good fits . these values are also in agreement with @xcite , who arbitrarily set @xmath223 in their four heuristic models of mfa in the precursor and which is , according to them , a reasonable estimate . we choose three best - fitting models , for injection parameter @xmath88 values 3.30 , 3.35 , 3.40 and 3.45 , respectively , denoting them with models a , b , c and d ( table [ tab : models ] and fig . [ fig : fit ] ) . we allow four different scenarios , although producing similar radio spectra for particular 2008 . epoch , in order to allow possible differences in simulations of radio flux temporal evolution , being the main goal of our paper . [ fig : fit ] indicates that most measurement 0.97 @xmath212 0.11 jy should be taken with caution as probably being subject to significant measurement errors . in order to reproduce observed radio flux spectra from 2008 , our simulations predict that the amplified magnetic field in downstream was then around @xmath224 . this value is in agreement with the value @xmath225 inferred for g1.9 + 0.3 from equipartition calculations @xcite and rapid variability in x - rays for notably older snr rx j1713.72@xmath2263946 , indicating amplification of the magnetic field by a factor of even more than 100 @xcite . from the simulated 2500 yr of evolution , the obtained amplified magnetic field in the downstream is @xmath227 ( see section [ sec : mfa ] for discussion ) . and a flux density of 1.23 jy on 2005 january 1 , originally obtained by @xcite . our simulations are shown with thin colour lines , namely model a ( red ) , model b ( blue ) , model c ( green ) and model d ( black ) , showing similar average flux gradient @xmath5 0.017 jy yr@xmath4 . ] fig . [ fig : spectra ] clearly shows that particle spectrum of accelerated particles changes from that predicted by standard linear dsa , which reads @xmath228 in momentum and corresponds to energy distribution @xmath229 in a relativistic regime . similarly to the cut - off for the electrons ( section [ sec : radio ] ) , we parametrize the turnover of protons also by multiplying their distribution by an exponential factor , in a form suggested by @xcite . for sufficiently large momenta , the electron distribution function additionally deviates from the spectrum predicted by nldsa , as a result of synchrotron losses . as we mentioned before , a radio light curve for g1.9 + 0.3 based on 25 epochs of observation with the most is available @xcite . these observations were taken with the same instrument , at constant frequency ( 843 mhz ) and comparable resolutions ( 43 @xmath207 91 or 43 @xmath207 95 arcsec@xmath230 ) . therefore , we run our numerical simulations for different model parameters shown in table [ tab : models ] and synthesize the total radio flux density at frequency 843 mhz during the period from 1985 until 2010 , in order to make comparison with observations ( fig . [ fig : radio - e ] ) . we obtained the average flux gradient of around 0.017 @xmath231 during this period ( 1.8 per cent yr@xmath4 ) , which is in a very good agreement with a least - squares fit of most observations which gives 0.015 @xmath232 ( 1.22@xmath233 per cent yr@xmath4 ) and also very close to the estimate of @xmath22 per cent yr@xmath4 made by @xcite , based on observations from a range of instruments , compiled from the literature . during the simulated part of the free expansion phase , derived dependence of the radio flux density is @xmath234 , corresponding to radio surface brightness dependence @xmath235 , while @xcite derive steeper dependence @xmath236 in free expansion . interestingly , x - ray flux brightening of g1.9 + 0.3 , measured by @xcite , is also close to simulated and observed radio values , namely 1.7 @xmath212 1.0 per cent yr@xmath4 . three 11 cm flux density measurements from the effelsberg 100-m radio telescope clearly show a strong flux density increase of g1.9 + 0.3 for more than 30 yr . these measurements are respectively : 0.44@xmath2120.05 jy from epoch 1983.48 @xcite , 0.61@xmath2120.02 jy from 2008.56 and 0.65@xmath2120.02 jy from 2016.72 ( private communication , courtesy of dr . wolfgang reich ) . the resulting rate of flux change for effelsberg data is therefore around 0.006 jy yr@xmath4 , while our model predicts rate 0.008 jy yr@xmath4 at frequency 2695 mhz , for the corresponding period . frequency independent flux expansion rate for effelsberg data @xmath51.4 per cent yr@xmath4 agrees well with other measurements and our simulations . we are also able to deduce the fs expansion rate from our simulations , for the evolution period from 1985 until 2010 , roughly covering available observations . our value of 0.9 per cent yr@xmath4 is in good agreement with expansion rate measurements @xmath50.65 per cent yr@xmath4 , from vla observations @xcite , and 0.64 @xmath212 0.05 per cent yr@xmath4 @xcite , obtained by comparing _ chandra _ x - ray images . in fig . [ fig : evol - compare ] , we plot time evolution of different characteristics of snr for period of 1000 yr and compare the evolution corresponding to efficient dsa , including mfa , with a tp case . the red line represents dsa with pronounced non - linear effects and strongly modified shock ( parameters from model a ) , while the blue line represents snr evolution with injection parameter @xmath237 leading to almost negligible amount of accelerated crs . the total compression in the tp case reduces to 4 and magnetic field downstream is amplified only due to gas compression , which is far below the value required for the observed radio emission . , and the red line represents nldsa with model a parameters ( the most efficient acceleration among models listed in table [ tab : models ] ) . ] in jy yr@xmath4 , averaged for each frequency and line colours having the same meaning as in the upper panel . the lower panel shows the annual flux density increase , @xmath238 , in per cent yr@xmath4 , which is independent of frequency . the maximum flux density is predicted around 600 yr , which is before the shock sweeps ism mass equal to @xmath239 , roughly marking the end of the free expansion phase in our simulation ( @xmath240 yr ) . ] , defined so that the flux density depends on frequency as @xmath241 . spectral index evolution is model dependent and due to this we denote different scenarios with colours , namely model a ( red line ) , model b ( blue ) , model c ( green ) and model d ( black ) . ] being the main purpose of this paper , we simulate the time dependence of flux densities @xmath242 of the radio synchrotron emission at different frequencies with its corresponding rate of change @xmath243 in jy yr@xmath4 and frequency - independent fractional change @xmath244 in percentage yr@xmath4 ( fig . [ fig : evol - s1 ] ) . our model predicts increasing radio emission from g1.9 + 0.3 during the part of the free expansion phase , reaching its maximum value around the age of 600 yr and then decreasing during the later free expansion and sedov phase . for the determined ambient density of 0.02 @xmath3 , radius around 11.3 pc marks the end of the free expansion ( ejecta dominated ) phase , which we assume to be when the swept - up mass is @xmath245 . in our simulations , this happens @xmath5 1700 yr after the sn explosion . model also predicts maximum radio flux densities @xmath2 4.3 , 3.1 and 1.5 jy , respectively for frequencies 843 , 1425 and 4860 mhz , being around three times higher than the present values . it can be inferred from fig . [ fig : evol - s1 ] that models with higher injection parameter @xmath88 ( less efficient acceleration ) give slightly higher flux densities close to maximum , for a chosen frequency . this is mainly due to the increasing efficiency of mfa in models from a to d ( see table [ tab : models ] ) , linked with the parameter @xmath78 . as for the rate of flux density change during time ( in jy yr@xmath4 ) , our model suggests a maximum at around @xmath246 yr followed by gradual slowing down of flux increase , until it starts to decline . interestingly , available measurements of radio light curve for g1.9 + 0.3 roughly coincide with this maximum @xcite , meaning they probably contain the fastest ever flux change for this snr . simulations also give insight into the radio spectral index @xmath213 evolution ( fig . [ fig : alpha ] ) , reflecting the evolution of the spectrum of accelerated electrons with energies around @xmath2 gev . evolution starts from the values close to @xmath215 , corresponding to the tp dsa solution , reaches maximum value ( the steepest radio spectra ) and then slowly decreases , making spectra shallower . evolutionary tracks for radio spectral index were obtained by implementing models from table [ tab : models ] and they seem strongly model dependent . higher injection efficiency ( lower @xmath88 parameter ) naturally leads to higher value for @xmath213 in maximum but also this maximum is reached earlier in the snr lifetime . this is in good agreement with a considerable amount of observational evidence for steep spectral indices of snrs being @xmath2 1000 yr old or even few times older , as radio spectral index slowly decreases after reaching maximum steepness . the greatest number of evolved snrs have spectral indices in the interval 0.5 @xmath247 @xmath213 @xmath247 0.6 , as the dsa predicts @xcite . synchrotron emission spans from the radio to the x - ray band . @xcite concluded that x - ray emission from g1.9 + 0.3 appears to be purely synchrotron radiation . we neglect x - ray emission due to thermal bremsstrahlung and synthesize the synchrotron spectrum up to the highest energies by using an electron spectrum obtained in our simulations ( fig . [ fig : xray ] ) and adopted to fit observations , as described in section [ sec : radio ] . magnetic field @xmath248 g inferred from our simulations for the snr age of @xmath249 yr in 2008 gives the position of the break in the electron spectrum around @xmath250 ( equation [ eq : eb ] ) . the best - fitting maximum value for the steepening @xmath141 is 0.5 , implemented through our toy model ( section [ sec : radio ] ) as uniformly growing function starting from momenta slightly before @xmath251 , to ensure physically more consistent and smoother transition from the uncooled to the cooled regime instead of a sharp break in the electron spectrum . the synchrotron spectrum in fig . [ fig : xray ] is obtained only for model a and it is obtained for the maximum electron cut - off momentum @xmath252 and the corresponding energy @xmath253 tev , obtained by assuming bohm diffusion . spectra for the remaining three models ( table [ tab : models ] ) were omitted because they are very similar . also , modelled spectra of g1.9 + 0.3 reveals concave - up curvature at millimetre and sub - millimetre wavelengths . this is expected and indeed observed by the _ _ planck _ _ telescope in the radio continuum of another young snr cas a @xcite . after investigating alternative explanations of the observed curvature , @xcite agree that non - linear effects of particle acceleration are mainly responsible for high - frequency curvature in the radio spectrum . following the approach described in section [ sec : gamma ] , we evolve the snr during the 2500 yr and calculate its 4 tev gamma - ray emission produced by pion decay and ic computed for the cmb photon field ( fig . [ fig : gamma ] ) . we chose to model 4 tev emission intentionally , as the highest cta sensitivity is expected around this energy . for the present snr age , the expected total tev gamma - ray emission is @xmath254 . such a flux is too low for possible h.e.s.s . or veritas detection in @xmath2 50 h , more than one order of magnitude below their sensitivities . on the other hand , present value from our model is slightly below the predicted cta ( southern site ) sensitivity limit of @xmath255 around tev energies , but expected to reach this limit within a decade or so . the pion decay flux is only about 1/4 of the ic gamma - ray flux , probably as a result of the low ambient gas density . the maximum tev gamma - ray flux is predicted to occur around the end of the free expansion phase , at the age of 1500 yr , and it reaches @xmath256 . this value is still below the sensitivity limit of h.e.s.s . , but probably visible in tev gamma - rays by future instruments , including the cta . however , more advanced broad - band modelling of g1.9 + 0.3 is out of the scope of this paper . the x - ray part of the spectrum and gamma - ray emission evolution are given above only in an illustrative way , to check how our model fits with observations in domains other than radio . more rigorous numerical treatment of synchrotron losses will be necessary in order to obtain evolution of the emission at energies higher than radio . we reserve a detailed modelling of snr evolutionary tracks at different wavelengths for future work .	snr g1.9 + 0.3 is the only known galactic snr with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now . we conclude that this is a general property of snrs in free expansion phase .	the radio evolution of , so far the youngest known , galactic supernova remnant ( snr ) g1.9 + 0.3 is investigated by using three - dimensional ( 3d ) hydrodynamic modelling and non - linear kinetic theory of cosmic ray ( cr ) acceleration in snrs . we include consistent numerical treatment of magnetic field amplification ( mfa ) due to resonant streaming instability . under the assumption that snr g1.9 + 0.3 is the result of a type ia supernova explosion located near the galactic centre , using widely accepted values for explosion energy 10 erg and ejecta mass 1.4 , the non - thermal continuum radio emission is calculated . the main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution . we estimate that the snr is now 120 yr old , expanding in an ambient density of 0.02 , and explain its steep radio spectral index only by means of efficient non - linear diffusive shock acceleration ( nldsa ) . we also make comparison between simulations and observations of this young snr , in order to test the models and assumptions suggested . our model prediction of a radio flux density increase of 1.8 per cent yr during the past two decades agrees well with the measured values . we synthesize the synchrotron spectrum from radio to x - ray and it fits well the very large array , molonglo observatory synthesis telescope , effelsberg , _ chandra _ and nustar measurements . we also propose a simplified evolutionary model of the snr in gamma rays and suggest it may be a promising target for gamma - ray observations at tev energies with the future generation of instruments like cherenkov telescope array . snr g1.9 + 0.3 is the only known galactic snr with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now . we conclude that this is a general property of snrs in free expansion phase . [ firstpage ] acceleration of particles hydrodynamics radiation mechanisms : non - thermal cosmic rays ism : individual objects : g1.9 + 0.3 ism : supernova remnants .
1702.07418	c	the peculiar nature of radio evolution of the youngest known galactic snr g1.9 + 0.3 is modelled by using blasi non - linear kinetic theory of cr acceleration in snrs coupled with 3d hydrodynamics , simultaneously solved with the pluto code . we assume this snr originated from a type ia supernova ( sn ) explosion located near the gc , with explosion energy 10@xmath0 erg and ejecta mass 1.4 m@xmath257 . hydrodynamic equations in the pluto code were adopted to use the space and time - dependent adiabatic index in order to account for the presence of energetic particles , making the fluid more compressible . our modelling and analysis leads to the following essential results . \(i ) from our 3d hydrodynamic simulations of snr evolution , including a deceleration of fs by the ambient medium and due to back reaction of crs , we estimate the current age of g1.9 + 0.3 snr to be slightly over 120 yr , expanding in an ambient density of 0.02 @xmath258 . \(ii ) efficient acceleration is necessary in order to explain observed spectral steepening of the radio spectra . namely , observations are well fitted for injection parameter @xmath88 between 3.45 and 3.30 , corresponding to an acceleration efficiency @xmath2590.51.1@xmath260 and magnetic field amplified more than 50 times from the assumed ambient value . \(iii ) following our models , it can be concluded that radio emission increasing brightness is a common property of young snrs . our model gives the average 843 mhz flux increase gradient during a 20-yr period of around 0.017 @xmath232 ( 1.8 per cent yr@xmath4 ) , which is in a very good agreement with most observations and also with other available observations from a range of instruments , compiled from the literature . simulations give the average 2695 mhz flux gradient of 0.008 jy yr@xmath4 during the past 30 yr , being in a good agreement with effelsberg measurements . \(iv ) numerical model predicts increasing radio emission from g1.9 + 0.3 during the free expansion phase , reaching its maximum value around the age of 600 yr and then decreasing during late free expansion and beginning of sedov phase around 1700 yr after the sn explosion . interestingly , it seems that we are currently witnessing approximately the fastest radio emission increase than it will ever be . \(v ) the radio brightness will grow according to prediction given in this paper , until its maximum flux densities of @xmath2 4.3 , 3.1 and 1.5 jy , respectively , for frequencies 843 , 1425 and 4860 mhz , being around three times higher than the present day values . \(vi ) the steep radio spectral index ( steeper than linear dsa prediction of @xmath215 ) for young snrs is explained only by means of efficient nldsa and accompanying strong mfa . the radio spectral index also shows qualitatively similar evolution as the radio flux , it reaches the steepest value @xmath261 and then becomes shallower ( trending towards the value of 0.5 ) . higher injection efficiency @xmath80 leads to higher @xmath261 but also causes this value to be reached earlier in the snr history . however , the temporal evolution of the radio spectral index turns out to be very sensitive to model parameters @xmath88 and @xmath78 . \(vii ) we implement a simple toy model for the synthesis of a broader synchrotron spectrum from radio to x - ray , by using the electron spectrum obtained in our simulations . this spectrum is modified in post - processing by introducing a break in the electron spectrum , to account for synchrotron losses and modelled x - ray emission fit well the _ chandra _ and nustar measurements . it agrees well with models of spectra containing more consistent , numerical calculation of synchrotron losses . \(viii ) we also implement approximative model of gamma - ray emission coming from the snr . we inspect time evolution of the total gamma - ray flux and conclude that it may be visible in tev gamma - rays by future instruments , including the cta . model predicts increasing tev gamma - ray emission during the entire free expansion phase , reaching the maximum value of @xmath256 at the age of around 1500 yr . our model enabled us to make important conclusions about the present and predictions about the future properties of radio emission from the youngest known galactic snr . we want to emphasize that , although the presented model contains robust implementation , all provided quantitative estimates should be taken with caution . besides our limited knowledge in physical descriptions of particle acceleration and snr evolution , a significant number of model parameters still remain weakly constrained . models of radio evolutionary tracks can be of the utmost importance for the future observers working on powerful radio telescopes such as alma and ska . these types of modelling can provide important information about the evolutionary stage of snrs , as well as to characterize the physical conditions in the shocks where the relativistic particles are accelerated .	the radio evolution of , so far the youngest known , galactic supernova remnant ( snr ) g1.9 + 0.3 is investigated by using three - dimensional ( 3d ) hydrodynamic modelling and non - linear kinetic theory of cosmic ray ( cr ) acceleration in snrs . we include consistent numerical treatment of magnetic field amplification ( mfa ) due to resonant streaming instability . under the assumption that snr g1.9 + 0.3 is the result of a type ia supernova explosion located near the galactic centre , using widely accepted values for explosion energy 10 erg and ejecta mass 1.4 , we estimate that the snr is now 120 yr old , expanding in an ambient density of 0.02 , and explain its steep radio spectral index only by means of efficient non - linear diffusive shock acceleration ( nldsa ) . our model prediction of a radio flux density increase of 1.8 per cent yr during the past two decades agrees well with the measured values . we synthesize the synchrotron spectrum from radio to x - ray and it fits well the very large array , molonglo observatory synthesis telescope , effelsberg , _ chandra _ and nustar measurements .	the radio evolution of , so far the youngest known , galactic supernova remnant ( snr ) g1.9 + 0.3 is investigated by using three - dimensional ( 3d ) hydrodynamic modelling and non - linear kinetic theory of cosmic ray ( cr ) acceleration in snrs . we include consistent numerical treatment of magnetic field amplification ( mfa ) due to resonant streaming instability . under the assumption that snr g1.9 + 0.3 is the result of a type ia supernova explosion located near the galactic centre , using widely accepted values for explosion energy 10 erg and ejecta mass 1.4 , the non - thermal continuum radio emission is calculated . the main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution . we estimate that the snr is now 120 yr old , expanding in an ambient density of 0.02 , and explain its steep radio spectral index only by means of efficient non - linear diffusive shock acceleration ( nldsa ) . we also make comparison between simulations and observations of this young snr , in order to test the models and assumptions suggested . our model prediction of a radio flux density increase of 1.8 per cent yr during the past two decades agrees well with the measured values . we synthesize the synchrotron spectrum from radio to x - ray and it fits well the very large array , molonglo observatory synthesis telescope , effelsberg , _ chandra _ and nustar measurements . we also propose a simplified evolutionary model of the snr in gamma rays and suggest it may be a promising target for gamma - ray observations at tev energies with the future generation of instruments like cherenkov telescope array . snr g1.9 + 0.3 is the only known galactic snr with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now . we conclude that this is a general property of snrs in free expansion phase . [ firstpage ] acceleration of particles hydrodynamics radiation mechanisms : non - thermal cosmic rays ism : individual objects : g1.9 + 0.3 ism : supernova remnants .
1610.08779	i	suppose we have a collection of units we want to rank by a certain feature of each unit : for example , we may wish to rank genes by the risk they cause of a particular condition ; we may wish to rank sportsmen by their success - rate at particular standardised trials ; we may wish to rank business opportunities by the profit they will generate . this is a very common inference problem first studied as a formal statistical problem by bechhofer ( 1954 ) and by gupta ( 1956 ) . typically , for each unit we wish to rank , we will have some data on the associated feature , but will not know the true value of that feature . based on our data , we will have a point estimate for the feature , and an associated error distribution . the amount of data we might have for different units can vary wildly , meaning that the associated error distributions can be very different for different units . this means that when we select the top units using only our point estimates , the units for which we have largest errors have a higher chance of appearing among the top units , because a large error increases the chance of the point estimate being large . we are therefore likely to select a large number of false positives if we select based solely on the point estimates . we can illustrate this with a simple example . suppose we have 300 coins , we toss 100 of them six times each , 100 of them eight times each , and the remaining 100 of them ten times each , and rank the coins by the proportion of heads observed . if the coins are all fair , then among the 100 that we toss six times each , there is likely to be at least one that achieves 100% heads . among the 100 that we toss eight times , there might be one that achieves 100% heads , and there are likely to be several that achieve 87.5% heads . among the 100 that we toss ten times each , it is fairly unlikely than any will exceed 80% , so the highest ranked units will almost certainly come from among the coins that we toss only six times . that is , the highest ranked units are almost all false - positives arising only out of chance . this is still true , even if one or more of the coins that are tossed ten times have a slightly higher probability of heads . on the other hand , if our main aim is to avoid false positives , we could use a testing - based approach , where for each unit , we perform an hypothesis test of whether the unit has some null status for example whether the probability of heads is 0.5 . we can then rank by the @xmath0-values of these tests . this has the advantage of minimising false positives , but in many cases there are a large number of true positives , but only a few of them are truly important . if we apply the testing approach , we will often select the units on which we have collected most data , simply because the more data we have , the more evidence that they are not null cases . this may lead to neglecting some units which have much higher underlying value , but for which we have less data . other approaches to the problem mainly take a bayesian approach . they assume that the true values of the relevant feature fall under some distribution . we can estimate this underlying distribution from all the data points . then for each observed unit , we use this distribution as a prior to estimate a posterior distribution of the true value for this unit . we then perform our ranking based on these posterior distributions and a choice of loss function . there are a range of different methods based on different loss functions . for example , posterior expected rank ( laird and louis , 1989 ) use a loss function the squared difference between the true rank of a unit ( based on the actual value of the feature ) and the estimated rank . the @xmath1-values method ( henderson and newton , 2015 ) , corresponds to a loss function the sum of absolute differences between estimated rank and true rank . both of these loss functions are based entirely upon ranks , with no consideration of the actual true values . that is , they consider mis - ranking two units with almost identical true values to be as bad as mis - ranking units with very different true values . for the vast majority of practical ranking problems , this will not be the case . gelman and price ( 1999 ) present the interesting case of looking for spatial patterns among the top - ranked units , where artificial patterns can arise from patterns in available sample sizes . for their purposes , the ideal ranking method would be in such a way that the distribution of rank is the same for all values of standard error . for a known prior , it is possible to calculate this rank , though we are not aware of any work applying such a ranking method . however , methods with loss functions based only on rank , rather than value might be expected to perform better on this criterion , since all errors in ranking can cause this issue equally . the aim of a ranking analysis is often to maximise the average true value from the selected units . for instance , in the business profit example , the aim would be to maximise the expected total profit . for these purposes , the loss function is the difference between the largest true values and the true values of selected units . this loss function is introduced in gupta and hsiao ( 1983 ) , with some additional thought given to the situation where the loss is different for the case of omitting a variable that should be included , from the case of including a variable that should be omited . they show that for this loss function with known prior the bayes rule is to rank by posterior mean ( though they are not very explicit about this , and include some unnecessary hypotheses ) . this posterior mean ranking is used for example in aitkin and longford ( 1986 ) . a range of other loss functions have also been considered , for example , lin _ et al_. ( 2006 ) summarise a range of choices of loss function . for this paper , we will be focussing on the posterior mean ranking method , and its corresponding loss function , although many of our methods can be easily adapted to other bayesian ranking methods . the key difficulty in bayesian ranking methods is to choose the form of the prior . two common choices are the conjugate prior ( which for normal error is normal ) , and a non - parametric prior , which can be calculated using the results of laird ( 1978 ) . figure [ motivatingproblem ] shows the sort of problem that can arise with this approach . the lines on that figure show points that are ranked equally by posterior mean under a normal prior estimated from the whole dataset . as can be seen in that plot , a lot of emphasis gets placed on points with small variance . the reason is that the normal prior is light - tailed , so large true values are deemed implausible , and discounted . however , the true prior distribution seems to be more heavy - tailed than the normal , so larger values should not be discounted so much . for example , consider the point in the red circle . while it does have a larger standard error , it is very significantly non - zero , and it is likely that the true log - odds ratio is high . intuitively , we would probably want to rank this data point among the very top - ranked units . however , the posterior mean under the normal prior ranks it below a lot of other points which , while certainly significantly non - zero , have very small effect size . for practical purposes , this is not desirable . we are usually interested in units with a large effect size . the aim of this paper is to study the effect that choice of prior can have on the ranking problem , and determine suitable choices of prior for such analyses . despite a fair amount of literature on bayesian ranking methods , there has been a noticeable lack of work on the question of choice of prior . in view of the fact that selecting a suitable model for the prior distribution is a very difficult problem in model selection , it is important to consider the effects of a misspecified prior distribution . as will become apparent later , certain choices of prior are inherently more robust to misspecification than others . furthermore , some choices of prior are more sensitive to parameter estimation than others . we describe the objective more formally as follows . a ranking problem consists of a collection of units with unobserved parameters @xmath2 . for each unit , we have a point estimate @xmath3 for @xmath2 . we assume that @xmath3 is normally distributed with mean @xmath2 and variance @xmath4 , where @xmath5 is known . it is straightforward to adapt our approach to a number of other error distributions , but for this paper , we will focus on the normal error case . we assume that the unobserved values @xmath2 follow what we will refer to as the _ true prior _ distribution . we will rank by posterior mean using what we will refer to as the _ estimating prior _ , which may or may not be the same as the true prior . we are interested in how choice of the estimating prior affects the ranking . the structure of this paper is as follows : in section [ theorysection ] , we develop some theory behind posterior mean ranking , and the loss from using the wrong estimating prior . in section [ sectionisotaxes ] , we give a visual representation of the effect of choice of estimating prior on posterior mean ranking . in section [ sectionnonparametric ] , we show that using the non - parametric mle as an estimating prior for posterior mean ranking produces a robust ranking . in section [ simulations ] , we apply our theory to some examples of misspecified estimating priors , and perform a simulation study to confirm the results are as expected . we show that an exponential estimating prior is a good general - purpose choice for posterior mean ranking . in section [ sectionrealdata ] , we apply this to some real data examples where we show the difference in the ranking between using a normal distribution for the estimating prior and using an exponential distribution . in section [ sectionconclusions ] , we make some concluding remarks and suggestions for further investigations .	this problem arises naturally in a number of contexts , such as business , where we may want to rank potential projects by profitability ; or science , where we may want to rank variables potentially associated with some trait by the strength of the association . there are a number of different approaches to this problem , based on different loss functions for mis - ranking units . however , little has been done on the choice of prior distribution . , we look in more detail at the effect of choice of prior distribution on bayesian ranking . we focus on the use of posterior mean for ranking , but many of our conclusions should apply to other ranking criteria , and it is not too difficult to adapt our methods to other choices of prior distributions . empirical bayes ; posterior mean ranking ; choice of prior	the ranking problem is to order a collection of units by some unobserved parameter , based on observations from the associated distribution . this problem arises naturally in a number of contexts , such as business , where we may want to rank potential projects by profitability ; or science , where we may want to rank variables potentially associated with some trait by the strength of the association . most approaches to this problem are empirical bayesian , where we use the data to estimate the hyperparameters of the prior distribution , then use that distribution to estimate the unobserved parameter values . there are a number of different approaches to this problem , based on different loss functions for mis - ranking units . however , little has been done on the choice of prior distribution . typical approaches involve choosing a conjugate prior for convenience , and estimating the hyperparameters by mle from the whole dataset . in this paper , we look in more detail at the effect of choice of prior distribution on bayesian ranking . we focus on the use of posterior mean for ranking , but many of our conclusions should apply to other ranking criteria , and it is not too difficult to adapt our methods to other choices of prior distributions . empirical bayes ; posterior mean ranking ; choice of prior
0809.3805	i	interest in the electromagnetic production of strangeness from few nucleon targets , such as the proton and the deuteron , dates back to the 1960 s @xcite , but it is comparatively recently that high quality data , suitable for quantitatively testing theoretical models , has become available @xcite . the strangeness degree of freedom imparts to these reactions the potential to provide fundamental information concerning both the strong and electromagnetic interactions beyond that obtainable from reactions involving just the non - strange baryons . within an effective lagrangian model , one could use these reactions to search for baryon resonances that decay to strange particles and possibly test su(3 ) symmetry relations among the couplings of resonances within the same su(3 ) multiplets . by comparing photoproduction and electroproduction results , one might be able to extract information concerning the electromagnetic form factors of baryon resonances . finally , with the aid of a quantitative model for electromagnetic strangeness production from the proton , one could , within the impulse approximation , use results for strangeness production from the deuteron and other light nuclei to study final state interactions involving the @xmath9 and @xmath4 baryons . much of the theoretical work over the past 20 years or so has been based on effective lagrangian models @xcite . recently , there have been several coupled channel analyses @xcite that have revealed the need for resonances that had not been previously included in many of the effective lagrangian models . until recently , the fits and models were largely based on older data , and often combined photoproduction data and electroproduction data to generate the fits . more recent fits have made use of various combinations of recent data from the saphir @xcite , clas @xcite , leps @xcite , and graal @xcite collaborations . in ref . @xcite , it was suggested that the photoproduction data and the electroproduction data should _ not _ be fit together ; rather one should first generate a model for the basic reaction using photoproduction data alone and then use that model , in conjunction with electroproduction data , to obtain information concerning the electromagnetic form factors of the various resonances in the model . this consideration , along with the abundance of new data , particularly , polarization data , has motivated us to develop a new model for the reaction @xmath0 over the energy range from threshold up to a center - of - momentum ( c.m . ) energy of 2.2 gev . although the clas data extends up to 2.6 gev , the lack of @xmath10-channel resonances in our model with masses above 2.2 gev precludes a reliable treatment of the higher energy data . as discussed in sec . [ sec - results ] , the fits involve a subtle interference between @xmath10-channel contributions to the reaction on the one hand and @xmath11 and @xmath12-channel contributions on the other hand , which , to be effective , requires that the @xmath10-channel resonances included in a particular fit have masses spanning the whole energy range of that fit . the model is similar to that described in refs . @xcite , but has been expanded to include spin @xmath2 baryon resonances in both the @xmath10 and @xmath11-channels , in addition to the spin @xmath13 and spin @xmath14 resonances included in the earlier work . the present model also includes several higher energy , less well - established resonances in the @xmath10-channel that were not included in the earlier work . finally , the fits described here are much more elaborate than those described in refs . @xcite in that both single and double polarization data are included in the present fits . the reaction model is described in some detail in sec . [ sec - model ] . two separate fits were generated . the first fit has su(3 ) symmetry constraints imposed on the born terms in all three channels . these constraints , along with inputted empirical values for the baryon magnetic moments , require particular relationships between the various born terms and also , in conjunction with other considerations , provide a range of values for the @xmath15 coupling . this is discussed more fully in sec . [ sec - fitting ] . in the second fit , the @xmath15 coupling was allowed to move outside the su(3 ) symmetry range and assume whatever value yielded the best fit to the data . the second fit obtained is nearly identical to the first fit and yielded a @xmath7 per degree of freedom that differs from that of the first fit by less than @xmath16 . for these reasons , only results derived from the first fit are presented here . we have used all recently published results for the spin observables , @xmath3 @xcite , @xmath4 @xcite , @xmath5 and @xmath6 @xcite in our fits . to avoid difficulties associated with inconsistencies between different data sets @xcite , only the most recent cross section data from the clas collaboration @xcite were used in the fits . further details concerning the fitting procedure are contained in sec . [ sec - fitting ] . the resulting fit , along with several figures illustrating the quality of the fits , are presented and discussed in sec . [ sec - results ] . [ sec - results ] also contains some concluding remarks and a brief discussion of future work .	the reaction has been investigated over the center - of - momentum energy , , range from threshold up to 2.2 gev in a tree - level effective lagrangian model that incorporates most of the well - established baryon resonances with spins equal to or below . two different fits were obtained : one that incorporates su(3 ) symmetry constraints on the born contributions to the reaction amplitude and one in which these constraints are relaxed . explicit numerical results are given only for the first fit since the two fits gave nearly identical results for the observables and the per degree of freedom obtained with the second fit was only marginally better than that of the first fit ( better ) . results are presented for the fitted observables at several different energies and center - of - momentum ( c.m . )	the reaction has been investigated over the center - of - momentum energy , , range from threshold up to 2.2 gev in a tree - level effective lagrangian model that incorporates most of the well - established baryon resonances with spins equal to or below . four less well - established nucleon resonances of higher mass are also included . the fitted parameters consist , for each resonance included , of the products of the coupling strengths at the electromagnetic and strong interaction vertices and , for the less - established nucleon resonances , the total decay width . for the well - established nucleon resonances , the energy and momentum dependence of the widths is treated within a dynamical model that is normalized to give the empirical decay branching ratios on the resonance mass shells . for the less - established resonances , the total decay width is treated as a single parameter independent of the reaction kinematics . the model is used to fit recent data for the unpolarized differential cross section ( clas ) , the induced hyperon polarization asymmetry , ( clas , graal , and saphir ) , the beam spin asymmetry , ( leps ) , and the double polarization observables and ( clas ) . two different fits were obtained : one that incorporates su(3 ) symmetry constraints on the born contributions to the reaction amplitude and one in which these constraints are relaxed . explicit numerical results are given only for the first fit since the two fits gave nearly identical results for the observables and the per degree of freedom obtained with the second fit was only marginally better than that of the first fit ( better ) . results are presented for the fitted observables at several different energies and center - of - momentum ( c.m . ) frame kaon angles .
1105.0593	i	the discovery of neutrino mass has provided a wealth of information regarding the flavour structure of nature ( for reviews see @xcite ; for the latest global fit see @xcite ) . however , key questions regarding the neutrino sector remain unanswered and , in particular , the underlying mechanism responsible for neutrino mass remains elusive . the seesaw mechanism provides a simple explanation for the lightness of the known neutrinos @xcite . in its standard implementation one assumes @xmath7 , where @xmath8 is the neutrino dirac mass , @xmath9 is the singlet majorana mass and @xmath10 is the @xmath11 boson mass . the result is a light standard model ( sm ) neutrino with mass @xmath12 and a heavy sterile neutrino with mass @xmath13 . despite the simplicity of this approach , it offers little hope of being experimentally verified due to the invocation of the typically ( very ) large scale @xmath9 . a number of alternative mechanisms invoke new physics to explain neutrino masses without relying on a large uv scale . these offer the advantage of being experimentally verifiable and one may hope that the requisite new physics appears at the tev scale . this can happen in models with radiatively - generated neutrino mass @xcite , and the mechanism of mass generation can even be connected to the weak scale in models with coleman - weinberg symmetry breaking @xcite . of course , nature is likely not concerned with our ability to experimentally ascertain its inner workings . nonetheless it is interesting to explore alternative approaches to neutrino mass that may lie within experimental reach ; particularly if they enable a natural realization and/or provide insight into the observed flavour structures . beyond being sm singlets , right - handed neutrinos can form part of a more complicated hidden sector , and may provide a link to the dark / hidden sector of the universe . this feature is used to advantage in models that invoke non - standard properties of the gauge - singlet neutrinos in an effort to understand the origin of neutrino mass . for example , interesting exceptions to the standard seesaw picture arise if the right - handed neutrinos are bulk fields in an extra dimension @xcite or if they are composite objects within a strongly coupled hidden sector @xcite . a recent work has proposed a `` mini - seesaw mechanism '' in which naturally suppressed dirac and ( sterile ) majorana masses are combined to achieve light sm neutrinos via a low - scale seesaw @xcite . this approach borrows elements from both the extra - dimensional scenario and the composite right - handed neutrino approach : the sterile neutrinos are bulk fields in a truncated slice of @xmath14 but , via the ads / cft correspondence @xcite , the model has a dual 4d description in which the right - handed neutrinos are the lightest composites of a strongly coupled hidden sector . a key feature of this approach is the presence of a tower of light ( order gev ) sterile neutrinos that can be thought of as either kaluza - klein modes or higher fermionic resonances of the cft ( with mass gap ) . in this work we consider the detailed bounds on these light sterile - neutrinos . we show that viable parameter space exists in which sm neutrino masses can be successfully generated without recourse to large ( supra - tev ) scales . furthermore , we show that it may be possible to observe the effects of the sterile neutrinos in forthcoming experiments : the most stringent constraints come from the fcnc process @xmath0 and , as we will show , the interesting region of parameter space corresponds to @xmath15 . this is right below the current experimental bound and within the region to be probed by the meg experiment @xcite . the meg collaboration recently reported that the best value for the number of signal events in their maximal likelihood fit is three @xcite . interestingly , this corresponds to @xmath16 which , as we show , is obtained via the mini - seesaw with neutrino yukawa couplings approaching the @xmath17 level . before proceeding we note that bulk gauge - singlet neutrinos in randall - sundrum ( rs ) models @xcite were considered in @xcite and bulk sm fermions in @xcite . subsequent studies of neutrino mass appeared in @xcite and for an incomplete list of recent works in this active field see @xcite . related work on right - handed neutrinos within a strongly coupled cft was undertaken in @xcite . our implementation within a sub - tev scale effective theory differs from these previous works . other works have also considered a low - scale warped hidden sector @xcite and for another use of bulk sterile neutrinos see @xcite . light sterile - neutrinos have been studied extensively within the context of the @xmath18msm @xcite and for a discussion of the low - scale ( gev ) seesaw see @xcite . ref . @xcite contains a review on light steriles and a detailed analysis of the bounds on kk neutrinos in add models appeared in @xcite . a recent work has studied a viable realization of the meg signal in a susy model @xcite and other related recent works include @xcite . the layout of this paper is as follows . section [ sec : setup ] describes the model and outlines the basic neutrino spectrum . in section [ sec : mass_eigenstates ] the sterile neutrino spectrum is considered in more detail and the mixing with the sm is determined . the analysis of the bounds follows . we study the neutrinoless double beta - decay rate and invisible @xmath1-decays in sections [ sec : nubb ] and [ sec : hid_z_decay ] respectively , a number of other bounds on active - sterile neutrino mixing in section [ sec : other_bounds ] ( e.g. collider constraints ) , and the lepton number violating decay @xmath0 in section [ sec : mu_to_e_gamma ] . finally we discuss the prospects for observing invisible higgs decays in section [ sec : higgs_decay ] and conclude in section [ sec : conc ] .	the recently proposed `` mini - seesaw mechanism '' combines naturally suppressed dirac and majorana masses to achieve light standard model neutrinos via a low - scale seesaw . a key feature of this approach is the presence of multiple light ( order gev ) sterile - neutrinos that mix with the standard model . in this work we show that viable parameter space exists and that , interestingly , key observables can lie just below current experimental sensitivities . neutrino mass and from a mini - seesaw michael duerr, damien p. george and kristian l. mcdonald + max - planck - institut fr kernphysik , + postfach 10 39 80 , 69029 heidelberg , germany + nikhef theory group , science park 105 , + 1098 xg amsterdam , the netherlands +	the recently proposed `` mini - seesaw mechanism '' combines naturally suppressed dirac and majorana masses to achieve light standard model neutrinos via a low - scale seesaw . a key feature of this approach is the presence of multiple light ( order gev ) sterile - neutrinos that mix with the standard model . in this work we study the bounds on these light sterile - neutrinos from processes like , invisible-decays , and neutrinoless double beta - decay . we show that viable parameter space exists and that , interestingly , key observables can lie just below current experimental sensitivities . in particular , a motivated region of parameter space predicts a branching fraction within the range to be probed by meg . neutrino mass and from a mini - seesaw michael duerr, damien p. george and kristian l. mcdonald + max - planck - institut fr kernphysik , + postfach 10 39 80 , 69029 heidelberg , germany + nikhef theory group , science park 105 , + 1098 xg amsterdam , the netherlands +
astro-ph0209607	c	an x - ray nucleus is detected in all the objects except for ngc 4550 and ngc 5866 . we test whether the detected x - ray sources are the high energy extension of the continuum source which powers the optical emission lines by examining the luminosity ratio @xmath6/@xmath15 . the h@xmath3 luminosities ( @xmath15 ) were taken from ho et al . ( 1997a ) and the reddening was estimated from the balmer decrement for narrow lines and corrected using the reddening curve of cardelli , clayton , & mathis ( 1989 ) , assuming the intrinsic h@xmath3/h@xmath50 flux ratio = 3.1 . the x - ray luminosities ( corrected for absorption ) in the @xmath51 kev band are used . the h@xmath3 luminosities and logarithm of the luminosity ratios @xmath6/@xmath15 are shown in table 5 . the @xmath6/@xmath15 ratios of most objects are in the range of agns ( @xmath52 @xmath6/@xmath15 @xmath16 12 ) and in good agreement with the strong correlation between @xmath6 and @xmath15 for llagns , luminous seyferts , and quasars presented in terashima et al . ( 2000a ) and ho et al . this indicates that their optical emission lines are predominantly powered by a llagn . note that this correlation is not an artifact of distance effects , as shown in terashima et al . ( 2000a ) . the four objects ngc 2787 , ngc 4550 , ngc 5866 , and ngc 6500 , however , have much lower @xmath6/@xmath15 ratios ( @xmath52 @xmath6/@xmath15 .5ex0 ) than expected from the correlation ( @xmath52 @xmath6/@xmath15 @xmath53 ) , and their x - ray luminosities are insufficient to power the h@xmath3 emission ( terashima et al . this x - ray faintness could indicate one or more of several possibilities such as ( 1 ) an agn is the power source , but is heavily absorbed at energies above 2 kev , ( 2 ) an agn is the power source , but is currently switched - off or in a faint state , and ( 3 ) the optical narrow emission lines are powered by some source(s ) other than an agn . we briefly discuss these three possibilities in turn . if an agn is present in these x - ray faint objects and absorbed in the hard energy band above 2 kev , only scattered and/or highly absorbed x - rays would be observed , and then the intrinsic luminosity would be much higher than that observed . this can account for the low @xmath6/@xmath15 ratios and high radio to x - ray luminosity ratios ( @xmath54(5 ghz)/@xmath6 ; table 5 and section 5.3 ) . if the intrinsic x - ray luminosities are about one or two orders of magnitude higher than those observed , as is often inferred for seyfert 2 galaxies ( turner et al . 1997 , awaki et al . 2000 ) , @xmath6/@xmath15 and @xmath54(5 ghz)/@xmath6 become typical of llagns . alternatively , the agn might be turned off or in a faint state , with a higher activity in the past being inferred from the optical emission lines , whose emitting region is far from the nucleus ( e.g. , eracleous et al . also , the radio observations were made a few years before the _ chandra _ ones . this scenario might thus explain their relatively low @xmath6/@xmath15 ratios and their relatively high @xmath55/@xmath6 ratios . if this is the case , the size of the radio core can be used to constrain the era of the active phase in the recent past . the upper limits on the size of the core estimated from the beam size ( @xmath56 2.5 mas ) are 0.16 , 0.19 , and 0.48 pc for ngc 2787 , ngc 5866 , and ngc 6500 , respectively ( falcke et al . therefore , the agn must have been active until @xmath570.52 , @xmath570.60 , and @xmath571.6 years , respectively , before the vlba observations ( made in 1997 june ) and inactive at the epochs ( 2000 jan 2002 jan , see table 1 ) of the x - ray observations . this is an ad hoc proposal and such abrupt declines of activity are quite unusual , but it can not be completely excluded . it may also be possible that the ionized gas inferred from the optical emission lines is ionized by some sources other than an agn , such as hot stars . if the observed x - rays reflect the intrinsic luminosities of the agn , a problem with the agn scenario for the three objects ngc 2787 , ngc 5866 , and ngc 6500 is that these galaxies have very large @xmath18(5 ghz)/@xmath6 ratios , and would thus be among the radio loudest llagns . the presence of hot stars in the nuclear region of ngc 6500 is suggested by uv spectroscopy ( maoz et al . maoz et al . ( 1998 ) studied the energy budget for ngc 6500 by using the h@xmath3 and uv luminosity at 1300 a and showed that the observed uv luminosity is insufficient to power the h@xmath3 luminosity even if a stellar population with the salpeter initial mass function and a high mass cutoff of 120@xmath58 are assumed . this result indicates that a power source in addition to hot stars must contribute significantly , and supports the obscured agn interpretation discussed above . the first possibility , i.e. , an obscured low - luminosity agn as the source of the x - ray emission , seems preferable for ngc 2787 , ngc 5866 and ngc 6500 , although some other source(s ) may contribute to the optical emission lines . additional lines of evidence which support the presence of an agn include the fact that all three of these galaxies ( ngc 2787 , ngc 5866 , and ngc 6500 ) have vlbi - detected , sub - pc scale , nuclear radio core sources ( falcke et al . 2000 ) , a broad h@xmath3 component ( in ngc 2787 , and an ambiguous detection in ngc 5866 ; ho et al . 1997b ) , a variable radio core in ngc 2787 , and a jet - like linear structure in a high - resolution radio map of ngc 6500 with the vlba ( falcke et al . only an upper limit to the x - ray flux is obtained for ngc 5866 . if an x - ray nucleus is present in this galaxy and its luminosity is only slightly below the upper limit , this source could be an agn obscured by a column density @xmath10@xmath59 @xmath12 or larger . if the apparent x - ray luminosity of the nucleus of ngc 5866 is _ much _ lower than the observed upper limit , and the intrinsic x - ray luminosity conforms to the typical @xmath6/@xmath15 ratio for llagn ( @xmath52 @xmath6/@xmath15 @xmath60 ) , then the x - ray source must be almost completely obscured . the optical classification ( transition object ) suggests the presence of an ionizing source other than an agn , so the low observed @xmath6/@xmath15 ratio could alternatively be a result of enhanced h@xmath3 emission powered by this other ionizing source . the x - ray results presented above show that the presence of a flat ( or inverted ) spectrum compact radio core is a very good indicator of the presence of an agn even if its luminosity is very low . on the other hand , ngc 4550 , which does not possess a radio core , shows no evidence for the presence of an agn and all the three possibilities discussed above are viable . if the _ rosat _ detection is real ( halderson et al . 2001 ) , the time variability between the _ rosat _ and _ chandra _ fluxes may indicate the presence of an agn ( see appendix ) . it is notable that type 2 liners without a flat spectrum compact radio core may be heterogeneous in nature . for instance , some liner 2s without a compact radio core ( e.g. , ngc 404 and transition 2 object ngc 4569 ) are most probably driven by stellar processes ( maoz et al . 1998 ; terashima et al . 2000b ; eracleous et al . 2002 ) . in our sample , we found at least three highly absorbed llagns ( ngc 3169 , ngc 3226 , and ngc 4548 ) . in addition , if the x - ray faint objects discussed in section 5.1 are indeed agns , they are most probably highly absorbed with @xmath10@xmath61 @xmath12 . among these absorbed objects , ngc 2787 is classified as a liner 1.9 , ngc 3169 , ngc 4548 , and ngc 6500 as liner 2s , and ngc 5866 as a transition 2 object . thus , heavily absorbed liner 2s , of which few are known , are found in the present observations demonstrating that radio selection is a valuable technique for finding obscured agns . along with heavily obscured llagns known in low - luminosity seyfert 2s ( e.g. , ngc 2273 , ngc 2655 , ngc 3079 , ngc 4941 , and ngc 5194 ; terashima et al . 2002a ) , our observations show that at least some type 2 llagns are simply low - luminosity counterparts of luminous seyferts in which heavy absorption is often observed ( e.g. , risaliti , maiolino , & salvati 1999 ) . however , some liner 2s ( e.g. , ngc 4594 , terashima et al . 2002a ; ngc 4374 , finoguenov & jones 2001 ; ngc 4486 , wilson & yang 2002 ) and low - luminosity seyfert 2s ( ngc 3147 ; section 4 and appendix ) show no strong absorption . therefore , the orientation - dependent unified scheme ( e.g. , antonucci 1993 ) does not always apply to agns in the low - luminosity regime , as suggested by terashima et al . . combination of x - ray and radio observations is valuable for investigating a number of areas of agn physics , including the `` radio loudness '' , the origin of jets , and the structure of accretion disks . low - luminosity agns ( liners and low - luminosity seyfert galaxies ) are thought to be radiating at very low eddington ratios ( @xmath62/@xmath63 ) and may possess an advection - dominated accretion flow ( adaf ; see e.g. , quataert 2002 for a recent review ) . a study of radio loudness in llagns can constrain the jet production efficiency by an adaf - type disk . earlier studies have suggested that llagns tend to be radio loud compared to more luminous seyferts based on the spectral energy distributions of seven llagns ( ho 1999 ) and , for a larger sample , on the conventional definition of radio loudness @xmath64(5 ghz)/@xmath8(b ) ( the subscript `` o '' , which stands for optical , is usually omitted but we use it here to distinguish from @xmath9 see below ) , with @xmath65 being radio loud ( kellermann et al . 1989 , 1994 ; visnovsky et al . 1992 ; stocke et al . 1992 ; ho & peng 2001 ) . ho & peng ( 2001 ) measured the luminosities of the nuclei by spatial analysis of optical images obtained with _ hst _ to reduce the contribution from stellar light . a caveat in the use of optical measurements for the definition of radio loudness is extinction , which will lead to an overestimate of @xmath66 if not properly allowed for . although ho & peng ( 2001 ) used only type 11.9 objects , some objects of these types show high absorption columns in their x - ray spectra . in this subsection , we study radio loudness by comparing radio and hard x - ray luminosities . since the unabsorbed luminosity for objects with @xmath10 .5ex@xmath11 @xmath12 can be reliably measured in the 210 kev band , which is accessible to _ asca _ , _ xmm - newton _ , and _ chandra _ , and such columns correspond to @xmath21 .5ex50 mag , it is clear that replacement of optical by hard x - ray luminosity potentially yields considerable advantages . in addition , the high spatial resolutions of _ xmm - newton _ and especially _ chandra _ usually allow the nuclear x - ray emission to be identified unambiguously , while the optical emission of llagn can be confused by surrounding starlight . in the following analysis , radio data at 5 ghz taken from the literature are used since fluxes at this frequency are widely available for various classes of objects . we used primarily radio luminosities obtained with the vla at .5ex@xmath67 resolution for the present sample . high resolution vla data at 5 ghz are not available for several objects . for four such cases , vlba observations at 5 ghz with 150 mas resolution are published in the literature ( falcke et al . 2000 ) and are used here . for two objects , we estimated 5 ghz fluxes from 15 ghz data by assuming a spectral slope of @xmath68 ( cf . nagar et al . the radio luminosities used in the following analysis are summarized in table 5 . since our sample is selected based on the presence of a compact radio core , the sample could be biased to more radio loud objects . therefore , we constructed a larger sample by adding objects taken from the literature for which 5 ghz radio , 210 kev x - ray , and @xmath69 measurements are available . first , we introduce the ratio @xmath70(5 ghz)/@xmath6 as a measure of radio loudness and compare the ratio with the conventional @xmath69 parameter . the x - ray luminosity @xmath6 in the 210 kev band ( source rest frame ) , corrected for absorption , is used . , which utilizes monochromatic b - band luminosities . this alternative provides completely identical results if the x - ray spectral shape is known and the range of spectral slopes is not large . for example , the conversion factor @xmath8(2 kev)/@xmath6 is 0.31 , 0.26 , and 0.22 kev@xmath2 for photon indices of 2 , 1.8 , and 1.6 , respectively , and no absorption . ] we examine the behavior of @xmath9 using samples of agn over a wide range of luminosity , including llagn , the seyfert sample of ho & peng ( 2001 ) and pg quasars which are also used in their analysis . @xmath69 parameters and radio luminosities were taken from ho & peng ( 2001 ) for the seyferts and kellermann et al . ( 1989 ) for the pg sample . the values of @xmath69 in kellermann et al . ( 1989 ) have been recalculated by using only the core component of the radio luminosities . the optical and radio luminosities of the pg quasars were calculated assuming @xmath71 and @xmath72 ( @xmath73 ) . the x - ray luminosities ( mostly measured with _ asca _ ) were compiled from terashima et al . ( 2002b ) , weaver , gelbord , & yaqoob ( 2001 ) , george et al . ( 2000 ) , reeves & turner ( 2000 ) , iwasawa et al . ( 1997 , 2000 ) , sambruna , eracleous , & mushotzky ( 1999 ) , nandra et al . ( 1997 ) , smith & done ( 1996 ) , and cappi et al . note that only a few objects ( ngc 4565 , ngc 4579 , and ngc 5033 ) in our radio selected sample have reliable measurements of nuclear @xmath8(b ) . 3 . compares the parameters @xmath69 and @xmath9 for the seyferts and pg sample . these two parameters correlate well for most seyferts . some seyferts have higher @xmath69 values than indicated by most seyferts . this could be a result of extinction in the optical band . seyferts showing x - ray spectra absorbed by a column greater than @xmath74 @xmath12 ( ngc 2639 , 4151 , 4258 , 4388 , 4395 , 5252 , and 5674 ) are shown as open circles in fig . at least four of them have a value of @xmath69 larger than indicated by the correlation . the correlation between @xmath75 and @xmath76 for the less absorbed seyferts can be described as @xmath75 = 0.88 @xmath77 + 5.0 . according to this relation , the boundary between radio loud and radio quiet object ( @xmath75 = 1 ) corresponds to @xmath78 . the values of @xmath69 and @xmath9 for a few obscured seyferts are consistent with the correlation , indicating that optical extinction is not perfectly correlated with the absorption column density inferred from x - ray spectra . the pg quasars show systematically lower @xmath69 values than those of seyferts at a given @xmath76 . for the former objects , @xmath79 corresponds to @xmath80 . this apparently reflects a luminosity dependence of the shape of the sed : luminous objects have steeper optical - x - ray slopes @xmath81 ( @xmath82 ; e.g. , elvis et al . 1994 , brandt , laor , & wills 2000 ) , where @xmath83 is often measured as the spectral index between 2200 a and 2 kev , while less luminous agns have @xmath84 ( ho 1999 ) . this is related to the fact that luminous objects show a more prominent `` big blue bump '' in their spectra . fig . 8 of ho ( 1999 ) demonstrates that low - luminosity objects are typically 11.5 orders of magnitude fainter in the optical band than luminous quasars for an given x - ray luminosity . note that none of the pg quasars used here shows a high absorption column in its x - ray spectrum below 10 kev . the definition of radio loudness using the hard x - ray flux ( @xmath85 ) appears to be more robust than that using the optical flux because x - rays are less affected by both extinction at optical wavelengths and the detailed shape of the blue bump , as noted above . further , measurements of nuclear x - ray fluxes of seyferts and llagns with _ chandra _ are easier than measurements of nuclear optical fluxes , since in the latter case the nuclear light must be separated from the surrounding starlight , a difficult process for llagns . 4 shows the x - ray luminosity dependence of @xmath9 . in this plot , the llagn sample discussed in the present paper is shown in addition to the seyfert and pg samples used above . this is an `` x - ray version '' of the @xmath75-@xmath86 plot ( fig . 4 in ho & peng 2001 ) . radio galaxies taken from sambruna et al . ( 1999 ) are also added and we use radio luminosities from the core only . our plot shows that a large fraction ( @xmath87% ) of llagns ( @xmath6@xmath88 ergs s@xmath2 ) are `` radio loud '' . this is a confirmation of ho & peng s ( 2001 ) finding . note , however , that our sample is not complete in any sense , and this radio - loud fraction should be measured using a more complete sample . since radio emission in llagns is likely to be dominated by emission from jets ( nagar et al . 2001 ; ulvestad & ho 2001 ) , these results suggest that , in llagn , the fraction of the accretion energy that powers a jet , as opposed to electromagnetic radiation , is larger than in more luminous seyfert galaxies and quasars . since llagns are thought to have an adaf - type accretion flow , such might indicate that an adaf can produce jets more efficiently than the geometrically thin disk believed present in more luminous seyferts . the three llagns with the largest @xmath9 in fig . 4 are the three x - ray faint objects discussed in section 5.1 ( ngc 2787 , ngc 5866 , and ngc 6500 ) and which are most probably obscured agns . if their intrinsic x - ray luminosities are 12 orders of magnitude higher than those observed , their values of @xmath9 become smaller by this factor and are then in the range of other llagns . even if we exclude these three llagns , the radio loudness of llagns is distributed over a wide range : the radio - loudest llagns have @xmath9 values similar to radio galaxies and radio - loud quasars , while some llagns are as radio quiet as radio - quiet quasars . a comparison with blazars is of interest to compare our sample with objects for which the nuclear emission is known to be dominated by a relativistic jet and thus strongly beamed . the average @xmath89 for high - energy peaked bl lac objects ( hbls ) , low - energy peaked bl lac objects ( lbls ) , and flat spectrum radio quasars ( fsrqs ) are 3.10 , 1.27 , and 0.95 , respectively , where we used the average radio and x - ray luminosities for a large sample of blazars given in table 3 of donato et al . the average @xmath76 for hbls is similar to that for llagns in our sample , while the latter two classes are about two orders of magnitude more radio loud than llagns . although llagns and hbls have similar values of @xmath89 , the spectral slope in the x - ray band is different : llagns have a photon index in the range 1.72.0 ( see also terashima et al . 2002 ) , while hbls usually show steeper spectra ( photon index @xmath32 2 , e.g. , fig . 1 in donato et al . 2001 ) , and the x - ray emission is believed to be dominated by synchrotron radiation . furthermore , blazars with a lower bolometric luminosity tend to have a synchrotron peak at a higher frequency and a steeper x - ray spectral slope than higher bolometric luminosity blazars ( donato et al . 2001 ) . we also constructed an @xmath9-@xmath6 plot ( fig . 5 ) using the _ total _ radio luminosities of the radio source ( i.e. including the core , jets , lobes , and hot spots , if present ) . the radio data were compiled from vron - cetty & vron ( 2001 ) , kellermann et al . ( 1989 ) , and sambruna et al . the pg sample and other quasars are shown with different symbols . this plot appears similar to fig . 4 for llagns , seyferts , and radio - quiet quasars since these objects do not possess powerful jets or lobes and off - nuclear radio emission associated with the agn is generally of low luminosity ( ulvestad & wilson 1989 , nagar et al . 2001 , ho & ulvestad 2001 , kellermann et al . 1989 ) . on the other hand , radio galaxies have powerful extended radio emission and consequently the @xmath9 values calculated using the total radio luminosities become higher than if only nuclear luminosities are used . we used the same x - ray luminosities as in fig . 4 , because jets , lobes , and hot spots are almost always much weaker than the nucleus in x - rays . in fact , in our observations of llagns , we found no extended emission directly related to the agn . thus , the differences between fig . 4 and fig . 5 result from the extended radio emission .	the results of _ chandra _ snapshot observations of 11 liners ( low - ionization nuclear emission - line regions ) , three low - luminosity seyfert galaxies , and one -liner transition object are presented . our sample consists of all the objects with a flat or inverted spectrum compact radio core in the vla survey of 48 low - luminosity agns ( llagns ) by nagar et al . the x - ray spectra are generally steeper than expected from thermal bremsstrahlung emission from an advection - dominated accretion flow ( adaf ) . the x - ray to h luminosity ratios for 11 out of 14 objects are in good agreement with the value characteristic of llagns and more luminous agns , and indicate that their optical emission lines are predominantly powered by a llagn . for three objects , this ratio is less than expected . comparing with properties in other wavelengths , we find that these three galaxies are most likely to be heavily obscured agn . in contrast to the usual definition of radio loudness ((5 ghz)/(b ) ) , can be used for heavily obscured ( .5ex , mag ) nuclei . further , with the high spatial resolution of _ chandra _ , the nuclear x - ray emission of llagns is often easier to measure than the nuclear optical emission .	the results of _ chandra _ snapshot observations of 11 liners ( low - ionization nuclear emission - line regions ) , three low - luminosity seyfert galaxies , and one -liner transition object are presented . our sample consists of all the objects with a flat or inverted spectrum compact radio core in the vla survey of 48 low - luminosity agns ( llagns ) by nagar et al . ( 2000 ) . an x - ray nucleus is detected in all galaxies except one and their x - ray luminosities are in the range to ergs s . the x - ray spectra are generally steeper than expected from thermal bremsstrahlung emission from an advection - dominated accretion flow ( adaf ) . the x - ray to h luminosity ratios for 11 out of 14 objects are in good agreement with the value characteristic of llagns and more luminous agns , and indicate that their optical emission lines are predominantly powered by a llagn . for three objects , this ratio is less than expected . comparing with properties in other wavelengths , we find that these three galaxies are most likely to be heavily obscured agn . we use the ratio(5 ghz)/ , where is the luminosity in the 210 kev band , as a measure of radio loudness . in contrast to the usual definition of radio loudness ((5 ghz)/(b ) ) , can be used for heavily obscured ( .5ex , mag ) nuclei . further , with the high spatial resolution of _ chandra _ , the nuclear x - ray emission of llagns is often easier to measure than the nuclear optical emission . we investigate the values of for llagns , luminous seyfert galaxies , quasars and radio galaxies and confirm the suggestion that a large fraction of llagns are radio loud .
astro-ph0209607	i	fourteen galaxies with a nuclear radio source having a flat or inverted spectrum have been observed with _ chandra _ with a typical exposure time of 2 ksec . an x - ray nucleus is detected in all but one object ( ngc 5866 ) . 11 galaxies have x - ray and h@xmath3 luminosities in good accord with the correlation known for agns over a wide range of luminosity , which indicates that these objects are agns and that the agn is the dominant power source of their optical emission lines . their x - ray luminosities are between @xmath0 and @xmath1 ergs s@xmath2 . the three objects ngc 2787 , ngc 5866 , and ngc 6500 have significantly lower x - ray luminosities than expected from the @xmath6-@xmath15 correlation . various observations suggest that these objects are most likely to be heavily obscured agns . these observational results show that radio and hard x - ray observations provide an efficient way to find llagn in nearby galaxies , even if the nuclei are heavily obscured . one object ( the liner 2 ngc 4550 ) , which does not show a radio core , was also observed for comparison . no x - ray nucleus is detected . if the x - ray source detected in this galaxy with _ rosat _ is indeed the nucleus , the nucleus must be variable in x - rays , which would indicate the presence of an agn . we have used the ratio @xmath90(5 ghz)/@xmath6 as a measure of radio loudness and found that a large fraction of llagns are radio loud . this confirms earlier results based on nuclear luminosities in the optical band , but our results based on hard x - ray measurements are much less affected by obscuration and the detailed shape of the `` big blue bump '' . we speculate that the increase in @xmath9 as @xmath6 decreases below @xmath91 ergs s@xmath2 may result from the presence of an advection - dominated accretion flow in the inner part of the accretion flow in low - luminosity objects . however , the steep x - ray spectra in our sample of llagns rule out high temperature thermal bremsstrahlung as the x - ray emission mechanism . is supported by the japan society for the promotion of science postdoctoral fellowship for young scientists . this research was supported by nasa through grants nag81027 and nag81755 to the university of maryland .	we use the ratio(5 ghz)/ , where is the luminosity in the 210 kev band , as a measure of radio loudness . we investigate the values of for llagns , luminous seyfert galaxies , quasars and radio galaxies and confirm the suggestion that a large fraction of llagns are radio loud .	the results of _ chandra _ snapshot observations of 11 liners ( low - ionization nuclear emission - line regions ) , three low - luminosity seyfert galaxies , and one -liner transition object are presented . our sample consists of all the objects with a flat or inverted spectrum compact radio core in the vla survey of 48 low - luminosity agns ( llagns ) by nagar et al . ( 2000 ) . an x - ray nucleus is detected in all galaxies except one and their x - ray luminosities are in the range to ergs s . the x - ray spectra are generally steeper than expected from thermal bremsstrahlung emission from an advection - dominated accretion flow ( adaf ) . the x - ray to h luminosity ratios for 11 out of 14 objects are in good agreement with the value characteristic of llagns and more luminous agns , and indicate that their optical emission lines are predominantly powered by a llagn . for three objects , this ratio is less than expected . comparing with properties in other wavelengths , we find that these three galaxies are most likely to be heavily obscured agn . we use the ratio(5 ghz)/ , where is the luminosity in the 210 kev band , as a measure of radio loudness . in contrast to the usual definition of radio loudness ((5 ghz)/(b ) ) , can be used for heavily obscured ( .5ex , mag ) nuclei . further , with the high spatial resolution of _ chandra _ , the nuclear x - ray emission of llagns is often easier to measure than the nuclear optical emission . we investigate the values of for llagns , luminous seyfert galaxies , quasars and radio galaxies and confirm the suggestion that a large fraction of llagns are radio loud .
astro-ph0006018	i	if the galactic dark halo were composed entirely of massive compact halo objects ( machos ) , the instantaneous probablity of microlensing ( the `` optical depth '' ) towards the large magellanic cloud ( lmc ) would have been @xmath15 ( pacznski 1986 ) . the most recent observational result for machos with masses up to about 1 @xmath5 is @xmath16 , which comes from an analysis of 5.7 years of lmc microlensing survey data ( alcock et al . thus an all - macho galactic dark halo is ruled out . however , the observed optical depth is significantly higher than the estimate for known galactic and lmc stellar populations , @xmath17 ( alcock et al . the excess lmc microlensing signal may be telling us the macho fraction of the galactic dark halo or revealing gaps in our understanding of the essential structure of the lmc and galaxy . critical discussions of the microlensing optical depth from known stellar populations have developed along two lines . one debate has been about the possible existence of a `` new '' stellar population which would account for the lmc microlensing result . some example suggestions include an intervening dwarf galaxy or tidal stream ( zhao 1998 ; zaritsky & lin 1997 , zaritsky et al . 1999 ) , and a very warped galactic disk ( evans et al . 1998 ) . these hypotheses have been tested , and in some cases ruled out ( alcock et al . 1997 ; beaulieu & sackett 1998 ; bennett 1998 ; gould 1998 , 1999 ; gyuk , flynn , & evans 1999 ; ibata , germaint , & beaulieu 1999 ; johnston 1998 ) . the second debate has been about the importance of lmc star - star `` self - lensing '' ( sahu 1994 ; wu 1994 ) . in particular , although the lmc is well represented by an exponential disk model which often serves as the basis for the self - lensing optical depth calculation , it may exhibit some important detailed structures . our paper is motivated by this lmc self - lensing problem . the line - of - sight velocity dispersion of lmc stars yields a strong constraint on star - star self - lensing from the virialized lmc disk : @xmath18 ( gould 1995 ) . gould s elegant limit is probably uncertain by no more than a factor of @xmath72 . however , several lmc models have been devised which would increase the self - lensing optical depth over the gould limit . one example of a detailed structure that might increase the self - lensing optical depth is a highly - inclined and flared lmc disk ( zhao 1999 ) . it has also been suggested that the oldest lmc disk stars have a very large characteristic scale height , or that the lmc harbors an as yet unseen but massive stellar spheroid 2 - 4 for the former , and a very large m / l for the latter ) , and the density profiles . ] ( e.g. aubourg et al . 1999 ; salati et al . 1999 ; evans & kerins 2000 ) . finally , it is possible that a nonvirialized stellar component ( i.e. , a shroud of tidal debris ; weinberg 2000 ) acts to increase the self - lensing optical depth ( zhao 1998 ) . kinematic studies play a critical role in testing these various proposed lmc models . for example , the flare of the lmc disk may be inferred from its velocity dispersion at different radii , and the existence of a non - equilibrium stellar component lying near the lmc might be proven with a large kinematic survey ( zhao 1999 ; graff et al . 1999 ; see also zaritsky et al . 1999 ; ibata et al . in addition , one could search directly for an lmc stellar population with a velocity dispersion of @xmath750 km s@xmath1 , the prediction for a spheroid or very thick disk . these latter components must be identified before their importance to the self - lensing optical depth can be assessed . the lmc rotation curve provides a framework for detailed kinematic studies such as these . the decomposition of the lmc rotation curve into disk and dark halo components has several implications for microlensing . first , as emphasized by gyuk et al . ( 1999 ) , the total mass of the lmc is an important constraint on self - lensing optical depth calculations . a high - mass model will typically predict a high self - lensing optical depth , with an additional dependence on whether the mass lies mostly in the disk or in a halo . unfortunately , recent analyses of the lmc rotation curve have lead to mass estimates that range over a factor of @xmath74 , which can be attributed primarily to different assumptions about a dark halo ( kim et al . 1998 , kunkel et al . 1997 , schommer et al . second , a massive lmc dark halo might significantly affect the lmc disk kinematics ( e.g. bahcall 1984 ) , with possible consequence for constraints on self - lensing or determining the flare of the disk . the influence of an lmc dark halo on the lmc disk kinematics has not been investigated in detail . we note that the interplay between the disk and dark halo is also of general interest for studies of galaxy formation and evolution . finally , if the lmc has a dark halo with a physical makeup similar to that of the galactic dark halo ( i.e. composed partly of machos ) , the macho fraction of the galactic dark halo implied by the observed optical depth would be lowered ( alcock et al . 2000 ) . motivated by the above considerations , we present a new analysis of the lmc rotation curve . in this work we are particularly concerned with the flare of the lmc disk . however , other issues pertinent to microlensing are discussed as our calculations and analyses permit . we refer extensively to the rotation curve recently presented by kim et al . ( 1998 ) and the impressive radial velocity dataset for lmc carbon stars summarized by kunkel , demers , irwin & albert ( 1997 ; hereafter kdia ) . a significant subset of these latter data are public ( kunkel , irwin & demers 1997 ) , and archived electronically at the cds . we also refer extensively to the analysis of the lmc space motion presented by kroupa & bastian ( 1997 ) . our paper is organized as follows . in 2 , we present the impetus for this work , a comparison of constant - thickness exponential disk models ( with no dark halos ) to the lmc disk velocity dispersions reported by kdia . in 3 , we reanalyze the lmc rotation curve and velocity dispersion curve using archived carbon - star radial - velocity data . in 4 , we present a multi - mass component kinematic model for the lmc . in 5 , we compare our carbon - star rotating disk solution to our model . we discuss the microlensing implications of our analyses in 6 and conclude in 7 .	the rotation curve is well fit by a truncated , finite - thickness exponential disk model with no dark halo , implying a total mass of 5.3 1.0 . our model does not include a nonvirialized component such as tidal debris . the instantaneous probability of microlensing from lmc stars in our model is , where is the disk inclination .	the rotation of the disk of the large magellanic cloud ( lmc ) is derived from the radial velocities of 422 carbon stars ( kunkel , irwin , & demers 1997 , a&as , 122 , 463 ) . new aspects of this analysis include the propagation of uncertainties in the lmc proper motion with a monte carlo , and a self - consistent modeling of the rotation curve and disk kinematics . the lmc rotation curve reaches a maximum circular velocity of 72 7 km s at kpc and then declines . the rotation curve is well fit by a truncated , finite - thickness exponential disk model with no dark halo , implying a total mass of 5.3 1.0 . the velocity dispersion in concentric radial bins from to 5.6 kpc decreases from 22 to 15 km s , then increases to km s at larger radii . constant - thickness disk models in virial equilibrium can not be reconciled with the data even if the effects of lmc or galactic dark halos are included . if the disk is virialized , the scale height rises from = 0.3 to 1.6 kpc over the range of = 0.5 to 5.6 kpc . thus the lmc disk is flared . we model the velocity dispersion at large radii ( 6 kpc ) as a maximal flared disk under the influence of the galactic dark halo , which favors a mean density for the latter of pc at the lmc distance . lmc stellar kinematics play an important role in elucidating the nature of machos , a dark population inferred from lmc microlensing . we have constructed a truncated and flared maximal disk model for the lmc which is kinematically based . our model does not include a nonvirialized component such as tidal debris . the instantaneous probability of microlensing from lmc stars in our model is , where is the disk inclination . our upper limit on the self - lensing optical depth is in good agreement with that obtained from less sophisticated models , and is an order of magnitude too small to account for the macho microlensing signal .
astro-ph0006018	c	the rotation of the disk of the lmc has been derived from the radial velocities of 422 carbon stars ( kunkel , irwin , & demers 1997 ) . we have propogated the uncertainty in the lmc space motion to the lmc rotation curve with a monte carlo calculation . the associated disk velocity dispersions found in each rotating disk zonal solution are less sensitive to systematic uncertainties from the lmc space motion than the circular velocities obtained . we note that our carbon star rotation curve is derived in a manner consistent with the rotation curve analysis by kim et al . ( 1998 ) ; thus our respective results are properly comparable . we have fit our carbon star rotation curve and the rotation curve with a truncated , maximal lmc disk model , yielding a total lmc mass of @xmath143 @xmath3 @xmath140 . we also conclude that the disk of the lmc is flared . extrapolating the flare inferred at small radii ( where tidal perturbations are small ) to the outer - disk , and accounting for the influence of the galactic dark halo , we are able to approximately reproduce the observed disk kinematics . this model favors an isothermal density profile for the galactic dark halo out to a distance of 50 kpc . our truncated and flared maximal disk model yields a limit on the spatially - averaged lmc self - lensing optical depth of @xmath206 . for plausible values of the lmc inclination , this low self - lensing rate compared to the measured microlensing rate allows for the existence of a dark lens population in the galactic halo ( alcock et al . 2000 ) . finally , we caution that we have not included in our analysis ( 1 ) the dynamical effects of an lmc bar , ( 2 ) large - scale non - circular motions , ( 3 ) non - uniform anisotropy of the disk velocity dispersions , or ( 4 ) arbitrary spatial distributions of tidal debris ( i.e. , a polar ring or stars out of virial equilibrium ) . despite these shortcomings , our truncated and flared maximal disk model successfully accounts for the general dynamical characteristics of the lmc , lending inferences from the model high weight .	the rotation of the disk of the large magellanic cloud ( lmc ) is derived from the radial velocities of 422 carbon stars ( kunkel , irwin , & demers 1997 , a&as , 122 , 463 ) . we have constructed a truncated and flared maximal disk model for the lmc which is kinematically based .	the rotation of the disk of the large magellanic cloud ( lmc ) is derived from the radial velocities of 422 carbon stars ( kunkel , irwin , & demers 1997 , a&as , 122 , 463 ) . new aspects of this analysis include the propagation of uncertainties in the lmc proper motion with a monte carlo , and a self - consistent modeling of the rotation curve and disk kinematics . the lmc rotation curve reaches a maximum circular velocity of 72 7 km s at kpc and then declines . the rotation curve is well fit by a truncated , finite - thickness exponential disk model with no dark halo , implying a total mass of 5.3 1.0 . the velocity dispersion in concentric radial bins from to 5.6 kpc decreases from 22 to 15 km s , then increases to km s at larger radii . constant - thickness disk models in virial equilibrium can not be reconciled with the data even if the effects of lmc or galactic dark halos are included . if the disk is virialized , the scale height rises from = 0.3 to 1.6 kpc over the range of = 0.5 to 5.6 kpc . thus the lmc disk is flared . we model the velocity dispersion at large radii ( 6 kpc ) as a maximal flared disk under the influence of the galactic dark halo , which favors a mean density for the latter of pc at the lmc distance . lmc stellar kinematics play an important role in elucidating the nature of machos , a dark population inferred from lmc microlensing . we have constructed a truncated and flared maximal disk model for the lmc which is kinematically based . our model does not include a nonvirialized component such as tidal debris . the instantaneous probability of microlensing from lmc stars in our model is , where is the disk inclination . our upper limit on the self - lensing optical depth is in good agreement with that obtained from less sophisticated models , and is an order of magnitude too small to account for the macho microlensing signal .
0909.0522	i	the first metrics one typically encounters in the study of general relativity are the minkowski spacetime metric and the schwarzschild spacetime metric , the latter given by @xmath0 where @xmath1 is the time coordinate , @xmath2 are spatial coordinates , and @xmath3 is some positive number . this represents the exterior region @xmath4 of a non - rotating black hole of mass @xmath3 in vacuum . a spacelike slice of this lorentzian metric can be obtained by taking a level set of @xmath1 ; under a coordinate transformation @xmath5 , the resulting 3-manifold is isometric to @xmath6 minus the ball of radius @xmath7 about the origin , with the conformally flat metric @xmath8 where @xmath9 is the usual flat metric on @xmath6 and @xmath10 . its boundary is in fact a minimal surface which represents the apparent horizon of the black hole . we will refer to this riemannian metric as the _ schwarzschild metric _ ( of mass @xmath3 ) . consider instead the metric @xmath11 with @xmath12 . this gives a riemannian metric on @xmath6 minus a closed ball of radius @xmath13 about the origin that approaches zero near its inner boundary . one may loosely think of this manifold as a slice of a spacetime with a single `` black hole of negative mass . '' in fact , this metric has a naked singularity , as the singularity on the inner boundary is not enclosed by any apparent horizon . in this paper we introduce a theory of such `` zero area singularities '' ( zas ) , modeled on the `` schwarzschild zas metric '' ( i.e. , @xmath11 with @xmath12 ) , yet far more general . some of the interesting problems we address are : when can such singularities be `` resolved '' ? what is a good definition of the mass of such a singularity ? can the adm mass of an asymptotically flat manifold of nonnegative scalar curvature be estimated in terms of the masses of its singularities ? to say another word about the third question , recall the positive mass theorem of schoen and yau @xcite which states that , under suitable conditions , the adm mass of an asymptotically flat 3-manifold is nonnegative , with zero mass occurring only for the flat metric on @xmath6 . the riemannian penrose inequality @xcite improves this to give a lower bound on the adm mass in terms of the masses of its `` black holes . '' here , the case of equality is attained by the schwarzschild metric with @xmath14 . see appendix a for details on asymptotic flatness and adm mass . the main theorem of this paper is the riemannian zas inequality ( see theorems [ thm_zas_ineq ] and [ thm_zas_ineq_full ] ) , introduced by the first author @xcite . it is an analog of the riemannian penrose inequality , but for zero area singularities instead of black holes . specifically , this inequality gives a lower bound for the adm mass of an asymptotically flat manifold in terms of the masses of its zas . its proof assumes an unproven conjecture ( conjecture [ conj_conformal ] ) regarding the outermost minimal area enclosure of the boundary , with respect to a conformal metric . while the conjecture is known to be true in a number of cases , proving it remains an open problem . although we shall write `` the '' riemannian zas inequality in this paper , we remark that other similar inequalities may be discovered in the future that also deserve this title . table [ table_thms ] illustrates how this theorem fits together with the positive mass theorem and riemannian penrose inequality . .the schwarzschild metric as a case of equality [ cols="<,<,<",options="header " , ] + by the above discussion of capacity , we see that @xmath15 if and only if @xmath16 . by theorem [ thm_pos_cap ] , if @xmath17 , then @xmath18 , since we saw above that the capacity of @xmath19 is positive . we now determine the mass of @xmath19 assuming @xmath20 . the first step is to compute the regular masses of the concentric spheres @xmath21 : @xmath22 we can use lhopital s rule to evaluate this limit ( of the form @xmath23 ) as @xmath24 : @xmath25 this limit is @xmath26 if @xmath27 , finite but nonzero if @xmath28 , and zero if @xmath29 . for @xmath29 , this shows that the mass of @xmath19 is zero . ( it is at least zero by our computation , but it is a priori at most zero . ) for @xmath30 , we claim the mass of @xmath19 is @xmath26 . given any sequence of surfaces @xmath31 converging in @xmath32 to @xmath19 , we will compare them to a sequence of round spheres . let @xmath33 be the minimum value of the @xmath34-coordinate that @xmath35 attains ; then @xmath35 encloses @xmath36 , so @xmath37 . also , since @xmath35 converges in @xmath32 , the ratio of areas @xmath38 converges to 1 . using the proof of theorem [ thm_pos_cap ] , we can estimate the regular mass of @xmath35 : @xmath39 where the last equality comes from equations @xmath40 and @xmath41 . taking @xmath42 of both sides ( and using @xmath43 ) , we have @xmath44 . ( we showed above that this limit is @xmath26 for concentric round spheres . ) thus , @xmath18 if @xmath27 . if @xmath45 , we will see below that @xmath19 is harmonically regular . by corollary [ cor_masses_agree ] , its mass is given by @xmath46 , which evaluates to @xmath47 . we now determine the values of @xmath48 for which @xmath19 is a regular zas . the zas @xmath19 of the metric @xmath49 with @xmath50 given by @xmath51 is regular if and only if @xmath28 . in this case , @xmath19 is harmonically regular . we find a necessary condition for @xmath19 to be regular . assume @xmath52 is some local resolution ; by spherical symmetry we may assume @xmath53 depends only on @xmath34 . by applying a conformal transformation , we may assume that the spheres @xmath54 have constant area @xmath55 in @xmath56 ( i.e. , @xmath57 ) . ( in other words , the metric @xmath56 is that of a round cylinder with spherical cross sections . ) then @xmath58 a necessary condition for a local resolution is that @xmath59 is positive and finite on @xmath19 . compute this normal derivative : @xmath60 this is positive and finite in the limit @xmath61 if and only if @xmath28 . thus , @xmath45 is necessary for the existence of a local resolution . if @xmath45 , then @xmath62 . a calculation shows that the arc length parameter for @xmath56 is given as @xmath63 . thus , @xmath64 , which is smooth on @xmath65 ; moreover , @xmath53 is @xmath56-harmonic . thus , @xmath52 is a local harmonic resolution . evidently the case @xmath28 is special . it is left to the reader to show that if the schwarzschild zas metric is written in the form @xmath66 , then to first order , @xmath67 is given by a constant times @xmath68 , where @xmath69 is the distance to @xmath19 . for our purposes a `` removable singularity '' is a point deleted from the interior of a smooth riemannian manifold . such singularities can be viewed as zas . for example the manifold @xmath70 with the flat metric @xmath71 has its interior `` boundary '' as a zas . to see this , let @xmath72 with the flat metric @xmath73 on its interior , which is isometric to @xmath70 . clearly the boundary @xmath74 is a zas . it is not difficult to see that the zas @xmath19 of the spherically symmetric metric @xmath51 is removable if and only if @xmath75 , which corresponds to a deleted point in flat space . ( see lemma 4.1 of chapter 1 in @xcite . ) in fact , it is straightforward to show that a collection of removable singularities has zero mass ; see @xcite . ( the key tool is the existence of a harmonic function that blows up at the removable singularities . ) however , not all zas with zero mass are removable , as seen in earlier examples . there is also a notion of a `` removable @xmath76 singularity '' ; this occurs when an embedded circle is removed from the interior of a smooth riemannian manifold . the resulting space has a zero area singularity that is topologically a 2-torus . it is left to the reader to verify that removable @xmath76 singularities have mass equal to @xmath26 ( at least for a circle deleted from @xmath6 ) . thus , our definition of mass is not well - adapted to studying these types of singularities . in this section , we prove by example that there exists a zas that has a local resolution but no local harmonic resolution ; we begin by showing that the problem of finding a local harmonic resolution is equivalent to solving a linear elliptic pde . let @xmath52 be some local resolution of a zas @xmath77 . suppose for now that there exists a local harmonic resolution @xmath78 of @xmath77 defined on a neighborhood @xmath79 . set @xmath80 , which is smooth and positive on @xmath81 by lemma [ lemma_smooth_extension ] . also , @xmath82 . apply formula @xmath83 from appendix b ( with @xmath84 playing the role of @xmath85 ) . this leads to the equation @xmath86 since @xmath84 is assumed to be @xmath87-harmonic . then @xmath88 satisfies @xmath89 , where @xmath90 . then @xmath88 satisfies the linear elliptic pde @xmath91 where @xmath92 . on the other hand , if @xmath88 is some positive solution to @xmath93 that is smooth up to and including the boundary , then the above discussion implies that @xmath78 is a local harmonic resolution of @xmath77 , where @xmath94 and @xmath95 . note that solutions of @xmath93 may lose regularity at the boundary if , for some local resolution @xmath52 , the function @xmath96 is not smooth at the boundary . now we exhibit such an example . consider a spherically symmetric metric @xmath56 given by @xmath97 and a function @xmath98 , both for @xmath99 . then @xmath52 is a local resolution of the zas of @xmath100 . we assume that if a local harmonic resolution exists , it is also spherically symmetric . by equation @xmath101 , the laplacian on functions of @xmath34 is given by @xmath102 thus , for our choice of @xmath103 , we have @xmath104 , so equation @xmath93 becomes @xmath105 where @xmath88 is the quotient of @xmath53 and the unknown harmonic resolution function . the general solution of this second order linear ode on @xmath106 is given by @xmath107 where @xmath108 and @xmath109 are arbitrary constants . to satisfy the condition @xmath110 , it must be that @xmath111 . however , in this case , @xmath112 does not extend smoothly to zero : @xmath113 which diverges at @xmath114 . thus , there exists no solution of @xmath93 for this choice of @xmath115 obeying the necessary boundary conditions and extending smoothly to the boundary . in other words , the zas @xmath19 admits no local harmonic resolution . the above discussion also appears in @xcite .	the schwarzschild spacetime metric of negative mass is well - known to contain a naked singularity . in a spacelike slice , we develop a theory of such `` zero area singularities '' in riemannian manifolds , generalizing far beyond the schwarzschild case ( for example , allowing the singularities to have nontrivial topology ) . we also define the mass of such singularities . the second author wrote the majority of the paper , with individual contributions cited throughout .	the schwarzschild spacetime metric of negative mass is well - known to contain a naked singularity . in a spacelike slice , this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area . we develop a theory of such `` zero area singularities '' in riemannian manifolds , generalizing far beyond the schwarzschild case ( for example , allowing the singularities to have nontrivial topology ) . we also define the mass of such singularities . the main result of this paper is a lower bound on the adm mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the masses of its singularities , assuming a certain conjecture in conformal geometry . the proof relies on the riemannian penrose inequality . equality is attained in the inequality by the schwarzschild metric of negative mass . an immediate corollary is a version of the positive mass theorem that allows for certain types of incomplete metrics . * authorship remarks * most of the definitions and results of this paper were the work of the first author , originally presented at a conference in 2005 under the heading `` negative point mass singularities '' . the second author wrote the majority of the paper , with individual contributions cited throughout .
0909.0522	c	the essence of this paper was to associate a quantity `` mass '' to the class of zero area singularities . the primary application of the theory was to estimate the adm mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the masses of its singularities . in 1997 , the first author , just out of graduate school , sat next to barry mazur at a conference dinner at harvard , who , quite characteristically , asked the first author a series of probing questions about his research , which at the time concerned black holes . one of the questions was `` can a black hole have negative mass , and if so , what properties would it have ? '' contemplating this natural question marked the beginning of an enjoyable journey leading to this paper . the second author would like to thank mark stern and jeff streets for helpful discussions .	the main result of this paper is a lower bound on the adm mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the masses of its singularities , assuming a certain conjecture in conformal geometry . * authorship remarks * most of the definitions and results of this paper were the work of the first author , originally presented at a conference in 2005 under the heading `` negative point mass singularities '' .	the schwarzschild spacetime metric of negative mass is well - known to contain a naked singularity . in a spacelike slice , this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area . we develop a theory of such `` zero area singularities '' in riemannian manifolds , generalizing far beyond the schwarzschild case ( for example , allowing the singularities to have nontrivial topology ) . we also define the mass of such singularities . the main result of this paper is a lower bound on the adm mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the masses of its singularities , assuming a certain conjecture in conformal geometry . the proof relies on the riemannian penrose inequality . equality is attained in the inequality by the schwarzschild metric of negative mass . an immediate corollary is a version of the positive mass theorem that allows for certain types of incomplete metrics . * authorship remarks * most of the definitions and results of this paper were the work of the first author , originally presented at a conference in 2005 under the heading `` negative point mass singularities '' . the second author wrote the majority of the paper , with individual contributions cited throughout .
1009.5997	i	in the years since @xcite first proposed a two component structure to the milky way disk , a large body of observational work has provided supporting evidence for contrasting thin and thick disk attributes . structurally , the thin disk scale height is shorter than thick disk scale height ( for reviews see * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , and the thick disk may have a longer scale length than the thin disk @xcite . kinematically , thick disk stars have larger velocity dispersions and lag the net rotation of the disk @xcite . additionally , thick disk stars are older and metal poor relative to their thin disk counterparts ( _ e.g. _ * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and at a given iron abundance thick disk stars are @xmath1-enhanced @xcite . moreoever , thin and thick disk attributes are not unique to the milky way but a ubiquitous feature for late type galaxies @xcite . recently , several sdss based studies have provided further strong observational constraints on the structural , kinematic and chemical properties of stars in the solar cylinder . * hereafter j08 ) used a photometric parallax method on sdss data to estimate distances to @xmath248 million stars and studied their spatial distribution . because sdss provides accurate photometry , which enables reasonably robust distances ( 1015% , @xcite ) , as well as faint magnitude limits ( @xmath3 ) and a large sky coverage ( 6500 deg@xmath4 ) , j08 were able to robustly constrain the parameters of a model for the global spatial distribution of stars in the milky way . the j08 model is qualitatively similar to previous work ( _ e.g . _ @xcite ) which identifies a clear change of slope in the counts of disk stars as a function of distance from the galactic plane ; this change in slope is usually interpreted as the transition from the thin to thick disk @xcite . * hereafter i08 ) further extended this global analysis of sdss data by developing a photometric metallicity estimator and by utilizing a large proper motion catalog based on sdss and palomar observatory sky survey data @xcite . i08 studied the dependence of the metallicity , [ fe / h ] and rotational velocity , @xmath5 , of disk stars on the distance from the galactic plane and detected gradients of both quantities over the distance ranging from several hundred parsecs to several kiloparsecs . such gradients would be expected in a thin / thick disk decomposition where the thick disk stars are a separate population defined by a bulk rotational velocity lag and a lower metallicity compared to those of the thin disk . however , such a model would also predict a correlation between the metallicity and the velocity lag , which is strongly excluded ( @xmath2@xmath6 level ) by the i08 analysis ( see figure 17 , i08 ) . in this work we turn to a more sophisticated galactic description an @xmath0body model to characterize stars within the sdss volume and solve this puzzle . over the past few decades , @xmath0body simulations have been used to provide supporting evidence for three distinct theories of thick disk formation : violent relaxation @xcite , substructure disruption @xcite , and heating by satellites @xcite . several works have recently redressed these ideas . @xcite and @xcite formed a thick disk in situ at high redshift during gas - rich mergers , where star formation is triggered by the rapid accretion of gas ; this result is consistent with the thick disk forming through violent relaxation of the galactic potential . in contrast , @xcite , @xcite , and @xcite investigated substructure disruption by using a cosmologically derived satellite accretion history to perturb a milky way - like disk ; subhalo - disk encounters increased the scale height of this disk at all radii effectively forming a thick disk . finally , @xcite showed that by tidally stripping / accreting satellites , the majority of the oldest stars in the thick disk could have formed externally rather than in situ . in this work , we study a new method of formation : radial migration . radial migration due to scattering from transient spirals was first described by @xcite . in this model energy and angular momentum changes occur from interactions with transient spiral arms , which move stars at the corotation resonance inward or outward in radius while preserving their nearly - circular orbits . * ; * ? ? ? * r08ab hereafter ) studied this phenomenon in n - body + smooth particle hydrodynamic ( sph ) simulations of disk formation , and showed that migrations are possible on short timescales . they explored the implications of radial mixing for stellar populations for a variety of stellar systems , including the solar neighborhood . here we extend their work by highlighting the vertical evolution that occurs as a result of migration . we note that in this paper , we are not testing the validity of the other models of formation . however , recently , @xcite proposed using the eccentricity of orbits of stars in the thick disk to constrain the thick disk s formation mechanism ; they presented the eccentricity distributions that result from four n - body simulations : @xcite , @xcite , r08b , and @xcite . they found that the distributions that result from heating , radial migration and mergers all had a strong peak at low eccentricity ( @xmath7 ) , while the distribution that results from accretion is centered at higher orbital eccentries ( @xmath8@xmath9@xmath10 ) . building on this , @xcite studied the eccentricity of orbits of stars in the thick disk observed in the radial velocity experiment ( rave ) @xcite and found these results to be inconsistent with expectations for the pure accretion simulation . @xcite also leveraged @xmath1 measurements from rave to conclude that the @xmath1 enhancement of the metal - poor thick disk implies that direct accretion of stars from dwarf galaxies did not play a major role in the formation of the thick disk . using sdss dr7 , @xcite showed that the eccentricity of orbits of stars in the thick disk implies the thick disk is unlikely to be fully populated by radially migrated stars . we note that we can not exclude that some fraction of the thick disk is a fossil of a past more violent history , nor can this scenario explain thick disks in all galaxies . however , in what follows , we show that a large fraction of the stars in the thick disk could have formed in situ and arrived at their present location via radial migration . the outline of this paper is as follows : in [ s : simul ] , we present two simulations , one with substantial migration and the other with relatively little migration . when we compare these two simulations we can show that migration can build a thick disk as first conceived by gilmore & reid ( 1983 ) : a component with a scale - height larger than that of the thin disk . in [ s : obs ] we qualitatively compare the milky way - like simulation ( with migration ) with the sdss observations to show that they match each other sufficiently well to pursue further comparison . in [ s : solar ] we present a detailed comparison between the simulation and the local sdss volume focusing on the reason for the lack of correlation between @xmath5 and [ fe / h ] ; in appendix [ s : spagna ] we reconsider recent observational claims concerning the lack of correlation between @xmath5 and [ fe / h ] . in [ s : obs_decomp ] we use the simulation as a proxy for the milky way to show that classifying stars as members of the thin or thick disk by either velocity or metallicity leads to an apparent separation in the other property as observed . in [ s : schoenrich ] we compare our results to recent theoretical work that used semi - analytics to investigate how the solar neighborhood could have been shaped by radial migration and chemical evolution effects . in [ s : predict ] we explore the correlation between [ @xmath1/fe ] and age to show the diagnostic power of [ @xmath1/fe ] as a stand - in for age . finally , in [ s : concl ] we summarize our results and conclusions .	the separation of the milky way disk into a thin and thick component is supported by differences in the spatial , kinematic and metallicity distributions of their stars . these differences have lead to the predominant view that the thick disk formed early via a cataclysmic event and constitutes fossil evidence of the hierarchical growth of the milky way . we show here , using-body simulations , how a double - exponential vertical structure , with stellar populations displaying similar dichotomies can arise purely through internal evolution . in this picture , stars migrate radially , while retaining nearly circular orbits , as described by sellwood & binney ( 2002 ) . as stars move outwards their vertical motions carry them to larger heights above the mid - plane , populating a thickened component . such stars found at the present time in the solar neighborhood formed early in the disk s history at smaller radii where stars are more metal - poor and-enhanced , leading to exactly the properties observed for thick disk stars . classifying stars as members of the thin or thick disk by either velocity or metallicity leads to an apparent separation in the other property as observed . this scenario is supported by the sdss observation that stars in the transition region do not show any correlation between rotational velocity and metallicity . although such a correlation is present in young stars because of epicyclic motions , the radial migration mixes stars , washing out the correlation . using the geneva copenhagen survey , we indeed find a velocity - metallicity correlation in the younger stars and none in the older stars . we predict a similar result when separating stars by [/fe ] . the good qualitative agreement between our simulation and observations in the milky way are especially remarkable because the simulation was not tuned to reproduce the milky way , hinting that the thick disk may be a ubiquitous galaxy feature generated by stellar migration . nonetheless , we can not exclude that some fraction of the thick disk is a fossil of a past more violent history , nor can this scenario explain thick disks in all galaxies , most strikingly those which counter - rotate with respect to the thin disk .	the separation of the milky way disk into a thin and thick component is supported by differences in the spatial , kinematic and metallicity distributions of their stars . these differences have lead to the predominant view that the thick disk formed early via a cataclysmic event and constitutes fossil evidence of the hierarchical growth of the milky way . we show here , using-body simulations , how a double - exponential vertical structure , with stellar populations displaying similar dichotomies can arise purely through internal evolution . in this picture , stars migrate radially , while retaining nearly circular orbits , as described by sellwood & binney ( 2002 ) . as stars move outwards their vertical motions carry them to larger heights above the mid - plane , populating a thickened component . such stars found at the present time in the solar neighborhood formed early in the disk s history at smaller radii where stars are more metal - poor and-enhanced , leading to exactly the properties observed for thick disk stars . classifying stars as members of the thin or thick disk by either velocity or metallicity leads to an apparent separation in the other property as observed . this scenario is supported by the sdss observation that stars in the transition region do not show any correlation between rotational velocity and metallicity . although such a correlation is present in young stars because of epicyclic motions , the radial migration mixes stars , washing out the correlation . using the geneva copenhagen survey , we indeed find a velocity - metallicity correlation in the younger stars and none in the older stars . we predict a similar result when separating stars by [/fe ] . the good qualitative agreement between our simulation and observations in the milky way are especially remarkable because the simulation was not tuned to reproduce the milky way , hinting that the thick disk may be a ubiquitous galaxy feature generated by stellar migration . nonetheless , we can not exclude that some fraction of the thick disk is a fossil of a past more violent history , nor can this scenario explain thick disks in all galaxies , most strikingly those which counter - rotate with respect to the thin disk .
1603.06885	i	redshift surveys and weak lensing maps are two powerful and independent tools for tracing the matter distribution in the universe . approaches to combining these two powerful tools are developing rapidly as dense redshift surveys access the intermediate redshift universe and as weak lensing maps become increasingly extensive ( geller et al . 2005 ; kurtz et al . 2012 ; shan et al . 2012 ; van waerbeke et al . 2013 ; chang et al . 2015 ) . the shels ( smithsonian hectospec lensing survey ) project began as a platform for exploring the combination of dense , complete foreground redshift surveys with lensing maps ( geller et al . 2005 ; geller et al . 2010 ; utsumi et al . shels consists of dense redshift surveys of two of the five fields of the deep lens survey ( wittman et al . 2006 ; dls ) , f1 centered at r.a.@xmath1 = 00@xmath253@xmath325.3@xmath4 , decl.@xmath1 = 12@xmath533@xmath655@xmath7 and f2 centered at r.a.@xmath1 = 09@xmath219@xmath332.4@xmath4 and decl.@xmath1 = + 30@xmath1800@xmath1900@xmath7 . each of the dls fields covers 4 square degrees . the shels redshift surveys of the two fields are more than 94% complete to an extinction corrected r@xmath0 = 20.2 . these two fields currently represent the most densely sampled surveys to this magnitude limit . the dense , complete sampling makes the surveys useful for a wide range of astrophysical applications . the hectospec , a 300-fiber spectrograph with a 1@xmath5 field of view mounted on the mmt , enables surveys like shels . kochanek et al . ( 2012 ) also carried out a large redshift survey , ages , with hectospec . their survey focuses on agn evolution . the ages survey covers a 7.7@xmath5 contiguous region with a complex sampling strategy in several photometric bands . to a extinction corrected limit of r@xmath0 = 20.2 ( we use the subscript @xmath0 throughout to denote an extinction corrected magnitude ) , the number density of ages redshifts is @xmath81350 galaxies deg@xmath20 in contrast with the shels mean averaged over the two fields of 1961 galaxies deg@xmath20 . shels and ages are thus complementary in both their geometry and selection . here we describe the shels survey of the f1 dls field . geller et al . ( 2014 ) describe the survey of the f2 field . the f1 field contains a total of 9426 new galaxy redshifts and is 94% complete to an extinction corrected r@xmath0 = 20.2 . the f2 survey is somewhat deeper ; it is 95% complete to an observed r = 20.6 and 97% complete to r@xmath0 = 20.2 . taken at face value , the two fields seem remarkably different ; the raw counts to r@xmath0 = 20.2 differ by @xmath831% . the f2 field contains a prominent complex of rich clusters associated with abell 781 ( abell 1958 ) and easily detected with weak lensing ; f1 contains no clusters detected with weak lensing in the entire volume covered by the redshift survey ( ascaso et a. 2014 ) . we compare these observed differences with the expected cosmic variance for these fields . we also provide a guide to the properties of the survey and to some of its potential uses . we have already used both the f2 and f1 shels data for a variety of applications . for essentially all of these applications , the straightforward , complete magnitude limited survey is a critical underpinning . in concert with the original intent of the surveys , we have used the f2 survey as a basis for testing weak lensing maps against a foreground redshift survey ( geller et al . 2005 ; geller et al . 2010 ; utsumi et al . 2014 ; see also viola et al . we have also compared x - ray , spectroscopic and lensing selection demonstrating that the most massive systems are detected robustly with all three techniques ( starikova et al . 2014 ) . the extensive shels spectroscopy enables exploration of a variety of benchmarks for tracking galaxy evolution including the evolution of the h@xmath21 luminosity function ( westra et al . 2010 ) , the faint end of the composite galaxy luminosity function ( geller et al . 2012 ) , the nature of star - forming galaxies detected with wise ( hwang et al . 2012 ) , the impact of close pairs on star formation ( freedman woods et al . 2010 ) , the determination of central velocity dispersions for individual galaxies ( fabricant et al . 2013 ) , and the evolution of the mass - metallicity relation ( zahid et al . 2013 ; 2014 ) . here we provide guides to the quality and potential uses of the shels surveys by revisiting the stellar mass metallicity relation ; we compare the determinations for the f1 and f2 fields separately and in combination . similarly , we compare the d@xmath104000 distributions as a function of stellar mass and redshift for the two fields . we describe the f1 data in section 2 with attention to the differences between the photometric bases for the f1 and f2 surveys . we compare the completeness of the shallower f1 survey with f2 and lay the foundation for comparing the surveys to the same limiting extinction corrected apparent magnitude . in section 3 we compare various aspects of the f1 and f2 survey regions including the mass metallicity relation ( section 3.1 ) , the d@xmath104000 distributions as a function of redshift and stellar mass ( section 3.2 ) , galaxy counts ( section 3.3 ) , and cluster observations ( section 3.4 ) . in sections 3.3 and 3.4 we consider whether the differences in galaxy and cluster counts are consistent with the expected cosmic variance for fields of this size . we conclude in section 4 . we adopt h@xmath0 = 70 km s@xmath22 mpc@xmath22 , @xmath23 and @xmath24 = 0.3 throughout . all quoted errors in measured quantities are 1@xmath11 .	both fields are more than 94% complete to a galactic extinction corrected r = 20.2 . here we describe the redshift survey of the f1 field centered at r.a. = 00.3 and decl. = 12 ; like f2 , the f1 field covers deg . we compare the mass metallicity relation and the distributions of d as a function of stellar mass and redshift for the two fields . surveys	the shels ( smithsonian hectospec lensing survey ) is a complete redshift survey covering two well - separated fields ( f1 and f2 ) of the deep lens survey . both fields are more than 94% complete to a galactic extinction corrected r = 20.2 . here we describe the redshift survey of the f1 field centered at r.a. = 00.3 and decl. = 12 ; like f2 , the f1 field covers deg . the redshift survey of the f1 field includes 9426 new galaxy redshifts measured with hectospec on the mmt ( published here ) . as a guide to future uses of the combined survey we compare the mass metallicity relation and the distributions of d as a function of stellar mass and redshift for the two fields . the mass - metallicity relations differ by an insignificant 1.6 . for galaxies in the stellar mass range 10 to 10m , the increase in the star - forming fraction with redshift is remarkably similar in the two fields . the seemingly surprising 31 - 38% difference in the overall galaxy counts in f1 and f2 is probably consistent with the expected cosmic variance given the subtleties of the relative systematics in the two surveys . we also review the deep lens survey cluster detections in the two fields : poorer photometric data for f1 precluded secure detection of the single massive cluster at that we find in shels . taken together the two fields include 16,055 redshifts for galaxies with r and 20,754 redshifts for galaxies with r 20.6 . these dense surveys in two well - separated fields provide a basis for future investigations of galaxy properties and large - scale structure . key words : cosmology : observations galaxies : abundances galaxies : distances and redshifts galaxies : evolution large - scale structure of universe surveys
1603.06885	c	the shels project covers two widely separated 4 square degree fields of the deep lens survey . these fields include 16,055 redshifts and they are both @xmath61 94% complete to an extinction corrected r@xmath0 = 20.2 . other surveys covering comparable areas to the same apparent magnitude limit are sparser and/or color - selected . the straightforward selection in apparent magnitude makes shels a useful benchmark for evaluating selection effects based on other approaches . the median redshift of both shels fields is z @xmath8 0.3 . the redshift histograms of the two regions nonetheless differ significantly . this difference is largely driven by differences in the details of the large - scale structure in each region , particularly the presence of several massive clusters of galaxies in f2 . we have previously used the shels data to determine the stellar mass - metallicity relation for the redshift interval 0.2@xmath42 . comparison of the relation determined for the f1 and f2 fields separately shows that the fiducial mass , m@xmath0 characterizing the relation changes insignificantly ( at the 1.6 @xmath11 level ) from one field to the other . the relation for the two fields is a remarkably robust estimate for this redshift range . we provide the metallicities and stellar masses as we did for f2 in geller et al . ( 2014 ) . as we did for the f2 field ( geller et al . 2014 ) we use the distribution of the spectral indicator d@xmath104000 as a proxy to discriminate between the star - forming and quiescent populations as a function of redshift and stellar mass . the behavior of the d@xmath104000 distributions for the two fields is remarkably similar with salient differences driven either by low redshift structures sampled to low stellar mass or to the presence of massive clusters of galaxies . for galaxy stellar masses in the range 10@xmath12 to 10@xmath13m@xmath14 , the star - forming population fraction as a function of redshift are remarkably similar for the two fields in spite of the difference in the overall mean galaxy density . these broadly binned results are a guide to the use of the data for more detailed analysis of the properties of galaxies as a function of their environment . as a result of the small redshift errors ( @xmath102 km s@xmath22 ) , the shels data are particularly well - suited to this task . in contrast with the stable population fractions , the raw counts of galaxies and massive clusters in the two fields seem , at first glance , to differ significantly . the procedures in observing the two fields were not identical thus complicating the comparison . however , the 31 - 38% difference in the counts to the limiting magnitude ( and the smaller 19% in the count of massive galaxies ) is probably consistent with the expected cosmic variance to within our ability to control for the relative systematics in the two surveys . comparing the abundance of massive clusters in the two fields is complicated by the much poorer data available for f1 . in the f2 field there are extensive x - ray observations and the weak lensing data is of higher quality than for f1 . in fact , the shels survey uncovers a cluster in f1 at z = 0.35 that probably should have been detected in f1 if the lensing data were of the same quality as for the f2 field . the difference in the cluster count is dominated by shot noise , but the apparent difference is accentuated by the poorer f1 lensing data . this comparison underscores the need for well - controlled calibration of surveys and underscores the subtle issues that enter the comparison of data for fields observed under different conditions and with different observational approaches . the shels survey covers 8 square degrees in two widely separated fields and includes 20,754 redshifts for galaxies with r@xmath17 20.6 along with 4457 redshifts for fainter objects . the complete surveys of the f1 and f2 fields provide a resource for many investigations of galaxy properties and their environments . the completeness of the surveys to the apparent magnitude limit provides benchmarks for color - selected surveys and for the development of new strategies based on combinations of imaging and spectroscopy . we appreciate a thoughtful , careful review by the referee that substantially improved this paper . we thank changbom park of kias for generous support that enabled completion of this project . we thank kairy herrera of brown university for examining images of faint galaxies with superimposed stars to refine the construction of table 4 . we thank warren brown for remeasuring two redshifts for two of the objects examined by kairy herrera . scott kenyon provided advice on numerical methods along with comments on the manuscript . perry berlind and mike calkins masterfully operated the hectospec . susan tokarz and sean moran assisted with the data reduction . the smithsonian institution supported the research of margaret geller , ho seong hwang , michael kurtz , daniel fabricant and jabran zahid . kias supported the research of ho seong hwang . ccccccccrc 12.324533 + 12.480500 & 1237678919673053653 & @xmath103 & @xmath104 & 1 & 2 & 0 & 1.76 & @xmath105 & ... + 12.324566 + 12.653818 & 1237678859550589594 & @xmath106 & @xmath107 & 1 & 2 & 0 & 1.23 & @xmath108 & 9.05 + 12.324614 + 12.798466 & 1237678859550589182 & @xmath109 & @xmath110 & 1 & 2 & 0 & ... & @xmath111 & ... + 12.325052 + 11.897449 & 1237678858476913241 & @xmath112 & @xmath113 & 1 & 2 & 0 & 1.82 & @xmath114 & ... + 12.325632 + 12.798472 & 1237678859550589183 & @xmath115 & @xmath116 & 1 & 2 & 0 & 1.28 & @xmath117 & ... + 12.327368 + 12.549498 & 1237678919673053413 & @xmath118 & @xmath119 & 1 & 2 & 0 & 1.96 & @xmath120 & ... + 12.327427 + 12.550200 & 1237678919673053412 & @xmath121 & @xmath122 & 1 & 2 & 0 & 1.78 & @xmath123 & ... + 12.327430 + 11.594275 & 1237678918599311681 & @xmath124 & @xmath125 & 1 & 2 & 0 & 1.01 & @xmath126 & 8.77 + 12.327575 + 12.491597 & 1237678919673053661 & @xmath127 & @xmath128 & 1 & 2 & 0 & 1.40 & @xmath129 & 9.14 + 12.327611 + 12.244888 & 1237678859013783788 & @xmath130 & @xmath131 & 1 & 2 & 0 & 1.22 & @xmath132 & ... + ccccccccrc 12.389126 + 13.290399 & 1237678920746795438 & @xmath133 & @xmath134 & 1 & 1 & 0 & 1.34 & @xmath135 & ... + 12.389223 + 13.548410 & 1237678860624396698 & @xmath136 & @xmath137 & 1 & 2 & 0 & 1.71 & @xmath138 & ... + 12.389453 + 13.234157 & 1237678860087525736 & @xmath139 & @xmath140 & 1 & 1 & 0 & 1.92 & @xmath141 & ... + 12.390178 + 12.722615 & 1237678859550654860 & @xmath142 & @xmath143 & 1 & 1 & 0 & 1.16 & @xmath144 & ... + 12.391906 + 12.125328 & 1237678919136182371 & @xmath145 & @xmath146 & 1 & 1 & 0 & 1.36 & @xmath147 & ... + 12.392926 + 13.139955 & 1237678860087525754 & @xmath148 & @xmath149 & 1 & 1 & 0 & 1.43 & @xmath150 & ... + 12.396500 + 12.704612 & 1237678859550654877 & @xmath151 & @xmath152 & 1 & 1 & 0 & 1.15 & @xmath153 & 8.77 + 12.396858 + 13.245761 & 1237678920746795610 & @xmath154 & @xmath155 & 1 & 1 & 0 & 1.34 & @xmath156 & ... + 12.397086 + 12.221524 & 1237678859013783938 & @xmath157 & @xmath158 & 1 & 1 & 0 & 1.79 & @xmath159 & ... + 12.397125 + 12.852595 & 1237678920209924690 & @xmath160 & @xmath161 & 1 & 1 & 0 & 1.31 & @xmath162 & ... + ccc 12.315080 + 12.318782 & 1237678859013718622 & @xmath163 + 12.339393 + 12.349747 & 1237678859013783808 & @xmath164 + 12.352705 + 13.175315 & 1237678860087525659 & @xmath165 + 12.358372 + 11.543474 & 1237678857940042136 & @xmath166 + 12.359576 + 12.377343 & 1237678859013783569 & @xmath167 + 12.360730 + 12.853304 & 1237678920209924618 & @xmath168 + 12.363524 + 13.473994 & 1237678860624396650 & @xmath169 + 12.363848 + 12.351914 & ... & @xmath170 + 12.365371 + 12.855583 & 1237678920209924173 & @xmath171 + 12.367078 + 12.860638 & 1237678920209924839 & @xmath172 + cccccc 12.311022 + 13.024869 & 1237678920209924333 & @xmath173 & @xmath174 & 2 & 2 + 12.322512 + 12.238044 & 1237678859013783624 & @xmath175 & @xmath176 & 1 & 2 + 12.326695 + 12.168094 & 1237678919136182450 & @xmath177 & @xmath178 & 1 & 2 + 12.331113 + 13.070127 & 1237678860087460426 & @xmath179 & @xmath180 & 1 & 2 + 12.331615 + 12.833143 & 1237678920209924451 & @xmath181 & @xmath182 & 2 & 2 + 12.334228 + 12.140061 & 1237678919136182455 & @xmath183 & @xmath184 & 2 & 2 + 12.339199 + 11.762720 & 1237678918599311568 & @xmath185 & @xmath186 & 1 & 1 + 12.343303 + 12.813752 & 1237678859550654681 & @xmath187 & @xmath188 & 1 & 1 + 12.350332 + 11.883782 & 1237678858476912807 & @xmath189 & @xmath190 & 1 & 1 + 12.355689 + 12.097490 & 1237678919136182468 & @xmath191 & @xmath192 & 1 & 1 + lccr e(b@xmath193v ) & 0.06 ( a@xmath194=0.16 ) & 0.02 ( a@xmath194=0.05 ) + survey area ( deg@xmath9 ) & 4.20 & 3.98 ( excludes masked area ) + n@xmath195 & 7261 & 9489 + n@xmath196 & 6839 & 9216 + completeness@xmath197 & 94.2% & 97.1% + z@xmath198 & 0.282 & 0.294 + n@xmath199 & 6626 & 9946 + n@xmath200 & 6345 & 9643 + completeness@xmath201 & 95.8% & 97.0% + n@xmath202 & 9207 & 13408 + n@xmath203 & 8049 & 12705 + completeness@xmath204 & 87.4% & 94.8% + n@xmath205 & 1515 & 2942 + n@xmath206 & 9564 & 16319 + lccl n@xmath207&1446&2131&3577 + log(m@xmath0/m@xmath14 ) & 9.56@xmath380.03&9.50@xmath380.02&9.52@xmath380.02 + z@xmath0 & 9.10@xmath380.01 & 9.10@xmath380.01&9.10@xmath380.004 + @xmath65&0.49@xmath380.03&0.52@xmath380.03&0.52@xmath380.02 + . , between the dls r - band f2 magnitude ( r ) and r@xmath208 ( equation 1 ) as a function of the sdss r - band petrosian magnitude , r@xmath209 . the typical magnitude errors are 0.01 ( dls r ) and 0.11 ( sdss r@xmath209 ) . [ magcomp],width=672 ] -value ( tonry & davis 1979 ) , a redshift quality indicator , as a function of redshift ( upper panel ) . the center panel shows apparent r@xmath0 magnitude as a function of redshift . we display only 50% 0f the data for clarity . the lower panel shows a redshift histogram in bins of @xmath210 . [ bfzxcr],width=672 ] magnitude . the color bar shows the completeness fractions for the spatial completeness displays in the lower two panels . the lower left panel shows the completeness in 12@xmath5112 arcminute bins for galaxies with r@xmath16 . the yellow points indicate galaxies in the photometric sample without a measured redshift . the right hand plot shows the completeness in the interval 20.2@xmath211r@xmath0@xmath212 in the same format . note that for the r@xmath16 survey the most significant incompleteness occurs at the corners and edges of the field . [ bfcomplete],width=672 ] magnitude ( upper panel ) . color - magnitude diagram for the 422 objects without a redshift ( middle panel ) with r@xmath16 . contours indicate the relative density of objects with a redshift ; the absence of a slope as a function of r@xmath0 suggests that there is little obvious color bias in these objects . the bottom panel shows the number of objects with redshifts in the shels survey ( open histogram ) and the number of unobserved galaxy candidates ( red hashed histogram ) as a function of the r@xmath0 magnitude . [ fcmr],width=624 ] 20.2 shels f1 survey projected on the r.a.@xmath1 direction . the color coding indicates the value of d@xmath104000 . in the low density regions , galaxies with d@xmath104000 @xmath89 1.5 predominate as expected . the online journal includes a video display of the data . the color - coding of the video is in broader bins : d@xmath104000 @xmath213 ( blue ) , 1.3 @xmath17 d@xmath104000 @xmath214 ( green ) , and d@xmath104000 @xmath215 1.7 ( red ) . [ brafcone],width=624 ]	the seemingly surprising 31 - 38% difference in the overall galaxy counts in f1 and f2 is probably consistent with the expected cosmic variance given the subtleties of the relative systematics in the two surveys . we also review the deep lens survey cluster detections in the two fields : poorer photometric data for f1 precluded secure detection of the single massive cluster at that we find in shels . taken together the two fields include 16,055 redshifts for galaxies with r and 20,754 redshifts for galaxies with r 20.6 . these dense surveys in two well - separated fields provide a basis for future investigations of galaxy properties and large - scale structure .	the shels ( smithsonian hectospec lensing survey ) is a complete redshift survey covering two well - separated fields ( f1 and f2 ) of the deep lens survey . both fields are more than 94% complete to a galactic extinction corrected r = 20.2 . here we describe the redshift survey of the f1 field centered at r.a. = 00.3 and decl. = 12 ; like f2 , the f1 field covers deg . the redshift survey of the f1 field includes 9426 new galaxy redshifts measured with hectospec on the mmt ( published here ) . as a guide to future uses of the combined survey we compare the mass metallicity relation and the distributions of d as a function of stellar mass and redshift for the two fields . the mass - metallicity relations differ by an insignificant 1.6 . for galaxies in the stellar mass range 10 to 10m , the increase in the star - forming fraction with redshift is remarkably similar in the two fields . the seemingly surprising 31 - 38% difference in the overall galaxy counts in f1 and f2 is probably consistent with the expected cosmic variance given the subtleties of the relative systematics in the two surveys . we also review the deep lens survey cluster detections in the two fields : poorer photometric data for f1 precluded secure detection of the single massive cluster at that we find in shels . taken together the two fields include 16,055 redshifts for galaxies with r and 20,754 redshifts for galaxies with r 20.6 . these dense surveys in two well - separated fields provide a basis for future investigations of galaxy properties and large - scale structure . key words : cosmology : observations galaxies : abundances galaxies : distances and redshifts galaxies : evolution large - scale structure of universe surveys
cond-mat0406221	i	we have discussed the spin - dependent transport in a resonant tunneling structure with ferromagnetic multi - terminal under dc and ac fields by means of the nonequilibrium green function technique . the general formulation of the time - dependent spintronic transport in this structure in the presence of ac and dc fields has been established , which might offer a fundamental basis for further discussions on the spin - dependent transport in such spintronic devices in an ac field . first , we have considered the resonant system with two fm terminals in which the magnetizations of the leads are noncollinearly aligned under a dc bias voltage , and have found that for small @xmath173 s where @xmath173 characterizes the asymmetry of the relaxation times of the electrons with different spin in the central region , the tmr is negative , and whose absolute magnitude increases with increasing @xmath139 ( the relative angle between the magnetizations of both leads ) ; when @xmath173 becomes larger , the tmr will be positive and increases with increasing @xmath139 . we have also investigated the tmr as a function of energy , the dc bias voltage and the gate voltage for different polarizations and energy levels of the central scattering region , respectively . the results are diverse , which manifest the effect of the resonant energy level on the tmr and the tunneling current , as discussed in detail in sec.ii . second , we have considered a three - terminal device under a dc bias , which is different from the standard three - terminal device discussed elsewhererefs.@xcite . in the present device , each terminal is applied with a source bias , suggesting that there is net current flowing through every terminal . regardless of the spin - flip scattering , the electrons in up - spin subbands in one terminal will be accepted by the up - spin subbands in another terminal . when the magnetizations of the first and second terminals are antiparallel , the change of @xmath139 which is the relative angle between the magnetizations of the first and third terminals may considerably change the current flowing out of the second terminal . it turns out that tuning @xmath139 the current can be remarkably enhanced , giving rise to the so - called magnetization configuration - induced enhancement of the current or the current ratio @xmath290 . it has been found that the @xmath284 , which is defined in this case by the current change ratio when the configuration of the magnetizations of the first and second terminals is turned from parallel to antiparallel , decreases with increasing @xmath139 . third , as an application of our general formulation we have investigated the time - dependent spintronic transport in a system with two terminals under an ac field . we have uncovered that , when a very small dc bias is applied to the two terminals but an ac field is applied to the central scattering region , the photonic sidebands are formed in the central region . when the sidebands meet with the fermi energy of the terminals , the photon - assisted tunneling will occur . it manifests as the resonant peaks in the etc versus @xmath8 . the tmr exhibits many resonant peaks at the main resonant level and the photonic sidebands . it has been found that the asymmetric factor @xmath173 may lead to additional peaks besides the photon - assisted resonant peaks . we would like to mention that the present study might open a way to control the spin - dependent transport in a spintronic device by applying a time - dependent electrical field .	the spin - dependent transport of the electrons tunneling through a resonant tunneling structure with ferromagnetic multi - terminal under dc and ac fields is explored by means of the nonequilibrium green function technique . a general formulation for the time - dependent current and the time - averaged current is established . as its application the systems with two and three terminals in noncollinear configurations of the magnetizations under dc and the asymmetric factor of the relaxation times for the electrons with different spin in the central region is uncovered to bring about various behaviours of the tmr . the asymmetric factor of the relaxation times is observed to lead to additional resonant peaks besides the photon - asisted resonances .	the spin - dependent transport of the electrons tunneling through a resonant tunneling structure with ferromagnetic multi - terminal under dc and ac fields is explored by means of the nonequilibrium green function technique . a general formulation for the time - dependent current and the time - averaged current is established . as its application the systems with two and three terminals in noncollinear configurations of the magnetizations under dc and ac biases are investigated , respectively . the asymmetric factor of the relaxation times for the electrons with different spin in the central region is uncovered to bring about various behaviours of the tmr . the present three - terminal device is different from that discussed in literature , which is coined as a spin transistor with source . the current - amplification effect is found . in addition , the time - dependent spin transport for the two - terminal device is studied . it is found that the photonic sidebands provide new channels for the electrons tunneling through the barriers , and give rise to new resonances of the tmr , which is called as the photon - asisted spin - dependent tunneling . the asymmetric factor of the relaxation times is observed to lead to additional resonant peaks besides the photon - asisted resonances .
cond-mat0312378	i	recently , the coexistence of ferromagnetism and superconductivity has been observed in a number of materials , including , uge@xmath0,@xcite urhge,@xcite and zrzn@xmath0.@xcite the experiments so far have ascertained the presence of bulk superconductivity , and various thermodynamic and transport properties have been measured , but little is known yet about the detailed nature of the superconducting state . an obvious possibility is spin - triplet pairing induced by ferromagnetic fluctuations , but other mechanisms have also been proposed.@xcite one interesting aspects of the experiments , which may provide a clue about the origin and the nature of the pairing , is that the superconductivity is observed only on the ferromagnetic side of the magnetic phase boundary . this is in sharp contrast to early theories of superconductivity induced by ferromagnetic fluctuations , which predicted that this type of superconductivity would be equally strong on the paramagnetic side of the magnetic phase boundary.@xcite however , in a recent paper,@xcite to be referred to as i , it has been shown that the presence of magnons in the ferromagnetic phase can lead to a drastic enhancement of the superconducting @xmath1 compared to the paramagnetic phase . clearly , more properties of the superconducting state must be studied in order to differentiate between different possible pairing mechanisms . in this context , an interesting result is the recent measurement of the specific heat in urhge.@xcite taken at face value , this experiment shows a single transition into a superconducting state , and a low temperature specific heat that is linear in the temperature , which suggests that a fraction of the electrons remain in a fermi - liquid state at low temperatures . similar behavior has been observed in uge@xmath0.@xcite to date all of the theoretical work has assumed only the simplest type of superconducting order for a given pairing mechanism , with the main goal being to determine the phase boundary for superconductivity . for example , in i the present authors assumed an ordering of spin - triplet cooper pairs with spins oriented in the direction of the magnetization . let us denote the gap function for this ordering by @xmath2 . previous work on helium-3 in a magnetic field@xcite suggests that at some point , the cooper pairs with spins oriented opposite to the magnetization , characterized by a gap function @xmath3 , will form as well . more generally , the complete phase diagram for these systems will likely be complicated and involve ferromagnetism coexisting with several types of superconducting order.@xcite our goal in this paper is three - fold . first , we develop a formal theory that enables us to consistently describe ferromagnetism coexisting with two types of superconducting order . the superconductivity in our theory is caused by ferromagnetic fluctuations . our goal is to derive an equation of state , analogous to the strong - coupling or eliashberg equations of conventional superconductivity , that describes both up - spin and down - spin superconducting order , as well as a consistent magnetic equation of state in the presence of superconductivity . a major complication is that , because the superconductivity is itself caused by a fluctuation effect , a simple mean - field theory is not sufficient , and fluctuations need to be taken into account . the fluctuations that cause superconductivity within our theory are described by the spin susceptibility tensor . our second goal is therefore to develop a theory for the spin susceptibility , both in a pure ferromagnetic phase , and in coexisting ferromagnetic and superconducting phases . the pairing potential for superconductivity involving only @xmath2 and @xmath3 is given by the longitudinal susceptibility , @xmath4 . however , the transverse susceptibilities , @xmath5 , are also needed because they enter the normal self energies , and because they couple to @xmath4 via mode - mode - coupling effects . in fact , as shown in i , within the framework of our theory it is this mode - mode - coupling mechanism , which exists only in a magnetically ordered state , that causes the superconductivity to be observable only in the ferromagnetic phase . we will see that the magnons , which are described by @xmath5 , have an interesting dispersion relation in the superconducting state and , under certain conditions , can become effectively massive . a striking feature of the mass is that it is proportional to the inverse square of the magnetization , and thus singular for small magnetization . we give estimates showing that this result should be observable with neutron scattering . our third goal is to discuss the phase diagram for superconductivity and magnetism , based on the above results . in a theory that allows for pairing of both up - spin and down - spin electrons , one expects a phase diagram that is qualitatively shown in fig . [ fig:1 ] . with decreasing temperature , one schematic phase diagram in the temperature - pressure plane showing a paramagnetic phase ( pm ) , a normal conducting ferromagnetic one ( ncfm ) , a superconducting ferromagnetic phase with up - spin pairing only ( scfm i ) , and a superconducting ferromagnetic phase with both up - spin and down - spin pairing ( scfm ii ) . the two superconducting phases have been drawn to end in the same point for simplicity , but this will not necessarily be the case.,width=226 ] oberves a transition from a paramagnetic ( pm ) phase to a normal conducting ferromagnetic ( ncfm ) one . with decreasing temperature , the system enters a ferromagnetic superconducting state where only up - spin electrons are paired ( scfm i ) . finally , with further decreasing temperature , down - spin electrons are paired as well ( scfm ii ) . in general the coupled magnetic and superconducting equations of state are very complicated to solve . for the points we want to make , however , a complete solution is not needed . our aim here is to compute , for our proposed pairing mechanism , the relative magnitudes of the transition temperatures @xmath6 and @xmath7 for the phase boundaries between the ncfm phase and the scfm i phase , and between the scfm i phase and the scfm ii phase , respectively . generically we find that these transition temperatures are close to one another . experimentally this suggests that , for example , any specific heat measurement should find two closely spaced transition signatures . this result is in conflict with the naive interpretation of the specific heat measurement in urhge noted above . a possible alternative interpretation of the data consistent with our theory will be discussed below . the plan of this paper is as follows . in section [ sec : ii ] we develop a formalism that allows for a consistent description of all components of spin - triplet superconductivity , induced by ferromagnetic fluctuations , in the presence of long - range ferromagnetic order . in section [ sec : iii ] we calculate the magnetic susceptibility in the ferromagnetic state in the presence of a non - unitary superconducting order parameter . in section [ sec : iv ] we solve the strong - coupling equations for superconductivity and determine the phase diagram containing phases with pure ferromagnetic order , ferromagnetic plus spin - up superconducting order , and ferromagnetic plus both spin - up and spin - down superconducting order , respectively . we discuss our results and their experimental implications in section [ sec : v ] . in appendix [ app : a ] we augment our microscopic approach with a more general landau - ginzburg - wilson theory and discuss the soft - mode structure of the magnetic superconducting phase . in appendix [ app : b ] we relate the physical spin susceptibility to the magnetization fluctuations that occur most naturally in the theory . some of our results have been reported before in ref ..	the split superconducting transition of up - spin and down - spin electrons on the background of ferromagnetism is studied within the framework of a recent model that describes the coexistence of ferromagnetism and superconductivity induced by magnetic fluctuations . this conclusion is discussed in relation to experimental results on urhge .	the split superconducting transition of up - spin and down - spin electrons on the background of ferromagnetism is studied within the framework of a recent model that describes the coexistence of ferromagnetism and superconductivity induced by magnetic fluctuations . it is shown that one generically expects the two transitions to be close to one another . this conclusion is discussed in relation to experimental results on urhge . it is also shown that the magnetic goldstone modes acquire an interesting structure in the superconducting phase , which can be used as an experimental tool to probe the origin of the superconductivity .
cond-mat0312378	c	let us further discuss several aspects of our theory and its implications . first , we consider in more detail our results regarding the magnetic susceptibility . in a normal conducting ferromagnetic phase , the transverse spin susceptibility is soft , displaying ferromagnetic magnons with a quadratic dispersion relation . the scale in the dispersion relation is set by the stoner gap or exchange splitting @xmath115 , which is proportional to the magnetization . in natural units , measuring wave numbers in units of the magnetic coherence length @xmath101 , which is on the order of the fermi wave number @xmath123 , we have @xmath124 at zero frequency , the dimensionless transverse magnetic susceptibility diverges for @xmath125 like @xmath126 for a given distance from the magnetic phase transition , @xmath127 is a number of order one whose exact value depends on the details of the model . the gaussian approximation we have employed correctly reflects these exact features , see eqs . ( [ eqs:3.1 ] ) . in the presence of an up - spin gap , the structure of the magnon changes qualitatively . the gaussian approximation for @xmath5 predicts a true gap , eqs . ( [ eqs:3.5 ] ) . this is a consequence of the fact that the gaussian approximation effectively treats the superconducting gap as a fixed external field . the lgw theory of appendix [ app : a ] shows that this does not correctly reflect the symmetry properties of the system , and that the static @xmath5 actually has the structure [ eqs:5.1 ] _ ( k ) = . [ eq:5.1a ] here @xmath128 is related to the coupling constant @xmath129 and the magnetic order parameter @xmath130 of the lgw theory by @xmath131 . this result shows that , in general , @xmath5 has a much more complicated structure than in the absence of spin - triplet superconductivity . at asymptotically small wave numbers , @xmath132 , @xmath128 drops out of the expression for @xmath5 , and we have _ ( k ) = . [ eq:5.1b ] restoring the frequency , the dispersion relation of the magnon then is @xmath133 \,{\bm k}^2\quad.\ ] ] we see that the magnon dispersion relation is substantially changed by the presence of @xmath2 as long as the condition expressed by eq.([eq : a.10 ] ) is fulfilled . namely , the magnon is much stiffer , i.e. , the frequency rises much faster with the wave number , than in a normal conducting ferromagnet . the magnitude of this effect will depend on the detailed parameters of the material in question , but it clearly can be substantial : assuming a value of @xmath2 on the order of the superconducting @xmath1 , or @xmath134 , a value of @xmath115 on the order of 10 times the magnetic @xmath1,@xcite or @xmath135 , and @xmath136 , we find that the prefactor in the dispersion relation is enhance by a factor of 100 over its value in the normal conducting phase . for larger wave numbers , @xmath137 , we have _ ( k ) . [ eq:5.1c ] using eqs . ( [ eqs : a.9 ] ) , we have the correspondence @xmath138 , so we recover the result of the gaussian theory , eqs.([eqs:3.5 ] ) . as long as eq . ( [ eq : a.10 ] ) is valid , @xmath5 thus displays a pronounced plateau as a function of the wave number , followed by a very steep increase at asymptotically small wave numbers . the gaussian theory approximates this behavior by a true gap , ignoring the asymptotic regime . in the limit @xmath99 the asymptotic regime shrinks to zero , and the gaussian theory becomes qualitatively correct . however , in this context one should note that the lgw theory of appendix [ app : a ] is valid only for wave numbers @xmath139 . within the lgw theory , the shoulder will lie in that regime provided the coupling constant @xmath129 is sufficiently small . while the above identification of @xmath129 with the parameters of the microscopic theory makes @xmath129 effectively of order unity , given the initial sharp rise of the magnon frequency with the wave number in the regime where the lgw is valid , a pronounced shoulder in the dispersion relation at intermediate wave numbers is inevitable . the wave number region where one expects this shoulder is given by g_^-2 < k^2 < g(_/)^2_m^-2 . [ eq:5.2 ] if we use the same numbers as above , and @xmath140 , @xmath141 , the upper limit of this wave - number range is given by @xmath142 . this is a factor of 3 below the smallest wave numbers currently observable with neutron scattering.@xcite however , in materials with smaller values of the exchange splitting @xmath115 the plateau should be in an observable regime . second , we add some comments about our prediction of two superconducting transitions that are separated only by a small temperature interval . within our model , we have found this prediction to be very robust , especially given that all of our approximations have a tendency to overestimate the suppression of @xmath7 compared to @xmath6 . even an ( artificial ) increase of the gap in the transverse susceptibility by a factor of 10 does not make a visible change in fig . [ fig:6 ] . this reflects the fact that the up - spin and down - spin pairing are mediated by the same effective potential , viz . , @xmath4 , see eq . ( [ eq:4.4a ] ) and the corresponding eq . ( 3.14a ) in i. while @xmath4 is modified by @xmath2 , the effect is not sufficiently large to lead to a substantial separation of @xmath6 and @xmath7 . this in turn means that the lower value of @xmath7 is overwhelmingly due to the lower value of the density of states at the down - spin fermi level . in this context we need to keep in mind that we have used a free - electron model with parabolic bands . a complicated band structure could lead to a drastically reduced value of @xmath143 , which in turn would lead to a much lower value of @xmath7 . if experiments on samples of improved quality should fail to show two transitions , this would be the most likely explanation . this would be of interest also with regard to distinguishing between the two proposed explanations for why the superconductivity is observed in the ferromagnetic phase only : sandeman et al.@xcite have proposed a mechanism based on an intricate structure of the density of states , while the explanation proposed in i is based on properties of the magnetic susceptibility . third , we come back to our discussion of the specific heat . the experiment of ref . shows that the observed superconductivity is indeed a bulk effect . what is not clear _ a priori _ is the origin of the large residual value of the specific heat coefficient . while the down - spin electrons remaining unpaired , as was suggested in ref . , is a possibility , normal - conducting regions within the sample would have the same effect and would also lead to the observed smearing of the discontinuity in the specific heat . with increasing sample quality , the discontinuity should become sharper , and a crucial question will be whether the residual value drops correspondingly . of course , the emergence of the predicted double feature from the narrowing peak will be the most direct test of our predictions regarding the specific heat . in this context it is interesting to note that such a split transition , with two closely spaced discontinuities in the specific heat , has been observed in upt@xmath144,@xcite but only after a long period of gradually increasing sample quality . ( upt@xmath144 is not ferromagnetic , though , and the split transition has a physical origin that is very different from what we have discussed . ) even in the best samples that show the split transition , however , there is a substantial residual specific heat coefficient , the origin of which is not quite clear . in a ferromagnetic superconductor , one also has to keep in mind that the ground state will not be homogeneous , due to the formation of a spontaneous vortex state.@xcite normal electrons in the vortex cores are a possible source of a residual specific heat coefficient . this effect has been neglected in the current theory and will be pursued in a future publication . fourth , we briefly comment on the fact that the mass , or pseudo - mass , induced in the transverse magnetic susceptibility by the superconductivity , is a singular function of the magnetization . this can be seen in eqs.([eqs:3.5 ] ) , and it also leads to the factor of @xmath145 in the relation between the phenomenological coupling constant @xmath129 in the lgw theory and the microscopic parameters , eq . ( [ eq : a.9c ] ) . this behavior can be traced back to the behavior of the integral in eq . ( [ eq:3.5c ] ) , and thus ultimately to the green functions and the soft particle - hole excitations that are characteristic for itinerant electron systems . the singularity is therefore a result of a coupling between the particle - hole excitations and the magnetic and superconducting goldstone modes . it is very similar in nature to , e.g. , the anomalous magnetization dependence of the magnon stiffness in a normal conducting ferromagnetic phase that was discussed in ref .. in conclusion , we summarize our results . we have presented a consistent and self - contained theory for the coexistence of superconductivity and ferromagnetism in itinerant electron systems . we have presented a field - theoretic formulation of this problem that allows for the determination of both the magnetic and the superconducting equation of state in a systematic loop expansion . this method , which utilizes ma s procedure for generating equations of state , remedies some shortcomings of the earlier theory presented in i , which relied on a minimization of the free energy . the self - contained character of the theory is achieved by means of explicit expressions for the magnetic susceptibility , which is needed as input for the generalized eliashberg equations . these expressions have been evaluated in ferromagnetic phases , both normal conducting and superconducting ones . this is a generalization of the theory for the magnetic susceptibility that was developed in i , and it explicitly takes into account the feedback effects that are characteristic for any purely electronic mechanism for superconductivity . we have explicitly evaluated this theory to one - loop order , and for a model that allows for two components of the superconducting order parameter , one each for cooper pairs consisting of up - spin electrons and down - spin electrons , respectively . the limitations of this one - loop approximation , which neglects superconducting fluctuations and uses a zero - loop expression for the magnetic susceptibility , have been discussed by means of a phenomenological lgw theory that complements our microscopic theory . we have found that , for generic parameter values , the two superconducting transitions that describe the pairing of up - spin and down - spin electrons , respectively , occur close to one another , with transition temperatures that typically differ by only on the order of 10% . this suggests that , if the superconductivity observed in urhge is indeed of a spin - triplet p - wave type mediated by ferromagnetic fluctuations , then the broad feature observed in the specific heat near the temperature of the resistive transition@xcite should contain two transitions that are close together . if samples of improved quality should show only one sharp discontinuity in the specific heat , then this would be a strong argument against the type of pairing we have assumed in this paper . a caveat is provided by our assumption of parabolic bands , however , as discussed above . the presence of spin - triplet superconductivity has further been shown to drastically change the structure of the dispersion relation of the ferromagnetic magnons . in materials with a small exchange splitting this effect is observable with neutron scattering , and can also be used as a probe for the nature of the superconductivity . we would like to thank meigan aronson , j. david cohen , and john toner for helpful discussions . we are indebted to thomas vojta for insisting that the question of goldstone modes warranted a more detailed discussion than we initially were prepared to give . this work was supported by the nsf grant under nos . dmr-01 - 32555 and dmr-01 - 32726 .	it is shown that one generically expects the two transitions to be close to one another . it is also shown that the magnetic goldstone modes acquire an interesting structure in the superconducting phase , which can be used as an experimental tool to probe the origin of the superconductivity .	the split superconducting transition of up - spin and down - spin electrons on the background of ferromagnetism is studied within the framework of a recent model that describes the coexistence of ferromagnetism and superconductivity induced by magnetic fluctuations . it is shown that one generically expects the two transitions to be close to one another . this conclusion is discussed in relation to experimental results on urhge . it is also shown that the magnetic goldstone modes acquire an interesting structure in the superconducting phase , which can be used as an experimental tool to probe the origin of the superconductivity .
1304.5902	c	the comparison with the considered molecular - line and dust - continuum studies of galactic mc complexes demonstrates the applicability of a statistical approach to derive the clmf presented in paper i. the results on fitting the observational clmf through our model are summarized in table [ table_fit ] . they are obtained by use of two different primary fitting criteria : fitting of the general cloud structure @xmath227 or direct fitting of the clmf . regardless of the type of observational data , the applied fitting criterion and of the variety of model cases , the best - fit parameters span relatively narrow ranges : * ` soft ' velocity scaling : @xmath228 * mainly solenoidal forcing : @xmath229 * mapping resolution from few percent to one tenth of the spatial scale : @xmath230 * typical temperatures for molecular gas phase : @xmath231 k. a small velocity scaling index @xmath61 , close or equal to the kolmogorov value for incompressible turbulence ( @xmath79 ) , may seem unrealistic in view of the high compressibility of interstellar turbulence which implies @xmath232 . in fact , numerical simulations of magnetized clouds show that the velocity power spectrum can be even shallower than in the kolmogorov theory . @xcite measured @xmath233 for thermal - to - magnetic pressure ratio in range @xmath234 . ( in our modeling , the latter value could be as low as @xmath235 in case ` wkin2mag ` ; see eq . [ eq_mag_scaling ] . ) apparently , the velocity scaling index for incompressible turbulence @xmath236 should not be necessarily treated as the lowest possible value from theoretical considerations . the best - fit range of the turbulent forcing parameter @xmath78 is narrower , with typical values @xmath237 , in most considered complexes . since @xmath78 can vary within a star - forming region , this result might be explained as a statistical effect . indeed , @xmath238 corresponds to a natural mixture between solenoidal and compressive modes as the latter represent longitudinal waves , occupying one of the three spatial dimensions ( see * ? ? ? * and fig . 8 there ) . the typical best - fit values of the mapping resolution parameter @xmath85 are about several percent . these are the expected values , appropriate to distinguish substructures which are significantly smaller than the spatial scale @xmath41 and significantly larger than the scale of dissipation . generally , our results lend support to a two power - law shape of the clmf : intermediate - mass and high - mass part , with two distinct values of the characteristic mass @xmath20 : @xmath143 and @xmath239 @xmath7 . ( the molecular - line study of rosette mc with its high @xmath20 is the only exception . ) the first value is consistent with model cases of a `` virial - like '' equipartition between gravitational and turbulent energy , possibly with contribution of the thermal energy at small scales and negligible contribution of the magnetic energy ( ` wkin2 ` , ` wkin2th2 ` ) . these equipartition relations are not sufficient to argue that the modeled clumps are in virial equilibrium @xcite but rather indicate their gravitational boundedness or contraction . on the other hand , if the considered model cases hold for a whole cloud , they are indicative for its global collapse @xcite . large characteristic masses of hundreds @xmath7 are obtained for strongly gravitating clumps , with possible magnetic support ( ` wkin4 ` , ` wkin2mag ` ) . such are evidently the cases in taurus , orion a , m17 and ngc7538 . the slope of the modeled intermediate - mass clmf is shallow and does not vary significantly from complex to complex ( @xmath240 ) while the variety is larger for the high - mass one : from typical slopes for fractal clouds to slopes , a bit steeper than the one of the stellar imf ( @xmath241 ) . it seems that the single power - law observational clmfs of slope @xmath242 derived from molecular - line studies in 1990s @xcite have been products of a combination between intermediate- and a few bins from high - mass clmf . on the other hand , the variety of high - mass clmf slopes probably reflects a real variety of physical conditions in individual complexes and the gravitational balance and evolution of the dense fragments in them . its model slope @xmath243 similar to that of the stellar imf when the clmf is time - weighted . when derived from molecular - line mapping of orion a @xcite or the dust - continuum studies of m17 and ngc7538 by @xcite , @xmath244 exceeds noticeably the salpeter value but lies still within the observed variability range @xcite . the dust extinction mapping of taurus , orion a and orion b by lal10 enabled us to make a link between the predicted general cloud structure and the clmf . we point out also the excellent agreement applying this criterion to the dust - continuum study of rosette , making use of a column density map of rosette ( fig . [ fig_rosette ] , top right , embedded ) obtained from herschel data ( see * ? ? ? * for details ) . ( note that the extinction map derived from near - ir extinction using 2mass @xcite delivers similar values for @xmath245 . ) generally , good agreement is found for the chosen scales of clump generation @xmath41 between @xmath246 and @xmath247 pc while in taurus the upper limit is about half of that . those are the conservative limits of the inertial range of turbulence , i ) ] that is a corner stone in our framework of clump description . the discrepancies for larger @xmath41 are to be expected and can be interpreted as reflecting changes in the physical conditions such scales may lie outside the inertial range and/or the assumption of isothermality does not hold for them ( e.g. * ? ? ? * ) . on the other hand , at @xmath248 pc the density pdf deviates from the lognormal shape and develops a power law tail in the high - density part @xcite . the predicted typical clump size in such density regimes approaches @xmath249 pc which is about the sonic scale for temperature range @xmath250 k , i.e. the assumption for supersonic turbulence as a generator of clumps breaks down . @l@ c@ c@ c@ c@ c@ c@ c@ c@ c@ c@ c@ c sf region & fc & mc & & & + & & & @xmath61 & @xmath78 & @xmath85 & @xmath99 [ k ] & @xmath251 & @xmath252 & @xmath244 & @xmath243 & @xmath253 & @xmath203 + + taurus & @xmath254 & ` wkin4 ` & 0.30 - 0.36 & 0.38 - 0.42 & 0.07 - 0.09 & 10 - 20 & @xmath255 & @xmath256 & & & @xmath257 & @xmath258 + orion a & @xmath254 & ` wkin2mag ` & 0.38 - 0.42 & 0.38 - 0.42 & 0.07 - 0.09 & 18 - 22 & @xmath259 & @xmath260 & @xmath261 & @xmath262 & @xmath263 & @xmath264 + orion b & @xmath254 & ` wkin2 ` & 0.30 - 0.36 & 0.30 - 0.36 & 0.055 - 0.065 & 10 - 15 & @xmath265 & & @xmath266 & @xmath267 & @xmath268 & @xmath269 + & @xmath254 & ` wkin2th2 ` & 0.30 - 0.36 & 0.30 - 0.36 & 0.050 - 0.065 & 10 - 15 & @xmath265 & & @xmath266 & @xmath270 & @xmath268 & @xmath271 + mc sample & clmf & ` wkin2 ` & 0.30 - 0.36 & 0.42 - 0.46 & 0.02 - 0.10 & 10 - 12 & @xmath272 & @xmath273 & @xmath274 & @xmath275 & @xmath276 & @xmath271 + & clmf & ` wkin2th2 ` & 0.42 - 0.46 & 0.36 - 0.40 & 0.02 - 0.10 & 8 - 10 & @xmath277 & @xmath278 & @xmath279 & @xmath280 & @xmath276 & @xmath281 + * m17 * & clmf & ` wkin4 ` & 0.43 - 0.45 & 0.37 - 0.40 & 0.02 - 0.10 & 28 - 35 & @xmath282 & @xmath283 & @xmath284 & @xmath285 & @xmath286 & @xmath287 + * rosette * & clmf & ` wkin2mag ` & 0.18 - 0.23 & 0.30 - 0.36 & 0.02 - 0.10 & 8 - 15 & @xmath288 & @xmath289 & @xmath290 & @xmath291 & @xmath292 & @xmath293 + + * m17 * & clmf & ` wkin4 ` & 0.40 - 0.44 & 0.37 - 0.40 & 0.02 - 0.10 & 28 - 35 & @xmath294 & @xmath295 & & & @xmath296 & @xmath297 + * m17+ & clmf & ` wkin4 ` & 0.43 - 0.46 & 0.38 - 0.42 & 0.02 - 0.10 & 28 - 35 & @xmath298 & @xmath299 & @xmath300 & @xmath301 & @xmath302 & @xmath303 + rosette * & clmf & ` wkin2 ` & 0.44 - 0.46 & 0.41 - 0.45 & 0.02 - 0.03 & 18 - 25 & @xmath304 & @xmath305 & @xmath306 & @xmath307 & @xmath308 & @xmath309 + & ( @xmath254 ) & & & & & & & & & & & + probed parameter spaces : @xmath310 ; @xmath311 ; @xmath312 ; @xmath313 k + inclusion of data from dust - continuum studies in the analysis of the clump mass - size ( @xmath201 ) diagrams confirms the results from molecular - line mappings ( sect . [ mr_diagrams ] ) : consistency between the slopes within 2@xmath314 and , occasionally , a shift by a factor of up to 3 on the size axis . generally , the agreement between the locations of the ` average clump ensemble ' and the observed clumps is better ; especially , for the combined clump sample from m17 and ngc7538 . the discrepancies on the @xmath201 diagrams could be attributed to the various clump - finding techniques used in the referred observational studies ( cf . table [ table_mc ] , column 10 ) and hence to different clump size definitions . the latter would not lead to substantially different mass estimates if a typical clump structure is a dense central region and diffuse outer shell . a careful comparative analysis of the basic clump - finding algorithms , applied to identical observational or numerical datasets , is necessary for a more comparison between our statistical clump description and the observed clumps in mc complexes . the role of the magnetic fields in shaping the physical characteristics of mcs and of their substructures can be accounted for more thoroughly in a further extension of this work . @xcite proposed an analytical model of the relation between the width of the pdf @xmath314 in magnetized turbulent medium . it includes a modification of equation [ eq_sigma_pdf ] , consistent with a scaling law of magnetic field @xmath57 ( equation [ eq_mag_scaling ] ) and can be easily incorporated in our modeling . finally we caution the reader that the predictions of our model hold for less evolved clumps of sizes @xmath315 pc and must not be compared with observational mass distributions of dense ( prestellar ) cores . the latter ones will be subject of another study which considers the high - density power - law tail of the density pdf ( cf . * ; * ? ? ? * ) in active star forming regions as a basis for cores description . the essence of this approach is presented in @xcite while the model is in process of development . such study may answer the question whether the difference between the clump mass function and the core mass function is physical or statistical .	the slope of the intermediate - mass clmf is shallow and nearly constant ( ) while the high - mass part is fitted by models that imply gravitationally unstable clumps and exhibit slopes in a broader range ( ) , centered at the value of the stellar initial mass function ( ) .	the statistical approach for derivation of the clump mass function ( clmf ) developed by donkov , veltchev & klessen is put to observational test through comparison with mass distributions of clumps from molecular emission and dust continuum maps of galactic cloud complexes , obtained by various authors . the results indicate gravitational boundedness of the dominant clump population , with or without taking into account the contribution of their thermal and magnetic energy . the clmf can be presented by combination of two power - law functions separated by a characteristic mass from about ten to hundreds solar masses . the slope of the intermediate - mass clmf is shallow and nearly constant ( ) while the high - mass part is fitted by models that imply gravitationally unstable clumps and exhibit slopes in a broader range ( ) , centered at the value of the stellar initial mass function ( ) . [ firstpage ] ism : clouds - ism : structure - turbulence - methods : statistical
astro-ph9805284	i	the pegasus dwarf irregular galaxy ( dig ) was first identified by a. wilson ( see holmberg 1958 ) and its status as a nearby dwarf was confirmed only with the detection of hi by fisher & tully ( 1975 ) . despite its small size , pegasus supports ongoing star formation as evidenced by the presence of luminous blue stars ( hoessel & mould 1982 , christian & tully 1983 , sandage 1986 ) and small hii regions ( hunter , hawley , & gallagher 1993 ) . pegasus is fairly typical of the least luminous digs detected in the local group and a few other nearby galaxy groups ( cf . karachentseva et al . 1987 ; miller 1996 ) . pegasus presents an interesting structural combination of a dwarf irregular system , with a chaotic appearance due to star formation , and a relatively symmetric dwarf elliptical ( de ) or dwarf spheroidal ( dsph ) galaxy , typically without young stars . pegasus has a smooth outer envelope with elliptical isophotes and a brighter core that contains at least two ob associations ( ivanov 1996 ) . it also has a relatively low amount of hi , as indicated by its moderate ( for a dig ) ratio of m@xmath5l@xmath10.4 ( hoffman et al . pegasus may therefore be a nearby example of a transition object between a dwarf galaxy dominated by current star - formation and one dominated by past star formation . while the evolution of very low mass galaxies is still unclear , one possibility is that brief epochs of very active star formation produce a significant fraction of the stellar mass over a few dynamical time scales , or @xmath01 gyr ( e.g. babul & ferguson 1996 ) . such events could disrupt or eject a small galaxy s ism , thereby inhibiting further star formation for a time ( e.g. dekel & silk 1986 , sandage & fomalant 1993 , marlowe et al . 1995 ) . under these conditions much of the metal - rich supernova ejecta will also be lost and so the remaining stellar populations are expected to be relatively metal - poor and may show little metal enrichment over time . it is interesting to see if any indications exist for epochs of enhanced star formation activity in the recent history of the pegasus dwarf , which might have led to its transitional morphological structure . this paper presents the first optical study of the stellar population of the pegasus dwarf based on observations obtained with the wide field planetary camera 2 ( wfpc2 ) on the _ hubble space telescope _ ( _ hst _ ) . supplementary ground - based data were obtained with the wiyn 3.5-m telescope . the pegasus dwarf is highly resolved into individual stars by wfpc2 . these data sets allowed us to obtain high quality color - magnitude diagrams ( cmds ) for the pegasus dwarf , which we analyze to derive its recent star formation history ( sfh ) . the next section reviews the global properties of pegasus and 3 describes our new observations . our analysis of the color - magnitude diagrams is covered in subsequent sections , the derived sfh is presented in 7 , and the results are summarized in 8 .	the stellar population of the pegasus dwarf irregular galaxy is investigated in images taken in the f439w ( b ) , f555w ( v ) , and f814w ( i ) bands with the wide field planetary camera 2 ( wfpc2 ) on the _ hubble space telescope_. with wfpc2 the pegasus dwarf is highly resolved into individual stars to limiting magnitudes of about 25.5 in b and v and 25 in i. these and ground - based data are combined to produce color - magnitude diagrams which show the complex nature of the stellar population in this small galaxy . a young ( age 0.5 gyr ) unique results can not be obtained for the star formation history over longer time baselines without better information on stellar metallicities and deeper photometry .	the stellar population of the pegasus dwarf irregular galaxy is investigated in images taken in the f439w ( b ) , f555w ( v ) , and f814w ( i ) bands with the wide field planetary camera 2 ( wfpc2 ) on the _ hubble space telescope_. with wfpc2 the pegasus dwarf is highly resolved into individual stars to limiting magnitudes of about 25.5 in b and v and 25 in i. these and ground - based data are combined to produce color - magnitude diagrams which show the complex nature of the stellar population in this small galaxy . a young ( age 0.5 gyr ) main sequence stellar component is present and clustered in two centrally - located clumps , while older stars form a more extended disk or halo . the colors of the main sequence require a relatively large extinction of a 0.47 mag . the mean color of the well - populated red giant branch is relatively blue , consistent with a moderate metallicity young , or older , metal - poor stellar population . the red giant branch also has significant width in color , implying a range of stellar ages and/or metallicities . a small number of extended asymptotic giant branch stars are found beyond the red giant branch tip . near the faint limits of our data is a populous red clump superimposed on the red giant branch . efforts to fit self - consistent stellar population models based on the geneva stellar evolution tracks yield a revised distance of 760 kpc . quantitative fits to the stellar population are explored as a means to constrain the star formation history . the numbers of main sequence and core helium - burning blue loop stars require that the star formation rate was higher in the recent past , by a factor of 3 - 4 about 1 gyr ago . unique results can not be obtained for the star formation history over longer time baselines without better information on stellar metallicities and deeper photometry . the youngest model consistent with the data contains stars with constant metallicity of z.001 which mainly formed 2 - 4 gyr ago . if stellar metallicity declines with increasing stellar age , then older ages are allowed of up to gyr . however , even at its peak of star forming activity , the intermediate - age dominated model for the pegasus dwarf most likely remained relatively dim with m . 0.5 cm
1512.08989	i	optomechanical systems , which are based on the interaction between optical and mechanical degrees of freedom , are currently under intense research focus @xcite . much of the interest in these systems is due to their ability to access quantum mechanics at more macroscopic scales than ever before . for example , a major accomplishment of the field has been the cooling of a microfabricated harmonic oscillator , consisting of roughly @xmath0 atoms , to its quantum mechanical ground state @xcite . optomechanical systems therefore provide an avenue for investigating fundamental quantum mechanical issues such as wave function collapse @xcite , superposition @xcite , decoherence @xcite , entanglement @xcite , backaction @xcite and planck - scale physics @xcite . furthermore , these optomechanical systems hold great potential as platforms for ultrasensitive measurement technologies . indeed , optomechanical principles underlie cutting - edge displacement @xcite and force @xcite sensors , phonon detectors @xcite , gravitational wave interferometers @xcite , thermometers @xcite , accelerometers @xcite , and magnetometers @xcite , to cite a few examples . while a variety of physical configurations are used in the investigations mentioned above , in almost all of them , the optical and mechanical degrees of freedom interact via the exchange of _ linear _ momentum . however , light can also exchange _ angular _ momentum with matter @xcite . since the pioneering experiment of beth , it has been known that light can carry spin angular momentum ( i.e. polarization ) , which in turn can exert torque on bulk matter @xcite . subsequently , a seminal paper by allen et al . in 1992 pointed out that photons could also carry orbital angular momentum ( oam ) , encoded as spatial structure in the transverse profile of the corresponding optical beam @xcite . unlike spin , which can only take values @xmath1 , photonic oam can take any value @xmath2 of importance to this tutorial is the fact that oam - carrying beams can exert torque on matter as well , with experiments demonstrating optical rotation effects on nanoparticles @xcite , liquid crystals @xcite , and bose - einstein condensates @xcite , for example . also of relevance is the fact that , due to their intrinsic spatial inhomogeneities , beams with oam can sense the circulation of material particles , via the rotational doppler shift @xcite . this has been verified in velocimetry experiments @xcite ( which have also been implemented with circularly polarized beams @xcite ) . further , it is relevant to mention that the practically infinite hilbert space corresponding to the virtually unlimited oam available per photon has proved to be an important resource for quantum information processing @xcite . lastly , oam carried by an optical beam is associated with the presence of singularities , i.e. vortices , in the beam profile . these structures have their own interesting dynamics and place oam - carrying beams into the larger arena of ` singular optics ' @xcite . there are many other applications of oam - carrying beams ; we have mainly mentioned those which are relevant to our discussion . this tutorial aims to introduce optomechanical systems which are based on angular momentum exchange between light and matter . for the optical fields , this will imply the consideration of photons carrying either polarization or oam . for the mechanics , torsional and free rotational motion will be of importance . to our knowledge , existing introductions to , and reviews of , the micromanipulation of matter with angular momentum - carrying beams largely deal with liquid media @xcite . in contrast , the present tutorial will consider instead only systems under vacuum . with few exceptions , we will consider beams carrying well - defined optical angular momentum per photon , and will neglect the effects of linear photonic momentum on mechanical torsional or free rotational motion @xcite . it is worth stating explicitly the interest behind considering the two types of mechanical motion mentioned above . torsional oscillators are often the instruments of choice for precision measurement experiments . for example , they were used in historic measurements of the static electric force by coulomb @xcite , of the gravitational force by cavendish @xcite , and of optical polarization by beth @xcite . furthermore , a key difference between linear and torsional oscillations is that the linear vibrational motion of an object is affected by its total mass , while the torsional oscillations are affected not only by the total mass but also by how that mass is distributed , i.e. by the moment of inertia . for example , the mass of a sphere of radius @xmath3 varies as @xmath4 , but the moment of inertia goes as @xmath5 thus , smaller objects are easier to move linearly , but even easier to move torsionally . these distinctions make it worthwhile to study torsional oscillations on their own . on the other hand , free mechanical rotation presents some entirely novel features , compared to linear or torsional oscillatory motion , especially in the quantum regime . for example , it is well known that since the harmonic oscillator is a linear system ( i.e. its equations of motion are linear in the dynamical variables , or equivalently , the energy eigenvalues are evenly spaced ) , quantum effects are quite difficult to observe . in other words , the quantum oscillator behaves , for the most part , like a classical oscillator . to observe quantum effects , one usually needs to introduce some sort of nonlinear interaction , for example , by coupling the oscillator to the mode of an electromagnetic field , or to a two - level system @xcite . the free rotor , in contrast , is a nonlinear system ( i.e. its equations of motion are nonlinear in the dynamical variables , or equivalently , its energy spectrum is anharmonic , see below ) , which suggests that it might be easier to observe quantum effects in its behavior without the use of any auxiliary systems . one such quantum effect , which would be interesting to verify at much larger than atomic mass scales , is the quantization of angular momentum , one of the central predictions of quantum mechanics @xcite . a second intriguing feature of the rotor is that , unlike the harmonic oscillator ( and other elementary quantum systems such as the square well , the delta function well , or the morse potential ) , it has no ground state energy @xcite . this can be seen from the hamiltonian of a particle of mass @xmath6 rotating in a circle of radius @xmath3 , @xmath7 where @xmath8 is the angular momentum of the particle , and @xmath9 is its moment of inertia . the eigenvalues of @xmath10 are @xmath11 thus , the ground state @xmath12 is perfectly rotationless . finally , the prospect of observing counter - rotating superpositions of mechanically rotating states @xcite is quite tantalizing , and is the neutral mechanical analog of counter - propagating persistent electronic currents in superconducting circuits @xcite . from a more practical point of view , freely rotating mechanical systems could possibly be used for gyroscopy @xcite and for storing photonic oam @xcite . conversely , optical beams carrying oam could be used to probe mechanical rotation , in a quantum - limited manner @xcite . the remainder of the tutorial is organized in the following way . we first introduce optomechanics based on electromagnetic modes confined to optical resonators . section [ sec : vco ] describes cavity - based vibrational optomechanics , and lays the ground for the formalism , basic physics and applications to follow later . section [ sec : oam ] then introduces oam - carrying beams . the material presented thus far is then utilized to explain cavity - based torsional and rotational optomechanics in sections [ sec : torsionalopto ] and [ sec : rco ] respectively . accounting for the more recent interest in cavityless optomechanical systems , we have included some material on this topic in section [ sec : cavless ] . the tutorial ends with a conclusion in section [ sec : con ] and acknowledgments in section [ sec : ack ] . the format for each section is to first introduce a basic physical configuration . this is done typically , but not in all cases , using work published by our own group , simply because we understand our own work best . subsequently , reference is made to other works in the field . although we have tried to be inclusive in making such references , we apologize to all authors whose works are not adequately cited .	the subject of optomechanics involves interactions between optical and mechanical degrees of freedom , and is currently of great interest as an enabler of fundamental investigations in quantum mechanics , as well as a platform for ultrasensitive measurement devices . subsequently , we will introduce optomechanical systems based on _ angular _ momentum exchange . in this context , optical fields carrying polarization and orbital angular momentum will be considered , while for the mechanics , torsional and free rotational motion will be of relevance .	the subject of optomechanics involves interactions between optical and mechanical degrees of freedom , and is currently of great interest as an enabler of fundamental investigations in quantum mechanics , as well as a platform for ultrasensitive measurement devices . the majority of optomechanical configurations rely on the exchange of linear momentum between light and matter . we will begin this tutorial with a brief description of such systems . subsequently , we will introduce optomechanical systems based on _ angular _ momentum exchange . in this context , optical fields carrying polarization and orbital angular momentum will be considered , while for the mechanics , torsional and free rotational motion will be of relevance . our overall aims will be to supply basic analyses of some of the existing theoretical proposals , to provide functional descriptions of some of the experiments conducted thus far , and to consider some directions for future research . we hope this tutorial will be useful to both theorists and experimentalists interested in the subject .
astro-ph9610082	c	new tf and fp measurements for the cluster a2634 and coma give compatible results for the relative distance and peculiar velocity of the two clusters . contrary to the findings of l91a , the peculiar velocity of a2634 with respect to the cmb reference frame is unlikely to exceed a few @xmath49 @xmath2 , and extremely unlikely to exceed @xmath50 @xmath2 . both tf and fp measurements suggest that the ratio of the distances to a2634 and to coma is @xmath51 , which is not too dissimilar from the ratio of systemic velocities in the cmb reference frame of 1.24 . our determinations are more accurate and reliable than those of previous work , thanks to ( a ) more accurate criteria for the assignment of cluster membership to individual galaxies and ( b ) significantly expanded samples . we have also obtained a new fp template , using for the first time i band photometry . the parameters of this template are in very good agreement with recent determinations of the fp obtained at shorter wavelengths ( gunn r ) , confirming that there is little dependence of the fp relation on the passband used for the photometric measurements . the uncertainty with which the fp can provide peculiar velocity estimates for single galaxies is @xmath10.43 mag in the distance modulus , or 20% of the distance . this uncertainty is slightly larger than the typical uncertainty that characterizes tf estimates , the latter being @xmath10.35 magnitudes . this disadvantage is however partly compensated by the fact that the sample incompleteness bias has a less severe effect on fp cluster distance estimates than it has on tf cluster distance estimates , and cluster membership is more readily established for early type objects . the original motivation for this study was provided by the desire to investigate the universality of the tf and fp relations , the discrepancy in peculiar velocity estimates reported by l91a making a2634 an extreme case study . our results restore a measure of trust in the reliability of those relations as cosmological tools . we would like to thank juan carrasco for the precious help he provided during the observing runs at palomar , and bill schoening for his assistance with the 0.9 m telescope at kpno . we are grateful to the kpno tac for the generous allocation of observing time . this research was partially supported by nsf grants ast9420505 to rg , and ast9023450 and ast9218038 to mph .	the tully - fisher ( tf ) and fundamental plane ( fp ) relations are used to obtain two independent estimates of the relative distance between the clusters a2634 and coma . previously published studies of a2634 showed a large discrepancy between the distance estimates obtained with the tf and the d relations , questioning the reliability of redshift - independent distances obtained using these relations . because of the importance of this issue , we have obtained new distance estimates for a2634 , based on much larger samples than previously used , and selected according to rigorous membership criteria . new i band ccd photometry for 175 galaxies , new 21 cm observations of 11 galaxies , and new velocity dispersion measurements for 62 galaxies are used together with previously published data in building these samples . as part of a larger project to compare the tf and fp distance - scales , we have obtained a new fp template using for the first time i band photometry . its parameters are in very good agreement with recent determinations of the fp obtained at shorter wavelengths . the uncertainty with which the fp can provide peculiar velocity estimates for single galaxies is.43 mag in the distance modulus , or 20% of the distance . this uncertainty is slightly larger than the typical uncertainty that characterizes tf estimates . however this disadvantage is partly compensated by the fact that the sample incompleteness bias has a less severe effect on fp cluster distance estimates than it has on the corresponding tf distance estimates . also , cluster membership is more readily established for early type objects than for spirals .	the tully - fisher ( tf ) and fundamental plane ( fp ) relations are used to obtain two independent estimates of the relative distance between the clusters a2634 and coma . previously published studies of a2634 showed a large discrepancy between the distance estimates obtained with the tf and the d relations , questioning the reliability of redshift - independent distances obtained using these relations . because of the importance of this issue , we have obtained new distance estimates for a2634 , based on much larger samples than previously used , and selected according to rigorous membership criteria . new i band ccd photometry for 175 galaxies , new 21 cm observations of 11 galaxies , and new velocity dispersion measurements for 62 galaxies are used together with previously published data in building these samples . as part of a larger project to compare the tf and fp distance - scales , we have obtained a new fp template using for the first time i band photometry . the template is derived using a sample of 109 e and s0 galaxies that are members of the coma cluster . its parameters are in very good agreement with recent determinations of the fp obtained at shorter wavelengths . the uncertainty with which the fp can provide peculiar velocity estimates for single galaxies is.43 mag in the distance modulus , or 20% of the distance . this uncertainty is slightly larger than the typical uncertainty that characterizes tf estimates . however this disadvantage is partly compensated by the fact that the sample incompleteness bias has a less severe effect on fp cluster distance estimates than it has on the corresponding tf distance estimates . also , cluster membership is more readily established for early type objects than for spirals . after the appropriate corrections for sample incompleteness have been taken into account , we find the tf and fp distance estimates to be in good agreement , both indicating that a2634 has a negligibly small peculiar velocity with respect to the cosmic microwave background reference frame . because of the high accuracy with which the two distance estimates have been obtained , their agreement strongly supports the universality of the tf and fp relations , and therefore their reliability for the estimate of redshift - independent distances .
1304.4457	c	we have emphasized that the uhf wave function can be written as a spin - contaminated _ pair _ wave function of the apsg form . the overlap of the alpha and beta corresponding orbitals of the uhf solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry . as a function of distance , or the ratio u / t , the uhf corresponding orbitals pair in a manner allowing a smooth evolution from a system with doubly occupied orbitals into one in which the @xmath0 and @xmath1 electrons segregate onto distinct sublattices . in this way the uhf wave function evolves from a regime in which the material behaves as a metal with delocalized spins , to one in which all the spins are localized antiferromagnetically . projecting the spin - contaminated uhf pair wave function recovers additional correlation energy in finite systems . the resulting multi - reference wave function , characterized by a single , deformed determinant , describes a pure spin state . the suhf wave function ( projecting @xmath88 by assuring rotational invariance in spin - space ) captures additional intra - pair correlation beyond uhf . the sghf wave function ( projecting @xmath88 and @xmath74 ) captures additional inter - pair correlation . by _ deliberately _ breaking and then restoring these symmetries , we describe strong correlation even at geometries where the uhf solution reduces to rhf or the ghf solution reduces to uhf . from simple calculations of one and two - dimensional finite lattices of hydrogen atoms , we have shown that the broken symmetry determinant characterizing our suhf solutions mirror the pairing schemes utilized extensively some years ago in amo theory to describe correlation in alternant pi - bonded networks . this early work did not address the questions of what happens as you dope the system away from half - filling , or in what manner the pairs respond . the pairs described here accounting for magnetic correlations are strongly orthogonal to one another , whereas the pairs of bcs theory overlap ; 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fox , d. j. gaussian development version revision h.01 . http://www.gaussian.com/ , gaussian , inc . , wallingford ct , 2009 amos , r. d. _ molecular physics _ * 1975 * , _ 29 _ , 11251135 the perfect geometric symmetry of the ring was broken slightly by adding a small ( @xmath152 a ) displacement to each succeeding atom along the vertical z - axis . this imposed helical distortion allows us to uniquely define each of the molecular orbitals of the system , as it lifts the perfect degeneracy in the @xmath153 symmetries , and removes the freedom of the diagonalization routine to rotate them in an arbritrary manner . pauncz , r. _ alternant molecular orbital method _ ; studies in physics and chemistry , no . 4 ; saunders , 1967 larson , e. g. ; thorson , w. r. _ the journal of chemical physics _ * 1966 * , _ 45 _ , 15391554 calais , j. l. _ arkiv fr fysik _ * 1965 * , _ 29 _ , 255 calais , j. l. _ arkiv fr fysik _ * 1965 * , _ 28 _ , 539 calais , j. l. _ arkiv fr fysik _ * 1965 * , _ 28 _ , 511 calais , j. l. _ arkiv fr fysik _ * 1965 * , _ 28 _ , 479	the uhf wave function may be written as a spin - contaminated _ pair _ wave function of the apsg form , and the overlap of the alpha and beta corresponding orbitals of the uhf solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry . we demonstrate this with calculations on one- and two - dimensional hydrogen clusters and make contact with the well studied hubbard model . the uhf corresponding orbitals pair in a manner that allows a smooth evolution from doubly occupied orbitals at small distance to one in which wave function breaks symmetry , segregating the and electrons onto distinct sublattices at large distances . by performing spin projection on these uhf solutions ,	the uhf wave function may be written as a spin - contaminated _ pair _ wave function of the apsg form , and the overlap of the alpha and beta corresponding orbitals of the uhf solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry . we demonstrate this with calculations on one- and two - dimensional hydrogen clusters and make contact with the well studied hubbard model . the uhf corresponding orbitals pair in a manner that allows a smooth evolution from doubly occupied orbitals at small distance to one in which wave function breaks symmetry , segregating the and electrons onto distinct sublattices at large distances . by performing spin projection on these uhf solutions , we address strong correlations that are difficult to capture at intermediate distances using a single determinant . approved for public release : la - ur-13 - 22691 .
0912.1731	i	lets consider that @xmath0 is a compact riemann surface . then we can define a green s function with respect to a metric and a divisor on @xmath0 . suppose that @xmath1 is a hyperbolic 3 - manifold with infinite volume and having compact riemann surfaces @xmath2 as its conformal boundaries at infinity . also choose a geometry on @xmath1 which bears a metric of constant negative curvature . the main new results of this paper express the green s functions on each @xmath3 in terms of the length of some certain geodesics in @xmath1 . manin has done this provided that @xmath1 has one boundary component ( i.e. n=1 ) and is uniformized by a schottky group in @xcite . in this work we will generalize manin s results in general case , @xmath1 has more than one boundary components and is uniformized by a fuchsian , quasi - fuchsian or kleinian group . + in this introduction we state the main definitions , motivation and the plan of doing the work . we start by introducing the definition of a green s function on a compact riemann surface for a divisor and with respect to a normalized volume form on it . let @xmath0 be a compact riemann surface and @xmath4 ( with @xmath5 integer number ) be a divisor on @xmath0 . we show the support of @xmath6 by @xmath7 . also lets consider that @xmath8 is a positive real - analytic 2 - form on @xmath0 . by a green s function on @xmath0 for @xmath6 with respect to @xmath8 we mean a real analytic function @xmath9 satisfying the following conditions : + ( i ) _ laplace equation : _ @xmath10 where @xmath11 , and @xmath12 is the standard @xmath13 - current @xmath14 . + ( ii ) _ singularities : _ let @xmath15 be a complex coordinate in a neighborhood of the point @xmath16 . then @xmath17 is locally real analytic . + a function satisfying these two conditions is uniquely determined up to an additive constant . and the third condition is \(iii ) _ normalization : _ @xmath18 which eliminates the remaining ambiguous constant . @xmath19 is additive on @xmath6 and for @xmath20 , @xmath21 is symmetric , i.e. @xmath22 . + lets consider that @xmath23 is another divisor on @xmath0 that is prime to the divisor @xmath6 . that means , @xmath24 . and put @xmath25 @xmath19 is additive and @xmath21 is symmetric , then @xmath26 is symmetric and biadditive in @xmath27 . + in general , the function @xmath28 depends on the metric @xmath8 , but in the case that both of the divisors are of the degree zero , from the condition ( i ) we see that @xmath29 depends only on @xmath30 . notice that , as a particular case of the general kahler formalism , to choose @xmath8 is the same as to choose a real analytic riemannian metric on @xmath0 compatible with the complex structure . this means that @xmath31 are conformal invariants when both divisors are of degree zero . also in the case that the divisor @xmath6 is principal , i.e. @xmath6 is the divisor of a meromorphic function like @xmath32 , then @xmath33 is a 1 - chain with boundary @xmath34 . the divisors of degree zero on the riemann sphere @xmath35 are principal . then this formula can be directly applied to divisors of degree zero on riemann sphere . + it is well known that the green s function of the degree zero divisors on a riemann surface of arbitrary genus can be expressed exactly via the differential of the third kind @xmath36 with pure imaginary periods and residues @xmath5 at @xmath16 when the divisor is @xmath37(see , @xcite , @xcite ) . then the generalization of the previous formula for arbitrary divisors @xmath27 of degree zero is @xmath38 in general , when the degree of the divisors are not restricted to zero , the basic green s function @xmath39 can be expressed explicitly via theta functions ( as in @xcite ) in the case when @xmath40 is the _ arakelov metric _ constructed with the help of an orthonormal basis of the differentials of the first kind on the riemann surface . the result of manin in @xcite which relates the arakelov green function on a compact riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with schottky uniformization , having the riemann surface as conformal boundary at infinity , was extremely innovative and influential and had a wide range of consequences in the arithmetic context of arakelov geometry as well as and in other contexts , ranging from p - adic geometry , real hyperbolic 3-manifolds , the holography principle and ads / cft correspondence in string theory , and noncommutative geometry . a natural question is to what extent the result of manin can be generalized to cases where , instead of dealing with a single riemann surface , one has several riemann surfaces whose union is the boundary of a hyperbolic 3-manifold , uniformized no longer by a schottky group , but by a fuchsian , quasi - fuchsian , or more general kleinian group . such a generalization is not only interesting because it is a very natural question to pass from kleinian - schottky groups to more general kleinian groups , but also for its potential applications to arakelov geometry , to the case of curves defined over number fields with several archimedean places , while manin s result was formulated for the case of arithmetic curves defined over the rationales . we have focused on the formula in manin s work , that expresses the arakelov green s function on a compact riemann surface in terms of a basis of holomorphic differentials of the first kind and of differentials of the third kind . in the case of schottky uniformization , when the limit set has hausdorff dimension strictly smaller than one , one can construct such differentials in terms of averages over the schottky group . while the same type of formula no longer holds in the fuchsian or quasi - fuchsian case , we use the canonical covering map relating fuchsian and schottky uniformization and the coding of limit sets for the fuchsian and schottky case , to express the green function in the fuchsian or quasi - fuchsian case in terms of the one in the schottky case . the approach we follow for the more general kleinian case is via a decomposition of the uniformizing group as a free product of quasi - fuchsian and schottky groups and applying the results we obtained for these cases individually . the paper consists of three chapters devoted to the cases that the hyperbolic 3-manifold @xmath1 have 1 , 2 and @xmath41 many boundary components at infinity respectively . first chapter pays to the one boundary component case and includes four subchapter devoted to the foundations and the genera 0,1 and @xmath42 respectively . also this chapter contains fundamental definitions and basic computations that are bases for the computations in the next chapters . the results of this chapter are a summary of the reference @xcite . all hyperbolic 3-manifolds with two boundary components with the same genera are uniformized by quasi - fuchsian groups ; the second chapter is devoted to this manifolds . in third chapter we consider the general case i.e. the case that @xmath1 is uniformized by some kleinian groups and have @xmath41 boundary components . finally , as a remark for the chapter three we show that for manifolds with @xmath43 many boundary components at infinity the situation is like the previous . i am grateful to matilde marcolli who suggested this problem , supported me in max - planck and hausdorff institute in bonn , and supervised me in all process . i also many thank saad varsaie for several useful and encouraging comments .	the work is motivated by a result of manin in , which relates the arakelov green function on a compact riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with schottky uniformization , having the riemann surface as conformal boundary at infinity . a natural question is to what extent the result of manin can be generalized to cases where , instead of dealing with a single riemann surface , one has several riemann surfaces whose union is the boundary of a hyperbolic 3-manifold , uniformized no longer by a schottky group , but by a fuchsian , quasi - fuchsian , or more general kleinian group . we have considered this question in this work and obtained several partial results that contribute towards constructing an analog of manin s result in this more general context .	the work is motivated by a result of manin in , which relates the arakelov green function on a compact riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with schottky uniformization , having the riemann surface as conformal boundary at infinity . a natural question is to what extent the result of manin can be generalized to cases where , instead of dealing with a single riemann surface , one has several riemann surfaces whose union is the boundary of a hyperbolic 3-manifold , uniformized no longer by a schottky group , but by a fuchsian , quasi - fuchsian , or more general kleinian group . we have considered this question in this work and obtained several partial results that contribute towards constructing an analog of manin s result in this more general context .
1011.4684	i	the @xmath0-bigraded toda hierarchy , denoted by @xmath0-bth , is an integrable system ( see e.g. @xcite ) , and its lax operator is given by @xmath6 where @xmath7 , @xmath8 is a shift operator which can be expressed as an infinite matrix in the form , @xmath9 . in terms of an infinite size matrix , the lax operator @xmath10 has the band structure with @xmath1 upper and @xmath2 lower nonzero diagonals . the @xmath0-bth is then defined by @xmath11 , & \quad { \rm if } \quad\gamma=\alpha= 1,2,\ldots , n,\\[1.5ex ] [ - ( { \mathcal{l}}^{n+1+\frac{\beta}{m}})_- , { \mathcal{l } } ] , & \quad{\rm if}\quad \gamma=\beta= -m+1,\ldots,-1,0 , \end{array}\right.\ ] ] here we call the @xmath12 numbers of the flows for @xmath13 the _ primaries _ of the bth which describe the small phase space of a topological field theory ( tft ) , and the flows with @xmath14 correspond to the gravitational descendants in this tft . in the case of @xmath15 , the @xmath3-bth is the original toda lattice hierarchy , and the primary flow is just the toda lattice equation @xcite . the @xmath0-bth with @xmath16 or @xmath17 is then considered as an extension of the original toda lattice hierarchy . one should also note that the case with infinite @xmath1 and @xmath2 corresponds to the two - dimensional toda hierarchy where we have two independent lax operators ( one defined near infinity and the other defined near zero in the spectral space , more precisely , one considers two cases with @xmath18 and @xmath19 ) . then the @xmath0-bth can be naturally considered as a reduction of the two - dimensional toda hierarchy by imposing an algebraic relation to those two lax operators ( see @xcite ) . in @xcite , we showed the integrability of an extended version of @xmath0-bth by writing the hierarchy as a bilinear identity , and introduced the @xmath20-functions . here the extension implies that the hierarchy has additional logarithmic flows , and this version is called the extended bth ( see @xcite ) . in this paper , we are interested in constructing several explicit solutions of the bth , and as a first step , we only consider the non - extended version of the bth based on our previous study @xcite . the paper is organized as follows . in section [ sec : toda ] , we give a brief summary of the original toda lattice hierarchy whose lax operator is given by a tri - diagonal matrix . we also discuss briefly @xmath21-bth as an extension of the toda hierarchy and describe the @xmath22-flow defined by the square root of the lax operator . in particular , we mention that there exists nonlocal terms in the equation , and make a remark that the flow also appears in the recent paper @xcite . in section [ sec : bth ] , we give the explicit form of @xmath0-bth and the @xmath20-functions . this section is a brief summary of our previous paper @xcite without the logarithmic flows . here we express the coefficient functions in the lax operator in terms of the @xmath20-functions in the similar manner discussed in @xcite . we also discuss some details of the @xmath23-bth as an example . in section [ sec : equivalent ] , we show the equivalence between the @xmath0- and @xmath5-bths by using the hirota bilinear equations found in @xcite and gauge transformation in @xcite . to be illustrative , we also give some simplest concrete examples of equivalence between flows of @xmath21-bth and @xmath24-bth . this equivalence is explicitly shown in the examples given in section [ sec : hirota ] . in section [ sec : hirota ] , we derive the hirota bilinear equations for the primaries of the @xmath0-bth . then we construct the @xmath20-functions in terms of the moment matrix defined naturally via the wave operators introduced in section [ sec : bth ] ( also see @xcite ) . in section [ sec : rational ] , we construct rational solutions based on the @xmath20-function formulas derived in the previous section . in particular , those rational solutions are given by the products of two schur polynomials depending on two different sets of flow parameters @xmath25 and @xmath26 in ( [ bthlax ] ) . contrary to the case of the original toda hierarchy where the rational solutions are given by the schur polynomials of rectangular young diagrams , the rational solutions of the bth are parametrized by non - rectangular young diagrams . finally , in section [ sec : conclusion ] , we summarize the results and give some discussions .	the-bigraded toda hierarchy is an extension of the original toda lattice hierarchy . the pair of numbers represents the band structure of the lax matrix which has upper and lower diagonals , and the original one is referred to as the-bigraded toda hierarchy . because of this band structure , one can introduce commuting flows which give a parametrization of a small phase space for a topological field theory . in this paper , we first show that there exists a natural symmetry between the- and-bigraded toda hierarchies . we then derive the hirota bilinear form for those commuting flows , which consists of two - dimensional toda hierarchy , the discrete kp hierarchy and its bcklund transformations . 37k05 , 37k10 , 37k20 .	the-bigraded toda hierarchy is an extension of the original toda lattice hierarchy . the pair of numbers represents the band structure of the lax matrix which has upper and lower diagonals , and the original one is referred to as the-bigraded toda hierarchy . because of this band structure , one can introduce commuting flows which give a parametrization of a small phase space for a topological field theory . in this paper , we first show that there exists a natural symmetry between the- and-bigraded toda hierarchies . we then derive the hirota bilinear form for those commuting flows , which consists of two - dimensional toda hierarchy , the discrete kp hierarchy and its bcklund transformations . we also discuss the solution structure of the-bigraded toda equation in terms of the moment matrix defined via the wave operators associated with the lax operator , and construct some of the explicit solutions . in particular , we give the rational solutions which are expressed by the products of the schur polynomials corresponding to non - rectangular young diagrams . `` mathematics subject classifications ( 2000 ) . 37k05 , 37k10 , 37k20 .
1011.4684	c	[ sec : conclusion ] we proved the equivalence between @xmath0-bth and @xmath5-bth , derived the primary hirota equations of the @xmath0-bth , and found several explicit formulas about solutions for the bth using orthogonal polynomials in the matrix form . we also constructed some rational solutions of the bth which are parameterized by the products of schur polynomials corresponding to non - rectangular young diagrams . it may be interesting to find their significance in terms of the representation theory , as in the case of the original toda lattice where the rational solutions are given by the schur polynomials of rectangular young diagrams and they are the virasoro singular vectors . + * acknowledgments : * this work was carried out under the guidance of professor yuji kodama during my visit to ohio state university . i would like to thank professor yuji kodama for his guidance and many useful discussions . i would also like to thank department of mathematics at ohio state university for providing me a generous support and making my visit so pleasant . i also thank professor jingsong he(nbu , china ) for useful discussions and his general support . g. carlet , the extended bigraded toda hierarchy , j. phys . a , 39(2006 ) , 9411 - 9435 , arxiv : math - ph/0604024 . c. z. li , j. s. he , k. wu , y. cheng , tau function and hirota bilinear equations for the extended bigraded toda hierarchy , journal of mathematical physics , 51(2010 ) , 043514 , arxiv:0906.0624 . m. toda , vibration of a chain with nonlinear interaction . 22(1967 ) , 431 - 436 . m. toda , nonlinear waves and solitons(kluwer academic publishers , dordrecht , holland , 1989 ) . k. takasaki , two extensions of 1-d toda hierarchy , j. phys . 43(2010 ) , 434032 , arxiv:1002.4688 . k. ueno , k. takasaki , toda lattice hierarchy , in _ `` group representations and systems of differential equations '' ( tokyo , 1982 ) _ , 1 - 95 , adv . stud . pure math . , 4 , north - holland , amsterdam , 1984 . t. milanov , h. h. tseng , the spaces of laurent polynomials , @xmath447-orbifolds , and integrable hierarchies , journal fr die reine und angewandte mathematik , 622 ( 2008 ) , 189 - 235 , ( also see , arxiv : math.ag/0607012 ) . g. f. yu , c. x. li , j. x. zhao , x. b. hu , on a special two - dimensional lattice by blaszak and szum : pfaffianization and molecule solutions , journal of nonlinear mathematical physics , 12 , 2(2005 ) , 316 - 332 .	we also discuss the solution structure of the-bigraded toda equation in terms of the moment matrix defined via the wave operators associated with the lax operator , and construct some of the explicit solutions . in particular , we give the rational solutions which are expressed by the products of the schur polynomials corresponding to non - rectangular young diagrams . `` mathematics subject classifications ( 2000 ) .	the-bigraded toda hierarchy is an extension of the original toda lattice hierarchy . the pair of numbers represents the band structure of the lax matrix which has upper and lower diagonals , and the original one is referred to as the-bigraded toda hierarchy . because of this band structure , one can introduce commuting flows which give a parametrization of a small phase space for a topological field theory . in this paper , we first show that there exists a natural symmetry between the- and-bigraded toda hierarchies . we then derive the hirota bilinear form for those commuting flows , which consists of two - dimensional toda hierarchy , the discrete kp hierarchy and its bcklund transformations . we also discuss the solution structure of the-bigraded toda equation in terms of the moment matrix defined via the wave operators associated with the lax operator , and construct some of the explicit solutions . in particular , we give the rational solutions which are expressed by the products of the schur polynomials corresponding to non - rectangular young diagrams . `` mathematics subject classifications ( 2000 ) . 37k05 , 37k10 , 37k20 .
1512.00942	i	ideal magnetohydrodynamics ( mhd ) , that reliable workhorse of plasma physics , has long been cast into noncanonical hamiltonian form @xcite . so has the theory from which it is usually derived , the two - fluid model @xcite . there are many advantages to a hamiltonian form : the discovery and classification of invariants ; the development of numerical algorithms that automatically preserve such invariants ; easily finding the equations of motion in curved coordinates ; conducting equilibrium and stability analysis . however , there are many theories intermediate in complexity between two - fluid theory and ideal mhd ; kimura and morrison @xcite describe eleven of them . two are particularly important : hall mhd , which accounts for the difference between the motion of the two species in a typical plasma , and lst s extended mhd @xcite , which includes all terms of first order in the ratio @xmath0 of species masses in the derivation from two - fluid electron - ion theory . recently , yoshida and hameiri @xcite formulated a noncanonical poisson bracket for hall mhd , and shortly later abdelhamid , kawazura and yoshida did so for extended mhd @xcite ; however , as often happens when working with hamiltonian systems , they had to simply posit a bracket and prove it satisfied all the desired attributes , such as antisymmetry and the jacobi identity . we will show how to derive these brackets , starting from action principles for each theory . these action principles have a long and distinguished history in fluids , originating with the work of lagrange in the 18th century @xcite . the action principle formulation has also been employed in plasma physics since the second half of the 20th century , as evident from the works of @xcite . for ideal magnetohydrodynamics ( mhd ) , the first action principle formulation was provided by newcomb in @xcite , shortly followed by other works in the same area @xcite . for extended mhd , an eulerian action principle was proposed by @xcite which was subsequently generalized to a eulerian - lagrangian action by @xcite . for recent overviews of action principle formulations of plasma models , we refer the reader to @xcite . the noncanonical hamiltonian formulations for these models can be found in the works of @xcite . in principle there is an easy process to construct a noncanonical poisson bracket , which goes as follows . first , construct an action whose variations give the correct equations of motion in some coordinate system . from this tangent - space action principle , derive a hamiltonian function via a legendre transform , and produce the corresponding phase - space action principle using the canonical momenta of the original action . the poisson bracket accompanying the phase - space action will be canonical . then simply change coordinates in order to produce the desired noncanonical bracket . this procedure is , indeed , what we use , but there are many complications along the way . to begin with , the canonical bracket for fluid theories requires lagrangian coordinates : those in which every fluid element is given a distinct label , and the equations of motion are expressed for a given labelled element , despite the fact that the element is changing position . however , fully lagrangian actions for hall and extended mhd have not yet been given . the closest are the mixed lagrangian - eulerian actions of ref . @xcite , `` eulerian '' coordinates being ones that observe fluid quantities at a fixed point rather than following a given element . in this paper we present fully lagrangian actions . another complication arises because the legendre transform fails to be invertible for either theory , and an expression for one of the velocities in terms of the phase - space variables must be inserted by hand . finally , the euler - lagrange map producing the noncanonical brackets requires prior knowledge of the generalized vorticities advected by the theories , so we must devote some time to their discovery and elucidation . these generalized vorticities turn out to be crucial to the structure of every hamiltonian mhd model . there are @xmath1 advected vorticities for a theory with @xmath1 distinct charged species , @xmath1 being two in our case . `` advected '' in this case means that the flux elements defined by the vorticities are carried along with the fluid , their corresponding two - forms obeying a lie - dragging equation . for ideal mhd , both generalized vorticities collapse down to the same quantity , the magnetic field , which is advected by the fluid velocity . for hall mhd , one generalized vorticity is the magnetic field , whose fluxes are carried along with the electron velocity , and the other is the magnetic field plus kinetic vorticity @xmath2 , advected by the ion velocity @xcite . for extended mhd they turn out to be almost the same , but differing from the hall mhd ones by terms of order @xmath0 in the curl of the current . both our actions and our derivations of noncanonical brackets would be impossible , but for the fact that we can eliminate the eulerian magnetic field terms in both the action and the euler - lagrange map in favor of fully lagrangian terms , an elimination wholly dependent on the existence of these advected fluxes . before moving on , we note a few ways in which our present work can be readily extended along the lines of past works that utilized these methods . one can incorporate finite larmor radius ( flr ) effects , such as the braginskii gyroviscosity @xcite . flr effects for reduced mhd @xcite and generalized fluid models @xcite were implemented via an action principle formulation , and evidently a similar treatment can be undertaken via our extended mhd action principles . further extensions include stability analyses @xcite , the systematic derivation of reduced extended mhd models ( with potential applications in collisionless reconnection ) , linear and nonlinear waves via a lagrangian approach @xcite , and mhd - like models ( ideal , hall , or extended ) for quasineutral plasmas with more than two charged species . the paper is organized as follows . section [ subsec : hamsys ] reviews the basic framework of hamiltonian systems , while section [ subsec : hammhd ] presents a specific example of that framework for ideal mhd , allowing comparisons with the related , but more complex constructions for hall and extended mhd . we begin our new material by focusing on the simpler theory , hall mhd , in section [ sec : hallmhd ] . section [ subsec : hallflux ] lays out the needed terminology and facts about hall mhd , which are then used in section [ subsec : hallactions ] to construct both tangent - space and phase - space actions . section [ subsec : hallliegauge ] is an interesting digression in which we lay out a useful gauge , producing not only advected fluxes but corresponding advected one - forms . finally , we reach the goal which motivates our entire paper , the derivation in section [ subsec : hallelmap ] of the noncanonical bracket . this derivation is carried out in more algebraic detail than might be necessary , in light of its unfamiliarity to many readers . we then pivot to extended mhd in section [ sec : exmhd ] , starting with a derivation of its fluxes in section [ subsec : exmhdflux ] . we give its actions in section [ subsec : exmhdaction ] , and derive its noncanonical bracket in section [ subsec : exmhdelmap ] . this derivation takes more work than that in [ subsec : hallelmap ] , but the procedure is identical , so this time we omit the details . we conclude in section [ sec : conclusion ] .	there are several plasma models intermediate in complexity between ideal magnetohydrodynamics ( mhd ) and two - fluid theory , with hall and extended mhd being two important examples . in this paper we investigate several aspects of these theories , with the ultimate goal of deriving the noncanonical poisson brackets used in their hamiltonian formulations . finally , using the euler - lagrange map , we show how to derive the noncanonical eulerian brackets from canonical lagrangian ones .	there are several plasma models intermediate in complexity between ideal magnetohydrodynamics ( mhd ) and two - fluid theory , with hall and extended mhd being two important examples . in this paper we investigate several aspects of these theories , with the ultimate goal of deriving the noncanonical poisson brackets used in their hamiltonian formulations . we present fully lagrangian actions for each , as opposed to the fully eulerian , or mixed eulerian - lagrangian , actions that have appeared previously . as an important step in this process we exhibit each theory s two advected fluxes ( in analogy to ideal mhd s advected magnetic flux ) , discovering also that with the correct choice of gauge they have corresponding lie - dragged potentials resembling the electromagnetic vector potential , and associated conserved helicities . finally , using the euler - lagrange map , we show how to derive the noncanonical eulerian brackets from canonical lagrangian ones .
1512.00942	c	we have accomplished many things in the course of deriving the noncanonical brackets for hall and extended mhd . the need for canonical momenta to serve as the backbone of the brackets led to actions for both theories : first the tangent - space ones and , then the phase - space ones and . essential to the actions were the advected generalized vorticities : the magnetic field and for hall mhd , and the two expressions for extended mhd . to go with these advected two - forms , we found advected one - form potentials and . for hall mhd , we found that the momentum equation could be restated in the form of an additional equation resembling ohm s law . similarly , in extended mhd , after recasting the complex original equations and into variables based around the various advected forms , we could produce the equivalent , but much simpler expressions . knowing these forms , we were also able to define the natural euler - lagrange maps and , and at last derive the noncanonical brackets and . a number of interesting concepts had to be used in order to produce these results . to begin with , the actions required a double label space in order to be fully lagrangian , and we may speculate that lagrangian theories incorporating @xmath1-fluid effects will require @xmath1 label spaces . moreover , padhye and morrison @xcite showed that , in ideal mhd , magnetic helicity is the noether invariant corresponding to the symmetry of relabelling . in each of hall and extended mhd , we have two label spaces , and we speculate that helicities corresponding to each theory s two generalized vorticities will arise from distinct relabelling symmetries on the doubled label space . this is a matter for future research . next , our expanded inventory of two - forms and one - forms , defined by their advection properties , allowed us to greatly simplify extended mhd . this shows that a firm understanding of the geometric nature of the objects appearing in a physical system will allow one to cut away much of its seeming complexity , as briefly noted in @xcite . finally , our implementation of the euler - lagrange map ( and the phase - space action principle ) required an unusual method of implementing a constraint , a method which may turn out to have broader applicability . prior to attempting work such as ours , one might have objected that hall and extended mhd are theories too specialized and inelegant to be a fruitful topic for mathematical physics . fortunately , we have found that it is precisely when investigating such specialized problems that one may discover ideas and methods useful in a broader context . from a practical perspective , we emphasize that our action principle for extended mhd ( and the concomitant noncanonical hamiltonian formulation ) can be applied to many problems of interest and relevance in diverse areas . we list a few examples in this category : topological invariants @xcite , particle relabelling symmetries @xcite , reconnection based on hamiltonian models @xcite , tearing modes @xcite , hamiltonian closures @xcite , nonlinear waves @xcite , weakly nonlinear dynamics @xcite , the derivation of gyrofluid and hybrid fluid - kinetic models @xcite , the properties of the equatorial electrojet @xcite , and the rapidly burgeoning field of variational integrators @xcite . thus , our work serves to advance and flesh out the mathematical foundations of extended mhd , whilst also paving the way for the applications of our methodology in fusion , space and astrophysical plasmas .	we present fully lagrangian actions for each , as opposed to the fully eulerian , or mixed eulerian - lagrangian , actions that have appeared previously . as an important step in this process we exhibit each theory s two advected fluxes ( in analogy to ideal mhd s advected magnetic flux ) , discovering also that with the correct choice of gauge they have corresponding lie - dragged potentials resembling the electromagnetic vector potential , and associated conserved helicities .	there are several plasma models intermediate in complexity between ideal magnetohydrodynamics ( mhd ) and two - fluid theory , with hall and extended mhd being two important examples . in this paper we investigate several aspects of these theories , with the ultimate goal of deriving the noncanonical poisson brackets used in their hamiltonian formulations . we present fully lagrangian actions for each , as opposed to the fully eulerian , or mixed eulerian - lagrangian , actions that have appeared previously . as an important step in this process we exhibit each theory s two advected fluxes ( in analogy to ideal mhd s advected magnetic flux ) , discovering also that with the correct choice of gauge they have corresponding lie - dragged potentials resembling the electromagnetic vector potential , and associated conserved helicities . finally , using the euler - lagrange map , we show how to derive the noncanonical eulerian brackets from canonical lagrangian ones .
cond-mat0211554	i	in this work we studied the effects of fano interference and aharonov - bohm phase on the diagonal and off - diagonal transport coefficients in an ab ring with an embedded quantum dot in the kondo regime . the transport properties shows crossover behavior from a high - temperature regime with no kondo correlation to a low - temperature regime with kondo correlation . the crossover behavior manifests itself in the amplitude of an ab oscillations in the diagonal transport coefficients , the electric and thermal conductances . the amplitude is small at high temperatures above @xmath0 but becomes enhanced below @xmath0 by the kondo correlation in the quantum dot . in the case of thermopower , the amplitude of an ab oscillation is strongest within the crossover region near the kondo temperature . the lorenz number , defined as the ratio of electric and thermal conductances , is fixed at the sommerfeld value near zero temperature , but also shows ab oscillations near the kondo temperature . the effect of the ab flux is more dramatic in the thermopower than in diagonal transport coefficients . in addition to the ab oscillations in magnitude , even the sign of thermopower can be modulated by the ab flux . in the case of weak direct tunneling amplitude , the sign change is not possible under the ab flux since the fano inference is weak . when the direct tunneling amplitude is increased , the ab flux can change the sign of the thermopower . most of studies in quantum dots have focused on the @xmath1 curves . charge confinement is relatively easy with the use of the gate voltages , but the heat confinement is a more difficult job possibly because of the easy transfer of heat via other excitations . with more advances in nanotechnology , thermoelectric transport coefficients will provide additional information about the quantum transport in quantum dot systems . this work is supported in part by the bk21 , in part by the national science foundation under grant no . dmr 9357474 , and in part by grant no . 1999 - 2 - 114 - 005 - 5 from the kosef .	thermoelectric effects are studied in an aharonov - bohm ( ab ) interferometer with an embedded quantum dot in the kondo regime . the sign and magnitude of thermopower can be modulated by the ab flux and the direct tunneling amplitude . in addition , the thermopower is anomalously enhanced by the kondo correlation in the quantum dot near the kondo temperature ( ) .	thermoelectric effects are studied in an aharonov - bohm ( ab ) interferometer with an embedded quantum dot in the kondo regime . the ab flux - dependent transmission probability has an asymmetrical shape arising from the fano interference between the direct tunneling path and the kondo - resonant tunneling path through a quantum dot . the sign and magnitude of thermopower can be modulated by the ab flux and the direct tunneling amplitude . in addition , the thermopower is anomalously enhanced by the kondo correlation in the quantum dot near the kondo temperature ( ) . the kondo correlation in the quantum dot also leads to crossover behavior in diagonal transport coefficients as a function of temperature . the amplitude of an ab oscillation in electric and thermal conductances is small at temperatures far above , but becomes enhanced as the system is cooled below . the ab oscillation is strong in the thermopower and the lorenz number within the crossover region near the kondo temperature .
0806.0695	i	the atacama large millimeter array ( alma ) is one of the largest ground - based astronomy projects of the next decade , which will revolutionize several fields of astronomy . a large community of scientists is expected to use alma to tackle several outstanding questions in astrophysics . however , mm / submm astronomy is often considered a field restricted to experts . in the case of students and young scientists in particular , the limited familiarity with mm / submm facilities and observations may prevent them to fully exploit the alma capabilities in the future . these lecture notes are aimed at providing students and young researches some background on mm / submm extragalactic astronomy , with a focus on the investigation of agns . i will first provide a quick overview of the current results obtained through extragalactic mm / submm observations , by focusing on agns ( [ sec_mm_astronomy ] ) . i will then summarize the currently available ( and forthcoming ) mm - submm facilities ( [ sec_current_facilities ] ) . then i will shortly describe alma and summarize its observing capabilities ( [ sec_alma ] ) . finally , i will discuss some of the alma prospects for extragalactic studies , and in particular for agns , both in the local universe and at cosmological distances ( [ sec_alma_prospects ] ) . these lecture notes are far from being exhaustive ; several scientific cases will not be discussed at all ; the main goal of these notes is only to provide an introduction to mm / submm extragalactic astronomy and to highlight some scientific cases that alma will be able to tackle .	these lecture notes provide an introduction to mm / submm extragalactic astronomy , focused on agn studies , with the final goal of preparing students to their future exploitation of the alma capabilities . i first provide an overview of the current results obtained through mm / submm observations of galaxies and agns , both local and at high redshift . then i summarize the main mm / submm facilities that are currently available . alma is then presented with a general description and by providing some details on its observing capabilities . finally , i discuss some of the scientific goals that will be achievable with alma in extragalactic astronomy , and for agn studies in particular .	these lecture notes provide an introduction to mm / submm extragalactic astronomy , focused on agn studies , with the final goal of preparing students to their future exploitation of the alma capabilities . i first provide an overview of the current results obtained through mm / submm observations of galaxies and agns , both local and at high redshift . then i summarize the main mm / submm facilities that are currently available . alma is then presented with a general description and by providing some details on its observing capabilities . finally , i discuss some of the scientific goals that will be achievable with alma in extragalactic astronomy , and for agn studies in particular . galaxies : active , evolution , formation , high - redshift , nuclei , quasars , seyfert , starburst , millimeter , submillimeter , instrumentation : high angular resolution , interferometers 95.85.fm , 95.85.bh , 98.54.-h , 98.54.cm , 98.54.ep , 98.54.kt
1012.3589	i	when a high - energy physics experiment enters the phase of data collection and analysis , the daily tasks of its postgraduate students are often centred not around the particle physics theories one is trying to test but rather on statistical methods . these methods are the tools needed to compare data with theory and quantify the extent to which one stands in agreement with the other . of course one must understand the physical basis of the models being tested and so the theoretical emphasis in postgraduate education is no doubt well founded . but with the increasing cost of hep experiments it has become important to exploit as much of the information as possible in the hard - won data , and to quantify as accurately as possible the inferences one draws when confronting the data with model predictions . despite efforts to make the lectures self contained , some familiarity with basic ideas of statistical data analysis is assumed . introductions to the subject can be found , for example , in the reviews of the particle data group @xcite or in the texts @xcite . in these two lectures we will discuss two topics that are becoming increasingly important : bayesian statistics and multivariate methods . in section [ sec : bayes ] we will review briefly the concept of probability and see how this is used differently in the frequentist and bayesian approaches . then in section [ sec : linefit ] we will discuss a simple example , the fitting of a straight line to a set of measurements , in both the frequentist and bayesian approaches and compare different aspects of the two . this will include in section [ sec : mcmc ] a brief description of markov chain monte carlo ( mcmc ) , one of the most important tools in bayesian computation . we generalize the treatment in section [ sec : fitsys ] to include systematic errors . in section [ sec : multivariate ] we take up the general problem of how to distinguish between two classes of events , say , signal and background , on the basis of a set of characteristics measured for each event . we first describe how to quantify the performance of a classification method in the framework of a statistical test . although the neyman pearson lemma indicates that this problem has an optimal solution using the likelihood ratio , this usually can not be used in practice and one is forced to seek other methods . in section [ sec : bdt ] we look at a specific example of such a method , the boosted decision tree . using this example we describe several issues common to many classification methods , such as overtraining . finally , some conclusions are mentioned in section [ sec : summary ] .	these lectures concern two topics that are becoming increasingly important in the analysis of high energy physics ( hep ) data : bayesian statistics and multivariate methods . in the bayesian approach in particular we will look at a method that has gained popularity in hep in recent years : the boosted decision tree ( bdt ) .	these lectures concern two topics that are becoming increasingly important in the analysis of high energy physics ( hep ) data : bayesian statistics and multivariate methods . in the bayesian approach we extend the interpretation of probability to cover not only the frequency of repeatable outcomes but also to include a degree of belief . in this way we are able to associate probability with a hypothesis and thus to answer directly questions that can not be addressed easily with traditional frequentist methods . in multivariate analysis we try to exploit as much information as possible from the characteristics that we measure for each event to distinguish between event types . in particular we will look at a method that has gained popularity in hep in recent years : the boosted decision tree ( bdt ) .
astro-ph9612216	c	we use the new eros microlensing survey data - set of 3 million two - color observations of about 500 cepheids in the lmc and smc to search for and derive the dependence of the optical pl relations on metallicity . we find that : + ( 1 ) the pl relations for both types of cepheids have the same zero - point offset ( but no slope difference ) , which is attributed to the effect of metallicity under a reasonable assumption about the extinction law . as expected from theory , this effect of metal content is manifested in a color shift of the instability strip . it amounts to about @xmath197 of the strip width , and we could detect it unambiguously thanks to the large number of cepheids and extremely well sampled light curves . + ( 2 ) with the known ensemble difference in metal content between lmc and smc cepheids , we derive a linear relation between the distance modulus correction and metallicity : @xmath173 it applies to distances which are inferred by using lmc as a base _ and _ using two color @xmath27 photometry of the cepheids to establish the reddening . the linearity of metallicity dependence is a good assumption , but needs to be confirmed empirically outside the range of application ( a factor of few lower than smc and higher than the galaxy ) . + ( 3 ) the first overtone cepheids have pl relations which provide distances fully consistent with the pl relations of fundamental mode cepheids . our result can be applied to the long - standing discrepancy between the low-@xmath5 scale and the high-@xmath5 scale . the host galaxies on which each of these scales relies appear to have systematically different metallicities . a simple application of our correction to several recent derivations makes the low-@xmath5 values ( sandage _ et al . _ 1994 ) @xmath7 and the high-@xmath5 values ( freedman _ et al . _ 1994b ) @xmath8 , thus bringing those discrepant estimates into agreement near @xmath9 km.s@xmath10@xmath11 . alcock c. , akerlof c.w . , allsman r.a . , axelrod t.s . , bennett d.p . , chan s. , cook k.h . , freeman k.c . , griest k. , marshall s.l . , park h - s . , perlmutter s. , peterson b.a . , pratt m.r . , quinn p.j . , rodgers a.w . , stubbs c.w , sutherland w. nature , 1993 , * 365 * , 621 aubourg e. , bareyre p. , brehin s. , gros m. , lachieze - rey m. , laurent b. , lesquoy e. , magneville c. , milsztajn a. , moscoso l. , queinnec f. , rich j. , spiro m. , vigroux l. , zylberajch s. , ansari r. , cavalier f. , moniez m. , beaulieu j.p . , ferlet r. , grison ph . , vidal - 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th-1514/96 ) , astro - ph/9611166 . pagel , b.e.j . , simonson , e.a . , terlevich , r.j . , & edmunds , m.g . 1992 , mnras , 255 , 325 pierce , m.j . , welch , d.l . , mcclure , r.d . , van den bergh , s. , racine , r. , & stetson , p.b . 1994 , nature , 371 , 385 press , w.h . , teukolsky , s.a . , vetterling , w.t . , & flannery , b.p . 1992 , _ numerical recipes _ , 2nd ed . , ( cambridge university press , cambridge ) press , w.h . 1996 , preprint , astro - ph/9604126 . riess , a.g . , press , w.h . , & kirshner , r.p . 1995 , apj , 438 , l17 saha , a. , labhardt , l. , schwengeler , h. , macchetto , f.d . , panagia , n. , sandage , a. , & tammann , g.a . 1994 , apj , 425 , 14 sandage , a. , saha , a. , tammann , g.a . , labhardt , l. , schwengeler , h. , panagia , n. , & macchetto , f.d . 1994 , apj * 423 * , l13 sandage , a. , saha , a. , tammann , g.a . , labhardt , l. , panagia , n. , & macchetto , f.d . 1996 , apjl , in press . schechter , p.l . 1980 , aj , 85 , 801 stift , m.j . 1982 , a&a , 112 , 149 stift , m.j . 1995 , a&a , 301 , 776 stothers , r. b. 1988 , apj , 329 , 712 tanvir , n.r . , shanks , t. , freguson , h.c . , & robinson , d.r.t . 1995 , nature , 377 , 27 zaritsky , d. , kennicutt , r.c . , & huchra , j. p. 1994 , apj , 420 , 87	our main result concerns the determination of distances to galaxies which are inferred by using the lmc as a base and using two color photometry to establish the amount of reddening . we attribute the color and the zero - point offset to the difference in metallicity between the smc and lmc cepheids . when applied to recent estimates based on cepheid observations , our metallicity dependence makes the low- values ( sandage _ et al . _ 1994 ) and the high- values ( freedman _ et al . _ 1994b ) , thus bringing those discrepant estimates into agreement near km.s .	this is an investigation of the period - luminosity relation of classical cepheids in samples of different metallicity . it is based on 481 cepheids in the large and small magellanic clouds from the blue and red filter ccd observations ( most similar to & ) of the french eros microlensing project . the data - set is complete and provides an excellent basis for a differential analysis between lmc and smc . in comparison to previous studies of effects on the pl - relation , the eros data - set offers extremely well - sampled light curves and well - filled instability strips . this allows reliable separation of cepheids pulsating in the fundamental and the first overtone mode and derivation of differential reddening . our main result concerns the determination of distances to galaxies which are inferred by using the lmc as a base and using two color photometry to establish the amount of reddening . we find a zero - point offset between smc and lmc which amounts to a difference between inferred and true distance modulus of 0.14 mag in the system . the offset is exactly the same in both sets of pl - relations of the fundamental and of the first overtone mode cepheids . no effect is seen on the slopes of the pl - relations , although the fundamental and the first overtone mode cepheids have different pl slopes . we attribute the color and the zero - point offset to the difference in metallicity between the smc and lmc cepheids . a metallicity effect of that small magnitude still has important consequencies for the inferred cepheid distances and the determination of . when applied to recent estimates based on cepheid observations , our metallicity dependence makes the low- values ( sandage _ et al . _ 1994 ) and the high- values ( freedman _ et al . _ 1994b ) , thus bringing those discrepant estimates into agreement near km.s .
astro-ph9605082	i	two of the most constraining observed properties of active galactic nuclei ( agn ) are their large luminosities over a broad range of energies ( @xmath1-ray through infrared ) and their rapid variability ( implying a small source size unless the emission is highly beamed ) . the inferred large energy densities have led to a standard model of the ultimate energy source being the release of gravitational potential energy of matter from an accretion disk surrounding a supermassive black hole ( e.g. , rees 1984 ) . although this general model has broad support , the specific physical processes that produce the complex , broadband spectral energy distributions ( seds ) observed from agn have not been clearly identified . it is believed that a mix of processes is important . the ultraviolet and optical emission may be primary radiation from an accretion disk ( shields 1978 ; malkan & sargent 1982 ; malkan 1983 ) . in low - luminosity objects starlight will contribute as well . thermal dust emission is an important ingredient of the infrared band ( barvainis 1987 ; sanders et al . the high - energy ( x - ray and @xmath1-ray)emission is not well understood . there are a variety of models for their origin ranging from electromagnetic cascades in an @xmath7 pair plasma ( zdziarski et al . 1990 ) to thermal comptonization models ( haardt & maraschi 1993 ; haardt , maraschi , & ghisellini 1994 ) . furthermore , gas near the central source may reprocess at least some of the primary radiation via compton scattering , absorption , and fluorescent processes ( guilbert & rees 1988 ; lightman & white 1988 ; george & fabian 1991 ; matt , fabian , & ross 1993 ) . determination of the mix of physical processes that produce these large , broadband luminosities is a major unresolved issue in agn research , and multi - waveband variability studies are potentially highly constraining . causality arguments imply that if emission in a secondary " band is produced when photons from a primary " band are reprocessed in material near the central engine , then variations in the secondary band could not be seen to lead those in the primary band . furthermore , if the emission in any given waveband is a combination of two independent components ( with presumably independent variability behavior ) , then measurement of broadband spectral variability might allow them to be separated . finally , if a characteristic variability time scale could be measured , it could be compared with those indicative of different physical processes ( e.g. , with the expected viscous , orbital , light - travel time scales ) . in spite of the potential power of this approach , it has not until recently been exploited because of the very large amount of telescope time required . in several experiments designed to measure the size of the broad - line region in the seyfert 1 galaxy ngc 5548 , variations at @xmath01400 were seen to track those at @xmath02800 and @xmath05000 to within @xmath212 day ( clavel et al . 1991 ; peterson et al . 1991 ; korista et al . this was taken to imply an ultraviolet - optical propagation time that is too short to be associated with any dynamics mediated by viscosity , such as variations in the mass inflow rate , in a standard @xmath8-disk ( krolik et al . 1991 ; but see 4.2 . similar problems were noted in ultraviolet and optical monitoring of ngc 4151 by ulrich et al . krolik et al . ( 1991 ) suggested that variation in the different wavebands in ngc 5548 were coordinated by a photon signal . nandra et al . ( 1992 ) suggested that this signal might be x - ray heating ( reprocessing ) . several authors constructed specific models of x - ray illuminated accretion disks to account for the ngc 5548 data ( collin - souffrin 1991 ; rokaki & magnan 1992 ; molendi , maraschi , & stella 1992 ; rokaki , collin - souffrin , & magnan 1993 ) as well as for ngc 4151 ( perola & piro 1994 ) . a strong test of the idea that the ultraviolet is produced by reprocessing x - ray photons could be made by measuring the time relationship between fluctuations in the ultraviolet and the x - rays , but previous attempts ( e.g. , clavel et al . 1992 ) lacked adequate temporal resolution . in order to attempt this test , an international consortium of agn observers undertook a campaign to intensively monitor a single seyfert 1 galaxy , ngc 4151 , at ultraviolet , x - ray , @xmath1-ray , and optical wavelengths for @xmath010 days in december 1993 . these data are described in detail in the three preceding papers ( paper i crenshaw et al . 1996 ; paper ii kaspi et al . 1996 ; and paper iii warwick et al . 1996 ) ; they are summarized in the following section . in this paper , the multi - wavelength data are analyzed in combination . the measurement of the multi - waveband variability , temporal correlations , phase lags , and the broadband optical through@xmath1-ray sed are analyzed in 3 and the scientific implications are briefly discussed in 4 .	if photons emitted at a primary " waveband are absorbed by nearby material and reprocessed " to produce emission at a secondary waveband , causality arguments require that variations in the secondary band follow those in the primary band . the tight interband correlation and limits on the ultraviolet and medium energy x - ray lags crenshaw , s . warwick , j . clavel , a.v . krolik , d . bertram,g.e . koratkar , o . kovo , a . penfold , e . rodrguez - pascual , e.l . rokaki , j . sadun , i . stirpe , r.e . ulrich , e . wagner , i . xue , a.a . zdziarski , w . zheng , and z .- department of astronomy , university of california , math - science building , los angeles , ca 90024 . department of astronomy , the ohio state university , 174 west 18th avenue , columbus , oh 43210 . department of astronomy , university of leicester , university road , leicester le17rh , united kingdom iso project , european space agency , apartado 50727 , 28080 madrid , spain . department of astronomy , university of california , berkeley , ca 94720 . school of physics and astronomy , university of st . department of physics and astronomy , university of kentucky , lexington , ky 40506 . department of physics and astronomy , the johns hopkins university , baltimore , md 21218 . laboratory for high energy astrophysics , nasa goddard space flight center , greenbelt , md 20771 . centre detudes de saclay , service dastrophysique , orme des merisiers , 91191 gif - sur - yvette cedex , france . department of physics and astronomy , colgate university , hamilton , ny 13346 . cary , il 60013 . deceased , 1994 november 15 . , mexico . department of physics and astronomy , university of nebraska , lincoln , ne 68588 . space telescope science institute , 3700 san martin drive , baltimore , md 21218 . harvard - smithsonian center for astrophysics , 60 garden street , cambridge , ma 02138 . v8x 4m6 , canada . naval research laboratory , code 4151 , 4555 overlook sw , washington , dc 20375 - 5320 . physics department , technion - israel institute of technology , haifa 32000 , israel . department of astronomy , university of michigan , dennison building , ann arbor , mi 48109 . department of physics and astronomy , georgia state university , atlanta , ga 30303 . sternberg astronomical institute , university of moscow , universitetskij prosp . istituto astronomico delluniversit , via lancisi 29 , i-00161 rome , italy . , lagrange , il 60525 . department of physics and astronomy , bowling green state university , bowling green , oh 43403 . oviedo , asturias , spain . instituto de astrofsica de canarias , e-38200 la laguna , tenerife , spain . box 50727 , 28080 madrid , spain . laeff , apdo . 50727 , e-28080 madrid , spain . steward observatory , university of arizona , tucson , az 85726 . hubble fellow . mailing address : rue elysee reclubus 1 bis . , 38100 grenoble , france . osservatorio astronomico di bologna , via zamboni 33 , i-40126 , bologna , italy . european southern observatory , karl schwarzschild strasse 2 , 85748 garching , germany . department of physics , keele university , keele st5 5bg , staffordshire , united kingdom . observatories of the carnegie institution of washington , 813 santa barbara street , pasadena , ca 91101 . = 0em = 1.5em	this paper combines data from the three preceding papers in order to analyze the multi - waveband variability and spectral energy distribution of the seyfert 1 galaxy ngc 4151 during the december 1993 monitoring campaign . the source , which was near its peak historical brightness , showed strong , correlated variability at x - ray , ultraviolet , and optical wavelengths . the strongest variations were seen in medium energy (.5 kev ) x - rays , with a normalized variability amplitude ( nva ) of 24% . weaker ( nva = 6% ) variations ( uncorrelated with those at lower energies ) were seen at soft-ray energies of kev . no significant variability was seen in softer ( 0.11 kev ) x - ray bands . in the ultraviolet / optical regime , the nva decreased from 9% to 1% as the wavelength increased from 1275 to 6900 . these data do not probe extreme ultraviolet ( 1200 to 0.1 kev ) or hard x - ray ( 250 kev ) variability . the phase differences between variations in different bands were consistent with zero lag , with upper limits of.15 day between 1275 and the other ultraviolet bands ,.3 day between 1275 and 1.5 kev , and day between 1275 and 5125 . these tight limits represent more than an order of magnitude improvement over those determined in previous multi - waveband agn monitoring campaigns . the ultraviolet fluctuation power spectra showed no evidence for periodicity , but were instead well - fitted with a very steep , red power - law ( ) . if photons emitted at a primary " waveband are absorbed by nearby material and reprocessed " to produce emission at a secondary waveband , causality arguments require that variations in the secondary band follow those in the primary band . the tight interband correlation and limits on the ultraviolet and medium energy x - ray lags indicate that the reprocessing region is smaller than.15 lt - day in size . after correcting for strong ( factor of ) line of sight absorption , the medium energy x - ray luminosity variations appear adequate to drive the ultraviolet / optical variations . however , the medium energy x - ray nva is 24 times that in the ultraviolet , and the single - epoch , absorption - corrected x - ray/-ray luminosity is only about 1/3 that of the ultraviolet / optical / infrared , suggesting that at most/3 of the total low - energy flux could be reprocessed high - energy emission . the strong wavelength dependence of the ultraviolet nvas is consistent with an origin in an accretion disk , with the variable emission coming from the hotter inner regions and non - variable emission from the cooler outer regions . these data , when combined with the results of disk fits , indicate a boundary between these regions near a radius of order lt - day . no interband lag would be expected as reprocessing ( and thus propagation between regions ) need not occur , and the orbital time scale of day is consistent with the observed variability time scale . however , such a model does not immediately explain the good correlation between ultraviolet and x - ray variations . * multiwavelength observations of * + * short time - scale variability in ngc 4151 . * + * iv . analysis of multiwavelength continuum variability * + 0.4 cm r.a . edelson , t . alexander , d.m . crenshaw , s . kaspi , m.a . malkan , b.m . peterson , r.s . warwick , j . clavel , a.v . filippenko , k . horne , k.t . korista , g.a . kriss , j.h . krolik , d . maoz , k . nandra , p.t . obrien , s.v . penton , t . yaqoob , p . albrecht , d . alloin , t.r . ayres , t.j . balonek , p . barr , a.j . barth , r . bertram,g.e . bromage , m . carini , t.e . carone,f .- z . cheng , k.k . chuvaev, m . dietrich , d . dultzin - hacyan , c.m . gaskell , i.s . glass , m.r . goad , s . hemar , l.c . ho , j.p . huchra , j . hutchings , w.n . johnson , d . kazanas , w . kollatschny , a.p . koratkar , o . kovo , a . laor , g.m . macalpine , p . magdziarz , p.g . martin , t . matheson , b . mccollum , h.r . miller , s.l . morris , v.l . oknyanskij , j . penfold , e . prez , g.c . perola , g . pike,r.w . pogge , r.l . ptak , b .- c . qian , m.c . recondo - gonzlez , g.a . reichert , j.m . rodrguez - espinoza , p.m . rodrguez - pascual , e.l . rokaki , j . roland , a.c . sadun , i . salamanca , m . santos - lle , j.c . shields,j.m . shull,d.a . smith , s.m . smith , m.a.j . snijders,g.m . stirpe , r.e . stoner , w .- h . sun , m .- h . ulrich , e . van groningen , r.m . wagner,s . wagner , i . wanders , w.f . welsh , r.j . weymann , b.j . wilkes , h . wu , j . wurster , s .- j . xue , a.a . zdziarski , w . zheng , and z .- l . zou 0.4 cm = 1.em = -1.em department of physics and astronomy , 203 van allen hall , university of iowa , iowa city , ia 52242 . electronic mail : edelson@spacly.physics.uiowa.edu school of physics and astronomy and the wise observatory , the raymond and beverly sackler faculty of exact sciences , tel - aviv university , tel - aviv 69978 , israel . astronomy program , computer sciences corporation , nasa goddard space flight center , code 681 , greenbelt , md 20771 . department of astronomy , university of california , math - science building , los angeles , ca 90024 . department of astronomy , the ohio state university , 174 west 18th avenue , columbus , oh 43210 . department of astronomy , university of leicester , university road , leicester le17rh , united kingdom iso project , european space agency , apartado 50727 , 28080 madrid , spain . department of astronomy , university of california , berkeley , ca 94720 . school of physics and astronomy , university of st . andrews , north haugh , st . andrews ky169ss , scotland , united kingdom . department of physics and astronomy , university of kentucky , lexington , ky 40506 . department of physics and astronomy , the johns hopkins university , baltimore , md 21218 . laboratory for high energy astrophysics , nasa goddard space flight center , greenbelt , md 20771 . center for astrophysics and space astronomy , university of colorado , campus box 389 , boulder , co 80309 . universitts - sternwarte gttingen , geismarlandstrasse 11 , d-37083 gttingen , germany . centre detudes de saclay , service dastrophysique , orme des merisiers , 91191 gif - sur - yvette cedex , france . department of physics and astronomy , colgate university , hamilton , ny 13346 . mailing address : lowell observatory , 1400 west mars hill road , flagstaff , az 86001 . computer sciences corporation , nasa goddard space flight center , code 684.9 , greenbelt , md 20771 . space sciences laboratory , university of california , berkeley , ca 94720 , and eureka scientific , inc . current address : 28740 w. fox river dr . , cary , il 60013 . center for astrophysics , university of science and technology , hefei , anhui , people s republic of china . crimean astrophysical observatory , p / o nauchny , 334413 crimea , ukraine . deceased , 1994 november 15 . landessternwarte , knigstuhl , d-69117 heidelberg , germany . universidad nacional autonoma de mexico , instituto de astronomia , apartado postal 70 - 264 , 04510 mexico d.f . , mexico . department of physics and astronomy , university of nebraska , lincoln , ne 68588 . south african astronomical observatory , p.o . box 9 , observatory 7935 , south africa . space telescope science institute , 3700 san martin drive , baltimore , md 21218 . harvard - smithsonian center for astrophysics , 60 garden street , cambridge , ma 02138 . dominion astrophysical observatory , 5071 west saanich road , victoria , b.c . v8x 4m6 , canada . naval research laboratory , code 4151 , 4555 overlook sw , washington , dc 20375 - 5320 . physics department , technion - israel institute of technology , haifa 32000 , israel . department of astronomy , university of michigan , dennison building , ann arbor , mi 48109 . astronomical observatory , jagiellonian university , orla 171 , 30 - 244 cracow , poland . canadian institute for theoretical astrophysics , university of toronto , toronto , on m5s 1a1 , canada . department of physics and astronomy , georgia state university , atlanta , ga 30303 . sternberg astronomical institute , university of moscow , universitetskij prosp . 13 , moscow 119899 , russia . department of physics and astronomy , university of calgary , 2500 university drive nw , calgary , ab t2n 1n4 , canada , and department of mathematics , physics , and engineering , mount royal college , calgary t3e 6k6 , canada . istituto astronomico delluniversit , via lancisi 29 , i-00161 rome , italy . mailing address : 816 s. lagrange rd . , lagrange , il 60525 . department of physics and astronomy , bowling green state university , bowling green , oh 43403 . shanghai observatory , chinese academy of sciences , people s republic of china . facultad de ciencias , dept . fsicas , universidad de oviedo , c/ calvo sotelo , s / n . oviedo , asturias , spain . nasa goddard space flight center , code 631 , greenbelt , md 20771 . instituto de astrofsica de canarias , e-38200 la laguna , tenerife , spain . esa iue observatory , p.o . box 50727 , 28080 madrid , spain . royal observatory edinburgh , university of edinburgh , blackford hill , edinburgh eh93hj , united kingdom . institut dastrophysique , 98 bis boulevard arago , f-75014 paris , france . department of physics and astronomy and bradley observatory , agnes scott college , decatur , ga 30030 . royal greenwich observatory , madingley road , cambridge cb3 0ez , united kingdom . laeff , apdo . 50727 , e-28080 madrid , spain . steward observatory , university of arizona , tucson , az 85726 . hubble fellow . jila ; university of colorado and national institute of standards and technology , campus box 440 , boulder , co 80309 . iram , 300 rue de la piscine , 38046 saint martin dheres , france . mailing address : rue elysee reclubus 1 bis . , 38100 grenoble , france . osservatorio astronomico di bologna , via zamboni 33 , i-40126 , bologna , italy . institute of astronomy , national central university , chung - li , taiwan 32054 , republic of china . european southern observatory , karl schwarzschild strasse 2 , 85748 garching , germany . astronomiska observatoriet , box 515 , s-751 20 uppsala , sweden . department of physics , keele university , keele st5 5bg , staffordshire , united kingdom . observatories of the carnegie institution of washington , 813 santa barbara street , pasadena , ca 91101 . beijing astronomical observatory , chinese academy of sciences , beijing 100080 , people s republic of china . n. copernicus astronomical center , bartycka 18 , 00 - 716 warsaw , poland . = 0em = 1.5em
astro-ph9605082	c	these results have important implications for models that attempt to explain the ultraviolet emission from agn . there are currently two broad classes of such models . the first hypothesizes that the bulk of the ultraviolet luminosity is produced internally by viscosity in the inner regions of an accretion disk surrounding a central black hole , and the second , that the observed ultraviolet emission is produced in gas illuminated and heated by the source that we observe at high energies . of course , the true picture could be a combination of these processes , a hybrid in which both intrinsic emission from an accretion disk and reprocessing of x - ray emission are important ( and , indeed , may feed back upon each other ) , or conversely , it may be that neither of these models is relevant . although the specific processes responsible for agn emission have not been clearly identified , there is broad support for the general model of a black hole and accretion disk ( see 1 ) . in this model , the emission from normal ( non - blazar , radio - quiet ) seyfert 1s like ngc 4151 is relatively isotropic , not significantly doppler - boosted or beamed towards earth . in this case , it is possible to use variability to place relatively model - independent limits on the central black hole mass ( and therefore the size scale ) . the most general is the eddington limit , which requires only that the source be gravitationally bound and possess a high degree of spherical symmetry . the minimum central mass given by this limit is @xmath74 where @xmath75 and @xmath76 are the eddington luminosity and mass , @xmath77 is the thompson cross - section , and @xmath78 is the proton mass . as the integrated luminosity of ngc 4151 is @xmath79 erg s@xmath18 , the eddington mass is @xmath80 . for a source surrounding a black hole of mass @xmath81 , and schwarzschild radius @xmath82 , the minimum variability time scale ( @xmath83 ) can be estimated from the size ( @xmath84 ) of the smallest stable orbit , which is @xmath85 for a schwarzschild black hole . for @xmath86 , this implies @xmath87 cm or @xmath88 sec , which is not a significant constraint on data which were sampled every hour . a larger but more model - dependent constraint assumes keplerian orbits and uses the correlation between the widths of emission lines and the distances estimated from their lags to estimate the central mass . in the form in which this estimate is generally presented , the inferred mass is the true mass if the clouds travel on circular orbits . if the clouds are gravitationally bound , but non - gravitational forces ( e.g. radiation pressure or hydrodynamics ) affect cloud motions , the real mass is greater than this estimate ; if the motions are unbound , the real mass is smaller than this estimate . clavel et al . ( 1987 , 1990 ) used this method to derive a central mass of @xmath89 for ngc 4151 . this corresponds to a smallest stable orbit of @xmath90 lt - min . again , this relatively weak constraint is not significant for these data . if the ultraviolet / optical continuum is optically thick thermal emission , the variability amplitudes can be used to constrain the temperature distribution . the simplest non - trivial general case is a flat , azimuthally symmetric disk with a local blackbody temperature that drops with radius as some power - law : @xmath91 . when @xmath8 is 3/4 , this is a fair approximation of a standard accretion disk , except at the smallest radii . by contrast , in a disk that radiates predominantly by reprocessed energy ( see 4.3 . ) , @xmath8 can be smaller , depending on the geometry of both the disk and the source of the primary radiation . if the local emission is described by a blackbody , the contribution of an annulus to the total disk flux density at a given frequency @xmath67 is @xmath92 where @xmath93 , and the starting and ending points of the integral are defined by the temperatures at the inner and outer radii of the ring . the increasing amplitude of variations with observing frequency is then naturally attributed to changing emission from the hotter regions ( that is , the inner disk radii ) . there is a test of the simplest case that produces simultaneous multi - wavelength variations , in which the emission from the outer disk ( @xmath94 ) is constant , and all of the variability is produced by a complete , simultaneous modulation of the emission from the inner disk ( @xmath95 ) . the only free parameter is the radius that separates the variable and constant parts of the disk , and this can be determined from the nva at a single wavelength . for example , using the 1275 variability amplitude of 8.6% gives @xmath96 for @xmath97 or @xmath98 for @xmath99 . this corresponds to a boundary at the disk radius where the temperature is 215,000 or 78,000 k , respectively . the last two columns of table 2 show how the percentage flux would drop if all of the emission inside this radius ( the putative variable component ) went to zero , including the effects of starlight . there is good agreement between the simple thermal model and the observed wavelength dependence of the variability amplitude for the standard accretion disk case , @xmath100 . this is not a strong function of how the inner boundary is chosen ; for the @xmath99 case , truncating the integration to between @xmath101 and @xmath98 changes the result by only 20% . the success of this simple exercise motivated the fitting of the ultraviolet / optical sed with a standard model of a geometrically thin , optically thick accretion disk ( e.g. , following the formalism of sun & malkan 1989 ) . aside from the starlight , no additional long - wavelength component was included in the models , so no attempt was made to fit fluxes longward of 2 @xmath102 m . if the disk is assumed to be viewed face - on , and the black hole is spinning rapidly ( kerr metric ) , the best - fit model parameters are @xmath103 and @xmath104 yr@xmath18 . if on the other hand the black hole is assumed stationary ( schwarzschild case ) , the best - fit parameters are @xmath105 and @xmath106 yr@xmath18 . in either case , the accretion rate corresponds to 0.6% of the eddington rate . the black hole mass inferred from the schwarzschild fit agrees with the keplarian value obtained by clavel et al . ( 1987 , 1990 ) . these fits give higher weight to the higher signal - to - noise optical continuum than to the ultraviolet continuum where the disk light dominates , which in turn requires a hotter disk and consequently a lower black hole mass ( @xmath107 ) . all the disk fits would give significantly larger black hole masses if the disk had a non - zero inclination . integrating the multi - waveband disk emission out to a boundary radius of @xmath108 lt - day shows that approximately 30% , 20% and 5% of the total disk flux at 1275 , 2688 , and 5125 is produced in the inner disk . ( these numbers refer to the kerr model , but are not very model - dependent ; malkan 1991 . ) after correcting for the effects of galactic starlight in the @xmath109 aperture , the 5125 emission from the inner disk falls to @xmath04% . for @xmath110 , this radius corresponds to @xmath111 these fractions are approximately the same as the largest peak - to - peak variations observed in these bands during the intensive 10 day multi - waveband monitoring campaign . thus , one consistent explanation for the decline in variability with increasing wavelength is that the variations occur entirely inside the inner disk . at a distance @xmath112 lt - day from a @xmath113 black hole , the orbital time scale is @xmath01 day , whereas the dominant fluctuations clearly occur on longer time scales ( i.e. , the 1275 peak - to - peak variation was only 42% over the entire 10 day intensive campaign ) . thus , they could be associated with either orbital mechanics or thermal fluctuations in the inner disk . it must also be noted that this simple disk model does not produce any x - ray emission , although this is also likely to originate within the inner regions . these data also can be used to constrain models in which the ultraviolet radiation is produced in gas that is heated by the same x - ray continuum that we observe directly at higher energies . in this model , time variations in the ultraviolet and high energy fluxes should be closely coupled : the ultraviolet becomes stronger shortly after the high energy flux rises , and the high energy flux may itself respond to changes in the ultraviolet flux if the ultraviolet photons provide seeds for compton upscattering into the higher energy band . the delays in both cases are essentially due to the light travel time between the two source regions . consequently , the ( reprocessed ) ultraviolet emission should vary simultaneously with the ( primary ) x - rays on time scales longer than the round - trip light - travel time between the emitting regions ( e.g. , clavel et al . the strong correlation between the ultraviolet and x - ray variations therefore supports the reprocessing hypothesis . the lack of any lag within the ultraviolet could be explained in two ways : either the sub - regions responsible for variations in different wavelengths are likewise very close to each other , or , as with the accretion disk model , only the hottest part of the region is varying . in the context of this model , the lack of any detectable lag implies that the x - ray and ultraviolet emitting regions are separated by @xmath20.15 lt - day , ( @xmath114 lt - day , because the light must travel in both directions ) , so the bulk of the reprocessing must occur in the central regions . perola & piro ( 1994 ) applied a more detailed reprocessing model to earlier x - ray / ultraviolet observations and predicted that high time resolution monitoring would measure lags of order 0.030.1 day ( rather close to but still formally consistent with the measured limits of @xmath20.150.3 day ) . the reprocessing model is supported by the broad profile of the iron k@xmath8 line , which suggests relativistic effects associated with an origin very close to a central black hole ( yaqoob et al . however , the _ asca _ observations ( and previous medium x - ray observations ) found no evidence for any significant hard tail " in the x - ray spectrum ( paper iii ; maisack & yaqoob 1991 ) . while the presence of the iron line implies reprocessing by some material , the lack of a `` reflection hump '' suggests that the material is not optically thick to compton scattering , as would be expected in the putative reprocessing disk . an associated problem is the overall energy budget . the total x - ray/@xmath1-ray flux must be adequate to produce the observed ultraviolet / optical / infrared flux , and the variable high energy flux must also equal or exceed that at lower energies . the observed , integrated 0.11 @xmath102 m flux is @xmath115 erg @xmath15 s@xmath18 . as strong ly@xmath8 and c iv emission indicates that the ultraviolet bump extends to wavelengths substantially shorter than 1000 , the intrinsic , integrated flux is probably larger by a factor of @xmath03 , corresponding to a total ultraviolet / optical / infrared flux of order @xmath116 erg @xmath15 s@xmath18 . the observed , integrated 12 kev and 210 kev fluxes are @xmath117 erg @xmath15 s@xmath18 and @xmath118 erg @xmath15 s@xmath18 , respectively after correction for line - of - sight absorption ( which is particularly important at 12 kev ) , the intrinsic , integrated fluxes rise to @xmath119 erg @xmath15 s@xmath18 and @xmath120 erg @xmath15 s@xmath18 , for a total of @xmath121 erg @xmath15 s@xmath18 . this is not adequate to power the lower energies , but inclusion of the gro data and interpolating between asca and gro yields a ( rather uncertain ) integrated 1200 kev flux of order @xmath122 erg @xmath15 s@xmath18 . this would be of order the amount necessary to power the lower energies . however , the fact that the @xmath1-ray variations differ from those in all other wavebands suggests that the bulk of the 10200 kev emission ( which dominates the x - ray/@xmath1-ray flux ) arises in a component that does not fully participate in the reprocessing . in this case , the x - ray/@xmath1-ray luminosity would still be a factor of order @xmath03 too small , so at most @xmath01/3 of the observed infrared / optical / ultraviolet flux could be due to reprocessing . however , this can not be independently verified because the _ asca _ sampling above 2 kev is inadequate to characterize the variability , and indeed the entire 10 - 50 kev spectrum is interpolated , not observed . although the absolute x - ray luminosity changes are observed to be small compared to those in the ultraviolet / optical , spectral fits indicate that the x - rays are highly ( factor of @xmath01520 ) absorbed , and the intrinsic , absorption - corrected variations have more than enough power to drive the ultraviolet / optical variations . however , the nva , which measures the fractional ( as opposed to absolute ) variations is 24% in the x - rays , while it is only 9% , 5% , 4% , and 1% at 1275 , 1820 , 2688 , and 5125 , respectively . this indicates that at most 35% , 20% , 15% , and 4% of the emission at 1275 , 1820 , 2688 , and 5125 could be due to reprocessing , with the rest coming from a component with different ( slower ) variability . as with the previous analysis , this would indicate that at most @xmath01/3 of the ultraviolet / optical / infrared can be reprocessed emission from higher energies . 1 . ngc 4151 showed significant variability over time scales of days , so the emitting region must be smaller than of order a few light days across , assuming the emission is not beamed . the limits on the interband lags indicate that , if there is reprocessing of flux between bands , none of the emission regions could be larger than @xmath00.15 lt - day . the lower limit to the central black hole mass derived from the eddington limit is small ( @xmath123 ) , corresponding to a minimum variability time of only 10 sec , which is not a significant constraint . accretion disk fits to the sed yield a central black hole with a mass of @xmath124 , accreting well below the eddington limit . the fact that the low nvas decrease from medium energy x - ray to ultraviolet to optical wavebands is consistent with the accretion disk model if the bulk of the variable ultraviolet / optical emission originates in a region @xmath00.07 lt - day ( @xmath125 ) from the center . this model gives is no immediate explanation of the link between ultraviolet and x - ray variations . the reprocessing model predicts a strong correlation between ultraviolet and x - ray variability , which is observed . because the nvas become systematically smaller at longer wavelengths , and because the absorption corrected x - ray/@xmath1-ray luminosity is only much smaller than in the ultraviolet / optical / infrared , and at most @xmath01/3 of the lower energy emission could be produced by reprocessing . this suggests that perhaps the ultraviolet arises in a disk powered partially by illumination by an x - ray source and partially by internal viscosity and accretion . determining the exact mix of these emission components will require probing the ultraviolet / x - ray bands at the shortest accessible time scales . it is of particular importance to extend the coverage to the gap at x - ray energies harder than 2 kev . this is the goal of the upcoming coordinated _ xte / iue_/ground - based observations of ngc 7469 , scheduled for the middle of 1996 , and it is hoped that they will shed further light on this important question . the work of bmp was supported by nasa grants nagw-3315 and nag5 - 2477 . the work of dmc and the _ iue _ data reduction were supported by nasa adp grant s-30917-f . the work of avf and lch was supported by nsf grant ast-8957063 . this research has also been supported in part by nasa grants nag5 - 2439 , nag5 - 1813 , and nagw-3129 . a96 alexander , t. 1996 , preprint a95 alloin , d. et al . 1995 , a&a , 293 , 293 a93 ayres , t. 1993 , pasp , 105 , 538 b87 barvainis , r. 1987 , apj , 350 , 537 b94 brinkmann , w. et al . 1994 , a&a , 288 , 433 c87 clavel , j. et al . 1987 , apj , 321 , 251 c90 clavel , j. et al . 1990 , mnras , 246 , 668 c91 clavel , j. et al . 1991 , apj , 366 , 64 c92 clavel , j. et al . 1992 , apj , 393 , 113 c91 collin - souffrin , s. 1991 , a&a , 249 , 344 g91 george , i. m. , & fabian , a. c. 1991 , mnras , 249 , 352 c95 courvoisier , t. et al . 1995 , apj , 438 , 108 c96 crenshaw , d.m . 1996 , submitted to apj ( paper i ) e87 edelson , r.a . , malkan , m , & rieke , g. 1987 , apj , 321 , 233 ek88 edelson , r.a . , & krolik , j.h . 1988 , apj , 333 , 646 ekp91 edelson , r.a . , krolik , j.h . , & pike , g.f . 1990 , apj , 359 , 86 e92 edelson , r.a . 1992 , apj , 401 , 516 e95 edelson r. et al . 1995 , apj , 438 , 120 e83 elvis , m. , briel , v. & henry , j.p . , 1983 , apj , 268 , 105 gp87 gaskell , c.m . , & peterson , b.m . 1987 , apjs , 65 , 16 gs86 gaskell , c.m . , & sparke , l.s . 1986 , apj , 305 , 175 g88 guilbert , p. w. , & rees , m. j. 1988 , mnras , 233 , 475 hm93 haardt , f. , & maraschi , l. 1993 , apj , 413 , 507 h94 haardt , f. , maraschi , l. , & ghisellini , g. 1994 , apj , 432 , l95 h80 holt , s. et al . 1980 , apj , 241 , l13 k96 kaspi , s. et al . 1996 , submitted to apj ( paper ii ) ko95 korista , k.t . 1995 , apjs , 97 , 285 kr95 kriss , g. et al . 1995 , apjl , 454 , l7 k91 krolik , j.h . , horne , k. , kallman , t.r . , malkan , m.a . , edelson , r.a . , & kriss , g.a . 1991 , apj , 371 , 541 l92 lee , g. , kriss , g. a. , & davidsen , a. f. 1992 , in testing the agn paradigm , ed . s. s. holt , s. g. neff , & c. m. urry ( new york : aip ) , 159 l88 lightman , a. p. , & white , t. r. 1988 , apj , 335 , 57 my91 maisack , m. & yaqoob , t. 1991 , a&a , 249 , 25 m83 malkan , m. a. 1983 , apj , 268 , 582 m91 malkan 1991 , in structure and emission properties of accretion disks ; editions frontieres , eds . bertout , collin , lasota , and van , p. 165 m82 malkan , m. a. , & sargent , w. l. w. 1982 , apj , 254 , 22 m93 matt , g. , fabian , a. c. , & ross , r. r. 1993 , mnras , 262 , 179 m95 morse , j.a . 1995 , apj , 439 , 121 n92 nandra , k. , pounds , k.a . , stewart , g.c . , george , i.m . , hayashida , k. , makino , f. , & ohasi , t. 1991 , mnras , 248 , 760 p95 papadakis , i.e. & mchardy , i.m . , 1995 , mnras , 273 , 923 p96 penton , s. et al . 1996 , apj , in preparation p86 perola , g. et al . 1986 , apj , 306 , 508 p94 perola , g. & piro , l. 1994 , apj , 281 , 7 p95 peterson et al . 1995 , pasp , 107 , 579 p91 peterson , b.m . 1991 , apj , 368 , 119 p78 press , w. 1978 , comments on astrophysics , 7 , 103 r84 rees , m.j . 1984 , araa , 22 , 471 r93 rokaki , e. , collin - souffrin , s. , & magnan , c. 1993 , a&a , 272 , 8 r92 rokaki , e. , & magnan , c. 1992 , a&a , 261 , 41 s89 sanders , d. b. , et al . 1989 , apj , 347 , 29 s78 shields , g. 1978 , nature , 272 , 706 sm89 sun , w .- h . , & malkan , m.a . 1989 , apj , 346 , 68 t89 tully , b. 1989 , nearby galaxy catalogue u91 ulrich , m .- h . , et al . 1991 , apj , 382 , 483 u93 urry , c. m. et al . 1993 , apj , 411 , 614 wds95 warwick , r.s . , done , c. , & smith , d.a . 1995 , mnras 275 , 1003 w96 warwick , r.s . 1996 , submitted to apj ( paper iii ) w94a weaver , k.a . et al . 1994a , apj , 423 , 621 w94b weaver , k.a . et al . 1994b , apj , 436 , l27 wp94 white , r.j . , & peterson , b.m . 1994 , pasp , 106 , 879 y89 yaqoob , t. , warwick , r.s . & pounds , k. 1989 , mnras , 236 , 153 y93 yaqoob , t. et al . 1993 , mnras , 262 , 435 y95 yaqoob , t. , edelson , r.a . , weaver , k.a . , warwick , r.s . , mushotzky , r.f . , serlemitsos , p.j . , & holt , s.s . 1995 , apj , 453 , l81 a90 zdziarski , a. , ghisellini , g. , george , i. m. , svensson , r. , fabian , a. c. , & done , c. 1990 , apj , 363 , l1 * figure 1 * continuum light curves during the 10 day intensive monitoring period , for wavebands centered on 100 kev , 1.5 kev , 1275 , 1820 , 2688 , and 5125 . the light curves are on a common scale , but shifted in flux to present them in one figure , so a 10% flux change is shown . the x - ray data showed the strongest variability but the poorest sampling ; the interruption in the second half of the campaign was due to a spacecraft malfunction . the apparent short flares in the 2688 light curve are probably due to instrumental effects , and not intrinsic variability . * figure 2 * plot of nva as a function of observing frequency . note the strong correlation in the optical / ultraviolet band , where the nva rises from @xmath01% in the optical to @xmath09% in the ultraviolet . the open circles refer to the total variability ( @xmath126 ) , and the filled circles are the nva ( @xmath24 ) , which represent the variability after correction for instrumental uncertainties . the strongest nva is seen in medium energy ( 12 kev ) x - rays , with an nva of 24% , while there is no significant variability observed in the softer x - ray bands , and weaker variations ( nva = 6% ) at 100 kev . * figure 3 * pds of the resampled ultraviolet light curves in four bands . the units of the pds ( co - ordinate axis ) are erg@xmath127 @xmath128 @xmath129 , while the units of the ordinate are day@xmath18 . the pds , which all appear the same to within the errors , show no signs of periodic variability . instead , they are well - fitted by a power - law with slope @xmath46 . * figure 4 * plots of the correlation between continuum fluxes at bands centered on 1275 and 100 kev , 1.5 kev , 1330 , 1820 , 2668 and 5125 . the ultraviolet and @xmath1-ray data are not significantly correlated , but all of the other bands show a significant correlation . the solid lines are unbiased least squares fits to the data . the regression lines with the long - wavelength ultraviolet have a positive y - intercept , while the ultraviolet1.5 kev x - ray regression has a positive x - intercept . * figure 5 * interpolated cross - correlation functions between 1275 and 1275 ( top panel ; autocorrelation ) , 1.5 kev ( second panel ) , 1820 ( third panel ) , 2688 ( fourth panel ) , and 5125 ( bottom panel ) . in all cases , the peaks are consistent with zero lag . * figure 6 * discrete cross - correlation functions between 1275 and 1275 ( top panel ; autocorrelation ) , 1.5 kev ( second panel ) , 1820 ( third panel ) , 2688 ( fourth panel ) , and 5125 ( bottom panel ) . in all cases , the peaks are consistent with zero lag . * figure 7 * spectral energy distribution of ngc 4151 . plotted quantities are monochromatic luminosity ( @xmath130 ) as a function of frequency . optical , ultraviolet , x - ray , and @xmath1-ray data are taken from observations made near mjd 26 . the asterisks show the rms variability in the observing bands listed in table 2 , in terms of monochromatic luminosity . lcccccccc + + & & & & & & & & & & & & & & & & + 50 - 150 kev & 9 & 8.10 & 8.9 & 6.4 & 6.1 & 119 & & 1 - 2 kev & 17 & 9.72 & 26.5 & 11.4 & 23.9 & 6.7 & & 0.5 - 0.9 kev & 17 & 9.72 & 3.5 & 6.6 & & & & 0.1 - 0.4 kev & 17 & 9.72 & 3.0 & 5.0 & & & & 1275 & 176 & 9.20 & 8.6 & 0.9 & 8.6 & 235 & 8.6 & 8.6 1330 & 176 & 9.20 & 8.2 & 1.0 & 8.2 & 241 & 8.1 & 7.4 1440 & 176 & 9.20 & 6.7 & 1.5 & 6.6 & 179 & 7.2 & 6.5 1730 & 176 & 9.20 & 6.1 & 1.4 & 6.0 & 172 & 5.5 & 4.1 1820 & 176 & 9.20 & 5.0 & 1.3 & 4.8 & 124 & 5.1 & 3.6 1950 & 176 & 9.20 & 4.9 & 2.0 & 4.5 & 106 & 4.5 & 3.1 2300 & 168 & 9.15 & 5.3 & 2.0 & 4.9 & 108 & 3.6 & 1.9 2688 & 168 & 9.15 & 3.9 & 1.1 & 3.7 & 89 & 2.7 & 1.3 4600 & 17 & 7.94 & 1.3 & 0.9 & 0.9 & 23 & 1.0 & 0.3 5125 & 18 & 9.33 & 1.1 & 0.9 & 0.7 & 14 & 0.9 & 0.2 6200 & 8 & 8.91 & 1.5 & 0.6 & 1.4 & 33 & 0.6 & 0.2 6925 & 8 & 8.91 & 1.6 & 0.7 & 1.4 & 36 & 0.4 & 0.1 + + lrccrr + + & & & & & + 100kev & 9 & 0.33 & 0.37 & 1.04 & 1kev & 17 & 0.60 & 0.56 & 2.64 & @xmath135 1330 & 176 & 0.96 & 0.95 & 38.11 & @xmath136 1820 & 176 & 0.90 & 0.86 & 22.54 & @xmath137 2688 & 168 & 0.69 & 0.70 & 12.47 & @xmath138 5125 & 18 & 0.65 & 0.59 & 2.95 & @xmath139 + + lccccc + + & & & & & & & & & & + @xmath59 & iccf & 0.82 & 0.87 & 0.70 & 0.69 & zdcf & 0.71 & 0.87 & 0.65 & 0.57 @xmath60 ( days ) & iccf & @xmath140 & @xmath141 & @xmath142 & @xmath143 & zdcf & @xmath144 & @xmath143 & @xmath145 & @xmath143 @xmath61 ( days ) & iccf & @xmath146 & @xmath147 & @xmath148 & @xmath149 & zdcf & @xmath150 & @xmath151 & @xmath152 & @xmath153 @xmath63 ( days)&zdcf & @xmath154 & @xmath155 & @xmath156 & @xmath157 + +	the source , which was near its peak historical brightness , showed strong , correlated variability at x - ray , ultraviolet , and optical wavelengths . the strongest variations were seen in medium energy (.5 kev ) x - rays , with a normalized variability amplitude ( nva ) of 24% . the nva decreased from 9% to 1% as the wavelength increased from 1275 to 6900 . these tight limits represent more than an order of magnitude improvement over those determined in previous multi - waveband agn monitoring campaigns . indicate that the reprocessing region is smaller than.15 lt - day in size . after correcting for strong ( factor of ) line of sight absorption , the medium energy x - ray luminosity variations appear adequate to drive the ultraviolet / optical variations . however , the medium energy x - ray nva is 24 times that in the ultraviolet , and the single - epoch , absorption - corrected x - ray/-ray luminosity is only about 1/3 that of the ultraviolet / optical / infrared , suggesting that at most/3 of the total low - energy flux could be reprocessed high - energy emission . the strong wavelength dependence of the ultraviolet nvas is consistent with an origin in an accretion disk , with the variable emission coming from the hotter inner regions and non - variable emission from the cooler outer regions . however , such a model does not immediately explain the good correlation between ultraviolet and x - ray variations . alexander , d.m . kaspi , m.a . malkan , b.m . peterson , r.s . filippenko , k . horne , k.t . kriss , j.h . maoz , k . nandra , p.t . albrecht , d . alloin , t.r . ayres , t.j . balonek , p . barr , a.j . barth , r . bromage , m . carini , t.e . carone,f .- z . cheng , k.k . chuvaev, m . dietrich , d . dultzin - hacyan , c.m . gaskell , i.s . glass , m.r . hemar , l.c . ho , j.p . huchra , j . hutchings , w.n . johnson , d . kazanas , w . kollatschny , a.p . laor , g.m . macalpine , p . magdziarz , p.g . martin , t . morris , v.l . oknyanskij , j . prez , g.c . perola , g . pike,r.w . pogge , r.l . qian , m.c . reichert , j.m . rodrguez - espinoza , p.m . roland , a.c . salamanca , m . shields,j.m . shull,d.a . smith , s.m . smith , m.a.j . snijders,g.m . stoner , w .- h . sun , m .- h . van groningen , r.m . wanders , w.f . welsh , r.j . wu , j . l . andrews , north haugh , st . andrews ky169ss , scotland , united kingdom . center for astrophysics and space astronomy , university of colorado , campus box 389 , boulder , co 80309 . universitts - sternwarte gttingen , geismarlandstrasse 11 , d-37083 gttingen , germany . current address : 28740 w. fox river dr . , center for astrophysics , university of science and technology , hefei , anhui , people s republic of china . landessternwarte , knigstuhl , d-69117 heidelberg , germany . universidad nacional autonoma de mexico , instituto de astronomia , apartado postal 70 - 264 , 04510 mexico d.f . canadian institute for theoretical astrophysics , university of toronto , toronto , on m5s 1a1 , canada . fsicas , universidad de oviedo , c/ calvo sotelo , s / n . royal observatory edinburgh , university of edinburgh , blackford hill , edinburgh eh93hj , united kingdom . institut dastrophysique , 98 bis boulevard arago , f-75014 paris , france . institute of astronomy , national central university , chung - li , taiwan 32054 , republic of china .	this paper combines data from the three preceding papers in order to analyze the multi - waveband variability and spectral energy distribution of the seyfert 1 galaxy ngc 4151 during the december 1993 monitoring campaign . the source , which was near its peak historical brightness , showed strong , correlated variability at x - ray , ultraviolet , and optical wavelengths . the strongest variations were seen in medium energy (.5 kev ) x - rays , with a normalized variability amplitude ( nva ) of 24% . weaker ( nva = 6% ) variations ( uncorrelated with those at lower energies ) were seen at soft-ray energies of kev . no significant variability was seen in softer ( 0.11 kev ) x - ray bands . in the ultraviolet / optical regime , the nva decreased from 9% to 1% as the wavelength increased from 1275 to 6900 . these data do not probe extreme ultraviolet ( 1200 to 0.1 kev ) or hard x - ray ( 250 kev ) variability . the phase differences between variations in different bands were consistent with zero lag , with upper limits of.15 day between 1275 and the other ultraviolet bands ,.3 day between 1275 and 1.5 kev , and day between 1275 and 5125 . these tight limits represent more than an order of magnitude improvement over those determined in previous multi - waveband agn monitoring campaigns . the ultraviolet fluctuation power spectra showed no evidence for periodicity , but were instead well - fitted with a very steep , red power - law ( ) . if photons emitted at a primary " waveband are absorbed by nearby material and reprocessed " to produce emission at a secondary waveband , causality arguments require that variations in the secondary band follow those in the primary band . the tight interband correlation and limits on the ultraviolet and medium energy x - ray lags indicate that the reprocessing region is smaller than.15 lt - day in size . after correcting for strong ( factor of ) line of sight absorption , the medium energy x - ray luminosity variations appear adequate to drive the ultraviolet / optical variations . however , the medium energy x - ray nva is 24 times that in the ultraviolet , and the single - epoch , absorption - corrected x - ray/-ray luminosity is only about 1/3 that of the ultraviolet / optical / infrared , suggesting that at most/3 of the total low - energy flux could be reprocessed high - energy emission . the strong wavelength dependence of the ultraviolet nvas is consistent with an origin in an accretion disk , with the variable emission coming from the hotter inner regions and non - variable emission from the cooler outer regions . these data , when combined with the results of disk fits , indicate a boundary between these regions near a radius of order lt - day . no interband lag would be expected as reprocessing ( and thus propagation between regions ) need not occur , and the orbital time scale of day is consistent with the observed variability time scale . however , such a model does not immediately explain the good correlation between ultraviolet and x - ray variations . * multiwavelength observations of * + * short time - scale variability in ngc 4151 . * + * iv . analysis of multiwavelength continuum variability * + 0.4 cm r.a . edelson , t . alexander , d.m . crenshaw , s . kaspi , m.a . malkan , b.m . peterson , r.s . warwick , j . clavel , a.v . filippenko , k . horne , k.t . korista , g.a . kriss , j.h . krolik , d . maoz , k . nandra , p.t . obrien , s.v . penton , t . yaqoob , p . albrecht , d . alloin , t.r . ayres , t.j . balonek , p . barr , a.j . barth , r . bertram,g.e . bromage , m . carini , t.e . carone,f .- z . cheng , k.k . chuvaev, m . dietrich , d . dultzin - hacyan , c.m . gaskell , i.s . glass , m.r . goad , s . hemar , l.c . ho , j.p . huchra , j . hutchings , w.n . johnson , d . kazanas , w . kollatschny , a.p . koratkar , o . kovo , a . laor , g.m . macalpine , p . magdziarz , p.g . martin , t . matheson , b . mccollum , h.r . miller , s.l . morris , v.l . oknyanskij , j . penfold , e . prez , g.c . perola , g . pike,r.w . pogge , r.l . ptak , b .- c . qian , m.c . recondo - gonzlez , g.a . reichert , j.m . rodrguez - espinoza , p.m . rodrguez - pascual , e.l . rokaki , j . roland , a.c . sadun , i . salamanca , m . santos - lle , j.c . shields,j.m . shull,d.a . smith , s.m . smith , m.a.j . snijders,g.m . stirpe , r.e . stoner , w .- h . sun , m .- h . ulrich , e . van groningen , r.m . wagner,s . wagner , i . wanders , w.f . welsh , r.j . weymann , b.j . wilkes , h . wu , j . wurster , s .- j . xue , a.a . zdziarski , w . zheng , and z .- l . zou 0.4 cm = 1.em = -1.em department of physics and astronomy , 203 van allen hall , university of iowa , iowa city , ia 52242 . electronic mail : edelson@spacly.physics.uiowa.edu school of physics and astronomy and the wise observatory , the raymond and beverly sackler faculty of exact sciences , tel - aviv university , tel - aviv 69978 , israel . astronomy program , computer sciences corporation , nasa goddard space flight center , code 681 , greenbelt , md 20771 . department of astronomy , university of california , math - science building , los angeles , ca 90024 . department of astronomy , the ohio state university , 174 west 18th avenue , columbus , oh 43210 . department of astronomy , university of leicester , university road , leicester le17rh , united kingdom iso project , european space agency , apartado 50727 , 28080 madrid , spain . department of astronomy , university of california , berkeley , ca 94720 . school of physics and astronomy , university of st . andrews , north haugh , st . andrews ky169ss , scotland , united kingdom . department of physics and astronomy , university of kentucky , lexington , ky 40506 . department of physics and astronomy , the johns hopkins university , baltimore , md 21218 . laboratory for high energy astrophysics , nasa goddard space flight center , greenbelt , md 20771 . center for astrophysics and space astronomy , university of colorado , campus box 389 , boulder , co 80309 . universitts - sternwarte gttingen , geismarlandstrasse 11 , d-37083 gttingen , germany . centre detudes de saclay , service dastrophysique , orme des merisiers , 91191 gif - sur - yvette cedex , france . department of physics and astronomy , colgate university , hamilton , ny 13346 . mailing address : lowell observatory , 1400 west mars hill road , flagstaff , az 86001 . computer sciences corporation , nasa goddard space flight center , code 684.9 , greenbelt , md 20771 . space sciences laboratory , university of california , berkeley , ca 94720 , and eureka scientific , inc . current address : 28740 w. fox river dr . , cary , il 60013 . center for astrophysics , university of science and technology , hefei , anhui , people s republic of china . crimean astrophysical observatory , p / o nauchny , 334413 crimea , ukraine . deceased , 1994 november 15 . landessternwarte , knigstuhl , d-69117 heidelberg , germany . universidad nacional autonoma de mexico , instituto de astronomia , apartado postal 70 - 264 , 04510 mexico d.f . , mexico . department of physics and astronomy , university of nebraska , lincoln , ne 68588 . south african astronomical observatory , p.o . box 9 , observatory 7935 , south africa . space telescope science institute , 3700 san martin drive , baltimore , md 21218 . harvard - smithsonian center for astrophysics , 60 garden street , cambridge , ma 02138 . dominion astrophysical observatory , 5071 west saanich road , victoria , b.c . v8x 4m6 , canada . naval research laboratory , code 4151 , 4555 overlook sw , washington , dc 20375 - 5320 . physics department , technion - israel institute of technology , haifa 32000 , israel . department of astronomy , university of michigan , dennison building , ann arbor , mi 48109 . astronomical observatory , jagiellonian university , orla 171 , 30 - 244 cracow , poland . canadian institute for theoretical astrophysics , university of toronto , toronto , on m5s 1a1 , canada . department of physics and astronomy , georgia state university , atlanta , ga 30303 . sternberg astronomical institute , university of moscow , universitetskij prosp . 13 , moscow 119899 , russia . department of physics and astronomy , university of calgary , 2500 university drive nw , calgary , ab t2n 1n4 , canada , and department of mathematics , physics , and engineering , mount royal college , calgary t3e 6k6 , canada . istituto astronomico delluniversit , via lancisi 29 , i-00161 rome , italy . mailing address : 816 s. lagrange rd . , lagrange , il 60525 . department of physics and astronomy , bowling green state university , bowling green , oh 43403 . shanghai observatory , chinese academy of sciences , people s republic of china . facultad de ciencias , dept . fsicas , universidad de oviedo , c/ calvo sotelo , s / n . oviedo , asturias , spain . nasa goddard space flight center , code 631 , greenbelt , md 20771 . instituto de astrofsica de canarias , e-38200 la laguna , tenerife , spain . esa iue observatory , p.o . box 50727 , 28080 madrid , spain . royal observatory edinburgh , university of edinburgh , blackford hill , edinburgh eh93hj , united kingdom . institut dastrophysique , 98 bis boulevard arago , f-75014 paris , france . department of physics and astronomy and bradley observatory , agnes scott college , decatur , ga 30030 . royal greenwich observatory , madingley road , cambridge cb3 0ez , united kingdom . laeff , apdo . 50727 , e-28080 madrid , spain . steward observatory , university of arizona , tucson , az 85726 . hubble fellow . jila ; university of colorado and national institute of standards and technology , campus box 440 , boulder , co 80309 . iram , 300 rue de la piscine , 38046 saint martin dheres , france . mailing address : rue elysee reclubus 1 bis . , 38100 grenoble , france . osservatorio astronomico di bologna , via zamboni 33 , i-40126 , bologna , italy . institute of astronomy , national central university , chung - li , taiwan 32054 , republic of china . european southern observatory , karl schwarzschild strasse 2 , 85748 garching , germany . astronomiska observatoriet , box 515 , s-751 20 uppsala , sweden . department of physics , keele university , keele st5 5bg , staffordshire , united kingdom . observatories of the carnegie institution of washington , 813 santa barbara street , pasadena , ca 91101 . beijing astronomical observatory , chinese academy of sciences , beijing 100080 , people s republic of china . n. copernicus astronomical center , bartycka 18 , 00 - 716 warsaw , poland . = 0em = 1.5em
1404.2670	i	many recent survey articles on the challenges of achieving exascale computing identify three issues to be overcome : exploiting massive parallelism , reducing energy usage and , in particular , coping with run - time failures @xcite . faults are an issue at peta / exa - scale due to the increasing number of components in such systems . traditional checkpoint - restart based solutions become unfeasible at this scale as the decreasing mean time between failures approaches the time required to checkpoint and restart an application . algorithm based fault tolerance has been studied as a promising solution to this issue for many problems @xcite . sparse grids were introduced in the study of high dimensional problems as a way to reduce the _ curse of dimensionality_. they are based on the observation that when a solution on a regular grid is decomposed into its hierarchical bases the highest frequency components contribute the least to sufficiently smooth solutions . removing some of these high frequency components has a small impact on the accuracy of the solution whilst significantly reducing the computational complexity @xcite . the combination technique was introduced to approximate sparse grid solutions without the complications of computing with a hierarchical basis . in recent years these approaches have been applied to a wide variety of applications from real time visualisation of complex datasets to solving high dimensional problems that were previously cumbersome @xcite . previously @xcite it has been described how the combination technique can be implemented within a _ map reduce _ framework . doing so allows one to exploit an extra layer of parallelism and fault tolerance can be achieved by recomputing failed map tasks as described in @xcite . also proposed was an alternative approach to fault tolerance in which recomputation can be avoided for a small trade off in solution error . in @xcite we demonstrated this approach for a simple two - dimensional problem showing that the average solution error after simulated faults was generally close to that without faults . in this paper we develop and discuss this approach in much greater detail . in particular we develop a general theory for computing new combination coefficients and discuss a three - dimensional implementation based on mpi and openmp which scales well for relatively small problems . as has been done in the previous literature @xcite , we use the solution of the scalar advection pde for our numerical experiments . the remainder of the paper is organised as follows . in section [ sec : back ] we review the combination technique and provide some well - known results which are relevant to our analysis of the fault tolerant combination technique . we then develop the notion of a general combination technique . in section [ sec : faults ] we describe how the combination technique can be modified to be fault tolerant as an application of the general combination technique . using a simple model for faults on each node of a supercomputer we are able to model the failure of component grids in the combination technique and apply this to the simulation of faults in our code . we present bounds on the expected error and discuss in how faults affect the scalability of the algorithm as a whole . in section [ sec : implem ] we describe the details of our implementation . in particular we discuss the multi - layered approach and the way in which multiple components work together in order to harness the many levels of parallelism . we also discuss the scalability bottleneck caused by communications and several ways in which one may address this . finally , in section [ sec : numres ] we present numerical results obtained by running our implementation with simulated faults on a pde solver . we demonstrate that our approach scales well to a large number of faults and has a relatively small impact on the solution error .	the approach is novel for two reasons , first it provides several levels in which one can exploit parallelism leading towards massively parallel implementations , and second , it provides algorithm - based fault tolerance so that solutions can still be recovered if failures occur during computation . we present a generalisation of the combination technique from which the fault tolerant algorithm is a consequence . using a model for the time between faults on each node of a high performance computer we provide bounds on the expected error for interpolation with this algorithm . a comparison with traditional checkpoint - restart methods applied to the combination technique show that our approach is highly scalable with respect to the number of faults . exascale computing , algorithm - based fault tolerance , sparse grid combination technique , parallel algorithms 65y05 , 68w10	this paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [ b. harding and m. hegland , _ anziam j. _ , 54 ( ctac2012 ) , pp . c394c411 ] . the approach is novel for two reasons , first it provides several levels in which one can exploit parallelism leading towards massively parallel implementations , and second , it provides algorithm - based fault tolerance so that solutions can still be recovered if failures occur during computation . we present a generalisation of the combination technique from which the fault tolerant algorithm is a consequence . using a model for the time between faults on each node of a high performance computer we provide bounds on the expected error for interpolation with this algorithm . numerical experiments on the scalar advection pde demonstrate that the algorithm is resilient to faults on a real application . it is observed that the trade - off of recovery time to decreased accuracy of the solution is suitably small . a comparison with traditional checkpoint - restart methods applied to the combination technique show that our approach is highly scalable with respect to the number of faults . exascale computing , algorithm - based fault tolerance , sparse grid combination technique , parallel algorithms 65y05 , 68w10
1404.2670	c	a generalisation of the sparse grid combination technique has been presented . from this generalisation a fault tolerant combination technique has been proposed which significantly reduces recovery times at the expense of some upfront overhead and reduced solution accuracy . theoretical bounds on the expected error and numerical experiments show that the reduction in solution accuracy is very small . the numerical experiments also demonstrate that the upfront overheads become negligible compared to the costs of recovery using checkpoint - restart techniques if several faults occur . there are some challenges associated with load balancing and efficient communication with the implementation of the combination technique . studying these aspects and improving the overall scalability of the initial implementation will be the subject of future work . as the ulfm specification continues to develop , the validation of the ftct on a system with real faults is also being investigated . , _ a robust combination technique _ , in s. mccue , t. moroney , d. mallet , and j. bunder , editors , proceedings of the 16th biennial computational techniques and applications conference , anziam journal , 54 ( ctac2012 ) , pp . c394c411 . , _ robust solutions to pdes with multiple grids _ , sparse grids and applications - munich 2012 , j. garcke , d. pflger ( eds . ) , lecture notes in computational science and engineering 97 , springer , 2014 , to appear . , _ a parallel fault tolerant combination technique _ , m. bader , a. bode , h .- j . bungartz , m. gerndt , g.r . joubert , f. peters ( eds . ) , parallel computing : accelerating computational science and engineering ( cse ) , advances in parallel computing 25 , ios press , 2014 , pp . 584592 . , _ global communication schemes for the sparse grid combination technique _ , m. bader , a. bode , h .- j . bungartz , m. gerndt , g.r . joubert , f. peters ( eds . ) , parallel computing : accelerating computational science and engineering ( cse ) , advances in parallel computing 25 , ios press , 2014 , pp . 564573 . , _ reducibility among combinatorial problems _ , in complexity of computer computations : proc . of a symp . on the complexity of computer computations , r. e. miller and j. w. thatcher , eds . , the ibm research symposia series , new york , ny : plenum press , 1972 , pp . 85103 . , _ fault - tolerant grid - based solvers : combining concepts from sparse grids and mapreduce _ , proceedings of 2013 international conference on computer science ( iccs ) , procedia computer science , elsevier , 2013 . , _ managing complexity in the parallel sparse grid combination technique _ , m. bader , a. bode , h .- j . bungartz , m. gerndt , g.r . joubert , f. peters ( eds . ) , parallel computing : accelerating computational science and engineering ( cse ) , advances in parallel computing 25 , ios press , 2014 , pp .	this paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [ b. harding and m. hegland , _ anziam j. _ , 54 ( ctac2012 ) , pp . c394c411 ] . numerical experiments on the scalar advection pde demonstrate that the algorithm is resilient to faults on a real application .	this paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [ b. harding and m. hegland , _ anziam j. _ , 54 ( ctac2012 ) , pp . c394c411 ] . the approach is novel for two reasons , first it provides several levels in which one can exploit parallelism leading towards massively parallel implementations , and second , it provides algorithm - based fault tolerance so that solutions can still be recovered if failures occur during computation . we present a generalisation of the combination technique from which the fault tolerant algorithm is a consequence . using a model for the time between faults on each node of a high performance computer we provide bounds on the expected error for interpolation with this algorithm . numerical experiments on the scalar advection pde demonstrate that the algorithm is resilient to faults on a real application . it is observed that the trade - off of recovery time to decreased accuracy of the solution is suitably small . a comparison with traditional checkpoint - restart methods applied to the combination technique show that our approach is highly scalable with respect to the number of faults . exascale computing , algorithm - based fault tolerance , sparse grid combination technique , parallel algorithms 65y05 , 68w10
1512.05669	i	the relationship between mathematics and physics at a basic level is of much interest to many . it was most clearly raised some time ago by wigner in a paper on `` the unreasonable effectiveness of mathematics in the natural sciences '' @xcite . this work resulted in much discussion about the relationship @xcite . there was also the suggestion that physics is mathematics @xcite . these ideas led to work towards a coherent theory of mathematics and physics together in which physics and mathematics are treated together as a coherent whole @xcite . the origin of continuing work on this topic @xcite was based on gauge theory considerations . the mathematical setup for these theories consists of vector spaces associated with each point of a space time manifold . unitary connections between these spaces express the concept , based on work by yang and mills @xcite , of the freedom of choice of bases in vector spaces . this work is based on an extension of the freedom of basis choice in vector spaces to the freedom of number value choice for the underlying scalar fields . the choice freedom is based on the observation that the value of a number at one space time point does not determine the value of the same number at another point . this results in the extension of gauge theory to include separate scalar fields associated with the vector spaces at each space time point . this localization of scalar fields follows from the representation of mathematical systems , such as vector spaces and scalar fields , as mathematical structures and relations between the structures @xcite . structures consist of a base set , a few basic operations and relations , and none or a few constants . they satisfy axioms relevant to the system type being considered . it can be shown that , for each number type , there exist many different structures that differ from one another by scaling factors . it follows that base set elements , as numbers , do not have intrinsic , structure independent values . they have different values in different scaled structures . this fact and the choice freedom of number values at different locations results in the existence of separate local scaled number structures at each point . the scaling used here is linear in that the sum of two scaled numbers equals the scaling of the sum of the numbers . this type of scaling has recently been generalized to nonlinear scaling of number structures @xcite . the additional complexity of this type of scaling makes it difficult to apply it to different areas of physics . these applications are work for the future . relations between number structures at different locations are implemented by a scalar scaling field . the value of the field at each location is the scaling factor for the number structure at each point . the field is not unitary as it is the product of a real factor and a phase factor . in earlier work extension of gauge theory to include the effect of the scaling scalar field was described . the effect of the scaling field and use of local scaled number structures was extended to briefly describe some other physical and geometric quantities @xcite . in this work the emphasis is on quantum mechanical quantities for one , two , and multiparticle systems . the definition of the scaling field is extended to apply to entangled states of two or more particles . fiber bundles @xcite have been much used in physics . they have been used to describe gauge theories @xcite and nonrelativistic quantum mechanics @xcite . the quantum descriptions include an introductory description @xcite , a detailed mathematical development @xcite and descriptions in which symmetry groups and semigroups serve as the base space @xcite . this paper uses fiber bundles to describe the effect of a scaling scalar field on one , two , and multiparticle quantum systems in nonrelativistic quantum mechanics . the description includes the effect of the field on multiparticle spatially entangled states . the plan of the paper is to first describe the scaling of scalar fields and vector spaces . this is done in the next section . local representations of these and other structures at each point of a space or space time manifold are conveniently described by use of fiber bundles . these are described in section [ fb ] . the bundle fibers are large in that they contain sufficient scaled mathematical structures to describe some aspects of quantum mechanics . in earlier work that was not based on fiber bundles @xcite , mathematical universes or the mathematics available to observers were the equivalent of fibers at different locations . the scalar scaling field is introduced in the next section on connections . the field is complex valued since it acts on hilbert spaces and on complex numbers as a scalar base for the hilbert spaces . section [ qm ] describes some aspects of the use of fiber bundles in quantum mechanics . the three subsections discuss one , two , and multiparticle particle states . the discussion includes entangled two and multiparticle states . the fiber bundles are used to describe a projection of a wave packet onto the bundle fibers . this is followed by the use of the scaling field connections to map the projected wave packet to a fiber at an arbitrary reference location . without the localization , the implied space integration of the wave packet amplitudes is undefined . an expansion of the definition of the connection for single particle states to accommodate two and multiparticle states is described . the discussion section [ d ] concludes the paper . some justification for the localization of quantum mechanics is given . also coupling and cosmological limitations on the scalar scaling field are noted .	this paper describes the effects of a complex scalar scaling field on quantum mechanics . the field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field . the extension is based on the idea that the value of a number at one space time point does not determine the value at another point . this , combined with the description of mathematical systems as structures of different types , results in the presence of separate number fields and vector spaces as structures , at different space time locations . complex number structures and vector spaces at each location , are scaled by a complex space time dependent scaling factor . the effect of this scaling factor on several physical and geometric quantities has been described in other work . here the emphasis is on quantum mechanics of one and two particles , their states and properties . multiparticle states are also briefly described . the effect shows as a complex , nonunitary , scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics .	this paper describes the effects of a complex scalar scaling field on quantum mechanics . the field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field . the extension is based on the idea that the value of a number at one space time point does not determine the value at another point . this , combined with the description of mathematical systems as structures of different types , results in the presence of separate number fields and vector spaces as structures , at different space time locations . complex number structures and vector spaces at each location , are scaled by a complex space time dependent scaling factor . the effect of this scaling factor on several physical and geometric quantities has been described in other work . here the emphasis is on quantum mechanics of one and two particles , their states and properties . multiparticle states are also briefly described . the effect shows as a complex , nonunitary , scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics . the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small . it also means that the gradient of the field must be very small in a local region of cosmological space and time . outside this region there are no restrictions on the field gradient .
1512.05669	c	the are many aspects of number scaling and the effects of scaling fields on quantum mechanics that should be discussed . one is the use of a complex number value structure as separate from the different scaled representation structures . this is done to make clear the distinction between number and number value . however this may not be necessary . the reason is that base set elements of representation structures automatically acquire values in any structure that satisfies the relevant axioms . another distinct value structure should not be needed to describe this . representations of base set elements of complex numbers that are based on rational number representations as lexicographically ordered symbol strings over an alphabet has been briefly described . more work is needed here because these representations may provide a connection between experiment outputs as numbers and their values in different scaled representations . this suggests that the value of the scaling field at the location at which an experiment or measurement is done will affect the value associated with the measurement outcome . note that a measurement outcome is a physical system in a specific state that is interpreted as a number . the value of the number may depend on the scaling field value at the measurement location . the representations of quantum mechanical states of two or more systems in fiber bundles with fibers base on two or more points in @xmath125 needs more work . one would like to have a single fiber bundle that includes quantum states of an arbitrary number of particles in each fiber . here one needs separate bundles for @xmath107 and @xmath484 particle states . one possible way to achieve this is to expand the treatment to apply to relativistic quantum mechanics . hopefully such an expansion would include quantum states in fock space . the projection of the integrand for @xmath485 particle states as a section on a fiber bundle has the result that the magnitude of contributions of the integrand for different @xmath125 locations depends on the locations and their separations . if the amplitude of the integrand as a vector field for a one particle state is very small at a location , then its contribution to the scaled wave packet at a reference location is very small . this excludes the effect of the connection in moving the magnitude to the reference location . the same argument holds for the dependence of the amplitude for two particle states on two reference locations and the distance between them . the choice of a reference location or locations for a fiber representation of the wave packet as an integral over the section is independent of the properties of the wave packet . the location or locations can be anywhere with arbitrary separations between the locations . a change of reference locations is a change of the location of the mathematical descriptions . it is entirely separate from any physical change or translation of the quantum state . there is a rather philosophical reason for restricting reference locations to points in cosmological space and time that are accessible to us as intelligent observers . for reference locations such as @xmath464 this includes the collapsing of @xmath464 to one @xmath125 location such as @xmath486 for @xmath487 the reason is that mathematical structures , as models of axioms , have meaning or value . they are semantic structures . the important point is that the concept of meaning is observer related . it is based on the idea that meaningfulness or value is a local concept associated with individual observers . mathematics in a textbook , described in a lecture , or on a computer screen , has no meaning or value until the information is transmitted by a physical medium , such as light or sound , to the observers brain . the concept of meaning or value is localized to the observers location . if the observer moves through space then the localization of meaning or value follows a path in @xmath125 . since meaningfulness or value applies to many observers , there are many points in @xmath125 that are observer reference locations . as noted before , interest in local representations of physical and geometric quantities and the attendant scaling has its origin in gauge theories . the gauge freedom in these theories requires the use of separate vector spaces at each space time point . unitary transformations between spaces at different locations represent the freedom of basis choice in each space . since scalar fields , as real or complex numbers , are part of the description of vector spaces , it seems natural to consider them also as localized . the freedom of choice of bases in vector spaces is expanded to include freedom of choice of scaling factors in the fields . since numbers play such an essential role in physics it seems worthwhile to extend this localization and scaling factor choice to other mathematical structures used in other areas of physics . this includes those structures that include numbers as part of their description . examples include vector spaces , algebras , group representations as matrices , and many other systems . this is what is done here for complex numbers as used in quantum mechanics . a very important open question concerns the physical existence , if any , of the scalar scaling field , @xmath160 . candidates include the higgs boson @xcite , dark matter @xcite , dark energy @xcite , inflaton @xcite , quintessence @xcite , etc . as noted elsewhere @xcite , the lack of direct physical evidence for the @xmath160 field means that the coupling constant of @xmath160 to fermion fields must be very small compared to the fine structure constant . this is required by the great accuracy of quantum electrodynamics without any @xmath160 field components . some intriguing points are worth noting . if the @xmath160 field has single particle excited states , then the particles would be scalar bosons , presumably of spin @xmath72 the only particle field with this property is the higgs boson . is the @xmath160 field related to the higgs boson ? another point concerns the relation of dark energy to the physical vacuum energy as expanding space time . the effect of scaling on geometric quantities as in @xcite is in some ways similar . as was noted , the number @xmath1 is unique as the only number whose value is independent of scaling . in this sense it is like a number vacuum . assume that the scaling factor is time dependent . then the distance between points in @xmath125 , as a number value in @xmath488 is a function of @xmath133 and @xmath24 . if @xmath489 is a distance of two points at time @xmath490 then the distance between the same points at time @xmath491 is @xmath492 @xcite . is this related to dark energy ? answers to these and other questions is work for the future . the lack of physical evidence for the effect of the @xmath160 field in quantum mechanics , as shown here , means that the variation of the @xmath160 field over the region of cosmological space and time in which experiments have been conducted is below experimental error . this is equivalent to the requirement that the vector field @xmath493 as the gradient of @xmath387 be so small as to have avoided detection in the region of experiments done to date . this is the region occupied by us as beings capable of carrying out experiments and making theory predictions . it is impossible to predict what the future will say about the @xmath160 field or its gradient . however it is the case that all experiments done by us , in the past , now , or in the future , will be done in a region of cosmological space and time that is either occupiable by us , or by other intelligent beings on distant planets with whom we can communicate effectively . one estimate @xcite of the size of this region is as a sphere of about @xmath494 light years in diameter that includes the solar system . the exact size of the region is not important . the only requirement is that it is small compared to the size of the universe . the result of these considerations is that there are no restrictions on the properties of the @xmath160 field in space and time regions outside of the occupiable one . nothing prevents the @xmath160 field from being very large with rapidly varying gradients in these regions . this applies to regions close to the big bang , about @xmath495 billion years ago , as well as to most of the universe . it is clear that there is much more work needed . this includes expansion of the manifold to space time to include special relativity and to a pseudo reimannian manifold for general relativity . one may hope that these expansions will offer some clues to the physical nature of the scalar scaling field .	the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small . it also means that the gradient of the field must be very small in a local region of cosmological space and time . outside this region there are no restrictions on the field gradient .	this paper describes the effects of a complex scalar scaling field on quantum mechanics . the field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field . the extension is based on the idea that the value of a number at one space time point does not determine the value at another point . this , combined with the description of mathematical systems as structures of different types , results in the presence of separate number fields and vector spaces as structures , at different space time locations . complex number structures and vector spaces at each location , are scaled by a complex space time dependent scaling factor . the effect of this scaling factor on several physical and geometric quantities has been described in other work . here the emphasis is on quantum mechanics of one and two particles , their states and properties . multiparticle states are also briefly described . the effect shows as a complex , nonunitary , scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics . the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small . it also means that the gradient of the field must be very small in a local region of cosmological space and time . outside this region there are no restrictions on the field gradient .
1507.07385	r	this section presents the experimental results of the two - dimensional measurement setup described in section [ sec : experimental_setup ] . the first subsection presents the far - field spatial cross - correlation function of the rss signals and estimate the spread of these spatial correlations . we then determine the spatial fourier transform of these cross - correlations to look for an upper bound at a spatial frequency of @xmath221 , in line with the spatial resolution being bounded by the diffraction limit . finally , we determine the global rmse of and show its asymptotic behavior to the diffraction limit with the increase of the density of sampling points . we compare this experimentally determined rmse with the rmse determined by the crlb for independent and correlated noise . we show that the crlb for independent noise underestimates the rmse computed from our measurements . [ fig : coherence ] shows the spatial cross - covariance function between power flows as a function of distance in wavelengths . the spatial cross - covariance function is calculated using the deviations from the lnsm expressed by and calibrated propagation parameters expressed by . hence , spatial cross - covariance and thus cross - correlations are distance independent by cross correlating the deviations from the calibrated lnsm . fig . [ fig : coherence ] shows that the spatial cross - correlations go to a minimum over a distance of roughly half the mean wavelength , which corresponds to the diffraction limit . the small difference between the black and red curve indicates that noise resulting from repetitive multiplexed measurements over time is negligible compared to the cross - correlated noise in the far field . [ t ] million rss measurements . the red curve shows the measured cross - correlations using @xmath20 rss measurement per reference radio position.,title="fig:",scaledwidth=48.0% ] [ t ] . theoretically , it is represented by tri(k ) , as it is the fourier transform of . the vertical line represents the spatial frequency that corresponds to the diffraction limit , which forms an upper bound in the spectrum.,title="fig:",scaledwidth=48.0% ] in the case of fisher information and thus crlb analysis , information is additive when measurements are independent @xcite . one usually assumes signal models with independent noise@xcite . hence , localization precision increases with an ever increasing amount of independent measurements over a finite measuring range . however , when measurements are correlated , information and localization precision gain decrease with increasing correlations . [ fig : coherence ] shows that when space - measurement intervals become as small as the diffraction limit , measurements become spatially correlated and mutually dependent . our measurements show that rss signal measurements are spatially correlated over a single - sided region of roughly half the mean wavelength . it corresponds to the diffraction pattern expressed by derived in section [ sec : noise ] . therefore , increasing reference radio density beyond one per half a wavelength has a negligible influence on fisher information gain and thus on localization precision . our experimental results in the next subsection confirm this . in case of independent measurements , fig . [ fig : coherence ] would show an infinitely sharp pulse ( dirac delta function ) . [ fig : fft ] shows the measured power spectrum of cross - correlated noise in rss signals , @xmath222 , i.e. the spatial fourier transform of the cross - covariance of fig . [ fig : coherence ] . theoretically , it is represented by the spatial fourier transform of . this figure shows that the energy is mainly located in lower spatial frequencies and it diminishes over a single - sided interval of @xmath223 . this upper bound corresponds to the diffraction limit . the nyquist sampling rate provides an estimate of the minimum sampling rate to fully reconstruct the power - flow signal over space without loss of information , which equals the single - sided bandwidth of our power spectrum . the vertical black line represents the spatial frequency associated with the nyquist sampling rate , which equals @xmath224 . our experimental results in the next subsection confirm this by showing that the localization precision does not increase by sampling beyond this sampling rate . in case of independent measurements , fig . [ fig : fft ] would show a uniform distribution . [ fig : localization ] shows the experimental results of our measurement setup described in section [ sec : experimental_setup ] . localization precision is given as the inverse of rmse , which is computed from . [ t ] independent rss measurement per reference radio position ( green curve).,title="fig:",scaledwidth=48.0% ] the red curve in fig . [ fig : localization ] shows the rmse as a function of the number of measurements per wavelength . the rmse decreases with increasing number of rss measurements over space until sufficient measurements are available . at a critical measurement density , the bound on localization precision becomes of interest . the rmse ( red and black curves ) converges asymptotically to roughly half the mean wavelength as one would expect from the diffraction limit . the rmse represented by the red curve is based on processing all @xmath225 rss signal measurements per reference radio position . the rmse represented by the black curve is based on processing one rss signal measurement per reference radio position . the negligible difference between the red and black curves shows that the number of repeated rss signal measurements per reference radio has a negligible influence on the rmse . the crlb for independent measurements starts deviating from the rmse ( red and black curves ) when the sampling rate is increased beyond one rss signal per half the mean wavelength ( see black dotted curve ) , as one would expect from the diffraction limit and the nyquist sampling rate over space @xcite . spatial correlations between rss signals increase rapidly with increasing rss measurement density beyond one sample per half the mean wavelength ( fig . [ fig : coherence ] ) . correlated rss signals can not be considered as independent . @xcite has shown that fisher information is upper bounded by uncertainty in line with . as @xmath226 is upper bounded in spatial frequencies by @xmath227 , the spread or uncertainty in position , @xmath228 , is lower bounded . hence its inverse is upper bounded , as is fisher information . coherence and speckle theory have shown that uncertainty is lower bounded by the diffraction limit . hence , the crlb at a sampling density of one sample per half the mean wavelength ( vertical dotted black curve ) should equal the measured bound on rmse . we define the measured bound on rmse as the rmse processing all 60 million measurements . our measurements show that the difference between this crlb and the measured bound on rmse is @xmath229-@xmath230% ( 1 mm ) . hence , our experiments validate the theoretical concepts introduced by @xcite . our experiments reveal evidence that the crlb can not be further decreased by increasing the number of measurements . on the other hand , at @xmath6 rss signal measurements per wavelength , the rmse is a factor of four higher than the one calculated by the crlb for independent noise . this difference can not be explained by the difference between the covariance of the estimator and the crlb ( see section [ sec : model ] ) . the difference can , however , be explained by calculating the degrees of freedom of our localization setup using bienaym s theorem and the lower bound on correlation length . when one substitutes this lower bound in the and substitutes in , one obtains the asymptotic behavior of the crlb with correlated noise as is shown in fig . [ fig : crlb ] . the measured asymptote in fig . [ fig : localization ] deviates @xmath229-@xmath230% from bienaym s theorem and from the crlb for correlated noise . all @xmath4 million power measurements and matlab files are arranged in a database at linkping university @xcite .	we experimentally and theoretically show that rss measurements are cross - correlated over a minimum distance that approaches the diffraction limit , which equals half the mean wavelength of the radiation . our experiments show that measuring rss beyond a sampling density of one sample per half the mean wavelength does not increase localization precision , as the root - mean - squared - error ( rmse ) converges asymptotically to roughly half the mean wavelength .	this paper experimentally and theoretically investigates the fundamental bounds on radio localization precision of far - field received signal strength ( rss ) measurements . rss measurements are proportional to power - flow measurements time - averaged over periods long compared to the coherence time of the radiation . our experiments are performed in a novel localization setup using 2.4ghz quasi - monochromatic radiation , which corresponds to a mean wavelength of 12.5 cm . we experimentally and theoretically show that rss measurements are cross - correlated over a minimum distance that approaches the diffraction limit , which equals half the mean wavelength of the radiation . our experiments show that measuring rss beyond a sampling density of one sample per half the mean wavelength does not increase localization precision , as the root - mean - squared - error ( rmse ) converges asymptotically to roughly half the mean wavelength . this adds to the evidence that the diffraction limit determines ( 1 ) the lower bound on localization precision and ( 2 ) the sampling density that provides optimal localization precision . we experimentally validate the theoretical relations between fisher information , cramr - rao lower bound ( crlb ) and uncertainty , where uncertainty is lower bounded by diffraction as derived from coherence and speckle theory . when we reconcile fisher information with diffraction , the crlb matches the experimental results with an accuracy of 97 - 98% . radio localization , cramr - rao bounds , fisher information , bienaym s theorem , sampling theorem , speckles , uncertainty principle .
astro-ph0007103	i	considering the fact that the majority of ( spiral ) galaxies is not completely isolated but located in an environment which enables repeated close encounters or even merging processes with small companions it seems to be meaningful to systematically investigate the properties of galaxies affected by such processes . the investigation of their structural and dynamical changes caused by tidal interactions or low - mass satellite infall hence `` minor merger '' can help to clarify how far the evolution of disk galaxies was modified or even dominated by environmental effects . several n - body simulations were performed during the last decade in order to study the influence of minor mergers on galactic disks in greater detail ( e.g. quinn et al . @xcite ; mihos et al . @xcite ; walker et al . it was possible to use more realistic , multiple - component models for the galaxy - satellite system usually consisting of disk , bulge , and halo as well as a large number of particles ( @xmath1 ) . one of the main conclusions was that even merging processes in the range between @xmath2 can cause a vertical thickening of the stellar disk component by a factor between 2 and 4 , depending on the galactocentric distance . it was found that this vertical heating is due to a gain of kinetic energy of the disk stars by enhanced two - body relaxation . according to a series of papers on the frequency of these so called `` soft merging '' events ( e.g. toth & ostriker @xcite ; zaritsky @xcite , @xcite ) a large number of present - day ( disk- ) galaxies were affected by merging- or accretion processes of this magnitude since they have formed . as a consequence , interactions and minor mergers within this mass range might modify our picture of galaxy formation and evolution . however , the enormous parameter space of such a complex scenario makes it difficult to derive general conclusions from a set of few specific simulations . the quantitative results still crucially depend on the chosen parameters such as the content and behaviour of gas in the disk , the mass ratio between bulge and disk , induced star formation , or the satellite orbit ( quinn et al . @xcite ; mihos et al . @xcite ; velazquez & white @xcite ) . statistical studies of galaxy interactions based on optical photometry of disk galaxies ( reshetnikov & combes @xcite , @xcite ) focused on the effects of tidally - triggered disk thickening between systems of comparable mass . they found that the ratio @xmath3 of the radial exponential scale length @xmath4 to the constant scale height @xmath5 is only about twice smaller for interacting galaxies a lower value than derived from the minor mergers simulations . however , the small number of objects in their sample ( 7 non - interacting and 24 interacting galaxies ) did not permit to study these questions in detail . therefore , we started a project based on a larger sample of edge - on disk galaxies in both optical and near infrared passbands . this combination offers a number of advantages : first , observations in the near infrared particularly benefit from the much lower dust extinction near the galactic plane , i.e. at small @xmath6 . second , the presence of a dust lane along the major axis of most edge - on disk galaxies still presents one of the best methods to determine precise inclinations of the disks two facts that will become very important in order to derive reliable scale parameters from a disk fitting procedure . third , this combination enables us to make conclusions on disk populations of different ages . the main questions of this study can be summarized as follows : * are interactions / minor mergers able to change the radial and vertical structure of affected galactic disks ? * is there a substantial vertical disk thickening ? * of which order are the differences and similarities in the disk parameter distribution for a sample of interacting / non - interacting galaxies , respectively ? * to what extent are the disk properties of galaxies in the local universe influenced by interactions / minor mergers ? due to the complexity of these questions the paper is split into three parts : in this first part ( paper i ) we present deep optical and near infrared photometric data of a total sample of 110 highly - inclined / edge - on disk galaxies . this sample consists of two subsamples of 61 non - interacting galaxies ( control sample ) and of 49 minor merging candidates . additionally , 41 of these galaxies were observed in the near infrared . in sect . 2 the criteria of the sample selection will be described briefly . 3 gives an overview on the observations and data reduction . the disk modelling- and fitting procedure applied to derive the disk parameters will be reviewed in sect . 4 . in sect . 5 we summarize and conclude the paper . in the second part ( schwarzkopf & dettmar @xcite , paper ii ) the results of a detailed analysis of the structure of galactic disks will be presented . the third part ( schwarzkopf & dettmar in preparation , paper iii ) will be focused on the influence of accompanying minor merger features like disk `` warping '' and `` flaring '' on the vertical disk structure . 1.55 mm llccccccccccccccccc & & + & & + & & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 + & & e & & e - s0 & s0 & & s0/a & sa & sa - b & sb & sb - c & & sc & & sc - irr & & irri & + & & e & & e - s0 & s0 & & s0-a & sa & sa - b & sb & sb - c & s ... & sc , sc - d & s ... /irr & sd & & irr & unknown + ( 8.8,7.7 ) ( 8.8,7.7 ) * fig . 1a and b. * the distribution of morphological types * ( a ) * for the total galaxy sample and * ( b ) * for both subsamples of non - interacting ( normal ) and interacting / merging galaxies ( merger ) .	surface photometry of the optical and near infrared data of a sample of 110 highly - inclined / edge - on disk galaxies are presented . this sample consists of two subsamples of 61 non - interacting galaxies ( control sample ) and of 49 interacting galaxies / minor merging candidates . additionally , 41 of these galaxies were observed in the near infrared .	this paper is the first part in our series on the influence of tidal interactions and minor mergers on the radial and vertical disk structure of spiral galaxies . we report on the sample selection , our observations , and data reduction . surface photometry of the optical and near infrared data of a sample of 110 highly - inclined / edge - on disk galaxies are presented . this sample consists of two subsamples of 61 non - interacting galaxies ( control sample ) and of 49 interacting galaxies / minor merging candidates . additionally , 41 of these galaxies were observed in the near infrared . we show that the distribution of morphological types of both subsamples is almost indistinguishable , covering the range between . an improved , 3-dimensional disk modelling- and fitting procedure is described in order to analyze and to compare the disk structure of our sample galaxies by using characteristic parameters . we find that the vertical brightness profiles of galactic disks respond very sensitive even to small deviations from the perfect edge - on orientation . hence , projection effects of slightly inclined disks may cause substantial changes in the value of the disk scale height and must therefore be considered in the subsequent study .