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1209.2420

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in the past decade it has become clear that the majority of galaxies have likely had one or more brief active periods , shifting our view of astrophysical black holes ( bhs ) from the role of exotic phenomena to fundamental ingredients of cosmic structures . the question of when and under which physical conditions the active galactic nuclei ( agn ) activate is important for understanding not only the origin and evolution of bhs but also the origin and evolution of galaxies . the clustering analysis can powerfully test theoretical model predictions and address which physical processes trigger agn activity . in the framework of the cold dark matter structure formation ( cdm ) , the spatial distribution of agn in the universe ( described by the correlation function , cf ) can be related to how agn are biased with respect to the underlying matter distribution and to the typical mass of dark matter halos ( dmhs ) in which they reside . there have been several studies of the bias evolution of optical quasars with redshift , based on survey such as 2qz and sdss @xcite . all the previous studies infer the picture that the quasar bias evolves with redshift following a constant mass evolution in the range log@xmath11 [ ] @xmath12 , i.e. halo masses similar to group scales , where the combination of low velocity dispersion and moderate galaxy space density yields to the highest probability of a close encounter @xcite . models of major mergers between gas - rich galaxies appear to naturally produce many observed properties of quasars , such as the shape and the evolution of the quasar luminosity function and the large - scale quasar clustering as a function of luminosity and redshift @xcite , supporting the scenario in which major mergers dominate the bright quasar populations . on the other hand , the majority of the results on the clustering of x - ray selected agn , suggest a picture where moderate - luminosity agn live in massive dmhs ( @xmath13 [ ] @xmath14 ) up to @xmath15 @xcite , i.e. x - ray selected agn samples appear to cluster more strongly than luminous quasars ( see * ? ? ? * for a review on the argument ) . the reason for this is not completely clear , but several studies argued that this large bias and dmh masses could suggest a different agn triggering mechanism with respect to bright quasars characterized by galaxy merger - induced fueling . several studies on the morphology of the agn host galaxies have demonstrated that major mergers of galaxies are not likely to be the single dominant mechanism responsible for triggering agn activity at low ( @xmath16 ) @xcite and high redshift ( @xmath17 2 ) @xcite . the theoretical understanding of galaxy clustering and bias factor has been greatly enhanced through the halo occupation distribution ( hod ) framework . in this framework , the virialised dmh with typical overdensities of @xmath18 ( defined w.r.t . the mean density ) are described in terms of the probability @xmath19 of a halo of given mass @xmath20 of having @xmath21 galaxies . a simple way to model the complicated shape of @xmath22 is by assuming the existence of two separate galaxy populations within halos , central and satellite galaxies . this method has been used extensively to interpret galaxy cfs @xcite to constrain how various galaxy samples are distributed among dmh as well as whether these galaxies occupy the centers of the dmhs or are satellite galaxies @xcite . these two populations can be modeled with an hod described by a step function above a halo mass limit for central galaxies , and a power - law for satellite galaxies . similarly , the problem of discussing the abundance and spatial distribution of agn can be reduced to studying how they populate their host halos . in fact the observed departure of the agn cf from a power law on small scales ( 1 - 2 ) can be physically interpreted in the language of the halo model , as the transition between two scales - from small scales lying within the dmhs ( 1-halo term ) to those larger than the halo ( 2-halo term ) . the 1-halo term constrains the hod of satellite agn and gives us the average profile of pairs of agn in groups and clusters of galaxies . the 2-halo term reflects the large - scale agn bias driven by the typical mass of the hosting halos . due to the low number density of agn , there have been few results in the literature studying the agn correlation function using hod modeling . previous works of @xcite at @xmath23 and @xcite at @xmath24 on qso using the hod modeling found that @xmath2525% and @xmath2610% of their qsos , respectively , are satellites . @xcite described for the first time the shape of the hod of x - ray selected agn . by using the cross correlation function of rosat - rass agn with sdss galaxies , they modelled the mean agn occupation of dmhs suggesting that the satellite agn fraction increases slow ( or may even decrease ) with @xmath6 , in contrast with the satellite hod of luminosity - limited samples of galaxies . cosmological hydrodynamic simulations have been performed in @xcite to study the mean occupation function of low - luminosity agn as function of redshift and luminosity . they used a softened step function for the central component plus a rolling - off power - law for the satellite component with @xmath27 depending on the redshift and agn luminosity . their results suggest a strong evolution of the agn occupancy in the redshift range @xmath28 estimated at three different luminosities @xmath29 s@xmath30erg . @xcite modelled the hod of sdss quasars at @xmath31 following this parametrization . they found that the satellite occupation becomes significant at mass @xmath32 , i.e. only the most massive halos host multiple quasars at this redshift and only a small satellite fraction ( @xmath33 ) of sdss quasars is required to fit the clustering signal at small scales . moreover , they measured that the quasars hod steepens considerably going from z=1.4 to 3.2 over halo mass scales @xmath34 and that the characteristic halo mass increases with z for central quasars . despite the diverse methods for studying the hod , counting the number of agn within galaxy groups can constrain quite directly the average agn number within a halo as a function of halo mass . the total mass of galaxy groups can be estimated via gravitational lensing and the distribution of agn within halos can be investigated in groups by means of the distribution of the agn host galaxies . separating the contribution to the occupation of halos from agn in satellite or central galaxies can advance our understanding of the co - evolution agn / galaxy and is related to the mechanism of agn activation . on the other hand , the cross - correlation ( ccf ) of agn with galaxy groups provides additional information about how galaxies and bh co - evolve in dense environments . in fact the physical processes that drive galaxy evolution , such as the available cold gas to fuel star formation and the bh growth , are substantially different in groups and clusters compared to the field . many studies over the past decade have presented an evidence that agn at @xmath35 are more frequently found in groups compared to galaxies ( georgakakis et al . 2008 , arnold et al . x - ray observations reveal that a significant fraction of high - z clusters show overdensities of agns in their outskirts ( henry et al . 1991 , cappi et al . 2001 , ruderman et al . 2005 , cappelluti et al . 2005 ) . in this paper , we perform the first direct measurement of the mean halo occupation of x - ray agn and of the projected cross - correlation function of agn with galaxy groups , using a sample of x - ray selected agn and galaxy groups in the cosmos field at @xmath0 , from xmm and _ chandra _ data . we use a @xmath36cdm cosmology with @xmath37 , @xmath38 , @xmath39 , @xmath40 . for comparison with previous measurements we refer to correlation lengths and distances in units of @xmath41 mpc comoving , where @xmath42 h km s@xmath30 mpc@xmath30 . agn luminosities and galaxy groups masses are calculated using @xmath43 = 0.72 .

we present the first direct measurement of the mean halo occupation distribution ( hod ) of x - ray selected agn in the cosmos field at , based on the association of 41 xmm and 17 c - cosmos agn with member galaxies of 189 x - ray detected galaxy groups from xmm and _ chandra _ data . we perform a measurement of the projected agn - galaxy group cross - correlation function , excluding from the analysis agn that are within galaxy groups and we model the 2-halo term of the clustering signal with the mean agn hod based on our results .

we present the first direct measurement of the mean halo occupation distribution ( hod ) of x - ray selected agn in the cosmos field at , based on the association of 41 xmm and 17 c - cosmos agn with member galaxies of 189 x - ray detected galaxy groups from xmm and _ chandra _ data . we model the mean agn occupation in the halo mass range = 13- 14.5 $ ] with a rolling - off power - law with the best fit index and normalization parameter . we find the mean hod of agn among central galaxies to be modelled by a softened step function at loglog while for the satellite agn hod we find a preference for an increasing agn fraction with suggesting that the average number of agn in satellite galaxies grows slower ( ) than the linear proportion ( ) observed for the satellite hod of samples of galaxies . we present an estimate of the projected auto correlation function ( acf ) of galaxy groups over the range of 0.1 - 40 at . we use the large - scale clustering signal to verify the agreement between the group bias estimated by using the observed galaxy groups acf and the value derived from the group mass estimates . we perform a measurement of the projected agn - galaxy group cross - correlation function , excluding from the analysis agn that are within galaxy groups and we model the 2-halo term of the clustering signal with the mean agn hod based on our results .

1209.2420

c

we have performed the first direct measurement of the mean halo occupation distribution of x - ray agn as function of halo mass , by directly counting the number of agn within x - ray galaxy groups with masses @xmath1 = 13- 14.5 $ ] , in the cosmos field at @xmath0 . our findings are summarized as follows . 1 . we identified 41 xmm - cosmos agn within galaxy groups , defined as agn located within 3 times the group line - of - sight velocity dispersion and within @xmath75 and 17 additional sources including in the analysis c - cosmos only selected agn . we measured the mean agn occupancy of galaxy groups as function of halo mass in the range log@xmath263 = 13- 14.5 $ ] and we modelled the data points with a rolling - off power - law with the best fit index @xmath264 and normalization parameter @xmath265 . 3 . using a galaxy membership catalog , we associated 22/58 and 36/58 agn to central and satellites galaxies , respectively . we constrained that the mean agn occupation function among central galaxies is described by a softened step function above log@xmath5 while the satellite agn hod increases with the halo mass ( @xmath266 ) slower than the satellite hod of sample of galaxies ( @xmath267 ) . we presented an estimate of the projected acf of galaxy groups over the range @xmath9 0.1 - 40 at @xmath10 . we verified that the bias factor and the corresponding typical halo mass estimated from the observed galaxy group acf , are in perfect agreement with the values @xmath220 and @xmath268 obtained by using the galaxy group mass estimates . in particular we found @xmath211 and log @xmath268 [ ] = 13.61@xmath269 , llllllllllll + 11 & 150.1898 & 1.65725 & 0.22 & 14.28 & -99 & 150.19864 & 1.671924 & 12390 & 0.228@xmath270 & 41.27 & 0 + 17 & 149.96413 & 1.68033 & 0.372 & 14.02 & 30744 & 149.96396 & 1.6805983 & -99 & 0.372 & 43.28 & 1 + 19 & 150.37282 & 1.60944 & 0.103 & 12.98 & 2021 & 150.37256 & 1.6093965 & 1678 & 0.104 & 41.22 & 1 + 20 & 150.32494 & 1.60313 & 0.22 & 13.38 & 2186 & 150.33601 & 1.6012201 & 1671 & 0.234@xmath270 & 41.88 & 0 + 35 & 150.2066 & 1.82327 & 0.53 & 13.70 & -99 & 150.20702 & 1.823398 & 1292 & 0.529 & 41.73 & 1 + 39 & 149.82381 & 1.8252701 & 0.531 & 13.63 & 5502 & 149.81248 & 1.8238187 & 219 & 0.529 & 42.37 & 0 + 52 & 150.44704 & 1.8828501 & 0.671 & 13.64 & 30681 & 150.44731 & 1.8832886 & 690 & 0.670@xmath270 & 42.75 & 1 + 69 & 150.42012 & 1.9708 & 0.862 & 13.49 & 5519 & 150.42473 & 1.9693011 & 1185 & 0.854@xmath270 & 42.77 & 0 + 78 & 150.27461 & 1.98884 & 0.838 & 13.61 & -99 & 150.27823 & 1.990302 & 685 & 0.838 & 42.35 & 1 + 78 & 150.27461 & 1.9888 & 0.838 & 13.61 & 206 & 150.27434 & 1.9884306 & 1100 & 0.673 & 42.57 & 0 + 79 & 150.44728 & 2.05392 & 0.323 & 13.77 & -99 & 150.44765 & 2.053961 & 2605 & 0.323 & 41.62 & 1 + 87 & 150.51109 & 2.0269899 & 0.899 & 13.60 & 2387 & 150.51036 & 2.0293686 & 496 & 0.899 & 43.15 & 1 + 93 & 149.6692 & 2.0740 & 0.338 & 13.59 & 417 & 149.6692 & 2.073962 & 168 & 0.34 & 42.76 & 0 + 110 & 150.17979 & 2.1103699 & 0.361 & 13.43 & 6 & 150.17978 & 2.1101542 & 42 & 0.360 & 43.19 & 1 + 118 & 149.63463 & 2.1357 & 0.962 & 13.70 & 411 & 149.63828 & 2.1494889 & 323 & 0.952 & 43.25 & 0 + 124 & 150.05656 & 2.2085 & 0.186 & 13.22 & 302 & 150.0571 & 2.2063098 & 1297 & 0.186 & 41.25 & 0 + 124 & 150.05656 & 2.20854 & 0.186 & 13.22 & -99 & 150.09554 & 2.2202671 & 1221 & 0.186 & 40.86 & 0 + 128 & 150.58435 & 2.1811 & 0.556 & 13.58 & 2855 & 150.57634 & 2.1812408 & 1634 & 0.554 & 42.41 & 0 + 127 & 150.44104 & 2.15873 & 0.377 & 13.32 & -99 & 150.44202 & 2.1551671 & 2313 & 0.376 & 41.24 & 1 + 130 & 150.02382 & 2.2032 & 0.942 & 13.84 & -99 & 150.02303 & 2.206567 & 2413 & 0.94 & 42.45 & 0 + 136 & 150.17493 & 2.2170 & 0.676 & 13.56 & -99 & 150.17592 & 2.2156539 & 877 & 0.667@xmath270 & 42.08 & 0 + 137 & 149.96271 & 2.2102399 & 0.425 & 13.32 & -99 & 149.96216 & 2.2102211 & 12011 & 0.425 & 41.44 & 1 + 138 & 149.50874 & 2.2614 & 0.943 & 13.97 & 5539 & 149.50914 & 2.261276 & -99 & 0.962 & 43.19 & 1 + 142 & 150.28798 & 2.2769 & 0.122 & 13.09 & 317 & 150.25331 & 2.2779887 & 3718 & 0.165 & 41.08 & 0 + 143 & 150.21454 & 2.2801 & 0.880 & 13.77 & 116 & 150.20604 & 2.2857771 & 22 & 0.874 & 43.33 & 0 + 149 & 150.41566 & 2.4302 & 0.124 & 13.85 & 45 & 150.33598 & 2.4335926 & 658 & 0.121 & 41.31 & 0 + 149 & 150.41566 & 2.4302001 & 0.124 & 13.85 & 73 & 150.416 & 2.4299896 & 634 & 0.124 & 42.00 & 1 + 161 & 149.95262 & 2.3418 & 0.941 & 13.74 & 430 & 149.95949 & 2.3560882 & 497 & 0.889 & 42.85 & 0 + 171 & 149.66328 & 2.2677 & 0.676 & 13.56 & 5411 & 149.66243 & 2.2693584 & 1646 & 0.676 & 42.76 & 0 + 173 & 150.05804 & 2.38045 & 0.347 & 13.48 & 241 & 150.05794 & 2.3805208 & 898 & 0.347 & 42.14 & 1 + 174 & 149.63988 & 2.3491 & 0.950 & 13.97 & 53937 & 149.64459 & 2.3587193 & -99 & 0.962@xmath270 & 42.88 & 0 + 175 & 150.24123 & 2.34835 & 0.723 & 13.55 & -99 & 150.24109 & 2.3483839 & 977 & 0.703 & 41.72 & 0 + 186 & 150.21748 & 2.4003 & 0.905 & 13.77 & 53303 & 150.21141 & 2.4022212 & 975 & 0.894@xmath270 & 42.62 & 0 + 194 & 149.69957 & 2.4028 & 0.354 & 13.45 & 135 & 149.70084 & 2.4025679 & 417 & 0.376 & 43.00 & 0 + 196 & 150.27898 & 2.4192 & 0.123 & 13.11 & -99 & 150.27975 & 2.4222209 & 1315 & 0.122 & 40.25 & 0 + 216 & 150.06664 & 2.6474 & 0.696 & 13.64 & 5113 & 150.06633 & 2.642817 & 143 & 0.693 & 42.45 & 0 + 217 & 150.00713 & 2.4534299 & 0.731 & 13.54 & -99 & 150.00188 & 2.4606521 & 1243 & 0.732 & 42.39 & 1 + 219 & 150.27148 & 2.5134399 & 0.704 & 13.54 & 158 & 150.27411 & 2.5117824 & 138 & 0.703 & 42.51 & 1 + 220 & 149.92343 & 2.5249 & 0.729 & 14.39 & 486 & 149.92007 & 2.5143571 & 562 & 0.698 & 42.52 & 0 + 220 & 149.92343 & 2.5249901 & 0.729 & 14.39 & -99 & 149.91588 & 2.52139 & 1310 & 0.729 & 42.38 & 0 + 231 & 150.05421 & 2.58885 & 0.675 & 13.73 & 8 & 150.05383 & 2.5896702 & 142 & 0.699 & 44.03 & 1 + 234 & 150.15816 & 2.6082 & 0.893 & 13.66 & -99 & 150.15796 & 2.6113441 & 727 & 0.863@xmath270 & 42.35 & 0 + 237 & 150.11774 & 2.6842501 & 0.349 & 14.00 & 5118 & 150.11783 & 2.6840661 & -99 & 0.349 & 42.18 & 1 + 259 & 149.65717 & 2.8195 & 0.703 & 13.73 & 60270 & 149.65953 & 2.8270493 & -99 & 0.708@xmath270 & 42.33 & 0 + 262 & 149.60007 & 2.8211 & 0.344 & 14.03 & 5320 & 149.63142 & 2.8174951 & -99 & 0.34 & 42.93 & 0 + 275 & 149.83878 & 2.6750801 & 0.259 & 13.45 & 5112 & 149.83847 & 2.6750875 & 1608 & 0.259 & 43.08 & 1 + 277 & 150.00462 & 2.63275 & 0.677 & 13.45 & 5091 & 150.00452 & 2.6328416 & 616 & 0.678 & 42.73 & 1 + 289 & 150.11256 & 2.5560 & 0.501 & 13.57 & 142 & 150.10342 & 2.5504889 & 148 & 0.498 & 42.62 & 0 + 292 & 150.03307 & 2.5524 & 0.747 & 13.48 & 398 & 150.02638 & 2.5620575 & 991 & 0.745 & 42.82 & 0 + 296 & 149.55516 & 2.0020 & 0.894 & 13.90 & 10732 & 149.56131 & 2.0087938 & 3549 & 0.930@xmath270 & 42.85 & 0 + 298 & 149.78191 & 2.1390 & 0.354 & 13.59 & 63 & 149.78223 & 2.1387713 & 313 & 0.355 & 42.57 & 0 + 298 & 149.78191 & 2.13906 & 0.354 & 13.59 & 392 & 149.79369 & 2.1256437 & 679 & 0.353 & 41.98 & 1 + 298 & 149.78191 & 2.13906 & 0.354 & 13.59 & -99 & 149.77357 & 2.141633 & 1498 & 0.354 & 41.34 & 0 + 300 & 149.72893 & 2.2373 & 0.381 & 13.47 & -99 & 149.74792 & 2.253087 & 2876 & 0.356 & 41.06 & 0 + 303 & 149.99364 & 2.2585399 & 0.660 & 13.53 & 19 & 149.99367 & 2.2585886 & 450 & 0.659 & 43.38 & 1 + 322 & 150.2254 & 2.26872&0.677 & 13.51 & -99 & 150.228 & 2.2698331 & 24 & 0.678 & 42.46 & 0 + 324 & 150.02414 & 2.36050&0.726 & 13.39 & 254 & 150.03079 & 2.358371 & 533 & 0.786 & 42.89 & 0 + 333 & 150.0423 & 2.6949 & 0.219 & 13.31 & 5075 & 150.04155 & 2.6945302 & 623 & 0.221 & 41.46 & 1 + allevato v. , et al . 2011 , , 736 , 99 avni , y. & bahcall , j. n. , 1980 , , 235 , 694 balogh , m. l. , et al . 2011 , , 412 , 2303 berlind a. a. , et al . 2003 , , 593 , 1 bierly , r. m. , et al . 2010 , a&a , 523 , 66 bonoli , s. , marulli , f. , springel , v. , et al . 2009 , , 396 , 423 brusa , m. , civano , f. , comastri , a. , et al . 2010 , , 716 , 348 cappelluti , n. , et al . 2007 , , 172 , 341 cappelluti , n. , brusa m. , hasinger g. , et al . 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we model the mean agn occupation in the halo mass range = 13- 14.5 $ ] with a rolling - off power - law with the best fit index and normalization parameter . we find the mean hod of agn among central galaxies to be modelled by a softened step function at loglog while for the satellite agn hod we find a preference for an increasing agn fraction with suggesting that the average number of agn in satellite galaxies grows slower ( ) than the linear proportion ( ) observed for the satellite hod of samples of galaxies . we present an estimate of the projected auto correlation function ( acf ) of galaxy groups over the range of 0.1 - 40 at . we use the large - scale clustering signal to verify the agreement between the group bias estimated by using the observed galaxy groups acf and the value derived from the group mass estimates .

we present the first direct measurement of the mean halo occupation distribution ( hod ) of x - ray selected agn in the cosmos field at , based on the association of 41 xmm and 17 c - cosmos agn with member galaxies of 189 x - ray detected galaxy groups from xmm and _ chandra _ data . we model the mean agn occupation in the halo mass range = 13- 14.5 $ ] with a rolling - off power - law with the best fit index and normalization parameter . we find the mean hod of agn among central galaxies to be modelled by a softened step function at loglog while for the satellite agn hod we find a preference for an increasing agn fraction with suggesting that the average number of agn in satellite galaxies grows slower ( ) than the linear proportion ( ) observed for the satellite hod of samples of galaxies . we present an estimate of the projected auto correlation function ( acf ) of galaxy groups over the range of 0.1 - 40 at . we use the large - scale clustering signal to verify the agreement between the group bias estimated by using the observed galaxy groups acf and the value derived from the group mass estimates . we perform a measurement of the projected agn - galaxy group cross - correlation function , excluding from the analysis agn that are within galaxy groups and we model the 2-halo term of the clustering signal with the mean agn hod based on our results .

1105.1792

i

little is known about the properties of the dense gas component on gmc scales in external galaxies yet it is dense gas ( @xmath5 @xmath6 ) that most directly correlates with global star formation rates ( e.g. , * ? ? ? * ; * ? ? ? * ) . to understand the evolution and regulation of current star formation in galaxies , dense gas properties need to be accurately characterized . in a recent imaging survey of millimeter - wave molecular lines in the nearby spiral nucleus of ic 342 , a surprising degree of morphological variation is observed in its dense gas @xcite , which was not anticipated from co or hcn ( e.g. , * ? ? ? * ; * ? ? ? these and other observations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) confirm that co and hcn fail to fully constrain excitation and chemical properties of the dense clouds . various probes of the dense component exist , each with various strengths and weaknesses ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? hcn(10 ) is the most commonly used dense gas tracer , primarily because it is bright , however , it is optically thick in most starburst environments ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , has a widely spaced rotational ladder with its j@xmath73 transitions in the submm and can be sensitive to chemical effects ( pdr effects and ir pumping ; e.g. * ? ? ? * ; * ? ? ? * ) . here we present a study of the physical conditions of the very dense gas component of a nearby starburst nucleus using hc@xmath0n . with its large electric dipole moment ( @xmath8 = 3.72 debye versus 3.0 debye for hcn ) , low opacity and closely spaced rotational ladder accessible to powerful centimeter and millimeter - wave interferometers , hc@xmath0n is well - suited to high resolution imaging of the structure and excitation of the densest component of the molecular gas ( eg . * ; * ? ? ? * ; * ? ? ? hc@xmath9n(54 ) has a critical density of @xmath10 @xmath6 and an upper level energy of e / k = 6.6 k ; the 1615 line has a critical density of @xmath11 @xmath6 and an upper level energy of e / k = 59 k. we have observed the j = 54 and j = 1615 lines of hc@xmath0n at @xmath122 resolution in ic 342 with the very large array ( vla ) and the plateau de bure interferometer ( pdb ) , respectively . ic 342 is one of the closest ( d@xmath133 mpc , or 2 = 29 pc ; eg . * ? ? ? * ; * ? ? ? * ) , large spirals with active nuclear star formation @xcite . it is nearly face - on , with bright molecular line emission both in dense clouds and a diffuse medium @xcite . the wealth of data and proximity of ic 342 permit the connection of cloud properties with star formation at sub - gmc spatial scales . the data published here represent the first high resolution maps of hc@xmath9n(54 ) and hc@xmath9n(1615 ) in an external galaxy . excitation is a key component in the interpretation of molecular line intensities . so these two maps are compared with the previously published lower resolution hc@xmath0n(109 ) map made with the owens valley millimeter array @xcite , to constrain the physical conditions of the densest component of the ism in the center of ic342 , and to correlate properties of the dense gas with star formation , diffuse gas , and chemistry .

we present the first images of the j=54 and j=1615 lines of the dense gas tracer , cyanoacetylene , hcn , in an external galaxy . the central 200 pc of the nearby star - forming spiral galaxy , ic 342 , was mapped using the vla and the plateau de bure interferometer . the j=1615 and 109 lines are also faint near the large hii region complex , but are brighter relative to the 54 line , consistent with higher excitation . the high excitation combined with faint emission towards the dense molecular gas at the starburst indicates that it currently lacks large masses of very dense gas .

we present the first images of the j=54 and j=1615 lines of the dense gas tracer , cyanoacetylene , hcn , in an external galaxy . the central 200 pc of the nearby star - forming spiral galaxy , ic 342 , was mapped using the vla and the plateau de bure interferometer . hcn(54 ) line emission is found across the nuclear mini - spiral , but is very weak towards the starburst site , the location of the strongest mid - ir and radio emission . the j=1615 and 109 lines are also faint near the large hii region complex , but are brighter relative to the 54 line , consistent with higher excitation . the brightest hcn emission is located in the northern arm of the nuclear minispiral , 100 pc away from the radio / ir source to the southwest of the nucleus . this location appears less affected by ultraviolet radiation , and may represent a more embedded , earlier stage of star formation . excitation temperatures are consistent with those determined from co ; the gas is dense , and cool , t k. so as to not violate limits on the total h mass determined from co , at least two dense components are required to model ic 342 s giant molecular clouds . these observations suggest that hcn(54 ) is an excellent probe of the dense , quiescent gas in galaxies . the high excitation combined with faint emission towards the dense molecular gas at the starburst indicates that it currently lacks large masses of very dense gas . we propose a scenario where the starburst is being caught in the act of dispersing or destroying its dense gas in the presence of the large hii region . this explains the high star formation efficiency seen in the dense component . the little remaining dense gas appears to be in pressure equilibrium with the starburst hii region .

1105.1792

r

continuum subtracted integrated intensity line maps of hc@xmath0n(54 ) , hc@xmath0n(109 ) and hc@xmath0n(1615 ) in ic 342 are shown in figure [ inti ] . figure [ inticont ] shows the 54 transition overlaid on the 7 mm continuum image generated from offline channels . locations of giant molecular cloud ( gmc ) cores @xcite and the optical clusters ( e.g. * ? ? ? * ) , compared with hc@xmath0n(54 ) and hcn(10 ) @xcite , are also shown in figure [ inticont ] . figure [ spec ] shows the hc@xmath9n(54 ) and hc@xmath0n(16 - 15 ) spectra ( in flux units ) taken over the same 2aperture centered on each cloud . hc@xmath0n(54 ) emission picks out most clouds seen in other dense gas tracers ( e.g hcn(10 ) . the only labeled cloud not clearly detected in hc@xmath9n(54 ) is gmc b , the cloud associated with the nuclear star - forming region ( @xmath29 ; * ? ? ? * ; * ? ? ? * ) . positions of the gmcs measured in hc@xmath0n are consistent with those fitted in c@xmath1o(2 - 1 ) to within a beam @xcite . an additional gmc is detected in hc@xmath0n(54 ) just south of gmc c3 , labeled c4 . unlike c@xmath1o(2 - 1 ) which peaks at gmc c2 , hc@xmath0n(54 ) emission peaks farther north , towards gmc c1 , at a distance of 105 pc from the nucleus suggesting changes in excitation across gmc c. gmcs a and d are resolved into two components , but we do not discuss them as separate entities given the lower signal - to - noise , other than to state that there is a clear difference in velocity centroid between the 54 and 1615 transitions ( e.g. figure [ spec ] ) indicating there is likely an excitation gradient across gmc a. no emission @xmath30 is detected towards the weak co(2 - 1 ) feature associated with the central nuclear star cluster @xcite . the j=1615 line intensity is comparable to that of j=54 line in all clouds . while dominated by gmc c , hc@xmath0n(16 - 15 ) is detected ( or tentatively detected ) towards all clouds , except gmc d. fluxes for gmcs d and d are quite uncertain since they are just inside the half power point of the pdbi primary beam . that gmc c is much brighter than the other clouds in both transitions indicates large quantities of dense gas are present in this cloud . hc@xmath0n(1615 ) favors c2 over c1 . gmc b , while still faint in an absolute sense , is significantly brighter in hc@xmath0n(1615 ) relative to 54 . this is not unexpected given the higher excitation requirements of the 1615 line and that both b and c2 have 7 mm continuum sources associated with massive star formation . comparisons of the hc@xmath9n ( 54 ) , ( 109 ) and ( 1615 ) maps provide a chance to establish the excitation of the densest molecular cloud gas component . line intensities from the j=54 and j=16 - 15 lines were measured over 2 apertures centered on each of the gmcs . table [ tinti ] records gaussian fits to each spectrum along with integrated line intensities . peak antenna temperature ratios are calculated for hc@xmath0n(1615)/hc@xmath0n(54 ) , hereafter denoted r@xmath32 . r@xmath32 ranges from less than 0.06 up to @xmath130.5 , with gmc b having the highest value ( table [ trat ] ) . the 54 and 1615 transitions generally bracket the peak of the level populations , so we achieve good constraints on gas excitation . lte excitation temperatures , t@xmath33 , implied by r@xmath32 range from @xmath1210 k to @xmath718 k ( where we have neglected t@xmath34 in this determination ) . excitation is lowest towards gmcs d , d and e. these excitation temperatures t@xmath33 are similar to those found from the presumably much less dense gas traced in c@xmath1o ( table 2 ; * ? ? ? * ) . only the gmc c clouds have significantly higher t@xmath33 in hc@xmath9n towards c1 - c3 t@xmath33(hc@xmath0n ) are about a factor of two greater than t@xmath33(c@xmath1o ) . the resolution of the hc@xmath0n(109 ) data is significantly lower than it is for the 54 and 1615 lines . to compare j=54 and j=10 - 9 line intensities , the 54 data were convolved to the resolution of the ( 109 ) data ( @xmath35 * ? ? ? * ) , then integrated intensity ratios , hereafter r@xmath36 , were sampled at the locations of r@xmath32 . though at lower resolution than r@xmath32 , we make the approximation that r@xmath36 does not change on these sub - gmc scales . while leading to larger uncertainties , this provides a way to include all three transitions in modeling dense gas excitation at very high resolution . @xmath37 range from 0.25 to 1.4 ( table [ tinti ] ) . gmc b has the highest value of 1.4 . the remainder of the gmcs have ratios of @xmath38 . excitation temperatures implied by these ratios range from t@xmath39 616 k , consistent with those derived from @xmath40 separately . t@xmath33 derived from r@xmath36 are similar to those derived from c@xmath1o . the only exception here is gmc a , the cloud where pdrs ( photon - dominated regions ) dominate @xcite . towards gmc a t@xmath33(c@xmath1o ) and t@xmath33(r@xmath32 ) are 12 - 13 k , twice that of t@xmath33(r@xmath36 ) . before modeling the densities implied by the line ratios , we test whether ir pumping can be responsible for the observed excitation . ir pumping is important if , @xmath41 where @xmath42 is the einstein @xmath43 of the corresponding @xmath44 vibrational transitions at @xmath45 m , @xmath46(45 @xmath8 m ) is the 45 @xmath8 m intensity as seen by the hc@xmath0n molecules and @xmath47 is the einstein @xmath48 of the rotational state ( e.g. * ? ? ? it is extremely difficult to estimate the applicable 45 @xmath8 m ir intensity , but it is expected to be most intense towards the starburst gmc ( b ) . a detailed assessment of ir pumping must await high resolution mir maps , but we constrain @xmath46(45 @xmath49 ) in several ways . first , we take the 45 @xmath8 m flux from @xcite and scale it by the fraction of total 20 @xmath8 m flux that comes from within 2.1@xmath28 of the starburst as found by @xcite and then average over that aperture . for the average @xmath46(45 @xmath8 m ) calculated this way , @xmath50(45 @xmath8 m ) is @xmath51 ( @xmath52 ) times too low to pump the 1615 ( 54 ) transition . alternatively if we ( very conservatively ) take the total mir luminosity from the central 30@xmath28 and assume it comes from a blackbody of the observed color temperature ( e.g. @xmath1350 k ; * ? ? * ) then @xmath46(45 @xmath8 m ) is still at least an order of magnitude too low to meet the inequality in eq . [ pump ] for both transition . ir pumping rates only become comparable to @xmath47 for the 54 transition if the total ir luminosity originates from a @xmath132.5 pc source with a source temperature of @xmath53100 k. we conclude that ir pumping is not important for the 1615 transition of hc@xmath0n in any reasonable geometry of the ir field . for the 54 transition to be sensitive to ir pumping , the ir source must be warm , opaque and extremely compact . therefore ir pumping is neglected for all clouds in the following discussion . the values of the excitation temperature constrain the density and kinetic temperatures , @xmath54 and @xmath55 , and the physical conditions of the clouds driving the excitation . a series of large velocity gradient ( lvg ) radiative transfer models were run to predict the observed intensities and line ratios for a given @xmath54 , t@xmath56 and filling factor , @xmath57 , of the dense component ( e.g. , * ? ? ? single component lvg models are instructive , particularly when lines are optically thin , as is the case for hc@xmath0n . the lvg model used is that of @xcite , adapted to hc@xmath0n , with levels up to j=20 included . collision coefficients are from @xcite . a range of densities , @xmath54 = 10@xmath5810@xmath59 , and kinetic temperatures , t@xmath56 = 0100 k , was explored . column densities based on lte excitation ( table [ trat ] ) , are calculated at 2@xmath28 resolution from : @xmath60 using molecular data of @xcite , hc@xmath0n(54 ) intensities , and t@xmath33(hc@xmath0n ) from table [ trat ] . hc@xmath0n abundances are found to be , @xmath61 , with the highest values towards c1 and d. while uncertain these abundances agree with those found in @xcite and are typical of galactic center hc@xmath0n abundances ( e.g. * ? ? ? * ; * ? ? ? * ) and good enough for constraining @xmath62 . the ratio of cloud linewidth to core size is @xmath63 for the gmcs . therefore , we adopt a standard model abundance per velocity gradient of @xmath62 = 10@xmath64 km s@xmath15 , but run models for values of @xmath65 - @xmath66 . antenna temperatures are sensitive to the unknown filling factor . in these extragalactic observations , the beam corresponds to scales large compared to cloud structure , and hence filling factors are not directly known . to first order , the line ratios , @xmath37 and r@xmath32 are independent of filling factor if we assume that hc@xmath0n(54 ) , ( 109 ) and ( 1615 ) originate in the same gas . so model ratios are compared to the observed data to constrain parameter space . for the parameter space implied by the line ratios model brightness temperatures are determined . a comparison of the model brightness temperature to the observed brightness temperature sets the required areal filling factors for that solution . figure [ lvg ] displays the results of the lvg modeling . acceptable @xmath67 ( t@xmath56,@xmath54 ) parameter spaces are shown for each line ratio ( r@xmath36 , thick solid gray line ; r@xmath32 , thick solid black line ) . also shown in figure [ lvg ] are the acceptable solutions obtained from the c@xmath1o(21)/c@xmath1o(10 ) line ratio ( thin gray lines ; * ? ? ? figure [ levels ] and table [ tlvg1 ] display the model flux versus upper j state of the line for the t@xmath68 = 10 k , 30 k and 50 k solutions ( also 70 k solutions for gmc b ) . hc@xmath0n(54 ) has a critical density of @xmath69 @xmath6 and an upper energy state of 6.55 k. hc@xmath0n(1615 ) has a critical density , @xmath70 @xmath6 and an upper energy state of 59 k. hc@xmath0n(109 ) values are intermediate . therefore @xmath37 and r@xmath32 are sensitive probes of @xmath54 between the range of @xmath71 and @xmath72 @xmath6 . observed ratios constrain @xmath54 to @xmath730.1 dex at a given t@xmath56 and to @xmath730.3 dex for all modeled t@xmath74 k. for t@xmath75 40 k , ratios are largely insensitive to t@xmath56 ( curves are horizontal ) . the lvg models do not constrain density when t@xmath56 is low . thus to narrow the range of possible solutions requires two or more line ratios , or an external constraint on one of the axes . kinetic temperatures of the dense component at 2@xmath28 scales in ic 342 remain largely unconstrained to date . one method of constraining the kinetic temperature is the peak t@xmath76 at this resolution of the optically thick co(2 - 1 ) line . using this method , t@xmath77 3545 k towards gmcs a , b and c , and t@xmath77 1520 k for gmcs d , d and e @xcite . these values are not highly discordant from arcminute resolution t@xmath78 k measurements from nh@xmath0 @xcite or the far - infrared dust temperature of 42 - 55 k @xcite . however , the co(2 - 1 ) traces gas with densities two to three orders of magnitude lower than these hc@xmath0n transitions , so it is not clear that this is the relevant t@xmath56 for the dense cores of the gmcs . valid solutions are found for the gmcs , with the exception of gmc d , which is the most uncertain due to its distance from the center of the field . ( no fit is attempted for gmc d because both hc@xmath0n(54 ) and hc@xmath0n(1615 ) are upper limits or tentative detections . ) the solutions show modest cloud excitations given the strong nuclear star formation . good agreement is observed between solutions found using r@xmath32 and r@xmath36 when kinetic temperatures are low ( t@xmath79 k ) . given uncertainties in line intensities and @xmath80 , higher temperatures can not be ruled out . while t@xmath56 itself is less well constrained the combination @xmath54t@xmath56 is well determined . since line brightnesses are the measured quantity , as gas temperatures are raised , densities or filling factors must decrease to compensate . the nature of the solutions are such that the densities decrease more than the filling factors ( table [ lvg ] ) . gmcs a , c1 and c3 are best fit with @xmath81 @xmath6 and t@xmath77 20 k. for t@xmath82 k derived densities drop to @xmath83 @xmath6 , while they drop to @xmath84 @xmath6 for t@xmath56 = 100 k. changes in @xmath62 do not strongly influence the derived solutions . towards these clouds filling factors are @xmath850.03 - 0.1 . for comparison , a 1 pc@xmath58 cloud would have @xmath86 0.0012 for the aperture size and ic 342 s distance . therefore these gmcs appear to have a few dozen dense clumps similar to the larger clumps found in galactic gmcs ( e.g. * ? ? ? * ; * ? ? ? gmc c2 appears to have similar densities but slightly elevated temperatures , t@xmath77 30k . in gmcs d and d densities are at least a factor of four lower than the other clouds . little can be said about the kinetic temperatures of these gmcs . gmc d is the only location with statistically discrepant solutions from r@xmath36 and r@xmath32 . here the ( 1615 ) line is somewhat brighter than would be expected from the r@xmath36 . the starburst gmc , b , is markedly different from the others . the combination of a low absolute hc@xmath0n brightness temperature and high ratios , @xmath37 and r@xmath32 , require higher densities of @xmath87 @xmath6 and a smaller ( @xmath880.02 ) filling factor . both line ratios seem to indicate a kinetic temperature of more than t@xmath77 40 k , and perhaps significantly higher , averaged over our 30 pc beam . the dense gas in gmc b , which is closest to the active star - forming region and ir source , is more compact , denser , and more highly excited than the other clouds . for our own galactic center it has long been argued that molecular clouds must be unusually dense , at least @xmath89 to withstand tidal forces ( eg . * ? ? ? * ) . if one assumes that gmc c , the most well defined cloud , is a point mass in a spherical mass potential of the galaxy , its roche limit would be at a radius of 25 pc . the radius of the combined c1-c2-c3 complex is @xmath725 pc . in ic 342 , the proximity to the nucleus where the strong noncircular velocity field @xcite together with feedback from the starburst @xcite suggests that these clumps have densities large enough to maintain their identity but likely will not remain gravitationally bound to each other . for all gmcs ( including gmc b ) , t@xmath33(hc@xmath0n ) @xmath21 t@xmath33(c@xmath1o ) . if a model in which all the h@xmath4 exists in one uniform component , then the similarity of t@xmath33 from both hc@xmath0n and c@xmath1o implies that the densities of the molecular clouds are high enough ( @xmath90 @xmath6 ) to thermalize both c@xmath1o and hc@xmath0n across the nucleus . ( lvg solutions for c@xmath1o j=21 and 10 lines from @xcite are shown with the hc@xmath9n solutions in figure [ lvg ] . ) in this monolithic model the low observed t@xmath33 of 1020 k demand that the thermalized clouds must be quite cool . these temperatures are similar to those of dark clouds in the disk of our galaxy , which is somewhat surprising given the elevated star formation rate in the nucleus of ic 342 . however this model of a monolithic , dense , cold ism seen in both hc@xmath0n and c@xmath1o runs into problems with total mass constraints . if the ism is uniformly this dense and cold then the total dense gas cloud mass implied by the required densities and filling factors become very large , greater than permitted based on the optically thin c@xmath1o line emission . in table [ tlvg1 ] the total mass of dense gas , @xmath91 , is approximated from the lvg solutions assuming @xmath92 , with r defined as @xmath93 . table [ trat ] lists the total molecular gas mass , @xmath94 , estimated from c@xmath1o(2 - 1 ) data ( see * ? ? ? * ) assuming @xmath95 . one can see that @xmath91 is typically larger than @xmath94 for t@xmath96 30 k and diverges rapidly as t@xmath56 drops towards the lvg favored values . in short if gmcs have uniformly such high densities and cold temperatures then the clouds would contain too much h@xmath4 mass for what is observed in c@xmath1o . to match the line ratios while not violating mass constraints requires a multi - component dense ism . a possible two component model of the dense gas is discussed in @xmath97 [ cloudsxco ] .

hcn(54 ) line emission is found across the nuclear mini - spiral , but is very weak towards the starburst site , the location of the strongest mid - ir and radio emission . the brightest hcn emission is located in the northern arm of the nuclear minispiral , 100 pc away from the radio / ir source to the southwest of the nucleus .

we present the first images of the j=54 and j=1615 lines of the dense gas tracer , cyanoacetylene , hcn , in an external galaxy . the central 200 pc of the nearby star - forming spiral galaxy , ic 342 , was mapped using the vla and the plateau de bure interferometer . hcn(54 ) line emission is found across the nuclear mini - spiral , but is very weak towards the starburst site , the location of the strongest mid - ir and radio emission . the j=1615 and 109 lines are also faint near the large hii region complex , but are brighter relative to the 54 line , consistent with higher excitation . the brightest hcn emission is located in the northern arm of the nuclear minispiral , 100 pc away from the radio / ir source to the southwest of the nucleus . this location appears less affected by ultraviolet radiation , and may represent a more embedded , earlier stage of star formation . excitation temperatures are consistent with those determined from co ; the gas is dense , and cool , t k. so as to not violate limits on the total h mass determined from co , at least two dense components are required to model ic 342 s giant molecular clouds . these observations suggest that hcn(54 ) is an excellent probe of the dense , quiescent gas in galaxies . the high excitation combined with faint emission towards the dense molecular gas at the starburst indicates that it currently lacks large masses of very dense gas . we propose a scenario where the starburst is being caught in the act of dispersing or destroying its dense gas in the presence of the large hii region . this explains the high star formation efficiency seen in the dense component . the little remaining dense gas appears to be in pressure equilibrium with the starburst hii region .

1105.1792

c

we have imaged the hc@xmath9n j=54 line in the nucleus of ic 342 with the vla and the hc@xmath0n(1615 ) line with the pdbi at @xmath141 resolution . these are the first maps of these transitions in an external galaxy . we have detected emission extended along the nuclear mini - spiral " in ( 54 ) and more concentrated emission in ( 16 - 15 ) , with relative abundance of @xmath142 . _ hc@xmath0n emission is not tightly correlated with star formation strength . _ dense gas _ excitation _ however , follows star formation more closely . gmc b , which is weak in all the hc@xmath0n lines , is relatively stronger in the higher j lines . lvg modeling indicates that the hc@xmath9n - emitting gas has densities of 10@xmath143 . in ic 342 , physical conditions of the densest component are fairly constant away from the immediate environment of the starburst , though beyond the central ring densities begin to fall . comparison with the c@xmath1o observations of @xcite reveal excitation temperatures similar to c@xmath1o values indicating either that the molecular gas is dense and cool ( t@xmath144 k ) or that there are multiple gas components where the densities and kinetic temperatures of each component conspire to give similar overall excitation . the strong over - prediction of the amount of gas mass present if densities are large and temperatures cool , favors a multi - component ism with at least two components beside the diffuse one seen in @xmath113co(21 ) . the actual ism is likely a continuum of cloud densities with different densities dominating different tracers . hc@xmath0n also differs in morphology from hcn(10 ) , with hcn(10 ) being much brighter towards the starburst . this is further evidence that there are multiple dense gas components . of particular interest , the starburst site ( gmc b ) exhibits the largest difference in intensity between hc@xmath0n ( both transitions ) and hcn(10 ) . the faintness of the hc@xmath0n here suggests that the brightness of hcn(10 ) is not due solely to large quantities of dense gas . a comparison between the gmcs with the largest star formation rates and similar dynamical environments , b and c , hint at an explanation . while gmc b shows higher excitation , the low brightness of this cloud indicates that it is composed of a relatively small amount of warm , dense clumps . the smaller amount of dense gas at the site of the strongest young star formation indicate high star formation efficiencies in the dense gas . towards gmc c , hc@xmath0n , ch@xmath0oh and nh@xmath0 are more intense and the fraction of millimeter continuum from dust is higher . this indicates that gmc c is in an early , less evolved ( hot core - like ) state . the extreme dense gas star formation efficiency observed towards gmc b reflects the fact the main burst is in a more evolved state . the dense clumps towards the starburst are being dispersed or destroyed in the presence of the hii region . the little dense gas remaining appears to be in pressure equilibrium with the hii region . the larger opacity of hcn(10 ) relative to hc@xmath0n elevates its brightness temperature in this warm gas and lowers its critical density permitting it to remain excited in the somewhat lower density component . we conclude that evla observations of hc@xmath0n(54 ) can be a powerful probe of dense , quiescent molecular gas in galaxies , and when combined with high resolution imaging of the higher j transitions of hc@xmath0n with current and upcoming mm interferometers ( like alma ) provide tight constraints on dense molecular gas properties in stronger or more widespread starbursts , where changes like those localized to gmc b are expected to permeate much of the ism . we thank chris carilli and miller goss for assistance with the vla observations . we also thank philippe salome and nemesio rodriguez for their help with the pdbi observations and data reduction . we thank the referee for several suggestions that improved the presentation . d.s.m . acknowledges support from the national radio astronomy observatory which is operated by associated universities , inc . , under cooperative agreement with the national science foundation and nsf grant ast-1009620 . this work is also supported by nsf grants ast-0307950 and ast-0506469 to j.l.t . aalto , s. , polatidis , a. g. , httemeister , s. , & curran , s. j. 2002 , , 381 , 783 aladro , r. , martn - pintado , j. , martn , s. , mauersberger , r. , & bayet , e. 2011 , , 525 , a89 becklin , e. e. , gatley , i. , mathews , k. , neugebauer , g. , sellgren , k. , werner , m. k. , & wynn - williams , c. g.1980 , , 236 , 441 brandl , b. r. , et al . 2006 , , 653 , 1129 bussmann , r. s. , et al . 2008 , , 681 , l73 costagliola , f. & aalto , s. , 2010 , , 515 , 71 dahmen , g. , huttemeister , s. , wilson , t. l. , & mauersberger , r. 1998 , , 331 , 959 de vicente , p. , martn - pintado , j. , neri , r. , & colom , p. 2000 , , 361 , 1058 downes , d. , radford , s. j. e. , giulloteau , s. , guelin , m. , greve , a. , & morris , d. 1992 , , 262 , 424 fuente , a. , martin - pintado , j. , cernicharo , j. , & bachiller , r. 1993 , , 276 , 473 gao , y. & solomon , p. m. 2004 , , 606 , 271 garca - burillo , s. , martn - pintado , j. , fuente , a. & neri , r. 2000 , , 355 , 499 garca - burillo , s. , martn - pintado , j. , fuente , a. & neri , r. 2001 , , 563 , l27 garca - burillo , s. , martn - pintado , j. , fuente , a. , usero , a. & neri , r. 2002 , , 575 , l55 graci - 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burillo , s. , fuente , a. , martn - pintado , j. & rodrguez - fernndez , n. j. 2004 , , 419 , 897 usero , a. , garca - burillo , s. , martn - pintado , j. , fuente , a. , & neri , r. 2006 , , 448 , 457 vanden bout , p. a. , loren , r. b. , snell , r. l. & wootten , a. 1983 , , 271 , 161 wall , w. f. 2007 , , 379 , 674 wu , j. , evans , n. j. , ii , gao , y. , solomon , p. m. , shirley , y. l. , & vanden bout , p. a. 2005 , , 635 , l173 zinchenko , i. , pirogov , l. , & toriseva , m. 1998 , , 133 , 337 lcccccccc a & 13@xmath1452.6 & 5.0@xmath1450.7 & 22@xmath1452 & 29@xmath1455 & 2.4@xmath1450.5 & 7.0@xmath1451.3 & 16@xmath1453 & 44@xmath14510 + b & @xmath125.3 & @xmath121.0 & & & 2.4@xmath1450.5 & 5.2@xmath1451.5 & 19@xmath1453 & 28@xmath14510 + c1 & 44@xmath1452.6 & 6.6@xmath1450.5 & 48@xmath1451 & 39@xmath1453 & 8.5@xmath1450.5 & 13@xmath1451.1 & 47@xmath1451 & 43@xmath1454 + c2 & 28@xmath1452.6 & 5.7@xmath1450.5 & 50@xmath1451 & 35@xmath1454 & 10@xmath1450.5 & 19@xmath1451.2 & 45@xmath1451 & 47@xmath1454 + c3 & 14@xmath1452.6 & 3.6@xmath1450.5 & 49@xmath1451 & 31@xmath1455 & 2.8@xmath1450.5 & 15@xmath1451.0 & 45@xmath1451 & 47@xmath1454 + d & 13@xmath1452.6 & 1.5@xmath1450.5 & 51@xmath1456 & 58@xmath14520 & @xmath121.0 & @xmath122.5 & & + d & 20@xmath1452.6 & 3.8@xmath1450.5 & 52@xmath1452 & 40@xmath1457 & @xmath1461.0 & 2.3@xmath1451.1 & 57@xmath1458 & 44@xmath14526 + e & 14@xmath1452.6 & 4.4@xmath1451 & 12@xmath1452 & 28@xmath1457 & @xmath121.0 & @xmath122.5 & & + [ tinti ] lcccccccc a & 0.55@xmath1450.2 & 8.8@xmath1451.5 & 0.14@xmath1450.03 & 12@xmath1450.6 & 13@xmath1454 & 4(22 ) & 1(-9 ) & 4.4(5 ) + b & 2.5@xmath1451 & 37@xmath14519 & @xmath530.52 & @xmath5318 & 19@xmath1458 & 4(22 ) & @xmath78(-10 ) & 7.6(5 ) + c1 & 0.80@xmath1450.1 & 11@xmath1451.0 & 0.20@xmath1450.03 & 13@xmath1450.6 & 8@xmath1453 & 7(22 ) & 3(-9 ) & 6.8(5 ) + c2 & 1.1@xmath1450.1 & 14@xmath1451.0 & 0.33@xmath1450.03 & 15@xmath1450.6 & 8@xmath1453 & 1(23 ) & 2(-9 ) & 1.0(6 ) + c3 & 1.0@xmath1450.1 & 13@xmath1451.3 & 0.42@xmath1450.07 & 17@xmath1451.3 & 8@xmath1453 & 5(22 ) & 1(-9 ) & 4.9(5 ) + d & @xmath1460.15 & @xmath135 & @xmath120.17 & @xmath1213 & 6@xmath1454 & 2(22 ) & 3(-9 ) & 6.4(5 ) + d & @xmath130.24 & @xmath136 & 0.061@xmath1450.04 & 10@xmath1451.8 & @xmath136 & 6(22 ) & 1(-9 ) & 5.8(5 ) + e & 1.1@xmath1450.3 & 14@xmath1453.1 & @xmath120.057 & @xmath1210 & 7@xmath1453 & 6(22 ) & 1(-9 ) & 1.1(6 ) + [ trat ] lccccccc a & 10 & 5.15 & 0.091 & 38 & 4.7(6 ) & 11 & 6.16 + & 30 & 4.63 & 0.051 & 6.9 & 6.0(5 ) & 1.4 & 6.11 + & 50 & 4.39 & 0.067 & 3.1 & 5.2(5 ) & 1.2 & 6.09 + b & 10 & 5.75 & 0.015 & 75 & 1.3(6 ) & 1.7 & 6.75 + & 30 & 5.22 & 4.7(-3 ) & 14 & 6.5(4 ) & 0.084 & 6.70 + & 50 & 4.87 & 6.0(-3 ) & 5.5 & 4.2(4 ) & 0.055 & 6.57 + & 70 & 4.81 & 5.4(-3 ) & 3.6 & 3.1(4 ) & 0.041 & 6.66 + c1 & 10 & 5.23 & 0.13 & 41 & 9.7(6 ) & 14 & 6.23 + & 30 & 4.69 & 0.066 & 7.4 & 1.0(6 ) & 1.5 & 6.17 + & 50 & 4.50 & 0.075 & 3.6 & 8.0(5 ) & 1.2 & 6.19 + c2 & 10 & 5.36 & 0.12 & 48 & 1.3(7 ) & 13 & 6.36 + & 30 & 4.80 & 0.056 & 8.4 & 1.0(6 ) & 1.0 & 6.28 + & 50 & 4.64 & 0.057 & 4.2 & 7.3(5 ) & 0.73 & 6.34 + c3 & 10 & 5.44 & 0.076 & 53 & 7.1(6 ) & 14 & 6.44 + & 30 & 4.86 & 0.033 & 9.0 & 5.3(5 ) & 1.1 & 6.34 + & 50 & 4.70 & 0.034 & 4.5 & 3.8(5 ) & 0.0.76 & 6.40 + d & 10 & @xmath124.49 & @xmath70.040 & & & & @xmath125.49 + & 30 & @xmath124.10 & @xmath70.040 & & & & @xmath125.58 + & 50 & @xmath123.88 & @xmath70.060 & & & & @xmath125.58 + d & 10 & & & & & & + & 30 & & & & & & + & 50 & & & & & & + e & 10 & 4.90 & 0.12 & 28 & 4.0(6 ) & 3.6 & 5.90 + & 30 & 4.36 & 0.096 & 5.1 & 8.3(5 ) & 0.75 & 5.84 + & 50 & & & & & & + [ tlvg1 ] lccccccc a & 30 & 2.6 & 0.015 & 3.01 & 1.1 & 0.62 & 4.0(45 ) + & 50 & 2.4 & 0.017 & 2.82 & 0.55 & 0.63 & 4.0(45 ) + b & 30 & 2.8 & 3.2(-4 ) & 2.83 & 0.87 & 0.078 & 5.2(46 ) + & 50 & 2.5 & 4.6(-4 ) & 2.54 & 0.37 & 0.097 & 4.2(46 ) + & 70 & 2.4 & 4.0(-4 ) & 2.44 & 0.24 & 0.092 & 4.4(46 ) + c1 & 30 & 2.4 & 0.017 & 3.03 & 1.1 & 0.77 & 1.9(45 ) + & 50 & 2.1 & 0.021 & 2.90 & 0.56 & 0.84 & 1.8(45 ) + c2 & 30 & 2.4 & 0.021 & 3.03 & 1.1 & 0.77 & 2.1(45 ) + & 50 & 2.1 & 0.013 & 2.87 & 0.54 & 0.83 & 1.9(45 ) + c3 & 30 & 2.3 & 5.0(-3 ) & 2.80 & 0.84 & 0.69 & 4.1(45 ) + & 50 & 2.1 & 6.3(-3 ) & 2.64 & 0.42 & 0.72 & 4.0(45 ) + d & 30 & @xmath122.5 & & & & & + & 50 & @xmath122.3 & & & & & + d & 30 & & & & & & + & 50 & & & & & & + e & 30 & 2.3 & 0.030 & 2.94 & 0.99 & 0.78 & 1.6(45 ) + & 50 & 2.0 & & & & & + [ tlvg2 ]

excitation temperatures are consistent with those determined from co ; the gas is dense , and cool , t k. so as to not violate limits on the total h mass determined from co , at least two dense components are required to model ic 342 s giant molecular clouds . this explains the high star formation efficiency seen in the dense component . the little remaining dense gas appears to be in pressure equilibrium with the starburst hii region .

we present the first images of the j=54 and j=1615 lines of the dense gas tracer , cyanoacetylene , hcn , in an external galaxy . the central 200 pc of the nearby star - forming spiral galaxy , ic 342 , was mapped using the vla and the plateau de bure interferometer . hcn(54 ) line emission is found across the nuclear mini - spiral , but is very weak towards the starburst site , the location of the strongest mid - ir and radio emission . the j=1615 and 109 lines are also faint near the large hii region complex , but are brighter relative to the 54 line , consistent with higher excitation . the brightest hcn emission is located in the northern arm of the nuclear minispiral , 100 pc away from the radio / ir source to the southwest of the nucleus . this location appears less affected by ultraviolet radiation , and may represent a more embedded , earlier stage of star formation . excitation temperatures are consistent with those determined from co ; the gas is dense , and cool , t k. so as to not violate limits on the total h mass determined from co , at least two dense components are required to model ic 342 s giant molecular clouds . these observations suggest that hcn(54 ) is an excellent probe of the dense , quiescent gas in galaxies . the high excitation combined with faint emission towards the dense molecular gas at the starburst indicates that it currently lacks large masses of very dense gas . we propose a scenario where the starburst is being caught in the act of dispersing or destroying its dense gas in the presence of the large hii region . this explains the high star formation efficiency seen in the dense component . the little remaining dense gas appears to be in pressure equilibrium with the starburst hii region .

1503.05340

i

it is well known that the virtual pair production and destruction occur always when the external field acts to the vacuum . further these virtual pair produced particles gain the energy from the external field and then these particles appear as real particles . in quantum electrodynamics ( qed ) or similar , in particular the case of electron - positron in the presence of the external electric field this is known as the schwinger effect @xcite and has been well analyzed theoretically . so far the analysis have been done by calculating the vacuum energy density @xmath4 and then the imaginary part @xmath5 is considered as the particle - antiparticle pair production rate defined as @xmath6 it is physically interpreted that the pair production is due to the tunnel effect , because the energy has the imaginary part . a direct physical clarification of the pair production in the background field was made by two of us of the present authors ( h.b.n . and m.n . ) @xcite . when the electric field is applied to the negative energy electrons in the dirac sea , the right - mover particles and left - mover holes gain the energy and are pumped up or down , the pair production occurs . this mechanism is depicted in figure [ pic : pair.prod-0 ] where the blue circle denotes the electron and the white circle is the positron . the purpose of the present article is twofold . the first purpose is to reveal in a quantum field theoretical method the dynamics of the pair production . we show in more detail and precisely that the pair production state is a superposition of all possible particle and antiparticle state . in fact we will show that the pair production state is indeed a superposition of one pair , two pairs , three pairs , ... of particle and antiparticle with various energies . the second theme of the present paper is a kind of new physical derivation of the weyl anomaly . in 1974 , d. m. capper and m. j. duff discovered the weyl anomaly @xcite that the trace of the energy - momentum tensor for a massless weyl fermion in a gravitational background is not as classically expected to be @xmath7 , but rather @xmath8 here @xmath9 is the square root of the determinant of the metric tensor and @xmath0 is the ricci scalar . later many recalculations of this anomaly has been made ( see the review , for example @xcite ) . the present article is an attempt to obtain a physical understanding of how this anomaly comes about , i.e. to reveal the mechanism that the pair production from the dirac sea leads the weyl anomaly . as such it is also inspired by the interpretation of the chiral anomaly as pumping up or down states from or to the dirac sea @xcite of two of us ( m.n and h.b.n ) . an another attempt to understand the @xmath10 dimensional weyl anomaly by our thinking on the dirac sea we presented in @xcite . as setting up we consider @xmath10 dimensional euclidean cylinder type space - time with the conformal flat metric @xmath11 . in this space - time we investigate the vacuum - to - vacuum transition amplitude of the massless dirac fermion which has weyl symmetric action . we then make a basis transformation of ( or , in other words , pull back ) the amplitude into the fock space in the space - time with another metric @xmath12 . then we can show that the dirac sea in the space - time specified by the primed metric @xmath13 ranging from @xmath14-past to @xmath15-future is expressed on the basis in the space - time with @xmath16 as a pair produced state on each time - slice . by summing up these pair production contribution from @xmath14-past to @xmath15-future , the difference between the vacuum ( or casimir ) energy in the space - time of the metric @xmath13 and that of the metric @xmath16 gives rise to the ricci scalar . in this way we finally obtain the weyl anomaly . the organization of this paper is as follows . in the following section [ sec1 ] we summarize the construction of the weyl particles and dirac sea in the gravitational background . in the section [ sec2 ] we then formulate the state description of the pair production and evaluate the weyl anomaly using the dirac sea formalism . in section [ sec3 ] we conclude and give an outlook as to how possibly to extend the use of our formalism . we have in addition three appendices .

when summing up with respect to the time the contribution of pair production of each time - slice we obtain the ricci scalar and then it is related to the trace part of the energy - momentum tensor to produce weyl anomaly . oiqp-15 - 03 * a state description of pair production from dirac sea + in gravitational field + physical interpretation of weyl anomaly * yoshinobu habara , holger b. nielsen and masao ninomiya okayama institute for quantum physics , 1 - 9 - 1 kyoyama , okayama 700 - 0015 , japan niels bohr institute , university of copenhagen , 17 blegdamsvej , dk2100 , denmark habara@yukawa.kyoto-u.ac.jp , hbech@nbi.dk , msninomiya@gmail.com pacs numbers : 04.60.kz , 11.10.-z , 11.10.kk , 11.10.gh , 11.30.-j keywords : field theory , pair production , gravitation , dirac sea , dirac fermion , weyl anomaly

we present the method that the pair production of particles is described as a fock space state vector , where the pair production stems from receiving energy from , as an example , gravitational background field . at the same time we show a sort of new mechanism that in the diffeomorphism - invariant dirac sea the weyl symmetry is broken due to the pair production and this provides us a new physical interpretation of the origin of weyl anomaly . in the present paper at the first place , we consider two kinds of background space - time which are connected each other by the weyl transformation . it is shown that the vacuum , i.e. dirac sea , in the curved " space - time making weyl transformation is nothing but the pair produced state provided we consider the state in terms of the fock space basis in the flat " space - time making the weyl transformation . when summing up with respect to the time the contribution of pair production of each time - slice we obtain the ricci scalar and then it is related to the trace part of the energy - momentum tensor to produce weyl anomaly . oiqp-15 - 03 * a state description of pair production from dirac sea + in gravitational field + physical interpretation of weyl anomaly * yoshinobu habara , holger b. nielsen and masao ninomiya okayama institute for quantum physics , 1 - 9 - 1 kyoyama , okayama 700 - 0015 , japan niels bohr institute , university of copenhagen , 17 blegdamsvej , dk2100 , denmark habara@yukawa.kyoto-u.ac.jp , hbech@nbi.dk , msninomiya@gmail.com pacs numbers : 04.60.kz , 11.10.-z , 11.10.kk , 11.10.gh , 11.30.-j keywords : field theory , pair production , gravitation , dirac sea , dirac fermion , weyl anomaly

1503.05340

c

in the present article we presented that when the dirac sea in the background space - time with the metric @xmath144 is expanded in terms of the fock space basis of the space - time with the metric @xmath41 there appears the state of the sum of the dirac sea and a state called @xmath78}$ ] . in particular , in the case of @xmath71 , the state @xmath145}$ ] describes the one of the particle - antiparticle pairs . in perturbation theory , between the formulation in terms of the empty vacuum and the formulation in terms of the dirac sea in which the negative energy states are all filled , there is no difference in the result . however in the case of the nonperturbative phenomena such as the particle - antiparticle pair production , there appears apparent difference as we have shown . the origin of this comes from the fact that the vacuum is not empty but there is a sea of the infinitely many negative energy particles and these are transformed under the weyl transformation . when the dirac sea , which is defined in a diffeomorphism invariant manner , is acted by the weyl transformation , the pairs of the particle and antiparticle are created and the weyl symmetry is broken . we have shown that this is precisely the origin of the weyl anomaly . in the fujikawa s method based on the path integral formalism @xcite , the path integral measure violates the symmetry and the weyl anomaly stems from the jacobian of the weyl transformation . in our operator formalism , the pair production from the dirac sea on each time - slice , which occurs during the transition from @xmath14-past to @xmath15-future , breaks the weyl symmetry . the weyl anomaly is obtained by summing up the breaking effects over all the time . in this manner , we show the formulation of the physical relation between the pair production state and the appearance of the weyl anomaly . our formulation can be applied to many physical phenomena , irrelevant to the detail of the models . for instance the state expression of the pair production can be used by changing the gravitational field to the electromagnetic field to investigate the dynamics of the electrons and holes in the materials . as for the physics of the high energy particle and the universe we are under investigation and some of the topics will be shown in the following section [ sec3.2 ] . really the main motivation for the present work is the hope that we may extend our formulation to slightly different but related issues : 1 . the pair production of bosons to generate the weyl anomaly : + in our previous works @xcite , we formulated the boson sea which is the vacuum being filled with negative energy bosons . if we set the background metric to the conformally flat one and transform the boson sea by the weyl transformation , we can construct the pair produced state from the boson sea vacuum , which would be the bosonic version of ( [ eq:2-weyl.dirac.a ] ) . all we should do may be parallel to the method shown in the present article . all other anomalies such as the gravitational anomaly being generated via the pair production from the sea : + we can apply our method to the physical interpretations of all anomalies and unify them in terms of the pair production from the sea vacuum . 3 . the hawking radiation and the gravitational wave : + when we consider the sea vacuum in the schwarzschild or de sitter space - time background , we can express the hawking radiation as the pair production state . in particular , in the case of the complex boson and the boson sea , we can represent the gravitational wave by using the pair production state as the hawking radiation , because the number of the degrees of freedom of the gravitational wave is two which is identical to that of the complex boson . then we may be able to evaluate the entropies of the black hole and the inflationary universe using the notion of the typicality @xcite or the formulation of statistical mechanics based on the thermal pure quantum states @xcite .

we present the method that the pair production of particles is described as a fock space state vector , where the pair production stems from receiving energy from , as an example , gravitational background field . at the same time we show a sort of new mechanism that in the diffeomorphism - invariant dirac sea the weyl symmetry is broken due to the pair production and this provides us a new physical interpretation of the origin of weyl anomaly . in the present paper at the first place , we consider two kinds of background space - time which are connected each other by the weyl transformation . it is shown that the vacuum , i.e. dirac sea , in the curved " space - time making weyl transformation is nothing but the pair produced state provided we consider the state in terms of the fock space basis in the

we present the method that the pair production of particles is described as a fock space state vector , where the pair production stems from receiving energy from , as an example , gravitational background field . at the same time we show a sort of new mechanism that in the diffeomorphism - invariant dirac sea the weyl symmetry is broken due to the pair production and this provides us a new physical interpretation of the origin of weyl anomaly . in the present paper at the first place , we consider two kinds of background space - time which are connected each other by the weyl transformation . it is shown that the vacuum , i.e. dirac sea , in the curved " space - time making weyl transformation is nothing but the pair produced state provided we consider the state in terms of the fock space basis in the flat " space - time making the weyl transformation . when summing up with respect to the time the contribution of pair production of each time - slice we obtain the ricci scalar and then it is related to the trace part of the energy - momentum tensor to produce weyl anomaly . oiqp-15 - 03 * a state description of pair production from dirac sea + in gravitational field + physical interpretation of weyl anomaly * yoshinobu habara , holger b. nielsen and masao ninomiya okayama institute for quantum physics , 1 - 9 - 1 kyoyama , okayama 700 - 0015 , japan niels bohr institute , university of copenhagen , 17 blegdamsvej , dk2100 , denmark habara@yukawa.kyoto-u.ac.jp , hbech@nbi.dk , msninomiya@gmail.com pacs numbers : 04.60.kz , 11.10.-z , 11.10.kk , 11.10.gh , 11.30.-j keywords : field theory , pair production , gravitation , dirac sea , dirac fermion , weyl anomaly

1609.06611

i

we have presented 21-cm line observations for a sample of four galactic cepheids . our goal was to search for circumstellar gas associated with previous or ongoing mass loss . if present , such matter would help to reconcile the persistent discrepancies of @xmath210 - 20% between the masses of cepheids derived from stellar evolution models versus those from the mass - dependent period - luminosity relation or orbital dynamics . we have discovered a shell - like structure near the long - period binary cepheid , t mon . the star lies in projection just outside the edge of this structure , with an offset from the geometric center in the direction of the star s space motion . at the distance of t mon , the shell would have an atomic hydrogen mass of @xmath186 and a size of @xmath22 pc . although we can not strictly exclude that the shell was formed during a red supergiant phase , or alternatively , that it represents a chance superposition of an interstellar cloud along the line - of - sight , its properties appear to be consistent with a fossil circumstellar shell that resulted from an earlier epoch of mass - loss during t mon s previous crossing of the instability strip . this interpretation would support a model where mass - loss on the cepheid instability strip is sporadic . assuming that approximately two - thirds of the shell s mass originated from a stellar outflow , the mass of the material would be sufficient to account for @xmath250% of the discrepancy between the pulsation and evolutionary mass of t mon . for the other three stars in our sample ( rs pup , x cyg , and @xmath0 gem ) , no emission was detected that could be unambiguously associated with the circumstellar environment . in all three cases , line - of - sight confusion precluded searches of portions of the observing band , with the effect being most severe for rs pup . for the undetected stars , we place model - dependent 3@xmath83 upper limits on the mass of circumstellar gas within a volume of radius 0.5 pc surrounding each star . the resulting upper limits correspond to @xmath1632 - 5% of the respective stellar masses . given typical cepheid mass discrepancies of @xmath210 - 20% , mass - loss through a neutral atomic wind therefore can not yet be excluded as making a significant contribution to reconciling the discrepancy between pulsation and evolutionary mass for these stars . furthermore , our upper limits on the mean mass - loss rates over their lifetimes on the instability strip [ @xmath6 yr@xmath4 ] are consistent with mean mass loss rates derived from previous studies of the rate of period change of large samples of cepheids . however , we emphasize that our current upper limits are dependent on uncertain assumptions about the properties of cepheid winds , including the predicted outflow velocity ( see section [ upperlimits ] ) . the findings here , together with the previous work of m12 , suggest that a deep survey of a larger sample of nearby galactic cepheids ( @xmath1881 kpc ) could provide additional new constraints on the role of mass loss during the cepheid evolutionary phase . an order of magnitude increase in sensitivity , such as could be achieved with next - generation interferometers , would be particularly valuable . additionally , the impact of confusion could likely be reduced in future observations through inclusion of data from longer baselines ( e.g. , le bertre et al . 2012 ) to help filter out the large - scale line - of - sight contamination . ldm is supported by grant ast-1310930 from the national science foundation . support to nre was provided from the _ chandra _ x - ray center nasa contract nas8 - 03060 . the observations presented here were part of nrao program am1087 ( vla/11b-035 ) . this research has made use of the simbad database , operated at cds , strasbourg , france .

the observations were aimed at detecting gas associated with previous or ongoing mass loss . near the long - period cepheid t mon , we report the detection of a partial shell - like structure whose properties appear consistent with originating from an earlier epoch of cepheid mass loss . at the distance of t we derive model - dependent upper limits on the mass - loss rates , averaged over their lifetimes on the instability strip , of yr and estimate the total amount of mass lost to be less than a few per cent of the stellar mass .

we present the results of a search for 21-cm line emission from the circumstellar environments of four galactic cepheids ( rs pup , x cyg , gem , and t mon ) based on observations with the karl g. jansky very large array . the observations were aimed at detecting gas associated with previous or ongoing mass loss . near the long - period cepheid t mon , we report the detection of a partial shell - like structure whose properties appear consistent with originating from an earlier epoch of cepheid mass loss . at the distance of t mon , the nebula would have a mass ( + he ) of , or% of the stellar mass . assuming that one - third of the nebular mass comprises swept - up interstellar gas , we estimate an implied mass - loss rate of yr . no clear signatures of circumstellar emission were found toward gem , rs pup , or x cyg , although in each case , line - of - sight confusion compromised portions of the spectral band . for the undetected stars , we derive model - dependent upper limits on the mass - loss rates , averaged over their lifetimes on the instability strip , of yr and estimate the total amount of mass lost to be less than a few per cent of the stellar mass .

astro-ph0311106

c

we have studied the cluster systems of dwarf irregular galaxies using hst / wfpc2 observations of 28 galaxies in the virgo and fornax clusters , 11 of which are confirmed members . in these 11 confirmed members we have found 237 cluster candidates and determined their magnitudes , core radii , and v - i colors . based on source counts of neighboring , empty , wfpc2 fields , we expect a contamination of 51 background and foreground sources , which were statistically subtracted from the data . the cluster candidates were divided by color in order to separate red ( with age @xmath53 1 gyr ) and blue ( age @xmath54 1 gyr ) cluster candidates . we consider the red cluster candidates to be globular cluster candidates . the main results presented here are : 1 . the red cluster candidates have the same magnitudes as expected for globular clusters . more specifically , the luminosity function of galactic globular clusters @xcite is well matched by the luminosity function of our red cluster candidates down to our 90% completeness limit at m@xmath55 -7 . 2 . the median color ( v - i = 1.0 ) of the red cluster candidates is bluer than the median colors of globular cluster systems in elliptical galaxies @xcite , even without a correction for internal reddening . this is consistent with the globular cluster systems in these dwarf irregular galaxies being metal - poor . the distribution of core radii for the red candidate clusters is significantly larger than for galactic globular clusters . larger radii are also seen in the globular clusters of the lmc and other local group dwarves @xcite suggesting that this might be a general property of globular clusters in dwarf galaxies . the blue cluster candidates are in general more compact and fainter than the red cluster candidates . based on single - stellar population models , they have masses ranging between 10@xmath2 and 10@xmath41 m@xmath3 . h@xmath0 data on 7 virgo cluster galaxies suggests that 26% of the blue cluster candidates are in fact hii regions . the specific frequencies for the galaxies exhibit a large scatter , but are surprisingly large , with 7 of the 11 galaxies having specific frequency values greater than two . these values are surprising when compared to local group dwarf irregulars and other nearby late - type galaxies , which have specific frequencies less than two . we note , however , that our specific frequency values are uncertain due to the possible presence of reddened young clusters , massive intermediate - age clusters and incompleteness . we plan to follow up this work with spectroscopic observations or infrared imaging of some of these cluster systems . these observations of the cluster candidates will test the accuracy of our photometric results by enabling accurate age and metallicity determination . this work was supported by the national optical astronomy observatory , which is operated by the association of universities for research in astronomy , inc . , under cooperative agreement with the national science foundation . it also has been supported by the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , on behalf of the international gemini partnership of argentina , australia , brazil , canada , chile , the united kingdom , and the united states of america . the authors would like to thank : paul hodge , for his guidance and help observing , peter stetson for help with daophot ii , eduardo bica , for providing us with his tables , nick suntzeff for his helpful comments , ricardo covarrubias , and armin rest . fcc 5 & 03:17:51.8 & -36:45:59 & & 22/10/98 & + fcc 41 & 03:25:35.9 & -32:57:35 & & 16/12/98 & + fcc 76 & 03:29:43.2 & -33:33:25 & 1808 & 12/03/99 & + fcc 120 & 03:33:34.2 & -36:36:21 & 887 & 14/12/98 & + fcc 128 & 03:34:06.9 & -36:27:52 & & 8/01/99 & + fcc 173 & 03:36:43.2 & -34:09:33 & & 31/07/97 & + fcc 224 & 03:39:32.8 & -31:47:32 & & 31/12/98 & + fcc 247 & 03:40:42.4 & -35:39:40 & 1097 & 21/02/99 & + fcc 282 & 03:42:45.5 & -33:55:13 & 1225 & 8/11/98 & + fcc 337 & 03:51:01.2 & -36:41:00 & & 16/12/98 & + vcc 72 & 12:13:02.2 & + 14:55:58 & 6351 & 18/12/98 & + vcc 83 & 12:13:33.5 & + 14:28:51 & 2441 & 18/12/98 & yes + vcc 280 & 12:18:14.6 & + 11:28:52 & & 16/12/98 & + vcc 328 & 12:19:11.1 & + 12:53:05 & 2179 & 4/01/98 & yes + vcc 364 & 12:19:44.0 & + 12:16:54 & & 16/12/98 & + vcc 666 & 12:23:46.1 & + 16:47:25 & & 2/01/99 & + vcc 888 & 12:26:18.3 & + 08:20:57 & 1096 & 13/12/98 & yes + vcc 899 & 12:26:27.4 & + 06:42:32 & 4198 & 11/12/98 & + vcc 1165 & 12:29:10.4 & + 09:16:01 & & 10/12/98 & + vcc 1227 & 12:29:46.8 & + 11:10:02 & & 14/12/98 & + vcc 1374 & 12:31:37.7 & + 14:51:38 & 2559 & 19/12/98 & yes + vcc 1413 & 12:32:07.7 & + 12:26:04 & & 17/12/98 & + vcc 1448 & 12:32:40.7 & + 12:46:16 & 2583 & 13/02/99 & yes + vcc 1822 & 12:40:10.4 & + 06:50:48 & 1012 & 7/12/98 & yes + vcc 1889 & 12:41:46.0 & + 11:15:01 & 4725 & 16/12/98 & + vcc 1992 & 12:44:09.7 & + 12:06:47 & 1010 & 21/03/99 & yes + fcc 5 & 17.5 & 0.09 & 24.38 & 5 & 4.92 @xmath51 2.59 + fcc 41 & 18.2 & 1.20 & 24.50 & 3 & 5.27 @xmath51 2.52 + fcc 76 & 14.6 & 0.04 & 24.38 & 24 & 4.69 @xmath51 2.53 + fcc 120 & 15.9 & 0.23 & 24.50 & 12 & 5.04 @xmath51 2.54 + fcc 128 & 16.3 & 0.02 & 24.50 & 7 & 5.23 @xmath51 2.63 + fcc 173 & 18.7 & 3.79 & 24.45 & 4 & 5.23 @xmath51 2.70 + fcc 224 & 16.4 & 0.17 & 24.49 & 17 & 5.30 @xmath51 2.62 + fcc 247 & 17.6 & 0.10 & 24.45 & 6 & 5.19 @xmath51 2.67 + fcc 282 & 14.2 & 0.01 & 24.36 & 25 & 4.46 @xmath51 2.52 + fcc 337 & 17.0 & 0.41 & 24.53 & 4 & 5.42 @xmath51 2.67 + vcc 72 & 16.2 & 0.07 & 24.30 & 7 & 4.54 @xmath51 2.50 + vcc 83 & 15.5 & 0.03 & 24.31 & 18 & 4.42 @xmath51 2.55 + vcc 280 & 18.4 & 1.58 & 24.29 & 6 & 4.31 @xmath51 2.36 + vcc 328 & 16.0 & 0.12 & 24.37 & 18 & 4.54 @xmath51 2.53 + vcc 364 & 16.9 & 0.05 & 24.31 & 10 & 4.27 @xmath51 2.39 + vcc 666 & 16.6 & 0.06 & 24.36 & 7 & 4.65 @xmath51 2.51 + vcc 888 & 15.3 & 0.06 & 24.22 & 16 & 4.19 @xmath51 2.38 + vcc 899 & 16.8 & 0.17 & 24.21 & 0 & 4.15 @xmath51 2.34 + vcc 1165 & 16.9 & 0.28 & 24.28 & 5 & 4.38 @xmath51 2.56 + vcc 1227 & 18.9 & 0.16 & 24.31 & 5 & 4.58 @xmath51 2.45 + vcc 1374 & 14.6 & 0.01 & 24.20 & 64 & 3.96 @xmath51 2.34 + vcc 1413 & 17.4 & 0.02 & 24.37 & 6 & 4.73 @xmath51 2.43 + vcc 1448 & 15.0 & 0.10 & 24.36 & 25 & 4.58 @xmath51 2.48 + vcc 1822 & 16.1 & 0.01 & 24.19 & 7 & 3.92 @xmath51 2.30 + vcc 1889 & 16.1 & 0.08 & 24.29 & 6 & 4.35 @xmath51 2.54 + vcc 1992 & 15.9 & 0.05 & 24.33 & 22 & 4.27 @xmath51 2.52 + lccccccc fcc76 & 11 & 13 & 2.3 @xmath51 0.9 & 1.36 & 3.1 @xmath51 1.0 & & + fcc120 & 5 & 7 & 2.4 @xmath51 2.0 & 1.28 & 3.0 @xmath51 2.2 & & + fcc247 & 1 & 5 & 3.7 @xmath51 7.1 & 1.31 & 4.9 @xmath51 7.5 & & + fcc282 & 15 & 10 & 1.1 @xmath51 0.6 & 1.36 & 1.5 @xmath51 0.6 & & + vcc83 & 10 & 8 & 2.5 @xmath51 1.7 & 1.40 & 3.5 @xmath51 1.8 & 11.0 & 0.009 + vcc328 & 14 & 4 & 0.5 @xmath51 1.9 & 1.36 & 0.7 @xmath51 1.9 & 7.1 & 0.006 + vcc888 & 13 & 3 & -0.1 @xmath51 0.9 & 1.47 & -0.2 @xmath51 0.9 & 6.3 & 0.005 + vcc1374 & 39 & 25 & 5.3 @xmath51 1.3 & 1.49 & 7.8 @xmath51 1.5 & 54.3 & 0.044 + vcc1448 & 4 & 21 & 6.1 @xmath51 1.7 & 1.36 & 8.3 @xmath51 1.9 & 0.0 & 0.0 + vcc1822 & 3 & 4 & 1.0 @xmath51 1.6 & 1.50 & 1.4 @xmath51 1.7 & 0.2 & 0.0002 + vcc1992 & 15 & 7 & 2.9 @xmath51 2.1 & 1.39 & 4.0 @xmath51 2.3 & 16.0 & 0.013 +

we present the results of a search for clusters in dwarf irregular galaxies in the virgo and fornax cluster using hst wfpc2 snapshot data . the galaxy sample includes 28 galaxies , 11 of which are confirmed members of the virgo and fornax clusters . in the 11 confirmed members , we detect 237 cluster candidates and determine their v magnitudes , v - i colors and core radii . although the values are uncertain , seven of the galaxies appear to have specific frequencies greater than 2 . these values are more typical of ellipticals and nucleated dwarf ellipticals than they are of spirals or local group dwarf irregulars .

we present the results of a search for clusters in dwarf irregular galaxies in the virgo and fornax cluster using hst wfpc2 snapshot data . the galaxy sample includes 28 galaxies , 11 of which are confirmed members of the virgo and fornax clusters . in the 11 confirmed members , we detect 237 cluster candidates and determine their v magnitudes , v - i colors and core radii . after statistical subtraction of background galaxies and foreground stars , most of the cluster candidates have v - i colors of -0.2 and 1.4 , v magnitudes lying between 20 and 25th magnitude and core radii between 0 and 6 pc . using h observations , we find that 26% of the blue cluster candidates are most likely hii regions . the rest of the cluster candidates are most likely massive ( m ) young and old clusters . a comparison between the red cluster candidates in our sample and the milky way globular clusters shows that they have similar luminosity distributions , but that the red cluster candidates typically have larger core radii . assuming that the red cluster candidates are in fact globular clusters , we derive specific frequencies ( s ) ranging from - 9 for the galaxies . although the values are uncertain , seven of the galaxies appear to have specific frequencies greater than 2 . these values are more typical of ellipticals and nucleated dwarf ellipticals than they are of spirals or local group dwarf irregulars .

0707.2249

i

clusters of galaxies represent the most massive bound systems in the cosmos . although they result from non - linear structure evolution , the departure from linear growth is modest compared to that for less massive objects . as a result , simple analytic models can provide an accurate indication of their expected number density at various redshifts . this is the primary reason why cluster of galaxies are considered to be valuable cosmological probes . cosmological attention has focused on the redshift - dependent number of clusters , @xmath1 , whose mass exceeds a certain threshold . this is one of the most straightforward observables , and is a function of the cluster mass function , @xmath2 , and the evolution of comoving volume @xmath3 . the mass function is obtained from the growth rate of density fluctuations , @xmath4 , numerically @xcite under the assumption of a particular theory of structure formation , e.g. the currently - popular cold dark matter ( cdm ) model . since both @xmath4 and @xmath3 are dependent on the cosmological model , useful constraints could be estimated by comparing @xmath1 with various model predictions . to make progress , e.g. on the dark energy equation of state parameter @xmath5 , data on several thousand clusters to @xmath61 is thought to be required @xcite , and maintaining an accurate and uniform mass threshold is critical . most early work focused on selecting clusters optically , with detection techniques that have improved over the decades : e.g. matched - filter @xcite , red - sequence @xcite , cut - and - enhance @xcite . optically selected samples have traditionally suffered from uncertainties in the optical richness - mass relation , although there has been recent progress in calibrating the closely related richness - velocity dispersion relation using the large maxbcg sample of clusters identified in the sloan digital sky survey @xcite . so far , x - ray samples have been the most popular cosmological probes e.g. @xcite , @xcite , @xcite . luminosity ( @xmath7 ) or temperature ( @xmath8)-limited samples offer simpler selection functions because the observables , @xmath7 , @xmath8 , are a fair estimate of the cluster mass , calibrated through empirical scaling relations . the derived mass does depend , however , on the assumed dynamical state of the system . unrelaxed clusters , arising for example from recent mergers , will introduce scatter in the scaling relation . a recent study by @xcite points out that at least half of 10 z @xmath9 0.2 cluster cores show unrelaxed features and a scatter of @xmath10 around the mean scaling relation . weak gravitational lensing , which analyses the coherent shear pattern of background galaxies , can potentially provide estimates of the cluster mass _ regardless of its dynamical state or the properties of the constituent galaxies_. for some years , the method has been used to calibrate mass obtained from x - ray data @xcite . @xcite concluded that x - ray mass measurements are consistent with those from weak lensing , particularly for relaxed systems which thus offer a useful cosmological probe@xcite . a natural extension of this progress is thus to consider selecting clusters directly from weak lensing signals . the development of panoramic imaging surveys has now made this a practical proposition . @xcite reported the first discovery of a cluster located from a weak lensing convergence map , during the course of conducting the deep lens survey @xcite . @xcite later undertook a systematic search of mass concentrations on a 2 deg@xmath0 field using the suprime - cam imager on subaru . they detected several significant ( s / n@xmath11 ) candidates , one of which was later spectroscopically identified as a cluster at @xmath12 = 0.41 . @xcite investigated 50 randomly - selected vlt fors1 fields , spanning 0.64 deg@xmath0 in total , and found 5 shear - selected candidates , each associated with an overdensity in luminosity . the first results from the deep lens survey , based on an area of 8.6 deg@xmath0 have also recently emerged @xcite . the above pioneering studies have demonstrated that clusters can be located directly via weak lensing . however , key issues , including the optimum selection threshold , the rate of spurious detection and the degree of mass completeness at a given redshift , crucial for any eventual cosmological application , remain unresolved . at the present time , theoretical studies offer the only insight into these issues . projection is one of the most troublesome aspects of a weak lensing survey , because of the relatively broad window function . unrelated structures contributing to the signal would lead to an overestimate of the cluster mass . moreover , as the noise in the convergence map arises largely from shot noise in the ellipticity distribution of background galaxies , some fraction of genuine clusters might be missed in a shear selected catalog . n - body and ray - tracing simulations @xcite have concluded that , for systems whose convergence signal lie above a 4 standard deviation ( @xmath13 ) threshold , 60 - 75% of clusters can reliably recovered ( completeness ) . likewise , for peaks detected in the simulated data using typically - used algorithms , 60 - 75 % represent genuine clusters ( efficiency ) . the difference in these figures between the various studies is largely due to differences in the lower mass limit adopted in the studies . this series of papers is motivated by the need to address these key issues observationally . the survey we describe is a natural and ongoing extension of the 2 deg@xmath0 survey of @xcite ; to date a total field of 21.82 deg@xmath0 has been imaged . this first paper describes the imaging survey and discusses the validation of the candidates found , both via spectroscopic verification and comparison with clusters located via x - ray techniques . later papers in the series will extend the spectroscopic follow - up to the full sample and will consider the feasibility of deriving cosmological constraints from both this survey and future enhanced versions . we note that a similary motivated program has been initiated by @xcite , @xcite and @xcite , all of which made used of the imaging data taken by 2.5 m vlt survey telescope . we compare the their conclusions with our own in this paper . we note that a similarly motivated program has been initiated by @xcite and @xcite whose conclusions we compare with our own in this paper . a plan of the paper follows . we discuss the imaging strategy and data analysis in 2 , including construction of the cluster catalog and its reliability . in 3 , we describe our initial spectroscopic follow - up with subaru and address the completeness by comparing x - ray selected clusters on one of our survey area where relevant x - ray data is available . we summarize our conclusions in 4 .

we present the results of an ongoing weak lensing survey conducted with the subaru telescope whose initial goal is to locate and study the distribution of shear - selected structures or _ halos_. using a suprime - cam imaging survey spanning 21.82 deg , we present a catalog of 100 candidate halos located from lensing convergence maps . all are confirmed as clusters of galaxies but two arise as the superposition of multiple clusters viewed along the line of sight . including data available in the literature and an ongoing keck spectroscopic campaign , a total of 41 halos now have reliable redshifts . of 15 halos detected in the xmm - lss field , 10 match with published x - ray selected clusters and a further 2 are newly - detected and spectroscopically confirmed in this work . although three halos have not yet been confirmed , the high success rate within the xmm - lss field ( 12/15 ) confirms that weak lensing provides a reliable method for constructing cluster catalogs , irrespective of the nature of the constituent galaxies or the intracluster medium .

we present the results of an ongoing weak lensing survey conducted with the subaru telescope whose initial goal is to locate and study the distribution of shear - selected structures or _ halos_. using a suprime - cam imaging survey spanning 21.82 deg , we present a catalog of 100 candidate halos located from lensing convergence maps . our sample is reliably drawn from that subset of our survey area , ( totaling 16.72 deg ) uncontaminated by bright stars and edge effects and limited at a convergence signal to noise ratio of 3.69 . to validate the sample detailed spectroscopic measures have been made for 26 candidates using the subaru multi - object spectrograph , focas . all are confirmed as clusters of galaxies but two arise as the superposition of multiple clusters viewed along the line of sight . including data available in the literature and an ongoing keck spectroscopic campaign , a total of 41 halos now have reliable redshifts . for one of our survey fields , the xmm lss field , we compare our lensing - selected halo catalog with its x - ray equivalent . of 15 halos detected in the xmm - lss field , 10 match with published x - ray selected clusters and a further 2 are newly - detected and spectroscopically confirmed in this work . although three halos have not yet been confirmed , the high success rate within the xmm - lss field ( 12/15 ) confirms that weak lensing provides a reliable method for constructing cluster catalogs , irrespective of the nature of the constituent galaxies or the intracluster medium .

1603.00947

i

we examined the x - ray properties of 16 young radio sources with _ chandra _ and observed variety of interesting characteristics , which we summarize below . * we found that our cso sample covers a wide range in x - ray luminosity , @xmath2@xmath3ergs@xmath4 and that the majority of sources contains a modest amount of the intrinsic absorption ( @xmath24010@xmath6@xmath7 ) . * we obtained the highest quality x - ray spectrum of the cso source to date in our long _ chandra _ observation of 0710@xmath10439 and found an ionized iron emission line , @xmath11kev . however , we were not able to determine the origin of the line , as it could be related to the emission from the hot ionized accretion disk illuminated by an external source , from a distant photoionized medium , or from a diffuse hot thermal plasma within the nuclear region . depending on the model , we derived ew of the line ranging from @xmath241ev ( model b ) to @xmath242kev ( model f ) . * we found a hard photon index of @xmath243 in 2021@xmath10614 and @xmath188 in 1511@xmath100518 consistent with either a compton thick absorber or non - thermal emission from compact radio lobes . * we discovered that the 210kev x - ray flux decreased by an order of magnitude since the 2008 _ xmm - newton _ observation of 1607@xmath1026 . future monitoring of this source is needed in order to characterize and understand the nature of the variability . * we examined the highest angular resolution x - ray images of the csos and detected extended x - ray emission in 1718@xmath8649 which needs to be studied with the deeper x - ray observations in the future . we found that short @xmath245ksec x - ray observations with @xmath244 have proven to be effective in detecting the csos sources and deriving their basic x - ray properties . with our _ chandra _ program , we observed six csos for the first time in x - rays , and we increased the size of the known csos sample with measured redshift , kinematic age , and x - ray information by @xmath2468% . the cso x - ray population can be further extended through snapshot _ chandra _ and/or _ xmm - newton _ observations of seven sources whose kinematic ages have been recently derived ( an & baan 2012 , figure [ fig : ages ] ) . however , it is apparent that deeper exposures are needed in order to study details of the csos environment ( e.g. , the amount of intrinsic absorption , the gaseous media co - spatial with the radio sources ) and the origin of the csos intrinsic x - ray emission ( diffused thermal vs. nuclear emission , evidence for reprocessing of the nuclear x - rays by a circumnuclear matter , thermal vs. non - thermal electron population generating the high - energy csos spectra , long term x - ray variability ) . deep x - ray observations are also necessary in order to place critical constraints on current theoretical models for the earliest stage of radio source evolution .

we observed six of them for the first time in x - rays using _ chandra _ , re - observed four with the previous _ xmm - newton _ or _ beppo - sax _ data , and included six other with the archival data . the sample covers a range in x - ray luminosity ,ergs , and intrinsic absorbing column density of . in particular , we detected extended x - ray emission in 1718 ; a hard photon index of in 2021 and 1511 consistent with either a compton thick absorber or non - thermal emission from compact radio lobes , and in 0710 an ionized iron emission line atkev and ew.4kev , and a decrease by an order of magnitude in the 2 - 10 kev flux since the 2008 _ xmm - newton _ observation in 1607 . we conclude that our pilot study of csos provides a variety of exceptional diagnostics and highlights the importance of deep x - ray observations of large samples of young sources . this is necessary in order to constrain theoretical models for the earliest stage of radio source evolution and study the interactions of young radio sources with the interstellar environment of their host galaxies .

we present the results of the first x - ray study of a sample of 16 young radio sources classified as compact symmetric objects ( csos ) . we observed six of them for the first time in x - rays using _ chandra _ , re - observed four with the previous _ xmm - newton _ or _ beppo - sax _ data , and included six other with the archival data . all the sources are nearby , with the age of their radio structures ( years ) derived from the hotspots advance velocity . our results show heterogeneous nature of the csos indicating a complex environment associated with young radio sources . the sample covers a range in x - ray luminosity ,ergs , and intrinsic absorbing column density of . in particular , we detected extended x - ray emission in 1718 ; a hard photon index of in 2021 and 1511 consistent with either a compton thick absorber or non - thermal emission from compact radio lobes , and in 0710 an ionized iron emission line atkev and ew.4kev , and a decrease by an order of magnitude in the 2 - 10 kev flux since the 2008 _ xmm - newton _ observation in 1607 . we conclude that our pilot study of csos provides a variety of exceptional diagnostics and highlights the importance of deep x - ray observations of large samples of young sources . this is necessary in order to constrain theoretical models for the earliest stage of radio source evolution and study the interactions of young radio sources with the interstellar environment of their host galaxies . [ firstpage ]

astro-ph0601634

i

structure formation and evolution in the universe and the formation and growth of supermassive black holes ( smbhs ) are two fundamental problems in astronomy which are still not fully understood . while recent progresses in the cosmic microwave background , the high redshift type ia supernovae survey , and the large optical surveys have significantly improved our understanding of the evolution of large scale structure , there are still several gaps in the picture of structure formation . the data at redshift of @xmath23 , where most of the cosmic star formation might have taken place , is still very limited . on scales of galaxies and cluster of galaxies , the feed back process from galaxies or agns could significantly alter structure formation models where gravitation is the only driving force . the clustering of active galactic nuclei ( agns ) provides unique path to the solution of these problems because ( 1 ) the agns are often bright compared to normal galaxies and are easily seen at large cosmological distance ; ( 2 ) agns trace the violent growth phase of smbhs and hence their clustering properties provide a link between the dark matter halo to the agn activity . large scale agn surveys have been traditionally carried out in the optical band with dedicated telescopes . the most recent of these are the sloan digital sky survey ( sdss , schneider et al . 2004 ) and the two degree field survey ( 2df , croom et al . 2005 , c05 hereafter ) . these surveys have demonstrated that the clustering of agns can be used to measure cosmological parameters ( croom et al . 2004 ; outram et al . 2004 ) , and to constrain gravitational lensing ( myers et al . 2003 ) . however , as has been found in recent _ chandra _ and _ xmm - newton _ deep surveys , a large fraction of x - ray detected agns show little or no activity in optical observations ( e.g. barger et al . 2005 ) , most probably due to obscuration ( fabian & iwasawa 1999 ) but possibly with some contribution from light dilution of the host galaxy ( moran , filippenko , & chornock 2002 ) , though barger et al . ( 2005 ) argue this is not a dominant factor . this results in a large fraction of agns being missed in the optical surveys . on the other hand , hard x - rays ( @xmath24 kev ) is almost unaffected by obscuring column densities @xmath25 @xmath26 , and the x - ray emission from the host galaxies is low compared to the agns . thus hard x - rays are at present the best energy band to find agns ( mushotzky 2004 ) . recent optical follow - ups of _ chandra _ deep surveys have revealed that the hard x - ray sources are mostly found around @xmath27 instead of @xmath28 as seen in optically selected quasar samples . the low redshift population is dominated by non - broadline objects , while broadline agns are found mostly at higher redshifts ( steffen et al . 2003 ) . given these new discoveries , it is important to know how the clustering properties of x - ray and optical selected agn differ . the most extensive x - ray agn surveys so far performed used the _ telescope ( mullis et al . 2004 ) . because the telescope is not sensitive above 2 kev , _ rosat _ misses a large fraction of hard x - ray sources . the relatively poor spatial resolution of rosat also limits the accuracy of optical identifications . most of the _ rosat _ detected agns show broad emission lines in their optical spectra . both the optical quasar surveys and the rosat surveys suggest that agns have correlation properties similar to the local galaxies . the results seem to be independant of the sample medium redshifts . this result is puzzling because agns are believed to be preferentially form in high density peaks where interactions between galaxies are more common , and interactions in turn are thought to be crucial in agn fueling ( di matteo , springel , & hernquist 2005 ) . the mass of the dark matter halos that host agns are hence likely to be more massive . the clustering results on hard x - ray agns are so far contradictory . earlier studies of a small number of individual _ chandra _ fields seem to indicate that the hard band number counts in these small fields has fluctuations larger than expected from poisson noise ( cowie et al . 2002 ; manners et al . 2003 ) but the result is contradicted with larger samples of _ chandra _ fields ( kim et al . basilakos et al . ( 2004 ) found a 4@xmath29 clustering signal in hard x - ray sources at @xmath30 using angular correlation functions on a xmm detected agn sample from a 2 deg@xmath0 survey . a similar result was also found earlier in our 0.4 deg@xmath0 _ chandra _ field ( see below ) using the count - in - cells technique ( yang et al . 2003 ) . using the limber equation basilacos et al . ( 2004 ) argue that the hard x - ray sources are likely to be more strongly clustered than the optically selected agns . gilli et al . ( 2003 ) reported the detection of large angular - redshift clustering in the chandra deep field south , which seems to be dominated by hard x - ray sources . using the projected correlation function for the optically identified x - ray sources from the chandra deep field north ( cdfn ) and south ( cdfs ) , gilli et al . ( 2005 ) found that the average correlation amplitude in the cdfs is higher than that in the cdfn , and the latter is consistent with the correlation amplitude found in optically detected quasars . in this paper , we report our spatial correlation function analysis of the optically identified x - ray sources in the _ chandra _ large area synoptic x - ray survey of the iso lockman hole northwest region ( clasxs ) . clasxs is so far the largest contiguous _ chandra _ deep field with a high level of spectroscopic identifications . the size of the field is chosen to reduce the cosmic variance in the x - ray background to @xmath31 ( yang et al . for comparison , we have also analyzed the correlation functions for the cdfn field , using the published x - ray catalog by alexander et al . ( 2003 ) and the optical catalog of barger et al . ( 2003 ) . because the two surveys use basically the same optical instruments in the follow - up observations , and thus have the same accuracy in redshift measurements , the comparison is relatively straight forward . the logn - logs of the cdfn agrees well with that of clasxs , also indicating that the cdfn is a `` typical '' field . the depth of the cdfn is very useful in probing the correlation function at small separations . in [ sec_obs_data ] we summarize our observations and data analysis . in [ sec_methods ] we discuss the methodology we use in the clustering analysis . the results of the correlation functions are presented in [ sec_results ] . the evolution of agn clustering is presented in [ sec_evolution ] . in [ sec_discussion ] we discussion the implications of our results . finally summarize our results in [ sec_conclusion ] . throughout this paper , unless noted otherwise , we assume @xmath32 and a flat universe with @xmath33 and @xmath34 .

we present the spatial correlation function analysis of non - stellar x - ray point sources in the _ chandra _ large area synoptic x - ray survey of lockman hole northwest ( clasxs ) . we find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2df survey .

we present the spatial correlation function analysis of non - stellar x - ray point sources in the _ chandra _ large area synoptic x - ray survey of lockman hole northwest ( clasxs ) . our 9 acis - i fields cover a contiguous solid angle of 0.4 deg and reach a depth of in the 28 kev band . we supplement our analysis with data from the chandra deep field north ( cdfn ) . the addition of this field allows better probe of the correlation function at small scales . a total of 233 and 252 sources with spectroscopic information are used in the study of the clasxs and cdfn fields respectively . we calculate both redshift - space and projected correlation functions in comoving coordinates , averaged over the redshift range of , for both clasxs and cdfn fields for a standard cosmology with , and ( km s mpc ) . the correlation function for the clasxs field over scales of 3 mpc 200 mpc can be modeled as a power - law of the form , with and mpc . the redshift - space correlation function for cdfn on scales of 1 mpc 100 mpc is found to have a similar correlation length mpc , but a shallower slope ( ) . the real - space correlation functions derived from the projected correlation functions , are found to be mpc , and for the clasxs field , and mpc , for the cdfn field . by comparing the real- and redshift - space correlation functions in the combined clasxs and cdfn samples , we are able to estimate the redshift distortion parameter at an effective redshift . we compare the correlation functions for hard and soft spectra sources in the clasxs field and find no significant difference between the two groups . we have also found that the correlation between x - ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between x - ray luminosity , blackhole mass , and dark halo mass . we study the evolution of the agn clustering by dividing the samples into 4 redshift bins over 0.1 mpc.0 mpc . we find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2df survey . we estimate the evolution of the bias , and find that the bias increases rapidly with redshift (and ) . the typical mass of the dark matter halo derived from the bias estimates show little change with redshift . the average halo mass is found to be .

astro-ph0601634

r

we calculate the redshift - space correlation function in the clasxs sample for non - stellar sources with @xmath82 and 28 kev fluxes @xmath83 , assuming constant clustering in comoving coordinates . the total number of sources in the sample is 233 . the median redshift of the sample is 1.2 . by comparing the number of detected pairs with separations @xmath84 mpc with that expected by simulation , we found that on scales of 20 mpc , the significance of clustering is @xmath85 . we use the maximum likelihood method in searching for the best - fit parameters ( cash 1979 ; popowski et al . 1998 ; mullis et al . the method is preferable to the commonly used @xmath86 method because it is less affected by arbitrary binning . the method uses very small bins so that each bin contains only 1 or 0 dd pair . in this limit , the probability associated with each bin is close to independent . the expected number of dd pairs in each bin is calculated using the dr , rr pairs using the mock catalog . the likelihood is defined as @xmath87 where @xmath88 is the expected number of pairs in each bin and @xmath89 is the observed number of pairs . the likelihood ratio defined as @xmath90 where @xmath91 is the maximum likelihood . the resulting @xmath92 approaches the usual @xmath86 distribution . since the maximum - likelihood does not provide a measure of the `` goodness - of - fit '' , we quote the @xmath93 derived from the binned correlation function ( as shown in the figures ) and the best - fit parameters from maximum - likelihood estimates . we fit the correlation functions over three separation ranges . in figure [ clasxs_cor ] we show the correlation function and the best - fit with 3 mpc@xmath7200 mpc . the best - fit parameters for all three separation ranges are listed in table [ z_space_cor ] . it is noticeable that the rather large @xmath93 seems to suggest that the single power - law model may not be a proper description of the data . for comparison , we also computed the correlation function of the x - ray sources in cdfn in the same redshift interval . we created a mock catalog 50 times larger than the observation . the positions and redshifts of the random sources are generated by randomizing the observed positions and redshifts . a large poisson noise was added to avoid artificial clustering in the mock catalog . such randomization is justified because the clustering signal in a small field like the cdfn mainly comes from clustering along the line - of - sight direction . the randomized sky coordinates are filtered using an image mask to take into account the edge effects . we include all the non - stellar sources in the same redshift interval as we use for clasxs , which results in 252 sources in the sample . the best - fit parameters for cdfn field over three scale ranges are also shown in table [ z_space_cor ] . the correlation function over 1 mpc@xmath7100 mpc is shown in figure [ cdfn_cor ] . there is a good agreement of the correlation lengths obtained in the two fields . there seems to be a systematic flattening of the slope at small separations ( @xmath94 mpc ) in both samples . when the correlation functions are fitted at small and large separations independently , the resulting @xmath93s are systematically smaller . the projected correlation function is computed using the methods described in [ subsec_corr_func ] . to test the method , we first compute the projected correlation function for the cdfn and compare the results with that published in gilli et al . we selected the same redshift interval for the clasxs field . a two dimensional correlation function is calculated on a @xmath95 grid on the ( @xmath96,@xmath59 ) plane . the 5 intervals along @xmath96 axis covers 0.1620 mpc . we integrate the resulting two dimensional correlation function along the line - of - sight to a @xmath97 mpc . our projected correlation function for cdfn is shown figure [ projected ] , and it agrees perfectly with that reported in gilli et al . ( 2005 ) for @xmath98 , validating the techniques used in this paper . we next compute the projected correlation function for the clasxs field . the correlation function is calculated on scales of @xmath99 mpc . the 2-d correlation function is integrated to @xmath100 mpc . the result is also shown in figure [ projected ] . the correlation functions of the cdfn and clasxs fields agree in general at @xmath101 mpc , where both surveys have very good s / n . the slope , however , appears to be flatter in the cdfn field . we perform a @xmath93 fit to the correlation functions using equation [ wp_n_real ] . the best - fit parameters for the cdfn are @xmath15 mpc , @xmath16 , and the reduced @xmath102 . this is in good agreement with the result from gilli et al . ( 2005 , @xmath103 mpc , @xmath104 ) . the quoted errors in that paper is smaller than we obtained , but since we adopt a bootstrap error instead of poisson error in this analysis , the difference is expected . the best - fit parameters for the clasxs field are @xmath13 mpc , @xmath105 , and the reduced @xmath106 . the correlation length appears to be higher than that of the cdfn , but agrees within the errors . the slope also seems steeper than that of the cdfn and agrees better with the slope of the redshift - space correlation function at @xmath107 mpc . since the clasxs sample does not cover separations @xmath108 mpc very well , it is hard to see a slope change in this sample alone . since the cdfn and clasxs connect very well at separations where both surveys are sensitive , we try to model the combined data points with a single power - law . this yields @xmath109 mpc , @xmath110 , and @xmath111 . the reduced @xmath93 is much worse than the two samples fitted separately , but does not reject the hypothesis of a single power - law fit . this seems to suggest that the slope of the correlation function flattens at small separations . such a trend need to be looked more closely with future large agn surveys with better signal - to - noise . redshift distortion affects the correlation function ( power - spectrum ) by increasing the redshift - space correlation amplitude and changing the shape of the 2-d redshift - space correlation function at small scales ( such as the well known `` finger - of - god '' effect , e.g. hamilton 1992 ) . since our data is too noisy at small separations to detect the effect , we only discuss the effect of the amplitude boosting of correlation function in redshift - space . kaiser ( 1987 ) showed that to the first order , @xmath112 where @xmath113 and @xmath114 is bias . in principle , the redshift - space distortion can be estimated by comparing @xmath115 and @xmath116 . to quantify the effect , we use the correlation function estimates at scales where both projected and redshift - space correlation functions are well determined . for the cdfn , we chose the correlation function estimates at 10 mpc and find @xmath117 , if the best - fit of @xmath115 on 1 - 100 mpc is used . the choice of this scale is justified given that the slope possibly changes below and above 10 mpc , as seen in the projected correlation function . since the slope of the redshift- and real - space correlation function is very similar in the cdfn , the ratio is almost constant . for the clasxs field , we chose to estimate the ratio at 20 mpc , where the s / n is the best . we find @xmath118 by using the best - fit on 1100 mpc for @xmath115 . the ratio changes slowly with the scales probed , but is within the errors . we find a general agreement between clasxs and cdfn . to avoid the arbitrary choice of scales , and to make the best use of the data , we combine the two samples to study the redshift distortion effect on @xmath119 . since the projected correlation function of cdfn and and clasxs agree in general , we are encouraged to assume that the the two samples , even with the vast difference in flux limits , generally trace the large scale structure in the same way . in figure [ z_distortion ] . we show the combined @xmath119 . the contours show no significant signature of nonlinear redshift distortion , such as the `` finger - of - god '' . we fit @xmath119 with equation [ distortion ] , assuming the best - fit parameters for the real - space correlation function from the combined sample ( @xmath120 mpc , @xmath121 ) , and ignoring the higher order redshift distortions . we generate the 2-d correlation function at each grid point . by minimizing @xmath93 by changing @xmath122 , we found the best - fit @xmath17 , corresponding to @xmath123 , which agrees with the estimates from individual fields above . by fixing @xmath124 , we can estimate the bias factor of x - ray selected agns from @xmath122 . the median redshift of the combined sample is 0.94 , and @xmath125 gives @xmath126 . this yields @xmath127 using the relation @xmath128 . we further test if there is any differences in clustering properties between the hard and soft spectra sources in the clasxs sample . we use the hardness ratio , defined as @xmath129 ( where @xmath130 is the count rate ) , to quantify the spectral shape of the x - ray sources . correlation functions of soft ( @xmath131 ) and hard ( @xmath132 ) sources are calculated the same way as above . the fraction of broad - line agns is 56.4% in the soft sample and 15.4% in hard sample . the median redshifts are 1.25 and 0.94 for soft and hard samples , respectively . we compute @xmath115 for both soft and hard sources over scales of 3200 mpc . using a maximum - likelihood fit , we found @xmath133 mpc , @xmath134 for hard sources and @xmath135 mpc , @xmath136 for soft sources . we found no significant difference in clustering between the soft and hard sources . this agrees with the results of gilli et al . it is noticeable that the soft sources have a higher median redshift than the hard sources . the interpretation of this result must include evolution effects . to avoid this complication , we restricted the redshift range to @xmath137 . the best - fit parameters are @xmath138 mpc ( @xmath139 mpc ) and @xmath140 ( @xmath141 ) for hard ( soft ) sources . the difference in clustering parameters between soft and hard sources are well within the measurement error . the same analysis on cdfn yields similar results . thus there is no significant dependence of clustering on the x - ray color . the cold dark matter ( cdm ) model of hierarchical structure formation predicts that massive ( and hence luminous ) galaxies are formed in rare peaks , and therefore should be more strongly clustered . this is seen in normal galaxies ( e.g. giavalisco & dickinson 2001 ) . whether this relation can be extended to x - ray luminosity of agns is unknown . this is because the x - ray luminosity relates to the dark matter halo mass in a more complex and not well understood way . the x - ray luminosity is directly linked to the accretion process , and the process is affected by factors such as accretion rate , radiative efficiency , blackhole mass and the details of the accretion process . we have shown that at least in broadline agns , where the blackhole mass can be inferred from the line - width and nuclear luminosity , the eddington ratio is close to constant over two decades of 28 kev luminosity ( barger et al . if this is the case for all x - ray selected agns , we should expect the agn luminosity to be mainly determined by the blackhole mass , which in turn , should be closely related to the halo mass ( ferrarese 2002 ) , even though the exact form of this relation is highly uncertain . however , optical quasar surveys such as 2df found little evidence of a correlation between clustering amplitude and ensemble luminosity ( c05 ) , perhaps due to the small dynamical range in luminosity these surveys probe . the x - ray luminosity of sources in the clasxs and cdfn cover a luminosity range of four orders of magnitudes , making it possible to make such a test . the 28 kev rest frame luminosity @xmath142 is calculated from the hard band fluxes , with a k - correction made assuming a power - law spectra with photon index @xmath143 . this yields @xmath144 where @xmath145 is the luminosity in observer s 2 - 8 kev band . in figure [ lum_dist ] we show @xmath142 vs. redshift for both clasxs and cdfn . for a better comparison of the correlation amplitude , we adopt the averaged correlation function within @xmath146 mpc , @xmath147 the quantity is chosen rather than @xmath148 because it measures the clustering ( directly linked to the rms fluctuations ) regardless of the shape of the correlation function . on scales of 20 mpc the clustering is in the linear regime of density fluctuations . the error in @xmath149 is from the single parameter @xmath150 confidence interval obtained by fixing the slope of the correlation function to the best - fit . we split the clasxs ( cdfn ) sample into two subsamples at @xmath151 ( @xmath152 ) so that each subsample contain similar number of objects . in table [ tab_lum ] we show the maximum - likelihood fits as well as @xmath149s . it should be noted that the correlation amplitude is biased in redshift space . the dominant part of this bias is characterized in equation [ distortion ] . comparing with other observations ( e.g. da ^ angela et al . 2005 ) , @xmath122 is likely a weak function of redshift in the redshift range probed by our sample , with @xmath153 ( [ sec_z_distortion ] ) , this translates to @xmath123 . we correct the @xmath149 s for this bias by dividing them by 1.3 . the correlation amplitude for the more luminous sources appears to be higher than that of the less luminous sources , which qualitatively agrees with expectations that x - ray luminosity reflects the dark matter halo mass . the correlation amplitude for the more luminous subsamples are @xmath154 and @xmath155 higher than that of the less bright subsample in the clasxs and cdfn fields , respectively . however , since the more luminous subsamples also are preferentially found at higher redshifts , the evolution in @xmath115 should be taken into account . to reduce this complication , we restrict ourselves to sources within the redshift range of 0.31.5 , where the evolution effect is relatively small ( see also [ sec_evolution ] ) . in figure [ lum_depend ] we show @xmath142 vs. @xmath149 for both clasxs and cdfn . by reducing the redshift range , the difference in correlation amplitude between the brighter and dimmer subsample is significantly reduced , in the cdfn sample , to merely @xmath150 . for the clasxs field , on the other hand , the correlation amplitude for both subsamples do not show significant change . for comparison , we also plot in figure [ lum_depend ] the correlation amplitude from the 2df survey ( c05 ) . the x - ray luminosities for the qsos in the 2df are obtained by dividing the bolometric luminosities by 35 ( elvis et al . we perform spearman s @xmath156 test for correlations between @xmath157 and @xmath158 . we found the correlation coefficient @xmath159 for x - ray samples , or a corresponding null probability of 20% , indicating a weak correlation between the two quantities . if the 2df samples are added , we found @xmath160 , and a null probability of 17% . this means that with the x - ray sample , we have detected a weak correlation between clustering and luminosity . we will discuss this in [ sec_xi_lx ] .

we calculate both redshift - space and projected correlation functions in comoving coordinates , averaged over the redshift range of , for both clasxs and cdfn fields for a standard cosmology with , and ( km s mpc ) . we compare the correlation functions for hard and soft spectra sources in the clasxs field and find no significant difference between the two groups .

we present the spatial correlation function analysis of non - stellar x - ray point sources in the _ chandra _ large area synoptic x - ray survey of lockman hole northwest ( clasxs ) . our 9 acis - i fields cover a contiguous solid angle of 0.4 deg and reach a depth of in the 28 kev band . we supplement our analysis with data from the chandra deep field north ( cdfn ) . the addition of this field allows better probe of the correlation function at small scales . a total of 233 and 252 sources with spectroscopic information are used in the study of the clasxs and cdfn fields respectively . we calculate both redshift - space and projected correlation functions in comoving coordinates , averaged over the redshift range of , for both clasxs and cdfn fields for a standard cosmology with , and ( km s mpc ) . the correlation function for the clasxs field over scales of 3 mpc 200 mpc can be modeled as a power - law of the form , with and mpc . the redshift - space correlation function for cdfn on scales of 1 mpc 100 mpc is found to have a similar correlation length mpc , but a shallower slope ( ) . the real - space correlation functions derived from the projected correlation functions , are found to be mpc , and for the clasxs field , and mpc , for the cdfn field . by comparing the real- and redshift - space correlation functions in the combined clasxs and cdfn samples , we are able to estimate the redshift distortion parameter at an effective redshift . we compare the correlation functions for hard and soft spectra sources in the clasxs field and find no significant difference between the two groups . we have also found that the correlation between x - ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between x - ray luminosity , blackhole mass , and dark halo mass . we study the evolution of the agn clustering by dividing the samples into 4 redshift bins over 0.1 mpc.0 mpc . we find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2df survey . we estimate the evolution of the bias , and find that the bias increases rapidly with redshift (and ) . the typical mass of the dark matter halo derived from the bias estimates show little change with redshift . the average halo mass is found to be .

astro-ph0601634

c

the bias evolution of optical quasar is extensively discussed in c05 . they found that the bias increases rapidly with redshift(@xmath166 ) . we will follow these arguments to estimate the bias evolution of the x - ray samples . on scales of 20 mpc , the clustering of dark matter and agns are both in the linear regime , i.e. , @xmath167 . this allows us to measure the bias , defined as the ratio of rms fluctuation of the luminous matter ( agns in our case ) and that of the underlying total mass , as a function of redshift by comparing the observed correlation function with the linear growth rate . in terms of correlation function , the bias can be written as @xmath168 the averaged correlation function of mass can be obtained using @xmath169 where @xmath170 $ ] , @xmath171 is the rms fluctuation of mass at @xmath172 obtained by _ wmap _ observation ( spergel et al . 2003 ) , and we choose the best - fit @xmath173 . @xmath174 is the linear growth factor , for which we use the approximation formula from carroll , press , & turner ( 1992 ) . the redshift - space distortion is taken into account to the first order through equation [ distortion ] and the bias factor is solved numerically . the result is shown in table [ tab_bias ] . the estimate of @xmath175 in the combined sample agrees with the result from the redshift - space distortion analysis in [ sec_z_distortion ] . in figure [ bias_mass](a ) we show the bias estimates for the cdfn and clasxs+cdfn samples . the best - fit model from c05 qualitatively agrees with the x - ray results . the simplest model for bias evolution is that the agns are formed at high redshift , and evolve according to the continuity equation ( nusser & davis 1994 ; fry 1996 ) . the model is sometimes called the _ conserving model _ or the _ test particle model_. by normalizing the bias to @xmath172 , the model can be written as @xmath176 this model is shown in figure [ bias_mass](a ) as dash - dotted line . the model produces a bias evolution which is slightly too shallow at high redshifts . the correlation function evolution based on this model is also shown in figure [ evolution_compare ] , where it underpredicts the observed @xmath177 . the model predicts a decrease of correlation function at high redshift , which is not true based on our results and that of the 2df . this implies that the agns observed in the local universe are unlikely to have formed at @xmath178 . one of the direct predictions of cdm structure formation scenario is that the bias is determined by the dark halo mass . mo & white ( 1996 ) found a simple relation between the minimum mass of the dark matter halo and the bias @xmath179 . by adopting the more general formalism by sheth , mo , & tormen ( 2001 ) we can compute the `` typical '' dark halo mass of the sample . it should be noted that the method assumes that halos are formed through violent collapse or mergers of smaller halos and hence is best applied at large separations , where the halo - halo term dominates the correlation function . this requirement is apparently satisfied by agns . following sheth , mo , & tormen ( 2001 ) , @xmath180 , \label{smt}\ ] ] where @xmath181 , a = 0.707 , c = 0.6 . @xmath182 is the critical overdensity . @xmath183 is the rms density fluctuation in the linear density field and evolves as @xmath184 where @xmath185 can be obtained from the power spectrum of density perturbation @xmath186 convolved with a top - hat window function @xmath187 , @xmath188 at the scale of interest ( @xmath189 mpc ) , the power spectrum can be approximated with a power - law , @xmath190 , with @xmath191 for cdm type spectrum . integrating equation [ sigma0 ] gives @xmath192 where @xmath193 is the mean mass within @xmath194 mpc . we can then solve equation [ smt ] for halo mass . the resulting mass is shown in table [ tab_bias ] and figure [ bias_mass](b ) . consistent with what s been found in c05 for the 2df , the halo mass does not show any evolution trend with redshift . we found @xmath195 , which is consistent with the 2df estimates ( c05 , grazian et al . 2004 ) . we have shown that over a very wide range of luminosity , the clustering amplitude of agns change very little . this allows us to put useful constrains on the correlations among x - ray luminosity , blackhole mass @xmath196 , and the dark matter halo @xmath197 . using the equivalent width of broad emission lines as mass estimators , barger et al . ( 2005 ) found that the eddington ratio of broadline agns may be close to constant . since the hard x - ray luminosity is an isotropic indicator of the bolometric luminosity , this implies that the blackhole mass is linearly correlated with x - ray luminosity . barger et al . ( 2005 ) found that @xmath198 where @xmath199 is @xmath142 in units of @xmath200 . a similar result is found at low redshift using a sample of broadline agns with mass estimates based on reverberation mapping relations ( kaspi et al . 2000 ; yang 2005 ) . the relation , however , is only tested for broadline agns . deviations from this relation is also expected at low luminosities since many low luminosity agns tend to have a low eddington ratio ( ho 2005 ) . blackhole mass have been shown to correlate with velocity dispersion of the spheroidal component of the host galaxies ( gebhardt et al . 2000 ; ferrarese & merritt 2000 ) . this leads to a linear correlation between @xmath196 and the mass of spherical component . this relation , however , could be different at high redshift ( akiyama 2005 ) . how these relationships translate to the @xmath201 relation is also unclear and could likely be nonlinear . ferrarese ( 2002 ) showed that @xmath196 @xmath197 can be modeled with a scaling law @xmath202 with @xmath203 and @xmath204 determined by the halo mass profile . combining the above and using equation [ smt ] , we can calculate the correlation amplitude as a function of x - ray luminosity . in figure [ lum_depend ] we show the model expectations compared with the observations from clasxs , cdfn and 2df . in calculating the bias we have assumed the nonlinear power - law index @xmath205 in equation [ sigma0_m ] ( peacock 1999 ) , with the best fit @xmath206 . the three lines represent three different halo profiles discussed in ferrarese ( 2002 ) . we found that the @xmath207 relation is in fact dominated by the very nonlinear relation between halo mass and correlation amplitude . the difference between different halo profiles is caused mainly by the normalization @xmath203 , or the fractional mass of blackhole mass , rather than the power - law index @xmath204 . one of the important model predictions is that the correlation between x - ray luminosity and clustering is weak below @xmath208 and increases rapidly above that . the lack of rapid change of correlation amplitude indicates the halo mass of agn can not be significantly higher than the corresponding threshold . under the assumed cosmology and bias model , the @xmath207 relation based on the weak lensing derived halo mass profile ( seljak 2002 ) is consistent with the data , while the nfw profile ( navarro , frenk , & white 1997 ) and the isothermal profile predicts a too steep correlation amplitude curve at high luminosity . however , we can not rule out these profiles as a reasonable descriptions of the agn host halo because of the uncertainty in the shape of the correlation function and the fractional blackhole mass in dark halos at the redshift of our sample . in figure [ lum_depend ] we also mark the model dark halo mass corresponding to the seljak ( 2002 ) mass profile . the average correlation amplitude of the combined optical and x - ray sample ( dotted - line ) corresponds to a halo mass of @xmath209 . while the luminosity in our sample ranges over five orders of magnitudes , the range of halo mass may be much smaller . the 2df sample has a high luminosity but has a similar or lower average correlation amplitude than that of the x - ray samples . it is possible that the optical selection technique tends to select sources with a higher eddington ratio . the correlation amplitude of the cdfn sample at @xmath210 , on the other hand , is higher than the model predictions . this is expected because many agns with such luminosities are liners which are probably accreting with a low radiative efficiency . it is now clear that the weak luminosity dependence of agn clustering is consistent with the simplest model based on the observed @xmath211 and @xmath201 relations , given the large error in the correlation functions . a large dynamical range in x - ray luminosity , as well as better measurements of correlation function , are needed to better quantify this relation . the luminosity range of the 2df survey is too small and the optical selection method also likely is biased to high eddington ratio sources . by increasing our current clasxs field by a factor of a few will be helpful in better determine the luminosity dependence of agn clustering , and to put tighter constrains on agn hosts . we look again at the @xmath196@xmath197 relation in the light of the mass estimates of the dark matter halos from _ chandra _ samples . if the ferrarese ( 2002 ) relation is independent of redshift , the nearly constant dark halo mass implies little evolution for the blackhole mass . on the other hand , strong luminosity evolution is seen since @xmath212 in hard x - ray selected agns ( barger et al . 2005 ) . this implies a systematic decrease of the ensemble eddington ratio with cosmic time . barger et al . ( 2005 ) showed that the characteristic luminosity of hard x - ray selected agns @xmath213 where @xmath214 and @xmath215 for @xmath216 . ueda et al . ( 2003 ) found a similar result with a slightly shallower slope . if the typical blackhole mass does not change with redshift , the observed luminosity evolution indicates the ensemble eddington ratio increase by a factor of @xmath189 from @xmath172 to @xmath217 . it is hard to understand such a change of the typical eddington ratio with redshift . one possibility is that a large number of compton thick agns at @xmath27 are missed in the _ chandra _ surveys ( e.g. worsley et al . 2005 ) , leading to the observed strong luminosity evolution . alternatively , instead of @xmath196@xmath197 being independent of redshift , the @xmath196@xmath218 could be unchanged with cosmic time , as suggested by shields et al . this is theoretically attractive because the feedback regulated growth of blackholes implies a constant @xmath196@xmath218 relation . this implies that @xmath196@xmath197 is in fact a function of redshift . wyithe & loeb ( 2003 ) proposed a model(wl model here after ) showing that the blackhole mass inferred from the halo mass increases with redshift . croom et al . ( 2005 ) show that this could lead to a close to constant eddington ratio in the 2df sample if the optical luminosity is used to compare with the derived @xmath196 . since the correlation function is only a weak function of luminosity , as we have demonstrated in [ sec_l_dependence ] , it is better to estimate the evolution of the eddington ratio using the characteristic mass of the blackholes from the wl model , and the characteristic luminosity from equation [ l_star ] . in figure [ eddington ] , we show the derived ensemble eddington ratio , assuming the dark halo mass to be constant and @xmath219 . ( we adopt the normalization of the wl model so that it matches the prediction of @xmath196 @xmath197 with a nwf type of halo profile . however , the choice of this normalization is not crucial ) . in the figure , we see a factor of @xmath220 change in the ensemble eddington ratio from @xmath172 to @xmath212 . this change , however , is smaller than the typical scatter in both the luminosity and halo mass . we now compare our clustering results with those for normal galaxies . using the sloan digital sky survey first data release , wake et al . ( 2004 ) found that the clustering of narrow - line agns in the redshift range @xmath221 , selected using emission - line flux ratios , have the same correlation amplitude as normal galaxies . our samples are not a very good probe at these redshifts , and the best clustering analysis at a comparable redshift for normal galaxies is from deep2 ( coil et al . 2004 ) . at effective redshift @xmath222 , they found @xmath223 h@xmath6 mpc , and @xmath224 , which translates to @xmath225 . the correlation amplitude from clasxs at @xmath226 is @xmath227 . the clustering of agns in clasxs field appear the same as the clustering of normal galaxies in deep2 . a higher correlation is found in the cdfn . the difference shows the large uncertainty of our correlation function estimates . at higher redshifts , the best estimate for galaxy clustering is from the so called `` lyman break galaxies '' , named after the technique by which they are found . adelberger et al . ( 1998 ) found , at a typical @xmath228 , these galaxies tend to have similar correlation function as galaxies in the local universe , indicating they are highly biased tracers of the large scale structure . in the @xmath229cdm cosmology , these authors found @xmath230 . this is very similar to the bias found in the highest bin of our _ chandra _ fields ( @xmath231 ) , which has a median redshift of @xmath232 . if we extrapolate the bias of the x - ray sources to @xmath233 , the bias of x - ray sources should be @xmath234 , consistent with the clustering strength of lymann break galaxies .

our 9 acis - i fields cover a contiguous solid angle of 0.4 deg and reach a depth of in the 28 kev band . the correlation function for the clasxs field over scales of 3 mpc 200 mpc can be modeled as a power - law of the form , with and mpc . we have also found that the correlation between x - ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between x - ray luminosity , blackhole mass , and dark halo mass . the typical mass of the dark matter halo derived from the bias estimates show little change with redshift .

we present the spatial correlation function analysis of non - stellar x - ray point sources in the _ chandra _ large area synoptic x - ray survey of lockman hole northwest ( clasxs ) . our 9 acis - i fields cover a contiguous solid angle of 0.4 deg and reach a depth of in the 28 kev band . we supplement our analysis with data from the chandra deep field north ( cdfn ) . the addition of this field allows better probe of the correlation function at small scales . a total of 233 and 252 sources with spectroscopic information are used in the study of the clasxs and cdfn fields respectively . we calculate both redshift - space and projected correlation functions in comoving coordinates , averaged over the redshift range of , for both clasxs and cdfn fields for a standard cosmology with , and ( km s mpc ) . the correlation function for the clasxs field over scales of 3 mpc 200 mpc can be modeled as a power - law of the form , with and mpc . the redshift - space correlation function for cdfn on scales of 1 mpc 100 mpc is found to have a similar correlation length mpc , but a shallower slope ( ) . the real - space correlation functions derived from the projected correlation functions , are found to be mpc , and for the clasxs field , and mpc , for the cdfn field . by comparing the real- and redshift - space correlation functions in the combined clasxs and cdfn samples , we are able to estimate the redshift distortion parameter at an effective redshift . we compare the correlation functions for hard and soft spectra sources in the clasxs field and find no significant difference between the two groups . we have also found that the correlation between x - ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between x - ray luminosity , blackhole mass , and dark halo mass . we study the evolution of the agn clustering by dividing the samples into 4 redshift bins over 0.1 mpc.0 mpc . we find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2df survey . we estimate the evolution of the bias , and find that the bias increases rapidly with redshift (and ) . the typical mass of the dark matter halo derived from the bias estimates show little change with redshift . the average halo mass is found to be .

astro-ph0601634

c

in this paper we study the clustering of the x - ray selected agns in the 0.4 deg@xmath0 _ chandra _ contiguous survey of the lockman hole northwest region . based on our previous study , the size of the clasxs field is large enough that the cosmic variance should not be important . we supplement our study with the published data from the cdfn . the very similar logn - logs of the clasxs and cdfn suggests that the cosmic variance should not be important when the cdfn is included in the analysis . the very deep cdfn gives a better probe of the correlation function at small separations . a total of 233 and 252 non - stellar sources from clasxs and cdfn respectively are used in this study . we use the correlation function in the redshift - space as a major tool in our clustering analysis . for the whole sample , we have also performed an analysis using the projected correlation function . this allows us to quantify the effect of redshift distortion . \1 . we calculated the redshift - space correlation function for sources with @xmath2 in both the clasxs and cdfn fields , assuming constant clustering in comoving coordinates . we found a @xmath85 clustering signal for pairs within @xmath235 mpc in the clasxs field . the correlation function over scale of 3 mpc@xmath7 200 mpc is found to be a power - law with @xmath9 and @xmath10 mpc . the redshift - space correlation function for cdfn on scales of 1 mpc@xmath7 100 mpc is found to have similar correlation length @xmath11 mpc , but the slope is shallower ( @xmath12 ) . we study the projected correlation function of both clasxs and cdfn . the best - fit parameters for the real - space correlation functions are found to be @xmath13 mpc , @xmath14 for clasxs field , and @xmath15 mpc , @xmath16 for cdfn field . our result for the cdfn shows perfect agreement with the published results from gilli et al . ( 2004 ) . fitting the combined data from both fields gives @xmath109 mpc and @xmath236 . \3 . comparing the redshift- and real - space correlation function of the combined clasxs and cdfn fields , we found the redshift distortion parameter @xmath17 at an effective redshift @xmath18 . under the assumption of @xmath229cdm cosmology , this implies a bias parameter @xmath127 at this redshift . we tested whether the clustering of the x - ray sources is dependent on the x - ray spectra in the clasxs field . using a hardness ratio cut at @xmath237 , we found no significant difference in clustering between hard and soft sources . this agrees with previous claims . \5 . with the large dynamic range in x - ray luminosity , we found a weak correlation between x - ray luminosity and clustering amplitude . using a simple model based on observations that links the agn luminosity and halo mass , we show that the observed weak correlation is consistent with the model , except at low luminosities , where sources are likely to have lower eddington ratio . the non - detection of a strong correlation between x - ray luminosity and clustering amplitude also suggests a narrow range of halo mass . we study the evolution of the clustering using the redshift - space correlation function in 4 redshift intervals ranging from 0.1 to 3.0 . we found only a mild evolution of agn clustering in both clasxs and cdfn samples . this qualitatively agrees with the results based on optically selected quasars from 2df survey . the x - ray samples , however , show a similar correlation amplitude as that of the 2df sample . this is consistent with the weak correlation between agn luminosity and the clustering amplitude found in this work . we estimate the evolution of bias by comparing the observed clustering amplitude with expectations of the linear evolution of density fluctuations . the result show that the bias increases rapidly with redshift ( @xmath238 and @xmath239 in clasxs field ) . this agrees with the findings from 2df . using the bias evolution model for dark halos from sheth , mo & tormen ( 2001 ) , we estimated the characteristic mass of agns in each redshift interval . we found the mass of the dark halo changes very little with redshift . the average halo mass is found to be @xmath240 . our results have demonstrated that deep x - ray surveys are a very useful tool in studying how agns trace the large scale structure . such knowledge provides an unique window to the understanding of agn activity , and its relation to structure formation . the higher spatial density and much better completeness compared to current optical surveys allows us to study clustering on scales only accessible to very large optical surveys such as the 2df and the sdss . the high spatial resolution and positional accuracy of _ chandra _ is critical for unambiguous optical identifications . since our results on the evolution of agn clustering could still be affected by a small number of large scale structures , as seen in chandra deep field south , larger _ fields are still needed to improve the measurements . we thank prof . alex szalay , dr . xaviar barcons and dr . takamitsu miyaji for very helpful conversations ; dr . chris mullis for discussions on his paper . we would like to thank the anonymous referee for his / her comments that help to improve the paper . this work is partially funded by the ids program of r. f. m. we also gratefully acknowledge support from nsf grants ast 02 - 39425 ( a.j.b . ) and ast 04 - 07374 ( l.l.c . ) , the university of wisconsin research committee with funds granted by the wisconsin alumni research foundation , the alfred p. sloan foundation , and the david and lucile packard foundation ( a.j.b . ) . lccclccc 10200 & @xmath241 & @xmath242 & 6.2/8 & 10100 & @xmath243 & @xmath244 & 7.9/8 + 330 & @xmath245 & @xmath246 & 3.8 /8 & 120 & @xmath247 & @xmath248 & 6.8/8 + 3200 & @xmath249 & @xmath250 & 10.6/8 & 1100 & @xmath251 & @xmath252 & 15.0/8 + [ z_space_cor ] cccccccc clasxs & 0.13.0 & 1.5 & @xmath253 & @xmath254 & @xmath255 & 7.2/8 & @xmath256 + & 0.13.0 & .73 & @xmath257 & @xmath258 & @xmath259 & 8.8/8 & @xmath260 + & 0.31.5 & 1.1 & @xmath261 & @xmath262 & @xmath263 & 9.2/8 & @xmath264 + & 0.31.5 & .81 & @xmath265 & @xmath266 & @xmath267 & 7.8/8 & @xmath268 + cdf - n & 0.13.0 & .98 & @xmath269 & @xmath270 & @xmath271 & 8.2/8 & @xmath272 + & 0.13.0 & .51 & @xmath273 & @xmath274 & @xmath275 & 11.9/8 & @xmath276 + & 0.31.5 & .96 & @xmath277 & @xmath278 & @xmath279 & 11.1/8 & @xmath280 + & 0.31.5 & .63 & @xmath281 & @xmath282 & @xmath283 & 8.4/8 & @xmath284 + [ tab_lum ] lcccccccc clasxs & 0.10.7 & 0.44 & 57 & @xmath265 & @xmath285 & @xmath286 & 4.1/8 & @xmath287 + & 0.71.1 & 0.90 & 60 & @xmath288 & @xmath289 & @xmath290 & 5.9/8 & @xmath291 + & 1.11.5 & 1.27 & 49 & @xmath292 & @xmath293 & @xmath294 & 1.6/3 & @xmath295 + & 1.53.0 & 2.00 & 67 & @xmath296 & @xmath297 & @xmath298 & 3.1/3 & @xmath299 + cdfn & 0.10.7 & 0.46 & 111 & @xmath300 & @xmath301 & @xmath302 & 12.5/8 & @xmath303 + & 0.71.1 & 0.94 & 91 & @xmath304 & @xmath305 & @xmath306 & 5.6/8 & @xmath307 + & 1.11.5 & 1.22 & 28 & @xmath308 & @xmath309 & @xmath310 & 2.9/8 & @xmath311 + & 1.53.0 & 2.24 & 22 & @xmath312 & @xmath313 & @xmath314 & 1.4/7 & @xmath315 + clasxs+cdfn & 0.10.7 & 0.45 & 168 & @xmath316 & @xmath317 & @xmath318 & 5.3/8 & @xmath319 + & 0.71.1 & 0.92 & 151 & @xmath320 & @xmath321 & @xmath322 & 5.5/8 & @xmath323 + & 1.11.5 & 1.26 & 77 & @xmath324 & @xmath325 & @xmath326 & 1.8/8 & @xmath327 + & 1.53.0 & 2.07 & 89 & @xmath328 & @xmath329 & @xmath330 & 4.2/7 & @xmath331 + [ tab_evolution ] cccccc 0.44 & @xmath332 & @xmath333 & 0.45 & @xmath334 & @xmath335 + 0.90 & @xmath336 & @xmath337 & 0.92 & @xmath338 & @xmath339 + 1.27 & @xmath340 & @xmath341 & 1.26 & @xmath342 & @xmath343 + 2.00 & @xmath344 & @xmath345 & 2.07 & @xmath346 & @xmath347 + [ tab_bias ] 200 mpc . maximum - likelihood contour for the single power - law fit . contour levels are @xmath348 , corresponding to @xmath150 , @xmath349 and @xmath350 confident levels for two parameter fits . [ clasxs_cor],title="fig : " ] 200 mpc . maximum - likelihood contour for the single power - law fit . contour levels are @xmath348 , corresponding to @xmath150 , @xmath349 and @xmath350 confident levels for two parameter fits . [ clasxs_cor],title="fig : " ] for the cdfn except that the correlation function is calculated for separations 1 mpc@xmath7100 mpc . [ cdfn_cor],title="fig : " ] for the cdfn except that the correlation function is calculated for separations 1 mpc@xmath7100 mpc . [ cdfn_cor],title="fig : " ] contours for the clasxs+cdfn sample , the clasxs sample , and the cdfn sample , respectively . are for @xmath150 , @xmath349 , and @xmath350 confident levels ; ( d ) the projected correlation function for clasxs ( open circles ) and cdfn ( black dots ) fields . lines are the best - fit shown in ( a)-(c ) . solid line : clasxs+cdfn ; dotted line : clasxs ; dashed line : cdfn [ projected ] ] of the combined clasxs and cdfn sample ( dashed - dotted contour ) . solid line shows the best - fit model . both the data and model correlation functions are smoothed using a @xmath351 boxcar to reduce the noise for visualization only . [ z_distortion ] ]

we supplement our analysis with data from the chandra deep field north ( cdfn ) . the addition of this field allows better probe of the correlation function at small scales . a total of 233 and 252 sources with spectroscopic information are used in the study of the clasxs and cdfn fields respectively . the redshift - space correlation function for cdfn on scales of 1 mpc 100 mpc is found to have a similar correlation length mpc , but a shallower slope ( ) . the real - space correlation functions derived from the projected correlation functions , are found to be mpc , and for the clasxs field , and mpc , for the cdfn field . by comparing the real- and redshift - space correlation functions in the combined clasxs and cdfn samples , we are able to estimate the redshift distortion parameter at an effective redshift . we study the evolution of the agn clustering by dividing the samples into 4 redshift bins over 0.1 mpc.0 mpc . we estimate the evolution of the bias , and find that the bias increases rapidly with redshift (and ) . the average halo mass is found to be .

we present the spatial correlation function analysis of non - stellar x - ray point sources in the _ chandra _ large area synoptic x - ray survey of lockman hole northwest ( clasxs ) . our 9 acis - i fields cover a contiguous solid angle of 0.4 deg and reach a depth of in the 28 kev band . we supplement our analysis with data from the chandra deep field north ( cdfn ) . the addition of this field allows better probe of the correlation function at small scales . a total of 233 and 252 sources with spectroscopic information are used in the study of the clasxs and cdfn fields respectively . we calculate both redshift - space and projected correlation functions in comoving coordinates , averaged over the redshift range of , for both clasxs and cdfn fields for a standard cosmology with , and ( km s mpc ) . the correlation function for the clasxs field over scales of 3 mpc 200 mpc can be modeled as a power - law of the form , with and mpc . the redshift - space correlation function for cdfn on scales of 1 mpc 100 mpc is found to have a similar correlation length mpc , but a shallower slope ( ) . the real - space correlation functions derived from the projected correlation functions , are found to be mpc , and for the clasxs field , and mpc , for the cdfn field . by comparing the real- and redshift - space correlation functions in the combined clasxs and cdfn samples , we are able to estimate the redshift distortion parameter at an effective redshift . we compare the correlation functions for hard and soft spectra sources in the clasxs field and find no significant difference between the two groups . we have also found that the correlation between x - ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between x - ray luminosity , blackhole mass , and dark halo mass . we study the evolution of the agn clustering by dividing the samples into 4 redshift bins over 0.1 mpc.0 mpc . we find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2df survey . we estimate the evolution of the bias , and find that the bias increases rapidly with redshift (and ) . the typical mass of the dark matter halo derived from the bias estimates show little change with redshift . the average halo mass is found to be .

0709.4512

i

rs ophiuchi ( rs oph ) is a member of a rare subclass of cataclysmic variable known as recurrent novae ( rn ) . as the name suggests , rn are systems which are observed to go into outburst more than once . nova outbursts are believed to be the result of thermonuclear runaway ( tnr ) on the surface of a white dwarf accreting material from a binary companion ( e.g. schatzman 1950 , starrfield et al . 1974 , prialnik et al . the tnr occurs once the pressure at the base of the shell of accreted material reaches a high enough value . following fujimoto ( 1982a ) the critical pressure required for the tnr ignition is given by @xmath5 where m@xmath6 and r are the mass and radius of the white dwarf , and @xmath7m@xmath8 is the mass of the accreted shell at the onset of the tnr . as long as accretion continues , all novae are expected to recur with timescales ranging from 10@xmath9 years to only a few decades . for systems hosting high mass white dwarfs , and those with higher accretion rates , critical envelope masses will be reached in a shorter time . therefore , the fact that we see the recurrent novae repeat at all during a human lifetime is an indication that we are dealing with higher mass white dwarfs . if the white dwarfs in recurrent novae can grow in mass with each subsequent accretion outburst cycle , they may eventually approach and even exceed the chandrasekhar limit . therefore , rn are interesting and important supernova ia progenitor candidates . rs oph went into its 6th recorded outburst on feb 12.83 , 2006 ( narumi 2006 ) , having previously been detected in outburst in 1898 , 1933 , 1958 , 1967 and 1985 . it is possible that other outbursts have occurred since the discovery of the system , but were missed by observers . long term lightcurves of rs oph obtained by the aavso show that the system undergoes a characteristic dimming just before the outburst , and an overshoot at the end of decay from maximum beyond the mean inter - outburst magnitude ( oppenheimer 1993 ) . schaefer ( 2004 ) reported that a reduction in magnitude was detected on plates obtained in 1907 , just after the end of the seasonal observing gap . he attributed these low values to the post - outburst dip observed in other events , and suggested that rs oph experienced an outburst in 1907 while it was hidden by the sun . similarly , dips in magnitude were detected both before and after the 1945 observing gap , suggesting another outburst was missed at that time ( oppenheimer & mattei 1996 ) . rs oph is believed to host a massive white dwarf accreting material from a red giant companion of spectral type k7 ( mrset & schmid 1999 ) . the most recent determination of the orbital period of the binary is 456 days ( fekel et al . 2000 ) . the secondary is believed to underfill its roche lobe , and so accretion proceeds through a wind and not through roche lobe overflow ( rlo ) , as in cataclysmic variables and classical novae ( e.g. dobrzycka et al . 1996 , hachisu et al . the distance to the system has been discussed extensively in the literature , and disagreements remain . bode ( 1987 ) gives 1.6 @xmath10 0.3 kpc . results from the current outburst give a distance ranging from 540 pc ( monnier et al . 2006 ) to 1.31.7 kpc ( hachisu et al . this large spread in distance makes the exact parameters of the system difficult to determine . we will follow bode in this work , and assume a distance of 1.6 @xmath10 0.3 kpc . the system was observed in x - rays by exosat on several occasions during the 1985 outburst ( mason et al . , 1987 ) . however , only low resolution spectra were obtained as x - ray grating spectroscopy was not available in 1985 . since then the situation has vastly improved , with no less than 4 active x - ray observatories equipped with advanced instrumentation capable of high resolution grating spectroscopy or microsecond timing accuracy . data have been obtained at frequent intervals by the rossi x - ray timing experiment ( rxte ) , the x - ray telescope ( xrt ) on board swift , and of course chandra and xmm - newton . in this paper , we present the chandra and xmm - newton data , which include the first grating spectra obtained of any of the recurrent novae . the temporal coverage offered by such an extensive set of observations allows us for the first time to test models of the evolution of an outburst in the rs oph system . we present a detailed timing analysis of the data set in an accompanying paper ( leibowitz et al .

we present the x - ray grating spectra of the recurrent nova rs ophiuchi during its 2006 outburst , obtained with the xmm - newton and chandra observatories . the absorption lines did not appear to be significantly blue - shifted as previously observed in another classical nova . therefore , rs oph may be an important type ia supernova progenitor .

we present the x - ray grating spectra of the recurrent nova rs ophiuchi during its 2006 outburst , obtained with the xmm - newton and chandra observatories . two weeks after optical maximum , the x - ray spectrum was hard and dominated by emission lines of h - like and he - like ions . the x - ray luminosity was 2.4 10 erg in the 0.33 - 10 kev range . the spectra indicate a collisionally dominated plasma with a broad range of temperatures . all the lines are blue - shifted , with the velocity shift increasing with lower ionization state and longer wavelength . two weeks later , the spectrum was still dominated by emission lines , although the line ratios present indicate cooling . during this observation , a soft x - ray flare occurred in which a new system of higher velocity emission lines appeared in the soft end of the spectrum . towards the end of the second month the emission spectrum became composite , with both absorption and emission features . the dominant component during the third month was the supersoft continuum with the broad absorption features of a hot white dwarf atmosphere . the absorption lines did not appear to be significantly blue - shifted as previously observed in another classical nova . a preliminary fit of an atmospheric model available in the literature indicates a white dwarf temperature slightly exceeding 800,000 k. the x - ray luminosity reached at least 9 10 erg in the 0.2 - 1 kev range , while the intrinsic nebular absorption decreased by a factor of five since the first observation . the spectral fits indicate a massive white dwarf , with a mass of at least 1.2 m . therefore , rs oph may be an important type ia supernova progenitor . we show that the data are consistent with mass loss ending before day 54 after the outburst , and nuclear burning ending around day 69 . a rapid decay in x - ray luminosity followed after week 10 . the x - ray luminosity 5 , 7 and 8 months after optical maximum dropped by more than two orders of magnitude , and the spectra are dominated by soft x - ray emission lines typical of a collisionally excited and ionized plasma . they do not appear to consistent with emission from an accretion disk .

astro-ph0108424

c

we have discovered two wide separation l - dwarf common proper motion companions to nearby stars and identified a third candidate from 2mass . spectral types assigned from optical spectroscopy were l0 v , l2.5 v , and l8 v. nir low resolution spectra of the companions were provided as well as a grid of known objects spanning m6 v t dwarfs to support spectral type assignment for these and future l - dwarfs in the _ zjhk _ bands . using published measurements , we estimated ages of the companions from physical properties of the primaries . these crude ages allowed us to estimate companion masses using theoretical low - mass star and brown dwarf evolutionary models . we found that gl 337c is a brown dwarf , hd 89744b is a vlm star , and gl 618.1b may be either . with the addition of these new l - dwarfs there are nine wide - binary ( @xmath0 au ) l - dwarf companions of nearby stars known . these discoveries improve the statistics of binaries involving low - mass stars and brown dwarfs . in particular they support initial conclusions that the brown dwarf desert seen at small separations around main sequence stars does not extend to wide separations . the discovery of these companions in low mass ratio systems ( @xmath248 ) , along with similar discoveries previously reported , will also significantly improve our understanding of the binary mass ratio distribution for @xmath10 . we thank the anonymous referee for helpful comments that led to a more concise manuscript , john carr for a careful reading of a previous draft , and adam burrows for providing his evolutionary curves in electronic format . we thank andrea richichi and isabelle baraffe for supplying filter curves , and isabelle baraffe and france allard for helpful discussions . we also wish to thank the palomar night assistants skip staples and karl dunscombe for their expertise and support . this publication makes use of data from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center , funded by the national aeronautics and space administration and the national science foundation . this research has also made use of the simbad database , operated at cds , strasbourg , france . dss images were obtained from the canadian astronomy data centre , which is operated by the herzberg institute of astrophysics , national research council of canada . allende prieto , c. & lambert , d. l. 1999 , , 352 , 555 arribas , s. & roger , c. m. 1989 , , 215 , 305 balachandran , s. 1990 , , 354 , 310 balachandran , s. 1995 , , 446 , 203 baliunas , s. & vaughan , a. 1985 , , 23 , 379 baliunas , s. & jastrow , r. 1990 , , 348 , 520 baliunas , s. , et al . 1995 , , 438 , 269 baliunas , s. , sokoloff , d. , & soon , w. 1996 , , 457 , l99 baraffe , i. , chabrier , g. , allard , f. , & hauschildt , p. h. 1998 , , 337 , 403 barnaby , d. , spillar , e. , christou , j. c. , & drummond , j. d. 2000 , , 119 , 378 barry , d. c. 1988 , , 334 , 436 bartkeviius , a. & lazauskait , r. 1996 , baltic astronomy , 5 , 1 basri , g. et al . 2000 , , 538 , 363 bertelli , g. , bressan , a. , chiosi , c. , fagotto , f. , & nasi , e. 1994 , astronomy & astrophysics supplement series , 106 , 275 binney , j. , dehnen , w. , & bertelli , g. 2000 , , 318 , 658 burgasser , a. j. , wilson , j. c. , kirkpatrick , j. d. , skrutskie , m. f. , colonno , m. r. , enos , a. t. , smith , j. d. , henderson , c. p. , gizis , j. e. , brown , m. e. , & houck , j. r. 2000 , , 120 , 1100 burrows , a. , marley , m. , hubbard , w. b. , lunine , j.i . , guillot , t. , saumon , d. , freedman , r. , sudarsky , d. , & sharp , c. 1997 , , 491 , 856 carney , b. w. 1979 , , 233 , 211 chandrasekhar , s. & mnch , g. 1950 , , 111 , 142 cutri , r. m. , et al . 2000 , explanatory supplement to the 2mass second incremental data release , http://www.ipac.caltech.edu/2mass/releases/second/doc/explsup.html de medeiros , j. r. , do nascimento , j. d. , jr . , & mayor , m. 1997 , , 317 , 701 delfosse , x. et al . 1997 , , 327 , l25 delfosse , x. , tinney , c. g. , forveille , t. , epchtein , n. , borsenberger , j. , fouqu , p. , kimeswenger , s. & tiphne , d. 1999 , a&ass , 135 , 41 delfosse , x. , forveille , t. , sgransan , d. , beuzit , j .- l . , udry , s. , perrier , c. , & mayor , m. 2000 , , 364 , 217 donahue , r. a. 1993 , phd thesis , new mexico state university duquennoy , a. & mayor , m. 1991 , , 248 , 485 , dm91 duquennoy , a. , mayor , m. , & mermilliod , j .- c . 1992 , in binaries as tracers of stellar formation , ed . m. duquennoy & m. mayor ( cambridge : cambridge univ . press ) , 52 edvardsson , b. , andersen , j. , gustafsson , b. , lambert , d. l. , nissen , p. e. , tomkin , j. 1993 , , 275 , 101 eggen , o. j. 1989b , , 101 , 366 eggen , o. j. 1998 , , 115 , 2397 epchtein , n. 1997 , in the impact of large - scale near - ir sky surveys , ed . f. garzon ( dordrecht : kluwer ) , 15 fukugita , m. , ichikawa , t. , gunn , j. e. , doi , m. , shimasaku , k. , & schneider , d. p. , 1996 , , 111 , 1748 gaidos , e. j. 1998 , , 110 , 1259 girardi , l. , bressan , a. , bertelli , g. , & chiosi , c. 2000 , astronomy & astrophysics supplementary series , 141 , 371 gizis , j. e. , monet , d. g. , reid , i. n. , kirkpatrick , j. d. , liebert , j. , & williams , r. j. 2000 , , 120 , 1085 gizis , j. e. , kirkpatrick , j. d. , burgasser , a. , reid , i. n. , monet , d. g. , liebert , j. & wilson , j. c. 2001a , , 551 , 163 gizis , j. e. , kirkpatrick , j. d. , & wilson , j. c. 2001b , , 121 , 2185 gliese , w. 1969 , catalogue of nearby stars ( 2nd ed . ; heidelberg : astron . rechen - institut ) gliese , w. & jahreiss , h. 1991 , preliminary version of the third catalogue of nearby stars ( heidelberg : astron . rechen - institut ) gonzalez , g. , laws , c. , tyagi , s. , & reddy , b. e. 2001 , , 121 , 432 hawley , s. l. , gizis , j. e. , & reid , i. n. 1996 , , 112 , 2799 henry , t. j. & mccarthy , d. w. , jr . 1993 , , 106 , 773 hoffleit , d. & warren , w. h. , jr . 1991 , the bright star catalogue , 5th revised ed . ( preliminary version ) hnsch , m. , schmitt , j. h. m. m. , sterzik , m. f. , & voges , w. 1999 , a&ass , 135 , 319 iben , i. , jr . 1967 , , 147 , 624 jones , h. r. a. , longmore , a. j. , jameson , r. f. , & mountain , c. m. 1994 , , 267 , 413 kirkpatrick , j. d. , henry , t. j. , & mccarthy , d. w. , jr . 1991 , , 77 , 417 kirkpatrick , j. d. , et al . 1999 , , 519 , 802 , k99 kirkpatrick , j. d. , reid , i. n. , liebert , j. , gizis , j. e. , burgasser , a. j. , monet , d. g. , dahn , c. c. , & nelson , b. 2000 , 120 , 447 , k00 kirkpatrick , j. d. , dahn , c. c. , monet , d. g. , reid , i. n. , gizis , j. e. , liebert , j. , & burgasser , a. j. 2001 , , 121 , 3235 klemperer , w. , norris , w. g. , & bchler , a. 1960 , , 33 , 1534 korzennik , s. g. , brown , t. m. , fischer , d. a. , nisenson , p. , & noyes , r. w. 2000 , , 533 , l147 lbre , a. , de laverny , p. , de medeiros , j. r. , charbonnel , c. , & da silva , l. 1999 , , 345 , 936 leggett , s. k. 1992 , , 82 , 351 lodders , k. 1999 , , 519 , 793 maggio , a. , sciortino , s. , vaiana , g. s. , major , p. , bookbinder , j. , golub , l. , harnden , f. r. , & rosner , r. 1987 , , 315 , 687 marcy , g. w. & butler , r. p. 2000 , , 112 , 137 mason , b. d. , mcallister , h. a. , & hartkopf , w. i. 1996 , , 112 , 276 mason , b. d. , wycoff , g. l. , & hartkopf , w. i. , the washington double star catalog , u. s. naval observatory , http://ad.usno.navy.mil/proj/wds/wds.html , updated 2001 mar 05 mclean , i. s. et al . 2000 , , 533 , l45 nelson , l. a. , rappaport , s. , & chiang , e. 1993 , , 413 , 364 ng , y. k. , & bertelli , g. 1998 , , 329 , 943 noyes , r. w. , hartmann , l. w. , baliunas , s. l. , duncan , d. k. , & vaughan , a. h. 1984 , , 279 , 763 oke , j. b. , et al . 1995 , , 107 , 375 perryman , m. a. c. et al . 1997 , , 323 , l49 pinsonneault , m. 1997 , , 35 , 557 pizzolato , n. , maggio , a. , & sciortino , s. 2000 , , 361 , 614 pourbaix , d. 2000 , a&as , 145 , 215 rebolo , r. , martn , e. l. , & magazz , a. 1992 , , 389 , l83 reid , i. n. et al . 1991 , , 103 , 661 reid , i. n. , hawley , s. l. , & gizis , j. e. 1995 , , 110 , 1838 reid , i. n. , kirkpatrick , j. d. , gizis , j. e. , dahn , c. c. , monet , d. g. , williams , r. j. , liebert , j. , & burgasser , a. j. 2000 , , 119 , 369 reid , i. n. & hawley , s. l. 2000 , new light on dark stars ( springer - verlag : berlin ) , 196 reid , i. n. , gizis , j. e. , kirkpatrick , j. d. , & koerner , d. w. 2001a , , 121 , 489 reid , i. n. , burgasser , a. j. , cruz , k. l. , kirkpatrick , j. d. , & gizis , j. e. 2001b , , 121 , 1710 richichi , a. , ragland , s. , calamai , g. , richter , s. , & stecklum , b. 2000 , , 361 , 594 saar , s. h. & brandenburg , a. 1999 , , 524 , 295 skrutskie , m. f. , et al . 1997 , in the impact of large - scale near - ir sky surveys , ed . f. garzon ( dordrecht : kluwer ) , 25 skumanich , a. 1972 , , 171 , 565 soderblom , d. r. 1985 , , 90 , 2103 testi , l. et al . 2001 , , 552 , l147 tinney , c. g. , mould , j. r. , & reid , i. n. 1993 , , 105 , 1045 tokunaga , a. t. , & kobayashi , n. 1999 , , 117 , 1010 vaughan , a. h. , preston , g. w. , & wilson , o. c. 1978 , , 90 , 267 walter , f. m. , & barry , d. c. 1991 , in the sun in time , ed . c. p. sonett , m. s. giampapa , & m. s. matthews ( tucson : univ . arizona press ) , 633 wilson , j. c. , skrutskie , m. f. , colonno , m. r. , enos , a. t. , smith , j. d. , henderson , c. p. , gizis , j. e. , monet , d. , & houck , j. r. 2001a , , 113 , 227 wilson , j. c. , gizis , j. e. , skrutskie , m. f. , miller , n. , j. davy kirkpatrick , monet , d. g. , & houck , j. r. 2001b , in preparation wilson , o. c. 1968 , , 153 , 221 york , d. g. , et al . 2000 , , 120 , 1579 zahn , j .- 1977 , , 57 , 383 2massw j0912145 + 145940 ( 2m0912 + 14 ) & 09:12:14.5 & + 14:59:40 & @xmath249 & @xmath250 & @xmath251 & @xmath252 + 2massw j1620261 - 041631 ( 2m1620 - 04 ) & 16:20:26.1 & -04:16:31 & @xmath253 & @xmath254 & @xmath255 & @xmath256 + 2massi j1022148 + 411426 ( 2m1022 + 41 ) & 10:22:14.8 & + 41:14:26 & @xmath257 & @xmath258 & @xmath259 & @xmath260 + 2m0912 + 14 ( gl 337c ) & 2000 may 10 & 4000 & palomar 60-inch & cormass + & 2000 dec 26 & 2400 & keck i & lris + 2m1620 - 04 ( gl 618.1b ) & 2000 may 9 & 3300 & palomar 60-inch & cormass + & 2000 oct 7 & 2400 & keck i & lris + 2m1022 + 41 ( hd 89744b ) & 2000 may 10 & 4550 & palomar 60-inch & cormass + & 2000 dec 26 & 900 & keck i & lris + m6 v & lhs 2034 & 1999 oct 27 & 600 & & 10.03 & & 0.97 & 1 + m8 v & vb 10 & 1999 aug 22 & 720 & & 8.80 & & 1.10 & 1 + m9 v & lhs 2924 & 2000 jun 16 & 2400 & & 10.67 & & 1.17 & 1 + m9.5 v & bri 0021 - 0214 & 1999 aug 24 & 1080 & & 10.64 & & 1.26 & 2 + l1 v & 2massw j0208183 + 254253 & 1999 aug 24 & 2700 & 12.58 & & 1.44 & & 3 + l2 v & 2massw j0015447 + 351603 & 2000 sep 18 & 3300 & 12.24 & & 1.58 & & 3 + l3.5 v & 2massw j0036159 + 182110 & 1999 aug 24 & 1440 & 11.03 & & 1.41 & & 4 + l5 v & 2massw j1507476 - 162738 & 2000 apr 20 & 2800 & 11.30 & & 1.52 & & 4 + l7 v & denis - p j0205.4 - 1159ab & 2000 sep 16 & 5100 & 12.99 & & 1.56 & & 5 + l8 v & 2massw j1632291 + 190441 & 2000 jun 14 & 5500 & 13.98 & & 1.88 & & 6 + t & 2massw j0559191 - 140448 & 1999 oct 24 & 2400 & 13.61 & & 0.22 & & 7 + lcccccccc spectral type & g8 v @xmath1 k1 v & 1 & & m0 v & 8 & & f7 iv - v & 11 + & 0.73 & 2 & & 1.4 & 9 & & 0.54 & 10 + distance ( pc ) & @xmath261 & 3 & & @xmath262 & 3 & & @xmath263 & 3 + @xmath264 & @xmath265 & 4 & & 0.67 & - & & @xmath266 & - + activity & & & & & & & & + @xmath267 & @xmath268 & 5,6 & & not detected & 6 & & @xmath269 & 12 + @xmath196 & & & & & & & @xmath270,@xmath271 & 10,13 + @xmath272 ( ew ) & & & & @xmath273 & 10 & & & + @xmath274 & & & & & & & 9 & 13 + period & & & & & & & flat & 14 + metallicity & & & & & & & & + @xmath275}$ ] & @xmath276 & 2,7 & & & & & + 0.24 & 15,16 + @xmath277}$ ] & & & & @xmath278 & 9 & & & + lithium abundance & & & & & & & & + @xmath279 & & & & & & & 2.07 & 16 + kinematics & & & & & & & & + @xmath280 & @xmath281 & 7 & & @xmath282 & 9 & & @xmath283 & 15 + @xmath284 & @xmath285 & 7 & & @xmath286 & 9 & & @xmath287 & 15 + @xmath288 & @xmath289 & 7 & & @xmath290 & 9 & & @xmath291 & 15 +

we present two confirmed wide separation l - dwarf common proper motion companions to nearby stars and one candidate identified from the two micron all sky survey . spectral types from optical spectroscopy are l0 v , l2.5 v , and l8 v. near - infrared low resolution spectra of the companions are provided as well as a grid of known objects spanning m6 v t dwarfs to support spectral type assignment for these and future l - dwarfs in the _ zjhk _ bands . using published measurements , we estimate ages of the companions from physical properties of the primaries . these crude ages allow us to estimate companion masses using theoretical low - mass star and brown dwarf evolutionary models .

we present two confirmed wide separation l - dwarf common proper motion companions to nearby stars and one candidate identified from the two micron all sky survey . spectral types from optical spectroscopy are l0 v , l2.5 v , and l8 v. near - infrared low resolution spectra of the companions are provided as well as a grid of known objects spanning m6 v t dwarfs to support spectral type assignment for these and future l - dwarfs in the _ zjhk _ bands . using published measurements , we estimate ages of the companions from physical properties of the primaries . these crude ages allow us to estimate companion masses using theoretical low - mass star and brown dwarf evolutionary models . the new l - dwarfs in this paper bring the number of known wide - binary ( au ) l - dwarf companions of nearby stars to nine . one of the l - dwarfs is a wide separation companion to the f7 iv - v extrasolar planet system hd89744ab .

1408.3778

i

it is well - known that many special functions , e.g. the airy , bessel , or legendre functions , originate as series solutions of _ linear _ ordinary differential equations ( odes ) . such functions play a crucial role in describing a wide range of important physical and mathematical phenomena . an essential point here is that for linear ordinary differential equations singularities of solutions can only occur at the points where the coefficients of the equation itself become singular . this makes it possible to talk about global properties of solutions ( and hence , of the corresponding special functions ) , and the asymptotic behavior of solutions near those fixed singular points . for nonlinear equations the situation is very different . although the cauchy existence theorem guarantees _ local _ existence of the solution to a given initial value problem at an ordinary ( regular ) point , in general the domain in which this solution is defined depends not just on the equation itself , but on the initial conditions as well solutions acquire _ movable _ ( i.e. , dependent on the initial values or , equivalently , on the constants of integration ) singularities . such singularities are called _ critical _ if a solution looses its single - valued character in a neighborhood of the singularity ( e.g. , when a singular point is a _ branch point _ ) . an ode is said to satisfy the _ painlev property _ if its general solution is free of _ movable _ critical singular points . otherwise , the riemann surface uniformizing such solution becomes dependent on the constants of integration , which prevents global analysis . thus , equivalently , the painlev property of an ode is the uniformizability of its general solution , see @xcite ( as well as the other excellent articles in the volume @xcite ) for a careful overview of these ideas . it is clear that liner equations satisfy painlev property . the importance of the painlev property for nonlinear equations is that , similar to the linear case , solutions of these equations give rise to new transcendental functions . in that sense , according to m.kruskal as quoted in @xcite , nonlinear equations satisfying this property are on the border between trivially integrable linear equations and nonlinear equations that are not integrable , and so the painlev property is essentially equivalent to ( and is a criterion of ) integrability . the search for new transcendental functions was the original motivation in the work of p.painlev who , together with his student b.gambier , had classified all of the rational second - order differential equations that have the painlev property , @xcite , @xcite , @xcite . among 50 classes of equations that they found , only _ six _ can not be reduced to linear equations or integrated by quadratures . these equations are now known as @xmath4 . solutions to these equations , the so - called _ painlev transcendents _ , are playing an increasingly important role in describing a wide range of nonlinear phenomena in mathematics and physics @xcite . almost simultaneously with the work of p.painlev and b.gambier , the most general painlev vi equation was obtained by r.fuchs @xcite in the theory of _ isomonodromic deformations _ of fuchsian systems . this theory , developed in the works of r.fuchs @xcite , l.schlesinger @xcite , r.garnier @xcite , and then extended to the non - fuchsian case by m.jimbo , t.miwa , and k.ueno @xcite , and also by h.flaschka and a.newell @xcite , as well as the related riemann - hilbert approach @xcite , @xcite , are now among the most powerful methods for studying the structure of the painlev transcendents . over the last thirty years a significant effort has been put towards understanding and generalizing results and methods of the classical theory of completely integrable systems to the _ discrete _ case . this is true for the theory of painlev equations as well . discrete painlev equations were originally defined as second order nonlinear difference equations that have usual painlev equations as continuous limits @xcite , @xcite . a systematic study of discrete painlev equations was started by b.grammaticos , j.hietarinta , f.nijhoff , v.papageorgiou and a.ramani , @xcite , @xcite , @xcite , and many different examples of such equations were obtained in a series of papers by grammaticos , ramani , and their collaborators by a systematic application of the singularity confinement criterion , see reviews @xcite , @xcite , and many references therein . discrete painlev equations also appear in a broad spectrum of important nonlinear problems in mathematics and physics , among which are the theory of orthogonal polynomials , quantum gravity , determinantal random point processes , reductions of integrable lattice equations , and , notably , as bcklund transformations of differential painlev equations . some of these problems are discrete anlogues or direct discretizations of the corresponding nonlinear problems , and some describe purely discrete phenomena . it turned out that classifying discrete painlev equations by their continuous limits , as well as the singularity confinement criterion , is not a very good approach , since such correspondence is far from being bijective . it is both possible for the same discrete equation to have different continuous painlev equations as continuous limits under different limiting procedures , and for different discrete equations to have the same continuous limit . in the seminal paper @xcite h.sakai showed that an effective way to understand and classify discrete painlev equations is through algebraic geometry . in this approach , to each equation , if we consider it as a two - dimensional first - order nonlinear system , we put in correspondence a family of algebraic surfaces @xmath5 , where @xmath6 is some collection of parameters that change , depending on the type of the equation , in an additive , multiplicative , or elliptic fashion as functions of a discrete `` time '' parameter . this family @xmath5 , by a slight abuse of terminology , is called the _ okamoto space of initial conditions _ ( that we often denote simply by @xmath7 omitting explicit dependence on parameters @xmath8 ) and it is obtained by resolving the indeterminacy points of the corresponding map @xmath9 via the blowing - up procedure . by sakai s theory , the complete resolution of indeterminacies is obtained by blowing up 9 ( possibly infinitely close ) points on @xmath10 ( or eight points on a birationally equivalent @xmath11 compactification of @xmath12 ) . the resulting surface @xmath7 has a special property that it admits a unique anti - canonical divisor @xmath13 of _ canonical type_. the orthogonal complement of @xmath14 in the picard lattice @xmath15 is described by the affine dynkin diagram @xmath16 that has two intersecting root subsystems of affine type : @xmath17 , that is generated by classes @xmath18 of irreducible components of the anticanonical divisor @xmath19 , and its orthogonal complement @xmath20 whose corresponding root lattice @xmath21 is called the _ symmetry sub - lattice_. then the _ type _ of the discrete painlev equation is the same as the _ type of its surface _ @xmath5 , which is just the type of an affine dynkin diagram describing the root system @xmath17 of irreducible components @xmath18 of @xmath19 ( essentially , the degeneration structure of the positions of the blowup points ) . moreover , nonlinear painlev dynamic now becomes a translation in the symmetry sub - lattice @xmath21 , and so it becomes `` _ _ linearized _ _ '' there , see @xcite for details . this is somewhat similar to the algebro - geometric integrability of classical integrable systems and soliton equations , where nonlinear dynamic is mapped to commuting linear flows on the jacobian of the spectral curve of the associated linear problem via the abel - jacobi map . one important observation from sakai s geometric approach is that in addition to _ additive _ ( difference ) and _ multiplicative _ ( @xmath22-difference ) _ discretizations _ of continuous painlev equations , there are some purely discrete painlev equations . it also led to the discovery of the master _ discrete painlev equation such that all of the other painlev equations can be obtained from it through degenerations ( which corresponds to more and more special configurations of the blow - up points ) . this degenerations can be described by the following scheme , where letters stand for the symmetry type of the equation ( which is the type of the affine dynkin diagram of the root subsystem @xmath20 ) , and the subscripts @xmath23 , @xmath22 , @xmath24 , and @xmath25 stand for elliptic , multiplicative , additive and differential painlev equations respectively , see figure [ fig : pain - diag ] . @xmath26 \matrix ( m ) [ matrix of math nodes , column sep={1pt},row sep={15pt } ] { \left(e^{(1)}_{8}\right)^{e } & & & & & & & \left(a_{1}^{(1)}\right)^{q } \\ \left(e^{(1)}_{8}\right)^{q } & \left(e^{(1)}_{7}\right)^{q } & \left(e^{(1)}_{6}\right)^{q } & \node{\left(d^{(1)}_{5}\right)^{q } } ; & \left(a^{(1)}_{4}\right)^{q } & \left((a_{1}\!\!+\!\ ! a_{2})^{(1)}\right)^{q } & \left((a_{1}\!\!+\!\!a_{1})^{(1)}\right)^{q } & \left(a_{1}^{(1)}\right)^{q } & \left(a_{0}^{(1)}\right)^{q } \\ \left(e^{(1)}_{8}\right)^{\delta } & \left(e^{(1)}_{7}\right)^{\delta } & \left(e^{(1)}_{6}\right)^{\delta } & \left(d^{(1)}_{4}\right)^{c,\delta } & \left(a^{(1)}_{3}\right)^{c,\delta } & \left((2a_{1})^{(1)}\right)^{c,\delta } & \left(a_{1}^{(1)}\right)^{c,\delta } & \left(a_{0}^{(1)}\right)^{c } \\ & & & & & \left(a_{2}^{(1)}\right)^{c,\delta } & \left(a_{1}^{(1)}\right)^{c,\delta } & \left(a_{0}^{(1)}\right)^{c } \\ } ; % \draw [ label = above ( m-1 - 1 ) : $ a$ ] \node [ blue ] at ( $ ( m-2-4.north ) + ( 0,0.1)$ ) { q-$p_{\text{vi}}$ } ; \node [ blue ] at ( $ ( m-3-4.south ) + ( 0,-0.1)$ ) { $ p_{\text{vi}}$,\ ! d-$p_{\text{v}}$ } ; \node [ blue ] at ( $ ( m-2-5.north ) + ( 0,0.1)$ ) { q-$p_{\text{v}}$ } ; \node [ blue ] at ( $ ( m-1-8.north ) + ( 0,0.1)$ ) { q-$p_{\text{i}}$ } ; \node [ blue ] at ( $ ( m-3-5.south ) + ( 0,-0.1)$ ) { $ p_{\text{v}}$,\ ! d-$p_{\text{iv}}$ } ; \node [ blue ] at ( $ ( m-3-5.south ) + ( 0,-0.4)$ ) { d-$p_{\text{iii}}$ } ; \node [ blue ] at ( $ ( m-2-6.north ) + ( 0,0.1)$ ) { q-$p_{\text{iv}}$,\ ! q-$p_{\text{iii}}$ } ; \node [ blue ] at ( $ ( m-3-6.south ) + ( 0,-0.1)$ ) { $ p_{\text{iii}}$ } ; \node [ blue ] at ( $ ( m-3-6.south ) + ( 0.1,-0.4)$ ) { alt.\ ! d-$p_{\text{ii}}$ } ; \node [ blue ] at ( $ ( m-4-6.south ) + ( 0,-0.1)$ ) { $ p_{\text{iv}}$,\ ! d-$p_{\text{ii}}$ } ; \node [ right , scale=0.8 ] at ( $ ( m-1-8.south east ) + ( -0.3,0.15)$ ) { $ { |\alpha|^{2}=8}$ } ; \node [ blue ] at ( $ ( m-4-7.south ) + ( 0,-0.1)$ ) { $ p_{\text{ii}}$,\ ! alt.d-$p_{\text{i}}$ } ; \node [ blue ] at ( $ ( m-4-8.south ) + ( 0,-0.1)$ ) { $ p_{\text{i}}$ } ; % \node [ right , scale=0.5 ] at ( $ ( m-1-8.south east ) + ( -0.5,0.05)$ ) { $ { |\alpha|^{2}=8}$ } ; \node [ right , scale=0.8 ] at ( $ ( m-2-7.south east ) + ( -0.95,0.02)$ ) { $ { |\alpha|^{2}=14}$ } ; \node [ right , scale=0.8 ] at ( $ ( m-2-8.south east ) + ( -0.65,0.02)$ ) { $ { |\alpha|^{2}=4}$ } ; \draw[- > ] ( m-1 - 1 ) edge ( m-2 - 1 ) ( m-2 - 1 ) edge ( m-3 - 1 ) ( m-2 - 2 ) edge ( m-3 - 2 ) ( m-2 - 3 ) edge ( m-3 - 3 ) ( m-2 - 4 ) edge ( m-3 - 4 ) ( m-2 - 5 ) edge ( m-3 - 5 ) ( m-2 - 6 ) edge ( m-3 - 6 ) ( m-2 - 7 ) edge ( m-3 - 7 ) ( m-2 - 8 ) edge ( m-3 - 8 ) ( m-3 - 5 ) edge ( m-4 - 6 ) ( m-3 - 6 ) edge ( m-4 - 7 ) ( m-3 - 8 ) edge ( m-4 - 8 ) ( m-2 - 7 ) edge ( m-1 - 8 ) ( m-1 - 8 ) edge ( m-2 - 9 ) ( m-2 - 9 ) edge ( m-4 - 8 ) ( m-2 - 8 ) edge ( m-4 - 7 ) % ( $ ( m-2-1.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-2.west ) + ( 0.05,0)$ ) ( $ ( m-2-2.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-3.west ) + ( 0.05,0)$ ) ( $ ( m-2-3.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-4.west ) + ( 0.05,0)$ ) ( $ ( m-2-4.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-5.west ) + ( 0.05,0)$ ) ( $ ( m-2-5.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-6.west ) + ( 0.05,0)$ ) ( $ ( m-2-6.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-7.west ) + ( 0.05,0)$ ) ( $ ( m-2-7.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-8.west ) + ( 0.05,0)$ ) % ( $ ( m-2-8.east ) + ( -0.15,0)$ ) edge ( $ ( m-2-9.west ) + ( 0.05,0)$ ) % ( $ ( m-3-1.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-2.west ) + ( 0.05,0)$ ) ( $ ( m-3-2.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-3.west ) + ( 0.05,0)$ ) ( $ ( m-3-3.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-4.west ) + ( 0.05,0)$ ) ( $ ( m-3-4.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-5.west ) + ( 0.05,0)$ ) ( $ ( m-3-5.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-6.west ) + ( 0.05,0)$ ) ( $ ( m-3-6.east ) + ( -0.15,0)$ ) edge ( $ ( m-3-7.west ) + ( 0.05,0)$ ) % ( $ ( m-4-6.east ) + ( -0.15,0)$ ) edge ( $ ( m-4-7.west ) + ( 0.05,0)$ ) ( $ ( m-4-7.east ) + ( -0.15,0)$ ) edge ( $ ( m-4-8.west ) + ( 0.05,0)$ ) % ( $ ( m-3-7.east ) + ( -0.15,0)$ ) - > ( $ ( m-3-8.west ) + ( 0.05,0)$ ) ; \draw [ - ] ( $ ( m-2-6.south ) + ( -0.48,0)$ ) to [ bend right = 50 ] ( $ ( m-4-6.north ) + ( -0.48,0.02)$ ) ; % \draw[->,gray , rounded corners ] ( kc ) -| node[auto , text = black , pos=.7 ] % { \(\partial\ ) } ( $ ( 01.east)+(.5,0)$ ) |- ( $ ( b)!.35!(b')$ ) -| % ( $ ( 02.west)+(-.5,0)$ ) |- ( ca ) ; \end{tikzpicture}\ ] ] the following question then becomes natural and important : _ how to represent these new purely discrete equations in the isomonodromic framework ? _ this question was posed by sakai in @xcite ( * problem a * for the difference case and * problems b , c * for the @xmath22-difference case ) . more precisely , in both continuous and discrete difference case we start with some fuchsian system and consider its isomonodromic deformations . in the continuous case , deformation parameters are locations of singular points of the system . the resulting isomonodromic flows on the space of coefficients of the fuchsian system are given by schlesinger _ equations_. in particular , for a @xmath27 fuchsian system with four poles , schlesinger equations reduce to the most general @xmath28 equation . in the discrete difference case , deformation parameters are the characteristic indices of the system and since the isomonodromy condition requires that the indices change by integral shifts , the resulting dynamic is indeed _ discrete_. it is expressed in the form of _ difference _ equations called schlesinger _ transformations_. it is also possible to get the isomonodromic description of difference and @xmath22-difference painlev equations by studying deformations of linear difference and @xmath22-difference analogues of fuchsian systems , see @xcite and @xcite for details . in @xcite we studied in detail a particular class of schlesinger transformations that are called _ these transformations change only two of the characteristic indices of the underlying fuchsian system ( and any other schlesinger transformation not involving characteristic indices with multiplicity can be represented as a composition of the elementary ones ) . in particular , we obtained explicit evolution equations governing the resulting discrete dynamic . our objective for the present paper is to carefully and very explicitly describe reductions of these _ discrete schlesinger evolution equations _ to the _ difference _ painlev equations . since the painlev equations are of second order , we focus on fuchsian systems that have two - dimensional moduli spaces ( coordinates on such moduli space are known as accessory parameters ) . it turns out that , modulo two natural transformations called _ katz s addition _ and _ middle convolution _ @xcite , that preserve the deformation equations @xcite , there are only four such systems , @xcite , that have the _ spectral type _ @xmath29 , @xmath30 , @xmath31 , and @xmath32 ( spectral type of a fuchsian system encodes the degeneracies of the characteristic indices , or eigenvalues of residue matrices at singular points , and it is carefully defined in the next section ) . isomonodromic deformations of a @xmath29 spectral type fuchsian system are well known continuous deformations reduce to painlev vi equation and schlesinger transformations reduce to the difference painlev d-@xmath33 equation , also known as d-@xmath34 , and in @xcite we showed that in this case our _ discrete schlesinger evolution equations _ indeed can be reduced to the standard form of d-@xmath33 . in @xcite p.boalch showed that for fuchsian systems with the spectral types @xmath30 , @xmath31 , and @xmath32 their schlesinger transformations reduce to difference painlev equations with the required symmetry groups @xmath1 , @xmath3 , and @xmath16 respectively , thus providing a theoretical answer to sakai s * problem a*. our goal for the present paper is to make this statement very concrete via explicit direct computation of reductions of discrete schlesinger evolution to difference painlev equations with symmetry groups @xmath1 and @xmath3 ( we plan to consider deformations of a fuchsian system of the spectral type @xmath32 with the symmetry group @xmath16 elsewhere ) . in addition to establishing that the resulting difference painlev equations have the required types d-@xmath35 and d-@xmath36 , we explicitly compare the resulting equations with the previously known instances of equations of the same type . we do so by finding an explicit identification between their okamoto spaces of initial conditions , which allows us to compute and compare the translation directions for different equations w.r.t . the same root basis , and also to match generic parameters to the characteristic indices of the fuchsian system , which in turn allows us to see and compare these different equations via their actions on the riemann scheme of our fuchsian system . we show that in both examples elementary schlesinger dynamic is indeed more elementary in the sense that standard examples of difference painlev equations can be realized as compositions of elementary schlesinger transformations . of particular interest here is the @xmath3 case which has two characteristic indices of multiplicity @xmath37 . we show that in that case the standard from of the equation can not be represented as a composition of elementary schlesinger transformations of rank one . thus we first generalize our discrete schlesinger evolution equations from @xcite to elementary schlesinger transformations of rank two , and then show how to represent the standard dynamic as a composition of two such rank two transformations . we also provide a lot of details on how to compute the okamoto space of initial conditions for our equations and how to identify two different instances of such spaces , hoping that this will be helpful for other researchers who are interested in the geometric approach to discrete painlev equations . the paper is organized as follows . in section [ sec : preliminaries ] we briefly describe our parameterization of a fuchsian system by its spectral and eigensystem data , define elementary schlesinger transformations , present evolution equations for elementary schlesinger transformations as a dynamic on the space of coefficient of our fuchsian system , and then show how to split them to get the dynamic on the space of eigenvectors of the coefficient matrices ( this is a brief overview of our paper @xcite ) . next we show how to generalize this to elementary schlesinger transformations of rank two , which is a new result . in section [ sec : reductions ] we consider two examples of reductions of the elementary schlesinger transformation dynamic . the first example of a difference painlev equation of type d-@xmath38 with the symmetry group @xmath39 was also briefly presented in @xcite , here we go into a lot more detail and show how the choice of good coordinates , which was essentially guessed in @xcite , is really forced on us by the geometric considerations . the next example of a @xmath40 fuchsian system of the _ spectral type _ @xmath41 ( i.e. , with three poles and two double eigenvalues at one pole ) is a first example that we have which has degenerate eigenvalues , and this is a completely new result . finally , we give a brief summary in section [ sec : conclusion ] . part of this work was done when a.d . was visiting t.t . at the tokyo university of marine science and technology and nalini joshi at the university of sydney , and a.d . would like to thank both universities for the stimulating working environment and , together with the university of northern colorado , for the generous travel support .

we present two examples of reductions from the evolution equations describing discrete schlesinger transformations of fuchsian systems to difference painlev equations : difference painlev equation d- with the symmetry group and difference painlev equation d- with the symmetry group . in both cases we describe in detail how to compute their okamoto space of the initial conditions and emphasize the role played by geometry in helping us to understand the structure of the reduction , a choice of a good coordinate system describing the equation , and how to compare it with other instances of equations of the same type .

we present two examples of reductions from the evolution equations describing discrete schlesinger transformations of fuchsian systems to difference painlev equations : difference painlev equation d- with the symmetry group and difference painlev equation d- with the symmetry group . in both cases we describe in detail how to compute their okamoto space of the initial conditions and emphasize the role played by geometry in helping us to understand the structure of the reduction , a choice of a good coordinate system describing the equation , and how to compare it with other instances of equations of the same type .

astro-ph0403103

i

interactions between the interstellar medium ( ism ) of a galaxy and the gas in the intracluster medium ( icm ) are believed to be one of the main processes which drive galaxy evolution in clusters ( gunn & gott 1972 ; poggianti 1999 ; van gorkom 2003 ; koopmann & kenney 2004 ) . gas stripping is likely responsible for the transformation of many cluster spirals into s0 s and sa s , and thus may help cause both the morphology - density relation ( dressler 1980 ) and the butcher - oemler effect ( butcher & oemler 1978 ; dressler etal 1997 ) . ism stripping is also significant for the evolution of the icm , as gas removed from the galaxies enriches the icm with heavy elements . there is widespread indirect evidence for icm - ism stripping in clusters from single dish hi observations which show many hi - deficient galaxies ( e.g. giovanelli & haynes 1983 ; helou etal 1984 ; solanes etal 2002 ) and resolved observations which show truncated hi ( warmels 1988 ; cayatte etal 1990 ) and h@xmath8 gas disks ( koopmann & kenney 1998 ; 2004 ) in spiral galaxies with fairly normal stellar disks . for most of these galaxies , it is not clear whether stripping is active or occurred in the past . there are several examples of cluster galaxies which are likely to be undergoing active icm - ism stripping , including some in virgo ( phookun & mundy 1995 ; vollmer etal 2001b ; yoshida etal 2002 ; tschoke etal 2001 ) , coma ( bravo - alfaro 2000 , 2001 ; vollmer etal 2001a ) and the a1367 clusters ( gavazzi et al . however there are few nearby galaxies which are unambiguously experiencing ram pressure stripping from an icm - ism interaction , and which can be studied with good sensitivity and high resolution . perhaps the clearest and nearest case of a cluster spiral with an ongoing icm - ism interaction is the highly inclined virgo galaxy ngc 4522 . the r - band and h@xmath8 imaging of kenney & koopmann ( 1999 ) revealed an undisturbed stellar disk and a selectively disturbed ism , with extraplanar filaments of ionized gas containing hii regions arising from the edge of a truncated star forming disk . based on the optical data kenney & koopmann conclude that ngc 4522 is experiencing active stripping of its ism by an interaction with the icm . in this paper we present new hi and radio continuum images of ngc 4522 from the very large array ( vla ) , which seem to confirm ongoing icm - ism stripping , and allow some of the details of this process to be studied . with detailed observations of a galaxy experiencing icm - ism stripping we can begin to learn what actually happens in an icm - ism interaction , the physics of the interaction , and the consequences for galaxy evolution . is there a shock , can the shock front be identified , and does the shock front partially protect the galaxy ? how does the complex multi - phase ism respond to an interaction with the icm , and what simplifying assumptions are reasonable for modelling ? how do molecular clouds , which may be too dense to strip directly , respond to the icm pressure ? what is the acceleration profile of the stripped gas ? can gas be pushed outwards from the local disk , but still be bound to the halo of the galaxy ? does gas pushed outwards sometimes fall back onto the galaxy ? when does the hi become ionized , and by what mechanism ? is star formation triggered by icm pressure , and if so when and where and under what conditions ? how do the rates of triggered star formation and gas removal by stripping compare ? in this paper , we address some of these issues , using the detailed morphological and kinematic information from the new vla hi data . the paper is organized as follows . in 2 we introduce the galaxy ngc 4522 . in 3 we discuss the observations . in 4 we present the hi data , discuss morphological and kinematic properties of the hi which are likely related to the interaction , and compare the hi with other ism tracers . in 5 we discuss the interpretation of the hi properties in terms of an icm - ism interaction , and compare the observations with simulations and theoretical expectations . we also compare ngc 4522 with other galaxies which are likely experiencing icm - ism interactions . a summary is presented in 6 . radio continuum maps of ngc 4522 are presented in a companion paper by vollmer etal ( 2004 ) .

we present vla hi observations at.5 kpc resolution of the highly inclined , hi - deficient virgo cluster spiral galaxy ngc 4522 , which is one of the clearest and nearest cases of ongoing icm - ism stripping . . forty percent of the total hi , corresponding to 1.5 m , is extraplanar and has likely been removed from the galaxy disk by an icm - ism interaction .

we present vla hi observations at.5 kpc resolution of the highly inclined , hi - deficient virgo cluster spiral galaxy ngc 4522 , which is one of the clearest and nearest cases of ongoing icm - ism stripping . hi is abundant and spatially coincident with the stellar disk in the center , but beyond r = 3 kpc the hi distribution in the disk is sharply truncated and the only hi is extraplanar , and all on the northwest side . forty percent of the total hi , corresponding to 1.5 m , is extraplanar and has likely been removed from the galaxy disk by an icm - ism interaction . the kinematics and the morphology of the hi appear more consistent with ongoing stripping , and less consistent with gas fall - back which may occur long after peak pressure . some of the extraplanar gas has linewidths ( fwzi ) of 150 km s , including a blueshifted tail of weaker emission , and much of the extraplanar gas exhibits a modest net blueshift with respect to the galaxy s disk rotational velocities , consistent with gas accelerated toward the mean cluster velocity . the sw side of the galaxy has less hi in the disk but more hi in the halo , suggesting more effective gas removal on the side of the galaxy which is rotating into the icm wind . in recent simulations of icm - ism interactions , large surface densities of extraplanar gas like that in ngc 4522 are seen at relatively early stages of active stripping , and not during later gas fall - back stages . the galaxy is 3.3 kpc from m87 , somewhat outside the region of strongest cluster x - ray emission . the ram pressure at this location , assuming a static smooth icm and standard values for icm density and galaxy velocity , appears inadequate to cause the observed stripping . we consider the possibility that the ram pressure is significantly stronger than standard values , due to large bulk motions and local density enhancements of the icm gas , which may occur in a dynamic , shock - filled icm experiencing subcluster merging . the hi and h distributions are similar , with both truncated in the disk at the same radius and hii regions located throughout much of the extraplanar hi . this implies that the star - forming molecular ism has been effectively stripped from the outer disk of the galaxy along with the hi . the inferred peak stripping rate of m yr is much larger than the galaxy s total star formation rate of.1 m yr , implying that the rate of triggered star formation due to icm pressure is presently minor compared to the rate of gas lost due to stripping .

astro-ph0403103

c

ngc 4522 is a clear case of ism gas selectively removed from an undisturbed stellar disk . the ism removal from the outer disk , and the existence of hi only on one side of the disk , argue strongly that the ism has been pushed out of the disk by icm - ism pressure , as the galaxy moves through the gas of the virgo intracluster medium . there is evidence that the galaxy is presently experiencing ram pressure ( this paper ; vollmer etal 2004 ) , but it is not clear whether present pressure is strong enough to produce the observed stripping , or whether is it in a post - peak pressure recovery phase with gas infall , as suggested by vollmer etal ( 2000 , 2001 ) . as explained below , the ram pressure required to produce the observed stripping is about an order of magnitude larger than the ram pressure calculated according to standard assumptions . thus either ngc 4522 is in a post - peak pressure phase with gas infall , or it is in an active phase and the ram pressure is significantly higher than the `` standard value '' . there are several recent simulations which show what may happen to spiral galaxies in icm - ism interactions ( abadi 1999 ; quilis 2000 ; vollmer etal 2001 ; schulz & struck 2001 ) . while it can not predict the detailed behavior of gas , a simple ram pressure formula indicates the important parameters , and the simulations indicate this formula yields a good first - order estimate of whether gas is stripped . gunn & gott ( 1972 ) proposed that gas from a galaxy disk is stripped if the ram pressure @xmath24@xmath25v@xmath26 exceeds the gravitational restoring force per unit area @xmath27 , for a face - on encounter . the resistance to stripping depends on galaxy properties including the ism gas surface density @xmath28 , the gravitational force per unit mass @xmath29 = 2@xmath30g@xmath31 , due to the vertical z - gradient in the gravitational potential @xmath32 , and the disk mass surface density @xmath31 , which is dominated by stars . the ram pressure from the icm wind depends on the icm density @xmath24@xmath25 , the velocity of the galaxy with respect to the icm v@xmath25 , and the encounter angle i between the disk and the icm wind direction . simulations suggest stripping rates which vary approximately as cos@xmath33i ( vollmer 2001 ; schulz & struck 2001 ) . the icm wind varies as a galaxy follows its orbital path within the cluster , and the present state of a galaxy depends on this orbital history . of particular importance is the time since ( until ) maximum ram pressure . since many hi - deficient galaxies in clusters have highly radial orbits ( dressler 1986 ; solanes 2001 ) , the ram pressure can vary by factors of 20 - 100 during the orbit ( vollmer etal 2001 ) . gas pushed outwards from the local disk will not necessarily be stripped from the galaxy , since the global gravitational potential ( including bulge , disk , and dark halo ) , is deeper than that from the disk alone . gas pushed outwards from the disk may hang up in the halo , and some of it might fall back into the disk ( schulz & struck 2001 ) , especially in the case of a time variable ram pressure ( vollmer etal 2001 ) . a different approximation for stripping gas from the entire galaxy is that the ram pressure must exceed the force per area from the radial gradient in the gravitational potential @xmath34=v@xmath35@xmath33/r , which includes contributions from all the mass components of the inner galaxy , not only the local disk . this is only an approximation , since for a face - on encounter the ram pressure is in the vertical direction , whereas the gravitational acceleration v@xmath35@xmath33/r is in the radial direction , so it does not strictly correspond to a restoring force . moreover , there is no guarantee that this pressure will accelerate gas to the escape speed v@xmath36=2@xmath37@xmath32@xmath37 , which is at least @xmath38 times larger than the circular speed v@xmath35 = @xmath39 , and includes contributions from mass outside the radius r. so the gunn & gott equation is a mininal stripping condition , but may be most appropriate for the extraplanar hi in ngc 4522 , which we know has been removed from the disk but may not be escaping . the 2 approximations yield similar values for the resistance of ngc 4522 to stripping . the r band surface brightness of ngc 4522 at r=3 kpc , corrected to face - on , is 22.8 mag arcsec@xmath15 ( koopmann etal 2001 ) . if we adopt a modest extinction correction of 0.3 mag , since the outer disk has relatively little gas and dust , then the surface brightness at 3 kpc is 25 l@xmath5 pc @xmath15 , and the stellar mass surface density is 100 m@xmath5 pc@xmath15 , assuming a mass - to - light ratio of 4 . this yields a gravitational force per unit mass in the vertical direction of @xmath29=9@xmath310@xmath23 cm s@xmath15 . this compares with a gravitational force per unit mass in the radial direction of of @xmath34=11@xmath310@xmath23 cm s@xmath15 , assuming a rotation speed of v@xmath35=103 km s@xmath6 at r=3 kpc ( rubin 1999 ) . is the present ram pressure on ngc 4522 sufficient to strip it ? we first assume a standard , smooth , static icm , with a density n@xmath25=@xmath24@xmath25/m@xmath40=10@xmath41 @xmath42 ( 5.2 ) , and a typical virgo galaxy velocity of v@xmath25= 1500 @xmath43 , and a typical gas surface density of @xmath28=10 m@xmath5 pc@xmath15 , and an encounter angle of 45@xmath7 . with these `` standard '' values , which are discussed below , the acceleration due to ram pressure @xmath24@xmath25v@xmath26cos@xmath33i/@xmath28 is 1@xmath310@xmath23 cm s@xmath15 , an order of magnitude less than needed to strip the gas at r=3 kpc in ngc 4522 . either the galaxy must presently be in a post - peak pressure phase , with the extraplanar gas now possibly falling back into the galaxy ( vollmer etal 2000 ) , or the ram pressure must be greater than that predicted from the nominal virgo icm parameters . here we discuss the nominal virgo icm parameters , and in the next section we discuss the possibility that the ram pressure presently experienced by ngc 4522 is significantly higher than the `` standard value '' . ngc 4522 s radial velocity of 2337 @xmath43 is on the high end of the distribution for virgo galaxies , implying that it has a velocity of at least 1300 @xmath43 with respect to the mean cluster velocity of 1050 @xmath43 ( binggeli , popescu , & tammann 1993 ) . there must also be a significant velocity component in the plane of the sky to cause the extraplanar filaments in this nearly edge - on galaxy , although it is unlikely that this component is as large as the extreme l - o - s component . if the plane - of - sky component is 700 @xmath43 , then the total velocity is 1500 @xmath43 , a typical orbital velocity for a virgo cluster galaxy . if the plane - of - sky velocity component is much larger , the galaxy would not be bound to the cluster . although some cluster galaxies could be given large orbital speeds through tidal interactions in merging subclusters , it is highly unlikely that ngc 4522 has an orbital speed as high as the 4000 km s@xmath6 needed to account for the observed stripping . the determination of the plane - of - sky icm motion and the disk encounter angle are coupled , with smaller plane - of - sky icm motions corresponding to more edge - on encounters . the encounter angle in ngc 4522 is likely in the 30 - 60@xmath7 range , since its large line - of - sight velocity and edge - on orientation insure that the encounter angle can not be too close to face - on , and the extraplanar filaments insure that it can not be too close to edge - on . simulations at various encounter angles i by vollmer ( 2001 ) find stripping rates which vary approximately as cos@xmath33i , except that for edge - on encounters the stripping rate is a few percent of the face - on case , rather than zero . simulations by schulz & struck ( 2001 ) show that while the initial ( first 200 myr@xmath01 dynamical time ) stripping rates do vary approximately as cos@xmath33i ( for i=0 - 60@xmath7 ) , the total stripping rates over longer times ( 500 myr ) have a much weaker i dependence , perhaps because viscosity effects become more important than ram pressure on longer timescales ( abadi etal 2001 ) . thus the pressure requirements are minimized for a face - on encounter , and 2 times higher for an encounter angle of 45@xmath7 . while ngc 4522 could be in a post - peak pressure phase , its orbit is not a simple radial orbit . it has an extreme line - of - sight velocity in the cluster , yet its projected location is not close to the center , as it would be if it were on a highly radial orbit bound to the cluster ( vollmer etal 2001 ) . ngc 4522 is one of the galaxies which gives the spirals in virgo a multi - peaked , non - gaussian velocity distribution , which is likely due to infalling galaxies , groups , and subclusters ( huchra 1985 ; schindler etal 1999 ; conselice etal 2001 ; vollmer etal 2001 ) . the galaxies in such systems have not yet reached dynamical equilibrium in the cluster . this is consistent with ngc 4522 being a recent arrival in the cluster . the radio continuum maps show enhanced polarization along the eastern edge ( vollmer etal 2004 ) , suggesting that the galaxy s plane - of - sky motion with respect to the icm is more toward the east than the south , as it would be for a highly radial orbit around m87 . it could be on an orbit whose closest approach to the cluster center brought it to the west of m87 on the near side of the cluster . if the present ram pressure is causing the observed stripping in ngc 4522 , the ram pressure must be stronger than suggested by standard assumptions . the icm gas density could be higher if there are gas lumps or cool gas , and the icm wind velocity could be higher if ngc 4522 has an unbound , high - velocity orbit or if the virgo cluster has bulk icm motions . recent observations ( dupke & bregman 2001 ) and simulations ( e.g. , ricker 1998 ; takizawa 2000 ; roettiger & flores 2000 ) have shown that the icm in many clusters , rather than being smooth and static , is instead shock - filled and dynamic , with bulk speeds of 1-few 1000 km s@xmath6 , due to ongoing subcluster mergers . this can cause significantly higher ram pressure for some of the cluster galaxies . the icm gas density is generally estimated from azimuthally - averaged radial surface brightness profiles of x - ray emission and gas temperature , and the assumption of a locally smooth gas distribution . these assumptions lead to an estimated icm density of n@xmath05@xmath310@xmath44 @xmath42 at a distance of 900 kpc from m87 , which corresponds to 3.3@xmath7 ( fabricant & gorenstein 1983 ) . however , the icm is not radially symmetric in virgo , and there are concentrations of x - ray emission around the giant ellipticals m87 , m86 , and m49 , as well as in a ridge extending between m87 and m49 ( bhringer 1994 ) where ngc 4522 is located ( figure 16 ) . asca x - ray spectroscopy show that icm gas at the western side of this ridge has unusually high temperatures , while the eastern side has temperatures similar to the rest of the cluster ( kikuchi etal 2000 ; shibata etal 2001 ) . thus the surface brightness enhancement of this ridge is due to both a density enhancement and a temperature enhancement , which are themselves probably due to shocks caused by the infall of the m49 sub - cluster toward m87 . the estimated gas density in this ridge region is n@xmath010@xmath41 @xmath42 ( kikuchi etal 2000 ) , which is perhaps a factor of 2 higher than the average value at this distance from m87 . thus ngc 4522 may have recently passed through a region of higher than average icm density in virgo . the hi morphology and radio continuum maps suggest that ngc 4522 s plane - of - sky motion is toward the east or southeast , and figure 16 shows that this direction is roughly away from the ridge of x - ray emission between m49 and m87 . the motions of the icm in virgo are not known , but the region between m49 and m87 , with evidence for icm shocks , could have large - scale icm motions , associated with the m49 sub - cluster merger ( schindler etal 1999 ; shibata etal 2001 ) . bulk icm motions which are comparable to , or larger than , those of the galaxies with respect to the cluster ( dupke & bregman 2001 ) , can increase the relative velocity between some galaxies and the icm by a factor of @xmath02 . shocks can cause local enhancements in gas densities of factors of @xmath02 - 4 . together , these dynamic icm effects can increase the ram pressure p@xmath45@xmath0@xmath24@xmath25v@xmath26 by as much an order of magnitude for some cluster galaxies . this would be enough to cause the observed stripping in ngc 4522 . it is also possible that the mean icm density is higher than that indicated by the x - ray emission , if there are significant amounts of cooler , 10@xmath46 - 10@xmath47 k gas in the cluster . outside of cluster cores , most of the baryons are believed to be in intergalactic gas at these temperatures ( cen & ostriker 1999 ; mathur , weinberg , & chen 2003 ) , and there may be signficant amounts of 10@xmath46 - 10@xmath47 k gas in at least the outskirts of clusters . there are several morphological and kinematic asymmetries in ngc 4522 which provide important clues about its interaction with the icm . in most cluster spirals , the disk encounters the icm wind at an intermediate angle between face - on and edge - on , and this should produce asymmetries in the galaxy , both because there are leading and trailing sides to the disk , and also because one side is rotating into the icm . as explained below , some of the asymmetries in ngc 4522 are naturally understood as the consequences of icm pressure plus rotation . the hi asymmetry in the disk , with relatively weak disk hi emission and a high ratio of extraplanar to disk emission for the sw side , could be naturally explained by gas being preferentially stripped on the sw side . the sw half of the disk is rotating into the oncoming icm , so the icm pressure should be highest on the sw side , and significantly less on the ne side . assuming a galaxy velocity through the icm of 1500 km s@xmath6 , and a rotation velocity of 100 km s@xmath6 , the sw side which is rotating into the oncoming icm , should experience a ram pressure ( 1600/1400)@xmath33=1.3 times stronger than the ne side , which is rotating away from the oncoming icm . this difference is less if the galaxy - icm velocity is significantly higher . the broad lines and the blueshifts could be natually explained by significant ongoing icm pressure , which would push the ism gas to lower , closer to cluster systemic , velocities . is the galaxy experiencing strong icm pressure now , or is it in a recovery phase with gas infall , as suggested by vollmer etal ( 2000 ) ? we have compared the hi morphology and kinematics with those of the n - body , sticky particle simulations of vollmer etal ( 2000 ) , who attempted to match the h@xmath8 data on ngc 4522 available at that time . in their favored simulation , the peak ram pressure occurred 650 myr in the past , and the simulated galaxy is presently experiencing gas infall . there are both similarities and differences between the data and the vollmer etal ( 2000 ) simulation . they have roughly similar radial and z extents of disk and extraplanar hi gas , and in both the ne extraplanar peak is weaker than the sw one . both exhibit an hi surface brightness asymmetry in the disk , although the details differs . the significance of the differences is limited because the simulations show all the gas , whereas the hi data shows only one component of the ism . there are also several features in the data which were not reproduced in the simulations . one key difference is that the amount of extraplanar gas is larger in the data than in the fall - back model . in the data , 40% of the hi is extraplanar , and the peak hi surface density in the extraplanar component is 67% of the peak in the disk . if all the molecular gas is assumed to be in the disk , then the corresponding values for the total gas mass distribution would be @xmath025% and less than 33% , respectively . in the vollmer etal ( 2000 ) model , 15% of the gas is extraplanar , and the peak gas surface density in the extraplanar component is 10% of the peak in the disk . large quantities of extraplanar gas located close to the truncation radius in the disk are generally seen only in early phases of stripping ( vollmer 2001 ; schulz & struck 2001 ) , and not during fall - back phases ( vollmer etal 2000 ; 2001 ) . since the angular momentum of the gas is not conserved , gas pushed outwards by ram pressure will generally not all return to the disk positions from which they originated . another difference in gas morphology concerns the existence in the data of an extraplanar hi surface density peak in the ne as well as the sw , each at a larger radius than the outermost disk emission , and both at the same height above the disk plane . this ne peak does not have a counterpart in the model . there are also significant differences in the kinematics . in the data , much of the extraplanar gas exhibits a blueshift with respect to the nearby disk emission . in particular , the sw extraplanar component is a bit blueshifted in the data , but the model shows similar or even redshifted velocities with respect to nearby disk emission . furthermore , in the data , some of the extraplanar gas has large linewidths , with blueshifted tails , whereas in the model , the extraplanar gas has fairly symmetric spectra and narrower linewidths . the broad lines and the blueshifts could be due to significant ongoing icm pressure . in summary , the vollmer etal ( 2000 ) simulations of ngc 4522 in a post - active stripping phase provide an approximate match to the observed projected radial and vertical extent of gas , but do not match the amount of extraplanar hi , the disk asymmetry , or the kinematics . new simulations by vollmer etal ( in prep ) of ngc 4522 in an active stripping phase with a ram pressure an order of magnitude higher than the `` standard value '' shows a much better match to all these properties . in the nearby virgo cluster , there are a few other galaxies with good evidence for ongoing icm - ism interactions , including ngc 4654 , ngc 4548 , ngc 4388 , and ngc 4569 ( phookun & mundy 1995 ; vollmer 2003 ; vollmer etal 2001b ; yoshida etal 2002 ; vollmer & hutchmeier 2003 ; tschoke etal 2001 ; kenney etal 2004 ) . these galaxies differ from ngc 4522 in the surface density of extraplanar hi , and in the extraplanar gas morphology . none of the other galaxies have a surface density of extraplanar hi as high as ngc 4522 . simulations generally show a high surface density of extraplanar gas only in the early phases of an icm - ism interaction ( vollmer etal 2001 ; schulz & struck 2001 ) . in each of ngc 4548 , ngc 4654 , and ngc 4569 , one extraplanar or outer disk gas arm emerges from the edge of a truncated gas disk . such an ism morphology resembles those in later phases of the simulations of vollmer etal ( 2001 ) and schulz & struck ( 2001 ) , in which a combination of rotation plus icm pressure produces a dominant gas arm in the outer galaxy . the extraplanar gas in ngc 4522 , however , does not have a simple spiral arm morphology , but more of a bow - shock type morphology . in simulations , this type of morphology is seen in earlier phases of the icm - ism interaction , before the arm morphology has time to develop . thus the differences in extraplanar gas density and morphology are both consistent with ngc 4522 being in an earlier phase of an icm - ism interaction than the other galaxies . is there direct evidence for a shock , or strong icm pressure currently on ngc 4522 ? there is enhanced polarized radio continuum emission on the eastern edge of the disk , on the opposite side from the extended extraplanar hi ( vollmer etal 2004 ) . this indicates a compressed magnetic field and probably enhanced icm pressure on this side . the same general region also has the flattest spectral index , indicating local acceleration of relativistic electrons . this suggests the existence of a shockfront . there is presently no optical or x - ray evidence for a shock at the icm - ism interface . deep h@xmath8 images do not show any diffuse emission outside the main body of the galaxy which might be associated with a shockfront ( kenney & koopmann 1999 ) , and ngc 4522 has not been detected as a localized source of x - ray emission ( 4.3 ) . the x - ray emission from an icm - ism interaction is generally expected to be modest compared with the icm x - ray background , since cluster galaxies are not moving highly supersonically in the icm , with expected mach numbers of @xmath01 - 5 ( stevens etal 1999 ; veilleux etal 1999 ) . stevens etal ( 1999 ) simulate an icm - ism interaction for a smooth ism in a spherical galaxy , which differs from the actual , lumpy , star - forming disk ism of a spiral galaxy , but their simulations provide a first - order estimate of the x - ray emission which might be expected in ngc 4522 . model 2c of stevens etal ( 1999 ) , which is the case most similar to ngc 4522 in virgo , predicts l@xmath48@xmath010@xmath49 erg s@xmath6 , assuming an emission region with 5 kpc radius . this is below the level observed by einstein , l@xmath48@xmath501.9@xmath310@xmath49 erg s@xmath6 ( fabbiano etal 1992 ) , but should be detectable with chandra or xmm . most of this x - ray emission is predicted to come from a tail of stripped gas , with much weaker emission arising from the shock front . thus the lack of observed x - ray emission in ngc 4522 is not inconsistent with ongoing icm pressure . more sensitive x - ray observations may provide a more definitive answer , although the weakness of the shock emission , as well as projection effects and confusion with disk emission , may make it difficult to clearly identify a shockfront . the response of a turbulent , multi - phase ism to ram pressure is difficult to assess , but a key question is the fate of molecular clouds , whose high surface densities of @xmath0200 m@xmath5 pc@xmath15 ( larson 1981 ; scoville etal 1987 ; solomon etal 1987 ) make them difficult to strip by ram pressure ( kenney & young 1989 ) . the similarity of the hi and h@xmath8 distributions in ngc 4522 ( 4.3 ) is significant because it implies that the star - forming ism has been effectively removed from the outer galaxy . while the hii regions in the extraplanar gas could have formed within molecular clouds formed in situ from gas that had lower densities when it was stripped , the absence of hii regions beyond the hi truncation radius indicates that even molecular gas has been effectively removed from the outer disk of ngc 4522 . the present result indicates that at least for ngc 4522 , the outer disk has been effectively stripped of all its gas . previous single dish co results indicate that hi deficient cluster galaxies have nearly normal co luminosities ( kenney & young 1989 ; boselli etal 1997 ) . considering the very different radial distributions of molecular and atomic gas in galaxies , with most hi in the outer parts of galaxies and most molecular gas in the inner parts ( e.g. kenney & young 1989 ; young & scoville 1991 ) it could be true that in general that hi deficient galaxies have virtually all the gas removed from their outer disks . thus low resolution observations which measure the global co luminosity are not that sensitive to outer disk molecular gas stripping . this , together with the fact that uncertainties in co deficiency are higher than those for hi deficiency ( boselli etal 1997 ) makes it hard to know whether strongly hi - deficient galaxies might be slightly h@xmath21-deficient . in many sc galaxies the co radial distribution resembles an exponential with a scale length similar to the optical starlight ( young & scoville 1991 ) . the hi stripping radius of 40@xmath1 is 1.33 times ngc 4522 s r - band exponential scale length of 30@xmath1 ( koopmann etal 2001 ) . since the central 1.33 scale lengths of an exponential disk contains 38% of the total flux , a galaxy completely stripped beyond 1.33 scale lengths would have a ( logarithmic ) co deficiency parameter of 0.4 . since ngc 4522 likely contains extraplanar molecular gas in addition to inner disk gas , its expected co deficiency would be somewhat less than this . the actual co deficiency parameter for ngc 4522 is 0.2 , corresponding to 63% of the average co luminosity for non - cluster spiral galaxies with the same optical diameter , according to the formulae in boselli etal ( 1997 ) . this is consistent with both the expected deficiency and with normalcy , given the large standard deviation of 0.3 ( in logarithmic units ) for the co luminosity of non - cluster spiral galaxies of a given optical size . even if molecular clouds are too dense to be directly and individually stripped , effective stripping of molecular clouds might occur in 3 ways . 1 . gmcs quickly evolve to a lower density state through the natural star formation - ism cycle , at which point they are stripped by ram pressure . the lifetimes of molecular clouds are estimated to be @xmath5110@xmath47 yrs ( larson 2003 ; hartmann 2003 ) , significantly shorter than the orbital and stripping timescales . the low density ism is stripped from around the denser molecular clouds , which are initially left behind , but are then ablated by hydrodynamic ( nulsen 1982 ; quilis etal 2000 ) or other effects . molecular clouds might be tied to the rest of the ism , e.g. by magnetic fields , so that the entire ism is stripped out together . whereas molecular gas in the outer disks of cluster spirals may be effectively stripped , inner galaxy regions could be different , although observationally the situation is unclear . the coma cluster spiral ngc 4848 is a possible although not clearcut case for low density hi stripped from the central part of a galaxy , while leaving , at least temporarily , the molecular gas behind ( vollmer etal 2001 ) . there is also suggestive evidence for high co / hi ratios and hi modest deficiencies in the central regions of globally hi - deficient virgo galaxies ( kenney & young 1989 ) , although because the co / hi ratio depends strongly on internal conditions in the ism , it is not clear that any gas has actually been lost from inner disks . the fate of molecular gas in stripping may depend on factors such as the local h@xmath21/hi ratio , and it may be easier to get effective stripping of molecular clouds if the local ism is hi - dominated . the global m@xmath52/m@xmath53 ratio in ngc 4522 is about 1 , and at the gas truncation radius of 3 kpc , the amount of molecular gas is probably less than the amount of hi . nearly normal co luminosities in hi deficient cluster spirals had been previously proposed to mitigate the impact of hi gas stripping on galaxy evolution ( kenney & young 1989 ; boselli etal 1997 ) . the present results indicate that molecular clouds do not prevent outer disks from being completely stripped of their ism , although they could still help the inner disk ism survive . recent simulations show that in significant ram pressure stripping events , most of the gas is stripped relatively quickly , in less than 10@xmath4 yrs ( abadi 1999 ; quilis 2000 ; vollmer etal 2001 ; schulz & struck 2001 ) , although significant stripping at lower rates may continue for a much longer time . ngc 4522 has lost over 10@xmath23 m@xmath5 of gas , so the peak stripping rate is @xmath010 m@xmath5 yr@xmath6 . the total star formation rate in the galaxy , based on the h@xmath8 luminosity with no extinction correction , is 0.1 m@xmath5 yr@xmath6 ( kenney & koopmann 1999 ) . since the galaxy is highly inclined , there must be a significant extinction correction , but with a global ratio of far - infrared luminosity to optical luminosity l@xmath54/l@xmath55 of 0.5 , the correction is unlikely to be more than a factor of a few . the rate of star formation triggered by the interaction is an unknown fraction of the total star formation rate . thus the peak gas stripping rate is @xmath02 orders of magnitude greater than the present rate of icm - triggered star formation . unless the peak star formation rate is much larger than the present star formation rate , gas loss due to icm pressure strongly dominates triggered star formation due to icm pressure . although the central star formation rate normalized by the optical luminosity is somewhat higher for ngc 4522 than the average for virgo cluster and isolated galaxies , it is within a factor of 2 of the median value for isolated spirals ( kenney & koopmann 1999 ) . the h@xmath8 equivalent width in the central 30% of the disk corresponds to a stellar birthrate parameter , defined as the ratio as the present to the past average star formation rate , of 0.1 - 0.2 , according to the precepts in kennicutt , tamblyn , & congdon ( 1994 ) and boselli etal ( 2001 ) . the lower value is based on the h@xmath8 flux with no extinction correction , and the upper value assumes a factor of 2 extinction correction . in terms of long - term galactic evolution , the outer disk of the galaxy would probably be closer to models which have star formation terminated abruptly in time , rather than a strong starburst followed by termination . however , since the central gas disk will likely survive , the global star formation rate will be reduced but not terminated , and the long - term evolution of the galaxy may resemble models in which the star formation is reduced over long timescales . we have reached the somewhat surprising conclusion that despite ngc 4522 s location somewhat outside the cluster core at 0.8 abell radii , it is an excellent candidate for ongoing strong ram pressure stripping . quite possibly the ongoing merger between the m49 group and virgo proper has stirred up the icm , locally enhancing the ram pressure . this would imply that the impact and reach of the icm is closely related to the dynamical state of the cluster . if this is indeed the case it may help explain a number of phenomena seen in the outskirts of clusters ( van gorkom 2003 ) , such as the hi deficiency seen out to 2 abell radii ( solanes et al 2001 ) , and suppressed star formation rates as far out as 2 r@xmath56 ( balogh et al . 1998 ; gomez et al . 2003 ; lewis et al .

the sw side of the galaxy has less hi in the disk but more hi in the halo , suggesting more effective gas removal on the side of the galaxy which is rotating into the icm wind . in recent simulations of icm - ism interactions , large surface densities of extraplanar gas like that in ngc 4522 are seen at relatively early stages of active stripping , and not during later gas fall - back stages . this implies that the star - forming molecular ism has been effectively stripped from the outer disk of the galaxy along with the hi .

we present vla hi observations at.5 kpc resolution of the highly inclined , hi - deficient virgo cluster spiral galaxy ngc 4522 , which is one of the clearest and nearest cases of ongoing icm - ism stripping . hi is abundant and spatially coincident with the stellar disk in the center , but beyond r = 3 kpc the hi distribution in the disk is sharply truncated and the only hi is extraplanar , and all on the northwest side . forty percent of the total hi , corresponding to 1.5 m , is extraplanar and has likely been removed from the galaxy disk by an icm - ism interaction . the kinematics and the morphology of the hi appear more consistent with ongoing stripping , and less consistent with gas fall - back which may occur long after peak pressure . some of the extraplanar gas has linewidths ( fwzi ) of 150 km s , including a blueshifted tail of weaker emission , and much of the extraplanar gas exhibits a modest net blueshift with respect to the galaxy s disk rotational velocities , consistent with gas accelerated toward the mean cluster velocity . the sw side of the galaxy has less hi in the disk but more hi in the halo , suggesting more effective gas removal on the side of the galaxy which is rotating into the icm wind . in recent simulations of icm - ism interactions , large surface densities of extraplanar gas like that in ngc 4522 are seen at relatively early stages of active stripping , and not during later gas fall - back stages . the galaxy is 3.3 kpc from m87 , somewhat outside the region of strongest cluster x - ray emission . the ram pressure at this location , assuming a static smooth icm and standard values for icm density and galaxy velocity , appears inadequate to cause the observed stripping . we consider the possibility that the ram pressure is significantly stronger than standard values , due to large bulk motions and local density enhancements of the icm gas , which may occur in a dynamic , shock - filled icm experiencing subcluster merging . the hi and h distributions are similar , with both truncated in the disk at the same radius and hii regions located throughout much of the extraplanar hi . this implies that the star - forming molecular ism has been effectively stripped from the outer disk of the galaxy along with the hi . the inferred peak stripping rate of m yr is much larger than the galaxy s total star formation rate of.1 m yr , implying that the rate of triggered star formation due to icm pressure is presently minor compared to the rate of gas lost due to stripping .

astro-ph0403103

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\1 . the virgo cluster sc galaxy ngc 4522 is a clear case of ism gas selectively removed from an undisturbed stellar disk by an icm - ism interaction . the existence of a one - sided distribution of extraplanar gas and an undisturbed stellar disk clearly indicates a non - gravitational external process which has selectively removed ism gas . hi is truncated within the disk at r=3 kpc = 0.4r@xmath11 . 40% of the hi appears to be extraplanar , and all the extraplanar gas is displaced toward one side of the major axis , extending 60@xmath1=5 kpc above the disk plane . the peak surface density of the extraplanar hi is 10 m@xmath5 pc@xmath15 , a high value for extraplanar gas . there is direct evidence for ongoing icm pressure on ngc 4522 from radio continuum maps ( vollmer etal 2004 ) , but it remains unclear whether the present ram pressure is sufficiently strong to to have caused the observed removal of the disk gas , or whether the galaxy may presently be observed some time after peak icm pressure . both the kinematics and the morphology of the hi are more suggestive of ongoing stripping than with gas fall - back which may occur long after peak pressure . the hi content within the disk is asymmetric , with 50% less emission on the sw , high - velocity half of the disk . an opposite asymmetry is observed in the halo , which has more hi in the sw than the ne . this could be due to the stronger icm pressure and enhanced stripping which is expected in the half of the disk which is rotating into the oncoming icm . much of the extraplanar hi exhibits a modest net blueshift with respect to the systemic velocity of the galaxy , consistent with stripped galaxy gas being accelerated toward the mean cluster velocity . extraplanar gas on the sw , high - velocity half of the disk shows large linewidths ( fwzi ) of 150 km s@xmath6 , including a tail of weaker emission extending to lower velocities . we suggest that the lower velocity tails represent gas which is accelerated toward the mean cluster velocity . the galaxy is 3.3@xmath7@xmath2800 kpc from m87 , which is somewhat outside the region of strongest x - ray emission , where the icm gas density is highest . assuming a smooth and static icm , the calculated ram pressure at this location appears inadequate by an order of magnitude to cause the observed stripping . we consider the possibility that in a dynamic , shock - filled icm with bulk motions and local density enhancements , the ram pressure presently on ngc 4522 may be significantly stronger than it would be in smooth , static icm . ngc 4522 has only @xmath025% of the hi expected for a galaxy of its mass , so @xmath075% , or 1.2@xmath310@xmath23 m@xmath5 of hi has presumably been stripped , heated , and ionized . the location and distribution of this gas is not known , but could in principle be traced by its x - ray emission , and if detected would provide evidence about the interaction history of ngc 4522 . . the inferred peak gas stripping rate of @xmath010 m@xmath5 yr@xmath6 is much larger than the galaxy s total star formation rate of @xmath00.1 m@xmath5 yr@xmath6 , implying that the present rate of triggered star formation due to icm pressure is minor compared to the peak rate of gas loss due to icm pressure . \8 . the hi and h@xmath8 distributions in ngc 4522 are similar . both are truncated at r=3 kpc in the disk , and they are coextensive in the extraplanar components . this implies that the star - forming ism , presumably including the molecular gas , has been effectively removed from the galaxy beyond a radius of r=3 kpc . if this result is general , it would indicate that molecular gas does not strongly mitigate the effect of stripping on cluster galaxy evolution . the outer disks of cluster spirals can be stripped clean by ram pressure stripping . in clusters with a denser icm and stronger ram pressure , most of the disk could be completely stripped , transforming spiral galaxies into lenticulars .

the kinematics and the morphology of the hi appear more consistent with ongoing stripping , and less consistent with gas fall - back which may occur long after peak pressure . some of the extraplanar gas has linewidths ( fwzi ) of 150 km s , including a blueshifted tail of weaker emission , and much of the extraplanar gas exhibits a modest net blueshift with respect to the galaxy s disk rotational velocities , consistent with gas accelerated toward the mean cluster velocity . the galaxy is 3.3 kpc from m87 , somewhat outside the region of strongest cluster x - ray emission . the ram pressure at this location , assuming a static smooth icm and standard values for icm density and galaxy velocity , appears inadequate to cause the observed stripping . we consider the possibility that the ram pressure is significantly stronger than standard values , due to large bulk motions and local density enhancements of the icm gas , which may occur in a dynamic , shock - filled icm experiencing subcluster merging . the hi and h distributions are similar , with both truncated in the disk at the same radius and hii regions located throughout much of the extraplanar hi . the inferred peak stripping rate of m yr is much larger than the galaxy s total star formation rate of.1 m yr , implying that the rate of triggered star formation due to icm pressure is presently minor compared to the rate of gas lost due to stripping .

we present vla hi observations at.5 kpc resolution of the highly inclined , hi - deficient virgo cluster spiral galaxy ngc 4522 , which is one of the clearest and nearest cases of ongoing icm - ism stripping . hi is abundant and spatially coincident with the stellar disk in the center , but beyond r = 3 kpc the hi distribution in the disk is sharply truncated and the only hi is extraplanar , and all on the northwest side . forty percent of the total hi , corresponding to 1.5 m , is extraplanar and has likely been removed from the galaxy disk by an icm - ism interaction . the kinematics and the morphology of the hi appear more consistent with ongoing stripping , and less consistent with gas fall - back which may occur long after peak pressure . some of the extraplanar gas has linewidths ( fwzi ) of 150 km s , including a blueshifted tail of weaker emission , and much of the extraplanar gas exhibits a modest net blueshift with respect to the galaxy s disk rotational velocities , consistent with gas accelerated toward the mean cluster velocity . the sw side of the galaxy has less hi in the disk but more hi in the halo , suggesting more effective gas removal on the side of the galaxy which is rotating into the icm wind . in recent simulations of icm - ism interactions , large surface densities of extraplanar gas like that in ngc 4522 are seen at relatively early stages of active stripping , and not during later gas fall - back stages . the galaxy is 3.3 kpc from m87 , somewhat outside the region of strongest cluster x - ray emission . the ram pressure at this location , assuming a static smooth icm and standard values for icm density and galaxy velocity , appears inadequate to cause the observed stripping . we consider the possibility that the ram pressure is significantly stronger than standard values , due to large bulk motions and local density enhancements of the icm gas , which may occur in a dynamic , shock - filled icm experiencing subcluster merging . the hi and h distributions are similar , with both truncated in the disk at the same radius and hii regions located throughout much of the extraplanar hi . this implies that the star - forming molecular ism has been effectively stripped from the outer disk of the galaxy along with the hi . the inferred peak stripping rate of m yr is much larger than the galaxy s total star formation rate of.1 m yr , implying that the rate of triggered star formation due to icm pressure is presently minor compared to the rate of gas lost due to stripping .

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because ngc 5466 resides at high galactic latitude , it suffers little if any reddening . though @xcite found a reddening of @xmath39 from the maps of dust ir emission , we adopted @xmath40 @xcite . for our interests in this paper , the small difference is of small importance . most of the comparisons below between observations and theory are _ relative _ , in which reference points ( like the turnoff ) are used to determine magnitude and/or color shifts . this has the benefit of minimizing the influence of uncertainties in reddening and distance modulus ( see below ) . as for abundances , there is only one high - resolution measurement for a cluster star , and it is for the anomalous cepheid v19 . @xcite find [ fe / h]@xmath41 , while @xcite find [ fe / h]@xmath42 using the same data . typically quoted metallicity values include [ fe / h ] @xmath43 @xcite from photoelectric photometry of integrated light in selected filter bands , and [ fe / h ] @xmath44 , which was derived by @xcite ( ultimately from low - resolution spectral scans by @xcite ) . when converted to the widely - used metallicity scale of @xcite , this becomes [ fe / h ] @xmath45 . more work could certainly be done on the composition of ngc 5466 stars , but the evidence so far points to an abundance [ fe / h ] @xmath46 . though the range in the above quoted metallicity values is relatively large for a globular cluster , the exact value is not critical for our purposes since we will primarily be concerned with _ relative _ comparisons . our photometry does not extend faint enough to derive a new distance modulus from subdwarf fitting to the main sequence . @xcite obtained @xmath47 by calibrating the observed luminosity level of the horizontal branch with the relation @xmath48}+0.80 $ ] and adopting a reddening , @xmath49=0.0 and a metallicity , [ fe / h]=@xmath50 . @xcite determined distance moduli @xmath51 from their zero - age hb estimate , assuming no reddening and metallicity on the @xcite scale . we will consider distance moduli in this range . most previous age estimates of ngc 5466 s age have it older than the recent determination of the age of the universe ( @xmath52 gyr ) obtained by the wilkinson microwave anisotropy probe ( wmap ) team @xcite . recent homogeneous studies of ggc indicate that ngc 5466 is coeval with clusters of similar metallicity @xcite . as a result , we will primarily consider ages in the range of 12 to 13 gyr . the color - magnitude diagrams ( cmds ) for ngc 5466 show well - defined rgb , agb , and hb sequences ( see fig . [ fig411 ] ) , and stars extending from the tip of the rgb down to @xmath53 . fiducial sequences for the ms and lower rgb were determined from the mode of the color distribution of stars in magnitude bins . the sgb position was determined using the magnitude distribution of the stars in color bins . the fiducial line for the rest of the rgb was obtained from the mean color of stars in magnitude bins . the fiducial points are listed in table [ tab34 ] . a comparison of the fiducial points derived for ngc 5466 with theoretical isochrones for a range of ages from the teramo @xcite , victoria - regina @xcite , and yonsei - yale @xcite groups is displayed in figures [ fig412 ] and [ rich ] . the isochrones have been shifted in color and magnitude ( aligning the turnoff colors and the magnitudes of the main sequence point 0.05 mag redder than the turnoff ) according to the technique of @xcite . this has the advantage of removing some of systematic uncertainties associated with the color-@xmath54 transformations . [ in our comparisons , we found that the yonsei - yale models could not match the fiducial line for any reasonable set of input parameters when the transformations of @xcite were used . therefore , we only utilize models using the green , demarque , & king ( 1987 ) transformations . even then , we could not find a match with the slope of the upper giant branch for reasonable metallicities ( [ fe / h ] @xmath55 ) . ] on the whole , the shape of the fiducial matches the models well on the main sequence , subgiant branch , and lower giant branch . neither the teramo nor the victoria - regina models include element diffusion processes , while the yonsei - yale isochrones only include he diffusion . however , differences in @xmath54-color transformations are likely to be the cause of some of the differences seen . the number of stars at a given luminosity in post - main - sequence phases is directly proportional to the lifetime spent at that luminosity . it is well known that the lf of the rgb probes the chemical stratification inside a star because the hydrogen abundance being sampled by the thin hydrogen - fusion shell affects the rate of evolution , and hence star counts on the rgb @xcite . setting aside the short pause at the rgb bump , rgb evolution accelerates in a very regular way that is ultimately related to the structure of degenerate core . the relationship between core mass and radius forces the fusion shell to function at strictly controlled density and temperature conditions , which leads to a relationship between core mass and luminosity . this causes the lf to be particularly sensitive to certain physical details , which we discuss in [ rgbms ] below . [ fig617 ] shows the observed luminosity function compared to theoretical lfs for the labeled values of metallicity , exponent of the initial mass function , and a range of age estimates for ngc 5466 , assuming our preferred distance modulus @xmath56 . the theoretical models were normalized to the observed lf at @xmath57 ( sufficiently faint that stellar evolution effects are minimized ) . the models agree well with the observed lf , implying an age of approximately 12 - 13 gyr . @xcite recently discussed theoretical luminosity functions calculated by different groups . one of the primary differences they noted was in the number of giant stars relative to main sequence stars . in order to show these differences in a parameter - independent way , we follow the method of @xcite . in fig . [ fig619 ] , the theoretical lfs were shifted so that a point on the main sequence 0.05 mag redder than the turnoff color point matched the corresponding point on the cluster fiducial line . the reason for using the point ( @xmath58 ) rather than the msto itself is that the ms has a significant slope and curvature at this point , making it possible to accurately measure the point in both observational data and isochrones @xcite . the theoretical models were normalized to the two bins in the observed lf on either side of the turnoff ( @xmath59 and 20.13 ) . as can be seen , age - related differences between the theoretical lfs nearly disappear when this procedure is applied ( see also @xcite ) . however , when different sets of models are compared , there are small differences in the number of rgb stars relative to ms stars , with the victoria - regina models predicting the smallest number of giants and the yonsei - yale models predicting the largest . to quantify the differences , we computed the ratio of the number of stars on the lower giant branch to the number of stars near the main sequence . @xcite introduced this ratio and showed that it is insensitive to age and heavy - element abundance . for the main sequence population , we used star counts in the two bins on either side of the turnoff ( @xmath60 ) , and for the red giant branch we used the counts in the range @xmath61 . we derived model values from the same magnitude ranges _ relative _ to the @xmath58 point on the main sequence . values are compared in table [ tabrat ] . the error in the observed value is dominated by poisson statistical scatter . the yonsei - yale models are in best agreement with the observations , the victoria - regina models are out of agreement by more than 2 @xmath37 , and the teramo models are in between . it is worth examining the possible causes of this difference both because it may help improve the physics inputs for the models and because red giant stars are some of the largest contributors to the integrated light of old stellar populations . @xcite tabulated most of the main physics inputs for the most widely - used model sets . earlier studies @xcite have shown that the lf - shifting method used above eliminates nearly all sensitivity to model input parameters like mass function , age , convective mixing length , and composition inputs with the exception of helium abundance , which we examine first . older models ( e.g. fig . 9 of ratcliff 1987 , fig . 7 of stetson 1991 , fig . 3 of @xcite ) seem to agree that an increase in _ initial _ helium abundance @xmath62 in non - diffusive models by 0.1 results in an increase in the relative number of stars on the rgb ( more precisely , a reduction in the relative number of main sequence stars ) by about 0.07 - 0.08 in @xmath63 . the teramo models ( @xmath64 ) predict about 12% more giant stars relative to main sequence stars compared to the victoria - regina models ( @xmath65)-element enhancement ( [ @xmath66/fe ] = 0.4 ) than the victoria - regina models ( [ @xmath66/fe ] = 0.3 ) , which would tend to _ reduce _ the number of giants relative to main sequence stars . however , because the relative number of rgb and ms stars is not sensitive to small differences in heavy element abundance , this difference is probably unimportant . ] . this difference corresponds to a shift of 0.05 in @xmath63 , which is about an order of magnitude too large for the helium abundance difference . the yonsei - yale models have the lowest assumed helium abundance ( @xmath67 ) , but are the only set of the three that include helium diffusion . the inclusion of helium diffusion reduces the age derived from the turnoff of a globular cluster by about 10 - 15% @xcite , thanks to the inward motion of helium . according to theoretical models ( e.g. fig . 8 of @xcite ) , diffusion has a small effect on the lfs ( @xmath68 a few times @xmath69 in @xmath63 , increasing for increasing age ) , but it does increase the number of giants relative to ms stars . he diffusion reduces the total core hydrogen fuel supply available to an ms star , but in itself this does not strongly modify the lf , just changes the brightness of the turnoff . this magnitude change is eliminated in our lf shifting procedure . the chemical composition profile left in the star after it leaves the main sequence has a greater impact . diffusion reduces the h abundance in the fusion regions , thereby decreasing the evolutionary timescale . according to the models of @xcite , the changes to the he abundance profile are most considerable immediately below the surface convection zone , and just outside the nuclear fusion regions ( where the composition gradient slows the inward settling of helium ) . however , over most of the star , the changes in @xmath62 are limited to 0.01 - 0.02 . because the core portion of the composition profile is consumed on the subgiant branch , the evolution timescales for giant stars are only affected in a minor way , and the appearance of a deep convection zone on the lower giant branch wipes out most of the effects of diffusion for the upper giant branch evolution . in spite of this , the yonsei - yale models have almost 23% more giants than the victoria - regina models , and more than 9% more giants than the teramo models ( relative to ms stars ) . the lower helium abundance in the yonsei - yale models compared to the other models should partially counteract what effects helium diffusion might have had on the rgb / ms ratio as well . thus , it appears that neither he abundance nor he diffusion can completely explain the differences between the yonsei - yale models and the other groups . we can ask whether the lfs show similar disagreements at other metallicities . @xcite made comparisons between the victoria - regina and yonsei - yale theoretical lfs and observational lfs for the clusters m3 @xcite , m5 @xcite , m12 , and m30 . the overall impression from those comparisons was again that the yonsei - yale models ( having he diffusion ) predict more giant stars relative to main - sequence stars than do the victoria - regina models . in fig . [ otherlfs ] , we compare the lfs for these clusters with the teramo models . the degree of agreement or disagreement can be quantified with number ratios of lower rgb and msto stars , similar to the ones we computed earlier for comparisons with ngc 5466 . our calculations are shown in table [ tabrat ] . as can be seen , uncertainties in the metallicity scale have some effect on the comparisons with the observations . the @xcite scale has higher [ fe / h ] values than the @xcite scale , and thus results in lower number ratios . [ rats ] shows the results of comparing the observed ratios with the models for different [ fe / h ] scales . on the @xcite scale ( right panels ) , the observed values seem to be in agreement to within about @xmath70 for most of the models , with the exception of the the lowest metallicity clusters ( m30 and ngc 5466 ) and the lowest helium abundance ( victoria - regina ) models . on the @xcite scale , the yonsei - yale models have the best overall agreement , although the teramo models only deviate noticeably for the lowest metallicity clusters . the victoria - regina models predict too few giants for all of the clusters . the differences from model to model ( as opposed to models versus observation ) point toward deficiencies elsewhere in the physics or computational algorithms used in the stellar evolution codes . the rgb lf is a robust prediction of the models because there is a strong core mass luminosity relationship : the conditions in the hydrogen fusion shell of the giant are strongly dependent on the structure of the degenerate core and are almost independent of the details of the mass or structure of the envelope . as a result of this , we can focus on factors affecting core structure . ( as a non - standard physics example , @xcite describe the way in which core rotation relieves a giant star of some of the need to support itself by gas pressure , which reduces the core temperature and lengthens the evolutionary timescale . ) because model - to - model differences appear even on the faint end of the giant branch , we can set aside factors that only become important to the structure of the star near the tip of the giant branch [ such as neutrino losses and conductive opacities ; see @xcite , for example ] , even though there are significant theoretical uncertainties in these quantities . nuclear reaction rates in the fusion shell can also be neglected , partly because the uncertainties in the reactions appear to be relatively small @xcite , but also because small changes in the reaction rates require only tiny changes in the shell temperature to get the same energy production . this leads us to examine the equation of state ( eos ) in the core . although the behavior of degenerate electrons is thought to be very well understood , their interactions with nuclei can have a measureable effect on the pressure . particles of like charge tend to cluster together , which modifies the free energy of the gas and reduces the gas pressure for given density and temperature . @xcite looked at the effects of the inclusion of coulomb interactions on giant stars , and their results are corroborated by those of @xcite . they found that for a given core mass the fusion shell temperature was higher when the coulomb interactions were included , which leads to faster processing of hydrogen . thus this is another example ( like core rotation ) where modification of the pressure support of the core affects the evolutionary timescales , which results in changes to the luminosity function . the coulomb corrections to the pressure become more important with increasing density for the core , but are small compared to the contribution of the degenerate electrons . all of the model sets we have considered here incorporate coulomb interactions in some form . the teramo group used the most sophisticated `` eos1 '' version of the freeeos , which incorporates coulomb corrections in a form that matches limits in both the weak ( debye - hckel ) and strong ( once - component plasma ) coulomb interaction limits as well as ( less importantly ) electron exchange interactions . the strong interaction limit is most relevant for giant star cores since the strong interaction parameter @xmath71 where @xmath72 is the rms nuclear charge and @xmath73 is the average internuclear distance . the yonsei - yale group used the opal eos tables @xcite , but falls back on the group s older eos [ e.g. @xcite ] for conditions for high densities and temperatures outside the opal tables . while the most recent opal tables probably contain the most complete physical description of the coulomb effect , the opal tables they used ( y .- c . kim , private communication ) were computed prior to recent improvements to account for relativistic electrons @xcite , and as a result cut off at @xmath74 . the yale eos at higher densities _ only _ includes the coulomb effect in the weak debye - hckel limit , which for the highest densities in the core . the victoria - regina models also use a modified version of the eff eos @xcite , with a correction for coulomb corrections in the weak debye - hckel limit @xcite . the differences in the implementation of the coulomb effect may explain the fact that the teramo models generally predict more giants ( relative to the main sequence ) than the victoria - regina models do . however , the smaller coulomb corrections in the yonsei - yale models would tend to result in fewer giants than the teramo models ( although the effects of helium diffusion work in the opposite direction ) . so , we are unable to completely reconcile the differences in the luminosity functions from the three groups . obviously more detailed study is needed by all of the modelling groups to identify the causes of the differences , but such a study is beyond the scope of this paper . still , we believe that helium diffusion and strong interaction coulomb corrections are physical effects that should be considered first . there is , for example , good evidence from helioseismology for helium diffusion in the sun @xcite , despite the surface convection and meridional flow ( e.g. , @xcite ) . it is expected that helium diffusion should also act in globular cluster stars . a detailed study of the effect of equation of state uncertainties has yet to be done [ see , for example , @xcite for a study of uncertainties in other physical inputs ] . use of freeeos would make a study of equation of state effects most stringent since it appears to be capable of modelling the most sophisticated tabular eos ( opal ) , while also having the flexibility to allow individual bits of the physics to be `` turned off '' . as a final warning about the observations , we should remember the lf of the cluster m10 . @xcite found that unusual variations in numbers of rgb stars at different brightness levels in m10 ( a virtual twin to m12 ) . in particular there seemed to a significant excess in the number of stars near the rgb bump in brightness , while the lower rgb appeared normal ( compared to victoria - regina and yonsei - yale models ) . a similar excess may be present in the rgb lf of m13 @xcite . these kinds of variations can not be explained by the `` global '' physics that should apply to all globular cluster stars . these anomalies point toward fluctuations in the stellar initial mass function or composition - dependent effects . a second feature of the lf presented here is a noticeable rgb bump . typically , the rgb bump appears as a peak in the differential lf and as a change of slope in the cumulative lf ( clf ) . the bump provides a measure of the maximum depth reached by the outer convection zone during first dredge - up since it is the result of a pause in the star s evolution when the shell fusion source begins consuming material of constant , lower helium content @xcite . unfortunately , the number of stars occupying the bump gets smaller and the luminosity of the bump increases as the metallicity of the cluster decreases , making the bump harder to detect in metal - poor clusters . a small peak appears in our differential lf at @xmath75 , and a significant ( @xmath76 ) change in slope occurs at the same position as the peak in the differential lf , as shown in fig . [ fig621 ] . the relative brightness of the bump can be measured by comparing to the @xmath13-magnitude of the hb at the level of the rr lyrae instability strip @xmath77 @xcite . this indicator is a function of the total metallicity and the age of the cluster : an increase in metallicity and/or a decrease in age are accompanied by a decrease in luminosity of the bump @xcite . we find @xmath78 mag , and @xmath79 ( from interpolation between the average magnitudes of non - variable hb stars at the blue and red ends of the rr lyrae instability strip ) , giving @xmath80 . in the compilation of @xcite , a zero - age hb reference point was calculated using the relation @xmath81}^2 + 0.236\mbox{[fe / h]}+0.193 $ ] . @xcite found @xmath82 , which is consistent with the value obtained here ( @xmath83 ) . our value of @xmath84 is considerably lower than tabulated values for other clusters with similar metallicities ( m68 : @xmath85 ; m92 : @xmath86 ; m15 : @xmath87 ) . in a separate compilation , @xcite measured a smaller value @xmath88 for m15 , in better agreement with the value for ngc 5466 . ( the difference is primarily because @xcite measured the bump position to be 0.16 mag fainter than @xcite . ) clearly there is still some need for more precise comparisons of bumps in metal - poors clusters with theory . we believe , however , that the brightness of the bump should ultimately be judged using _ hydrogen - fusing _ stars as references because it avoids any effects of the poorly - understood physical processes ( such as the helium flash and/or mass loss ) associated with the creation of an hb star . using the cluster lf ( as seen in figure [ fig619 ] ) , we again find that the observed rgb bump is fainter than model values by at least 0.3 mag when the models are shifted to match the cluster s main sequence . @xcite did similar comparisons between theoretical models and luminosity functions for m3 , m5 , m12 , and m30 taken from the literature . with the exception of m30 ( because the bump could not be identified ) , the position of the bump relative to the turnoff region agreed well with theory . ngc 5466 is thus the most metal - poor cluster this comparison has been done for . so at present we are left with the question of whether this might result from the cluster s low metallicity , or whether we have been the unfortunate victims of a fluctuation in the number of giant stars in this low - mass cluster . we therefore encourage the examination of the luminosity function of more massive metal - poor clusters to settle the question . two recent papers @xcite reported the discovery of tidal streams covering many degrees around ngc 5466 in sloan digital sky survey images . @xcite examined the milky way globular clusters and found ngc 5466 to be a cluster that has probably been strongly affected by disk shocking in the recent past . in our examination of the lf , we found a rather low value for the global main sequence mass function slope . the mass function for a cluster is typically expressed as a power law ( @xmath89 ) , where the slope @xmath90 is the standard salpeter value . generally , the present - day power - law index @xmath91 varies from cluster to cluster . the mass function slopes that best fit the upper lf of ngc 5466 around and above the msto have @xmath92 . ( note that the best fit slope does depend on the models being used : the yonsei - yale models require a flatter slope than the victoria - regina and teramo models . ) such a shallow mass function slope is unusual for a metal - poor cluster . for example , the cluster ngc 5053 has similar metallicity , position relative to the galactic center and plane , and density structure , but still has a steep @xmath93 mass function @xcite . @xcite found that mass function slopes in the range of @xmath94 are influenced primarily by the cluster s position in the galaxy , and to some extent by cluster metallicity . based on both of those factors , ngc 5466 should have a larger mass function slope ( @xmath95 according to the multivariate formula in @xcite ) . like other halo clusters , ngc 5466 s orbit is quite eccentric and will take the cluster more than 30 kpc away from the galactic center @xcite , but it is currently on its way back into the halo after two relatively recent passes through the galactic disk . recent losses of low - mass stars may explain the recent identification of strong tidal tails near the cluster by @xcite .

we present wide - field photometry for about 11,500 stars in the low - metallicity cluster ngc 5466 . we have detected the red giant branch bump for the first time , although it is at least 0.2 mag fainter than expected relative to the turnoff . the number of red giants ( relative to main sequence turnoff stars ) is in excellent agreement with stellar models from the yonsei - yale and teramo groups , and slightly high compared to victoria - regina models . ngc 5466 also has an unusually low central density compared to clusters of similar luminosity . in spite of this , the specific frequency of blue stragglers that puts it right on the frequency

we present wide - field photometry for about 11,500 stars in the low - metallicity cluster ngc 5466 . we have detected the red giant branch bump for the first time , although it is at least 0.2 mag fainter than expected relative to the turnoff . the number of red giants ( relative to main sequence turnoff stars ) is in excellent agreement with stellar models from the yonsei - yale and teramo groups , and slightly high compared to victoria - regina models . this adds to evidence that an abnormally large ratio of red giant to main - sequence stars is not correlated with cluster metallicity . we discuss theoretical predictions from different research groups and find that the inclusion or exclusion of helium diffusion and strong limit coulomb interactions may be partly responsible . we also examine indicators of dynamical history : the mass function exponent and the blue straggler frequency . ngc 5466 has a very shallow mass function , consistent with large mass loss and recently - discovered tidal tails . the blue straggler sample is significantly more centrally concentrated than the hb or rgb stars . we see no evidence of an upturn in the blue straggler frequency at large distances from the center . dynamical friction timescales indicate that the stragglers should be _ more _ concentrated if the cluster s present density structure has existed for most of its history . ngc 5466 also has an unusually low central density compared to clusters of similar luminosity . in spite of this , the specific frequency of blue stragglers that puts it right on the frequency cluster relation observed for other clusters .

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examinations of the luminosity functions of globular clusters continue to produce interesting tests of astrophysics . in this study , we found that ngc 5466 has a luminosity function that is in better overall agreement with theoretical models than the anomalous cluster m30 , which has a similar low metallicity . in addition , we found that the relative numbers of red giant and main sequence stars may produce a fairly sensitive test of the physics near the core of red giants specifically , helium diffusion and coulomb interactions . however , we are not yet able to fully explain the differences between sets of theoretical models . recent discoveries of large tidal tails associated with ngc 5466 suggest that this cluster has been strongly disrupted by interactions with the galaxy . our measured flat ( @xmath117 ) main - sequence luminosity function is unusual for a low - metallicity halo cluster . it is , however , consistent with the emerging picture of mass - segregation followed by tidal stripping . we have thoroughly re - examined the blue straggler population in the cluster , and detected a total of 94 . the radial distribution of stragglers is clearly more centrally concentrated than the rgb and hb populations . the frequency of blue stragglers in the cluster is relatively low consistent with the observed anti - correlation between frequency and cluster luminosity , in spite of the cluster s very low central density . we would like to thank the anonymous referee for helpful comments on the manuscript , y. jeon for providing us with an electronic copy of his photometric dataset , y .- c . kim for information on the yonsei - yale isochrones , and s. cassisi for providing us with access to the teramo set of models . this work has been funded through grants ast 00 - 98696 and 05 - 07785 from the national science foundation to e.l.s . and m.b . adelberger , e. g. , et al . 1998 , rev . 70 , 1265 bahcall , j. n. , pinsonneault , m. h. , & wasserburg , g. j. 1995 , 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2002 , , 576 , 1064 rogers , f. j. , swenson , f. j. , & iglesias , c. a. 1996 , , 456 , 902 rood , r. t. , et al . 1999 , , 523 , 752 rosenberg , a. , aparicio , a. , saviane , i. , & piotto , g. 2000 , , 145 , 451 sabbi , e. , ferraro , f. r. , sills , a. , & rood , r. t. 2004 , , 617 , 1296 salaris , m. , riello , m. , cassisi , s. , & piotto , g. 2004 , , 420 , 911 salaris , m. , & weiss , a.2002 , , 388 , 492 sandage , a. r. 1953 , , 58 , 61 sandquist , e. l. , bolte , m. , langer , g. e. , hesser , j. e. , & mendes de oliveira , c. 1999 , , 158 , 262 sandquist , e. l. , bolte , m. , stetson , p. b. , & hesser , j. e. 1996 , , 470 , 910 sandquist , e. l. 2005 , , 635 , 73 schlegel , d. j. , finkbeiner , d. p. , & davis , m. 1998 , , 500 , 525 searle , l. , & zinn , r. 1978 , , 225 , 357 spergel , d. n. , et al . 2006 , submitted stetson , p. b. 2000 , , 112 , 925 stetson , p. b. 1991 , asp conf . ser . 13 : the formation and evolution of star clusters , 13 , 88 stetson , p. b. 1990 , , 102 , 932 stetson , p. b. 1987 , , 99 , 191 straniero , o. , chieffi , a. , & limongi , m. 1997 , , 490 , 425 vandenberg , d. a. , bergbusch , p. a. , & dowler , p. d. 2006 , , 162 , 375 vandenberg , d. a. , bolte , m. , & stetson , p. b. 1990 , , 100 , 445 vandenberg , d. a. , & clem , j. l. 2003 , , 126 , 778 vandenberg , d. a. , larson , a. m. , & de propris , r. 1998 , , 110 , 98 vandenberg , d. a. , richard , o. , michaud , g. , & richer , j. 2002 , , 571 , 487 vandenberg , d. a. , swenson , f. j. , rogers , f. j. , iglesias , c. a. , & alexander , d. r. 2000 , , 532 , 430 warren , s. r. , sandquist , e. l. , & bolte , m. 2006 , , 648 , 1026 zaggia , s. r. , piotto , g. , & capaccioli , m. 1997 , , 327 , 1004 zoccali , m. , cassisi , s. , piotto , g. , bono , g. , & salaris , m. 1999 , , 518 , l49 zoccali , m. , & piotto , g.2000 , , 358 , 943 zinn , r. & west , m. j. 1984 , , 55 , 45 zinn , r. 1980 , , 241 , 602 rrrrr 1995 may 4 & @xmath23,@xmath13 & 1,1 & 60 & 1.01,1.12 + 1995 may 4 & @xmath23 & 2 & 300 & 1.03 , 1.03 + 1995 may 4 & @xmath23,@xmath13 & 2,1 & 600 & 1.0,1.11,1.0 + 1995 may 5 & @xmath23,@xmath14 & 2,2 & 300 & 1.03,1.01,1.02,1.01 + 1995 may 9 & @xmath23,@xmath13,@xmath14 & 1,1,1 & 60 & 1.12,1.13,1.14 + rrrr 13.532 & 0.5005 & 0.1761 & 0.3010 + 13.832 & @xmath118 & 0.3010 & 1.0000 + 14.132 & @xmath118 & 0.3010 & 1.0000 + 14.432 & 0.5975 & 0.1605 & 0.2575 + 14.732 & 0.8985 & 0.1193 & 0.1651 + 15.032 & 0.6767 & 0.1487 & 0.2279 + 15.332 & 0.6767 & 0.1487 & 0.2279 + 15.632 & 0.5976 & 0.1606 & 0.2575 + 15.932 & 0.8986 & 0.1193 & 0.1651 + 16.232 & 1.2410 & 0.0839 & 0.1041 + 16.532 & 1.0127 & 0.1063 & 0.1411 + 16.832 & 1.0451 & 0.1029 & 0.1351 + 17.132 & 1.3306 & 0.0764 & 0.0928 + 17.432 & 1.4432 & 0.0678 & 0.0804 + 17.732 & 1.4777 & 0.0728 & 0.0876 + 18.032 & 1.6136 & 0.0630 & 0.0738 + 18.332 & 1.7575 & 0.0540 & 0.0617 + 18.632 & 1.7577 & 0.0540 & 0.0617 + 18.932 & 1.9624 & 0.0433 & 0.0481 + 19.232 & 2.2928 & 0.0301 & 0.0324 + 19.532 & 2.5143 & 0.0236 & 0.0249 + 19.832 & 2.6996 & 0.0192 & 0.0201 + 20.132 & 2.7738 & 0.0178 & 0.0185 + 20.432 & 2.8830 & 0.0159 & 0.0165 + 20.732 & 2.9327 & 0.0151 & 0.0157 + 21.032 & 3.0036 & 0.0142 & 0.0146 + 21.332 & 3.0496 & 0.0137 & 0.0142 + 21.632 & 3.1179 & 0.0132 & 0.0136 + rrr 22.198 & 0.578 & 518 + 21.999 & 0.564 & 598 + 21.798 & 0.549 & 724 + 21.596 & 0.532 & 710 + 21.398 & 0.498 & 673 + 21.200 & 0.470 & 670 + 21.004 & 0.459 & 653 + 20.802 & 0.450 & 614 + 20.600 & 0.431 & 568 + 20.400 & 0.418 & 546 + 20.199 & 0.404 & 470 + 20.001 & 0.395 & 453 + 19.805 & 0.396 & 382 + 19.599 & 0.403 & 273 + 19.400 & 0.436 & 235 + 19.206 & 0.495 & 155 + 19.005 & 0.543 & 84 + 18.823 & 0.586 & 70 + 18.588 & 0.607 & 43 + 18.401 & 0.616 & 52 + 18.204 & 0.621 & 40 + 17.989 & 0.636 & 34 + 17.820 & 0.647 & 31 + 17.586 & 0.654 & 23 + 17.403 & 0.672 & 20 + 17.194 & 0.677 & 19 + 16.988 & 0.693 & 11 + 16.784 & 0.722 & 10 + 16.613 & 0.725 & 6 + 16.400 & 0.752 & 12 + 16.199 & 0.771 & 16 + 16.066 & 0.779 & 5 + 15.825 & 0.809 & 7 + 15.602 & 0.827 & 4 + 15.407 & 0.857 & 6 + 15.111 & 0.917 & 1 + 15.006 & 0.930 & 5 + 14.786 & 0.946 & 2 + 14.590 & 0.986 & 11 + 14.438 & 1.044 & 2 + lcclll ngc 5466 & @xmath60 & @xmath119 & & @xmath120 & + vr & & & 0.235 & 0.132 & @xmath50 + vr & & & 0.235 & 0.130 & @xmath121 + t & & & 0.245 & 0.148 & @xmath50 + t & & & 0.245 & 0.146 & @xmath121 + yy & & & 0.230 & 0.162 & @xmath50 + yy & & & 0.230 & 0.160 & @xmath121 + m3 & @xmath122 & @xmath123 & & @xmath124 & + vr & & & 0.235 & 0.170 & @xmath125 + vr & & & 0.235 & 0.158 & @xmath126 + t & & & 0.246 & 0.181 & @xmath125 + t & & & 0.248 & 0.170 & @xmath126 + yy & & & 0.230 & 0.185 & @xmath125 + yy & & & 0.230 & 0.162 & @xmath126 + m5 & @xmath127 & @xmath128 & & @xmath129 & + vr & & & 0.235 & 0.106 & @xmath130 + vr & & & 0.235 & 0.097 & @xmath131 + t & & & 0.248 & 0.114 & @xmath130 + t & & & 0.251 & 0.106 & @xmath131 + yy & & & 0.230 & 0.119 & @xmath130 + yy & & & 0.230 & 0.105 & @xmath131 + m12 & @xmath132 & @xmath133 & & @xmath134 & + vr & & & 0.235 & 0.144 & @xmath130 + vr & & & 0.235 & 0.118 & @xmath135 + t & & & 0.248 & 0.155 & @xmath130 + t & & & 0.251 & 0.144 & @xmath135 + yy & & & 0.230 & 0.150 & @xmath130 + yy & & & 0.230 & 0.137 & @xmath135 + m30 & @xmath136 & @xmath137 & & @xmath138 & + vr & & & 0.235 & 0.174 & @xmath139 + vr & & & 0.235 & 0.153 & @xmath140 + t & & & 0.245 & 0.173 & @xmath139 + t & & & 0.246 & 0.165 & @xmath140 + yy & & & 0.230 & 0.194 & @xmath139 + yy & & & 0.230 & 0.180 & @xmath140 + rrrrrrrrrrcl + 1 & 137.74 & 32.86 & 19.1477 & & 19.0038 & & & & 605 & j & + 1 & 137.74 & 32.86 & 19.1446 & 0.0122 & 19.0182 & 0.0280 & 18.7606 & 0.0400 & 809 & k & + 2 & @xmath141 & @xmath142 & & & 18.7591 & 0.0116 & 18.5972 & 0.0061 & 10313 & c & + 2 & @xmath141 & @xmath142 & 18.8461 & 0.0147 & 18.7209 & 0.0258 & 18.6245 & 0.0504 & 2176 & k & + 3 & @xmath143 & 14.99 & & & 19.1710 & 0.0100 & 18.9595 & 0.0059 & 9339 & c & sx phe ( 3 ) + 3 & @xmath143 & 14.99 & 19.4373 & 0.0155 & 19.2441 & 0.0296 & 19.1073 & 0.0563 & 2129 & k & + 4 & @xmath144 & 83.56 & 19.2057 & & 19.0546 & & & & 646 & j & + 4 & @xmath144 & 83.56 & 19.2266 & 0.0123 & 19.0548 & 0.0256 & 18.8465 & 0.0460 & 2880 & k & + 5 & @xmath145 & 65.06 & 18.5511 & & 18.2697 & & & & 389 & j & + 5 & @xmath145 & 65.06 & 18.5632 & 0.0121 & 18.2740 & 0.0243 & 17.8309 & 0.0255 & 2895 & k & + 7 & @xmath146 & @xmath147 & 18.8010 & & 18.7046 & & & & 504 & j & + 7 & @xmath146 & @xmath147 & 18.8482 & 0.0113 & 18.7379 & 0.0217 & 18.5538 & 0.0386 & 3289 & k & + 8 & @xmath148 & 3.07 & 18.8436 & & 18.6640 & & & & 498 & j & + 8 & @xmath148 & 3.07 & 18.8726 & 0.0120 & 18.6345 & 0.0234 & 18.3367 & 0.0298 & 3358 & k & + 9 & @xmath149 & 83.38 & 19.1757 & & 19.0256 & & & & 626 & j & + 9 & @xmath149 & 83.38 & 19.1385 & 0.0144 & 18.9711 & 0.0257 & 18.7508 & 0.0387 & 2973 & k & + 10 & @xmath150 & 96.04 & 19.3627 & & 19.1882 & & & & 751 & j & + 10 & @xmath150 & 96.04 & 19.4145 & 0.0139 & 19.2190 & 0.0261 & 18.9077 & 0.0494 & 2520 & k & +

we discuss theoretical predictions from different research groups and find that the inclusion or exclusion of helium diffusion and strong limit coulomb interactions may be partly responsible . ngc 5466 has a very shallow mass function , consistent with large mass loss and recently - discovered tidal tails . the blue straggler sample is significantly more centrally concentrated than the hb or rgb stars .

we present wide - field photometry for about 11,500 stars in the low - metallicity cluster ngc 5466 . we have detected the red giant branch bump for the first time , although it is at least 0.2 mag fainter than expected relative to the turnoff . the number of red giants ( relative to main sequence turnoff stars ) is in excellent agreement with stellar models from the yonsei - yale and teramo groups , and slightly high compared to victoria - regina models . this adds to evidence that an abnormally large ratio of red giant to main - sequence stars is not correlated with cluster metallicity . we discuss theoretical predictions from different research groups and find that the inclusion or exclusion of helium diffusion and strong limit coulomb interactions may be partly responsible . we also examine indicators of dynamical history : the mass function exponent and the blue straggler frequency . ngc 5466 has a very shallow mass function , consistent with large mass loss and recently - discovered tidal tails . the blue straggler sample is significantly more centrally concentrated than the hb or rgb stars . we see no evidence of an upturn in the blue straggler frequency at large distances from the center . dynamical friction timescales indicate that the stragglers should be _ more _ concentrated if the cluster s present density structure has existed for most of its history . ngc 5466 also has an unusually low central density compared to clusters of similar luminosity . in spite of this , the specific frequency of blue stragglers that puts it right on the frequency cluster relation observed for other clusters .

1206.5563

i

in the last decades , the angular momentum of light has received much attention from very diverse areas of physics . from experimental astrophysics proposals for the detection of exotic cosmic objects @xcite to the use of light beams to rotate atoms @xcite , through the exploitation of the infinite number of possible angular momentum values for increasing the capacity of optical communication networks @xcite or developing new concepts in quantum information @xcite . the list of applications is long indeed @xcite . the availability of appropriate theoretical tools for the study of light beams with angular momentum and their interactions with matter is crucial for the development of such a wide and promising range of applications . the current state - of - the - art theoretical framework is based on the separation of angular momentum @xmath0 in its orbital ( @xmath1 ) and spin ( @xmath2 ) components : @xmath3 . in the paraxial approximation the value of the total angular momentum along the optical axis can be split into a term which depends on the azimuthal spatial phase of the field and a term which depends on the polarization @xcite . several efforts have been undertaken to rigorously extend this approach to the non - paraxial regime , but have encountered fundamental difficulties @xcite . strongly non - paraxial tightly focused light fields are the bread and butter of applications where light is made to interact with nano - structures , molecules and atoms . the mechanism of spin to orbit angular momentum conversion ( sam to oam ) , also referred to as spin - orbit interaction , is the explanation of choice for numerically obtained observations in focusing @xcite and remarkable results in scattering experiments @xcite . for example , the presence of optical vortices in tightly focused fields and in scattered fields is explained by conversions between the two types of angular momenta . rigorously speaking , though , the separation between sam and oam can not be made on firm physical grounds . consequently , a conversion between the two quantities is not a fully satisfactory explanation for physical phenomena . the separate consideration of @xmath2 and @xmath1 is known to pose fundamental problems for the electromagnetic field @xcite and its quantum excitations @xcite , @xcite . from the point of view of quantum field theory only the total angular momentum operator is a valid observable property of the photon . even more generally , the strict non - separability is not restricted to photons . for example , it also applies to the electron since only in the non - relativistic limit can the orbital and spin parts of its angular momentum be separately considered @xcite . the fundamental reason for such non - separability is the geometry of rotations of vectors and spinors . such a restriction also applies to rotations of classical electromagnetic fields @xcite . in this article we put forward an alternative theoretical framework for the general and rigorous treatment of the angular momentum of light and its role in light - matter interactions . our approach solves the theoretical difficulties of the current framework , draws its predictive power from symmetry considerations , and can be simply applied in practice . by using it , we discover that the actual physical reason responsible for the presence of optical vortices in tightly focused beams is totally unrelated to the one responsible for the appearance of optical vortices in scattering experiments . in the current state - of - the - art framework , both cases are explained as sam to oam conversion . our proposal is based on total angular momentum and helicity . the role of helicity ( @xmath4 ) in light matter interactions has recently been considered @xcite . the macroscopic maxwell equations have been shown to be invariant under generalized electromagnetic duality transformations , and helicity has been identified as the generator of those transformations . by exploiting this connection , helicity can be used within the powerful formalism of symmetries and conserved quantities for the study of light matter interactions when the approximations implicit in the macroscopic maxwell equations hold @xcite . the use of symmetries and conserved quantities for the study of electromagnetic problems is the paradigm used in this article for the development of its theoretical concepts and their application to practical situations . in section [ sec : context ] we outline the paradigm , mathematical concepts and notation used throughout the paper . in section [ sec : lzsz ] we summarize the different aspects involved in the separation of sam and oam . in section [ sec : framework ] we outline our proposal . first , we discuss the concept of helicity and its associated symmetry and comment on a result from @xcite , which shows that , upon scattering , helicity transforms independently of the geometry of the scatterer . then we show that the combined use of angular momentum and helicity solves the problems associated with the separation of sam and oam in a way that is simpler than the existing theoretical solutions and comment on the practical applicability of our ideas . finally , we establish a relationship between helicity eigenstates and the transverse electric ( te ) and transverse magnetic ( tm ) components of the field . using this relationship we express the conservation law for helicity as a function of the partial scattering matrices in the te - tm basis . this expression becomes useful in the practical application of the framework . in section [ sec : spintoorbit ] we use the developed ideas to revisit the concept of sam to oam conversion in focusing and scattering . we are able to clearly identify the underlying reasons for the presence of optical vortices in focused and scattered fields , which happen to be two totally different physical phenomena connected to the breaking of two independent fundamental symmetries : transverse translational symmetry in focusing and electromagnetic duality in scattering . up to now , the two are explained by sam to oam conversion . during section [ sec : spintoorbit ] , we provide the analytical tools necessary for the practical application of our framework . section [ sec : conc ] contains our conclusions and discussion .

the fundamental problem of spin and orbital angular momentum separability is avoided , predictions are made based on the symmetries of the systems , and the practical application of the concepts is straightforward . finally , the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries : transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering .

we propose a new theoretical and practical framework for the study of light - matter interactions and the angular momentum of light . our proposal is based on helicity , total angular momentum , and the use of symmetries . we compare the new framework to the current treatment , which is based on separately considering spin angular momentum and orbital angular momentum and using the transfer between the two in physical explanations . in our proposal , the fundamental problem of spin and orbital angular momentum separability is avoided , predictions are made based on the symmetries of the systems , and the practical application of the concepts is straightforward . finally , the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries : transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering .

1403.6405

i

the investigation of single - photon properties has experienced an increasing interest over the last years @xcite . one of the reasons has to be sought in the escalating request , in many quantum information and cryptography protocols @xcite , for highly accurate manipulations of spatial and polarization single - photon properties . the most appropriate description of single - photon observables is the subject of an ongoing debate . photon position , in particular , has been considered a controversial concept since t.d . newton and e.p . wigner first stated @xcite that no position operator can be defined in the usual sense for particles with mass @xmath1 . later , a.s . wightman @xcite extended the search for a notion of photon localization based on a projection - valued measure ( pvm ) , again obtaining a negative result . this evidence suggested k. kraus to define the single - photon position observable as a positive- operator valued measure ( povm ) @xcite . after the appearance of k. kraus seminal work , several authors proposed alternative definitions of the photon position povm relying on the theory of quantum estimate @xcite or on explicit models describing actual measurements performed in photocounting experiments @xcite . despite such remarkable achievements , the most appropriate single - photon description remains controversial , since the above approaches were conceived to solve the specific problem of photon localization , and do not appear amenable of an immediate generalization to all other single - photon observables . in particular , the photon spin is another notoriously delicate topic@xcite , often ignored in favor of the more familiar notions of helicity and polarization . a renewed interest , due to recent experimental developments especially concerning quantum cryptography protocols @xcite , for the spin of single photons nevertheless calls for an appropriate and manageable description of such observable , in a common picture with that of position . in the present work , we generalize k. kraus construction of the single - photon position observable , given within g. ludwig s axiomatic formulation of quantum mechanics @xcite , to a formalism in which _ all _ the fundamental single - photon observables are given in a unified way in terms of povms @xcite . following the construction of the single - photon hilbert space given by k. kraus and h. moses @xcite , based on the representation theory of the poincar group for mass @xmath1 and spin @xmath2 particles , given by e. p. wigner @xcite , we interpret the notorious suppression of @xmath0-helicity photon states as a projection from an extended hilbert space onto the single - photon hilbert space . extending k. kraus construction of the single - photon position observable , we show that all single - photon observables are described by povms obtained by applying this projection to pvms defined on the extended hilbert space and mutuated from the well - established quantum description of relativistic massive particles . we provide explicit expressions for the povms describing the joint measurement of spin and momentum , and of spin and position . the results show that momentum and helicity are described by pvms , while spin and position by povms . such difference naturally reflects the well - known@xcite circumstance that povms describe _ unsharp _ observables reflecting either practical limits in the precision of measurements ( in which case povms typically correspond to coarse - grained version of pvms ) or inherent difficulties in realizing a preparation in which the value of an observable is perfectly defined @xcite . in particular , the intrinsic unsharpness of position and spin results from the coupling between momentum and spin introduced by the suppression of @xmath0-helicity states , a specific consequence of the mass @xmath1 and spin @xmath2 of the photon . we finally apply this formalism to assess the increase of the statistical character of single - photon observables naturally brought along by the intrinsic _ unsharpness _ of povms @xcite . for this purpose we investigate preparation uncertainty relations for position and momentum , as well as the spin probability distribution . these quantities are analytically calculated for a broad class of physically meaningful single - photon states , namely gaussian states with definite polarization and projections of gaussian states with definite spin . the reasons behind the choice of gaussian states range from their great theoretical and experimental relevance to the fact that , in the non - relativistic context , they saturate the notorious inequality @xmath3 , identifying themselves as the most suitable candidate to investigate the increment of the statistical character of quantum theory brought into stage by the povms . our results show that the emergence of povms systematically increases the randomness of the outcomes@xcite . in particular , the inequality @xmath3 is saturated only in the limiting case of infinitely sharp states in the momentum space ; for any finite gaussian width , we observe instead an increase in the product @xmath4 , of which we give a fully analytic estimate . we observe a similar increase of randomness in the spin probability distribution . such increment appears to be a manifestation of the unsharpness of position and spin , and of the inherent impossibility of sharply localizing a single photon in a bounded space region @xcite , and of preparing it with definite spin along a spatial direction independent on its momentum @xcite . the paper is organized as follows : in section [ sec : formalism ] the quantum mechanical description of a single free photon is reviewed ; in section [ sec : uncertainty ] the procedure for constructing single - photon observables is delineated and the povms and probability densities of such observables are explicitly given . finally , in section [ sec : results ] , a detailed study of the preparation uncertainty relations for position and momentum and of the spin probability distributions of gaussian states is presented , and conclusions are drawn in section [ sec : conclusions ] .

we propose a procedure for defining all single - photon observables in terms of positive - operator valued measures ( povms ) , in particular spin and position . we identify the suppression of-helicity photon states as a projection from an extended hilbert space onto the physical single - photon hilbert space . we show that all single - photon observables are in general described by povms , obtained by applying this projection to opportune projection - valued measures ( pvms ) , defined on the extended hilbert space . we finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin , exploring single photon gaussian states for several choices of spin and polarization .

we propose a procedure for defining all single - photon observables in terms of positive - operator valued measures ( povms ) , in particular spin and position . we identify the suppression of-helicity photon states as a projection from an extended hilbert space onto the physical single - photon hilbert space . we show that all single - photon observables are in general described by povms , obtained by applying this projection to opportune projection - valued measures ( pvms ) , defined on the extended hilbert space . the povms associated to momentum and helicity reduce to pvms , unlike those associated to position and spin , this fact reflecting the intrinsic unsharpness of these observables . we finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin , exploring single photon gaussian states for several choices of spin and polarization .

0812.1785

i

the last enzyme of the respiratory chain of animal cells and bacteria , cytochrome @xmath0 oxidase ( cco ) , operates as an efficient nanoscale machine converting electron energy into a transmembrane proton electrochemical gradient @xcite . the atp ( adenosine triphosphate ) synthase enzyme uses this energy to synthesize atp molecules serving as the energy currency " of the cell . the process of energy conversion starts when a molecular shuttle , cytochrome @xmath0 , delivers , one by one , high - energy electrons to a dinuclear copper center , cu@xmath1 , located near a positive side ( p@xmath2side ) of the inner mitochondrial membrane ( see fig . 1 ) . in recent time - resolved optical and electrometric studies @xcite of the cco transition from the oxidized ( o ) state to the one - electron reduced form ( e ) , a _ single _ electron is donated to the cu@xmath1 redox center by a laser - activated molecule of ruthenium bispyridyl ( rubipy ) . thereafter , in a few microseconds ( @xmath310 @xmath4s ) , a major part of an electron density ( @xmath370% ) is transferred from the cu@xmath1 center to the low - spin heme @xmath5 ( fe-@xmath5 ) . heme @xmath5 is located within the membrane domain at a distance about 2/3 of the membrane width , @xmath6 , counting from the n - side @xcite . within a time interval of approximately 150 @xmath4s , about 60% of the electron population is transferred from heme @xmath5 to heme @xmath7 ( fe-@xmath7 ) . heme @xmath7 , jointly with the next electron acceptor in line , a copper ion cu@xmath8 , form a binuclear center ( bnc , sites @xmath9 and @xmath10 in fig . 1 ) , serving as an active catalytic site for dioxygen reduction to water . the redox centers @xmath11 @xmath12 and cu@xmath8 , are located approximately at the same distance @xmath13 from the n - side of the membrane as heme @xmath5 . the next phase ( with a time scale of the order of 800 @xmath4s ) is characterized by a complete electron transfer to the copper ion cu@xmath8 . time - resolved measurements @xcite show that the first 10 @xmath4s " phase of the electron transfer process is not accompanied by a proton transfer , but the slowness " of the second 150 @xmath4s " and the third 800 @xmath4s " phases hints to the proton participation during phases . the proton path from the negative side of the membrane ( n - side ) toward the p - side ( for pumped protons ) and toward the binuclear center ( for substrate or chemical " protons ) goes through the residue @xmath14 ( for the @xmath15 enzyme @xcite ) . these residues are located at the end of the so - called d - pathway ( fig . 1 ) . a fraction of the substrate protons can also be delivered to the bnc via an additional k - pathway , which we will not consider here . the proton to be pumped is supposed to move from @xmath14 ( schematically shown as the site @xmath16 " in fig 1 ) to an unknown protonable pumping " site @xmath17 ( likely a heme @xmath7 propionate ) , located above the bnc @xcite , and , thereafter , via an additional protonable site @xmath18 @xcite , to the p - side of the membrane . after a fast reprotonation from the d - channel , the residue @xmath14 can donate a substrate proton to the catalytic site near the bnc ( probably , to an oh@xmath19 ligand of cu@xmath8 @xcite ) . it is assumed @xcite that during the second 150 @xmath4s " phase , the first ( pre - pumped ) proton moves from the residue @xmath14 ( the site d " in fig . 1 ) to the pump site @xmath17 , whereas in the third 800 @xmath4s " phase , the second ( substrate or chemical ) proton populates a catalytic site @xmath20 near the bnc . in the final phase , which occurs in 2.6 ms , the first proton ( in @xmath17 ) is translocated ( via @xmath18 ) to the p - side , which is characterized by a higher electrochemical potential than the n - side of the membrane . as a result of all these processes , two protons are taken from the n - side of the membrane , and one electron is taken from the p - side , and eventually one proton is pumped to the p - side . moreover , one proton and one electron are consumed at the catalytic site to finally produce a water molecule around the bnc . it should be noted that kinetic phases with similar time scales ( @xmath21s@xmath22s@xmath23s ) have been revealed in other cco enzymes at various transition steps between the states of the enzyme @xcite . kinetic data obtained in experiments @xcite reflect important details of the still elusive proton pumping mechanism in cytochrome @xmath0 oxidase . to extract these details and gain a deeper insight into the operating principles of the cco proton pump , it is necessary to compare results of experiments with theoretical predictions . in ref . @xcite , a simplified empirical valence bond ( evb ) effective potential was combined with a modified marcus equation to model time - dependent electron and proton transfers in cco in the range of milliseconds . however , this approach was applied to the single transfer event , not to the sequence of events , and the obtained time scale ( one microsecond ) differs by orders of magnitude from the experimental data ( about 100 microseconds ) . a computational analysis of the cco energetics was presented in refs . @xcite with molecular models reproducing energetic barriers for the proton transfer steps @xcite . the obtained energetic map of the proton and electron pathways in the cco enzyme can be converted into a set of rate constants , which qualitatively explains the kinetics and unidirectionality of the pumping process . however , these studies do not result in a quantitative model of the efficient cco proton pump . moreover , the error range of these semi - microscopic calculations ( @xmath3 2 kcal / mol ) is sometimes higher than the difference between the energy barriers @xcite . kinetic models of the proton pumping process were also discussed in ref . @xcite . within the master equation approach , it was shown that the proton pumping effect can be achieved in a simplified system having one redox and two proton sites and , with a higher efficiency , @xmath24 0.9 , for the design with two redox and two protonable sites , which are electrostatically coupled to each other . however , this work does not contain any predictions for the kinetics of the pumping process in more realistic set - ups , with at least four redox sites ( cu@xmath1 , heme @xmath5 , heme @xmath7 , and cu@xmath8 ) and two protonable sites ( a residue @xmath14 and a pump site @xmath17 ) . to find proper parameters for the proton pump , the authors of ref . @xcite resort to a monte carlo search in a multidimensional parameter space . it is hard to imagine , however , that a random search can provide a reasonable set of parameters which will comply with all physical restrictions of real pumps . in general , for comprehensive theoretical studies , it is preferable to determine the relevant parameters of the system using detailed microscopic calculations ( see , e.g. , refs . @xcite ) . however , the huge computational complexity of biological structures makes such an approach extremely difficult . in our paper , we include reasonable estimates for the system parameters into a model describing almost simultaneous electron and proton transfer processes and compare the obtained kinetics to experimentally observed time scales and site populations of cytochrome c oxidase @xcite . the time evolution of the proton pumping process in cco , related to the experimental data of refs . @xcite , was discussed in refs . @xcite . in these works , the kinetics of the electron - proton system is broken down into a cascade of quasi - equilibrium states characterized by distributions of electrons and protons over the sites , as well as by a set of transition rates corresponding to specific kinetic phases . it should be emphasized , however , that many electron and proton transfers can be separated by only a nanosecond time scale , and , consequently , the experimentally observed kinetic rates comprise contributions of several almost - simultaneous individual electron and proton transfer events @xcite . correspondingly , an approach taking into account the kinetic inseparability of electron and proton transitions can be useful for understanding recent experimental findings @xcite . we note that kinetic coefficients used in the theoretical analysis of refs . @xcite were deduced from experiments without independent microscopic calculations of the heights of individual electron and proton barriers . in the present paper , we analyze electron and proton kinetics in cytochrome @xmath0 oxidase within a simple physical model including four redox centers and four protonable sites electrostatically coupled to each other in the presence of a dissipative environment . using the master equation approach , we reproduce all four kinetic phases observed in ref . @xcite for a reasonable set of parameters . it should be emphasized that we have performed extensive numerical studies for a wide range of parameters and we found that our model of proton pumping is quite robust to significant variations of the parameters . the specific set of parameters presented below gives a very good agreement with the experimental data of ref . we consider a single cycle of events , which starts at @xmath25 with one electron transfer to the cu@xmath1 center and finishes at the moment @xmath26 , when the redox site cu@xmath8 is completely reduced . notice that the injection of additional high - energy electrons is necessary to maintain this nonequilibrium state of the cco enzyme . we also determine the efficiency of the proton pumping for our model and its dependencies on the temperature and transmembrane voltage . the rest of paper is structured as follows . our model and its parameters are presented in section ii . results of numerical studies are shown in section iii and discussed in section iv . section v contains the conclusions of our work . the detailed derivation of the master equations and the measurable variables is presented in the appendix . it should be noted that while the results of this paper are obtained in the _ classical _ regime , our approach ( based on quantum transport theory ) can be used to examine fine _ quantum _ effects and , consequently , the detailed derivation is worth presenting here .

we propose a simple model of cytochrome c oxidase , including four redox centers and four protonable sites , to study the time evolution of electrostatically coupled electron and proton transfers initiated by the injection of a single electron into the enzyme . we derive a system of master equations for electron and proton state probabilities and show that an efficient pumping of protons across the membrane can be obtained for a reasonable set of parameters .

we propose a simple model of cytochrome c oxidase , including four redox centers and four protonable sites , to study the time evolution of electrostatically coupled electron and proton transfers initiated by the injection of a single electron into the enzyme . we derive a system of master equations for electron and proton state probabilities and show that an efficient pumping of protons across the membrane can be obtained for a reasonable set of parameters . all four experimentally observed kinetic phases appear naturally from our model . we also calculate the dependence of the pumping efficiency on the transmembrane voltage at different temperatures and discuss a possible mechanism of the redox - driven proton translocation .

cond-mat0703049

i

during the last decade , ultrafast light - induced magnetization dynamics has been a subject of many experimental studies , which have yielded results of interest from both the insight into the basic physical processes occurring in ferromagnets at short time - scales , and from the possible practical implications for ultrafast writing of magnetic memories . the seminal discovery @xcite of sub - picosecond demagnetization in ni has challenged the previously held belief that the fastest time - scale of magnetization dynamics is the spin - lattice relaxation time , which is of the order of at least tens of picoseconds.@xcite since then , such an ultrafast magnetization quenching process in transition metals has been confirmed by various time - resolved magneto - optical techinques @xcite as well al other experimental methods , such as magnetic second harmonic generation,@xcite spin - resolved photoemission,@xcite and thz light emission @xcite . recently , an analogous phenomenon of light - induced demagnetization , including a complete destruction of ferromagnetic order in less than a picosecond , has been observed in ( iii , mn)v ferromagnetic semiconductors.@xcite apart from magnetization quenching , which is caused by absorption of light , there has recently been significant progress in nonthermal ( coherent ) light manipulation of magnetic order . @xcite coherent manipulation on the sub - picosecond time scale has been shown in antiferromagnetic @xcite and ferrimagnetic materials.@xcite theories of coherent manipulation of magnetization by strong off - resonant light have been put forth for ( iii , mn)v ferromagnetic semiconductors @xcite and for closely related undoped paramagnetic ( ii , mn)vi materials.@xcite in this paper we are interested in ultrafast demagnetization , which is an incoherent process involving strong excitation . the laser pulse heats up the carrier population , and we analyze the magnetization dynamics induced by such a hot gas of electrons or holes . ultrafast demagnetization experiments in transition metals were initially interpreted using a phenomenological three - temperature model.@xcite in this approach the system is divided into three reservoirs : carriers , lattice , and spins . excitation by light injects energy into the carrier system . each reservoir is described by its temperature , and phenomenological equations are written down for heat flow between each pair of reservoirs . physical underpinnings and time - scales of two of the couplings , carrier - lattice ( electron - phonon ) and spin - lattice interactions are known ( for the latter see ref . ) . a new ingredient , a direct carrier - spin coupling has to be postulated in order to explain the ultrafast demagnetization . in addition to the lack of detailed microscopic understanding of such carrier - spin coupling , there are two major deficiencies of the three - temperature model . the first is that treating carriers and spins as separate entities might not be a good starting point for the transition - metal itinerant ferromagnets . if such an approach is possible , the nature of an effective separation into subsystems should be elucidated . the second shortcoming is the fact that only the energy transfer between reservoirs is considered . as the key phenomenon to be explained is the change of magnetization , a correct physical description should involve the mechanism by which the angular momentum ( spin and orbital ) is exchanged between the subsystems.@xcite recently,@xcite koopmans et . al . proposed a simplified model of a transition - metal ferromagnet in which spinless electrons induce spin - flips in a magnetic subsystem separate from the electronic system . another proposed theory of demagnetization,@xcite in which the cooperative effect of a coherent laser field and the spin - orbit coupling is calculated , seems to be more suitable for the case of coherent manipulation of antiferromagnets.@xcite a model of ferromagnetism ideally suited for investigation of magnetization quenching induced by excitation of carriers is the sp - d model . in this approach , most of the macroscopic magnetization comes from the localized d - shell spins ( or f shells , in case of the rare earths ) , which are coupled by an exchange interaction to itinerant s or p carriers . this model was introduced independently by zener @xcite and by vonsovskii @xcite in order to describe the transition metals , but was abandoned when the above - mentioned lack of sharp separation into s carriers and d spins was understood . later , the s - d(f ) model was succesfully applied to magnetic semiconductors such as the chalcogenides of europium.@xcite recently , it has been again used in itinerant ferromagnets in order to analyze the situations in which an interplay between the transport and magnetic properties is critical . examples include spin - transfer torque @xcite and an enhancement of gilbert damping in a magnet due to pumping of spin currents into adjacent non - magnetic material.@xcite finally , and most importantly for us , the p - d model is used to describe the basic physics of ferromagnetism in ( iii , mn)v semiconductors,@xcite such as ga@xmath0mn@xmath1as or in@xmath0mn@xmath1as . ferromagnetic ( iii , mn)v semiconductors are created by doping a small ( @xmath25% ) molar fraction of mn into a iii - v semiconductor such as gaas or inas . the mn ions , which substitute the cations , are acceptors and their d shells can be treated as well - localized @xmath3 spins.@xcite hybridization between mn d orbitals and anion p states leads to a kinetic p - d exchange interaction @xcite , which couples localized d spins to spins of p holes in the valence band . these holes are a source of indirect mn - mn spin coupling . at large hole densities ( typically @xmath4@xmath5@xmath6@xmath7 ) a mean - field theory of zener @xcite has been successful in describing many features of ferromagnetism in these materials . it correctly predicts the critical temperature @xmath8 , increasing trend in @xmath8 with the density of carriers , and magnetic anisotropies.@xcite the strong correlation between the presence of the delocalized ( or at least weakly localized ) holes and ferromagnetic ordering of mn spins , has been firmly established experimentally . the optical induction of ferromagnetic transition ( through cw photoinjection of holes ) has been shown,@xcite and the critical temperature and the coercive field have been altered by changing the density of holes in inmnas by applying a gate voltage.@xcite most relevant for this article is the observation of the sub - picosecond light induced demagnetization in inmnas @xcite and gamnas.@xcite a complete quenching of ferromagnetic order was achieved in inmnas for pump fluences above 10 mj/@xmath9 . this should be contrasted with behavior in ni , where the demagnetization saturates at higher fluences while not reaching the complete demagnetization.@xcite since the carrier concentration is much lower in ferromagnetic semiconductors as compared to metals , their magnetization is more amenable to manipulation by external stimuli . these experiments led us to a preliminary investigation of the spin dynamics induced by strong incoherent excitation within the framework of the sp - d model,@xcite and to a proposal of the `` inverse overhauser effect '' as the physical basis of the observed phenomenon . in this scenario , the rate of spin - flip scattering between the localized spins and the mobile carriers is enhanced by the non - equilibrium distribution of excited carriers . this triggers the transfer of angular momentum from the localized spin system to the carriers , leading to demagnetization of the localized spins . for this process to be sustained , the angular momentum transferred into the carriers system has to be efficiently dissipated into the lattice by spin - orbit interaction assisted scattering , and we have stressed that the expected short spin relaxation time of holes in ferromagnetic semiconductor is essential for the explanation of measured changes in magnetization . in this article , we present a detailed theory of ultrafast demagnetization within the sp - d model . we concentrate on ferromagnetic semiconductors , specifically , we discuss photoexcitation processes specific to these materials , and we perform calculations using an effective hamiltonian @xcite model of the spin - split valence band . we assume that the indirect ( carrier - mediated ) exchange interaction between localized spins dominates over short - range antiferromagnetic d - d superexchange ( it has been argued@xcite that in the presence of holes the superexchange is suppressed ) . we also neglect the mn interstitials@xcite which can form antiferromagnetically coupled pairs with nearby substitutional mn spins,@xcite as we are only interested in mn spins which participate in ferromagnetic order . furthermore we work in the regime of strong carrier excitation , in which the carrier mediated mn - mn correlations beyond the mean - field level are averaged out . the localized spins flip independently in the common mean field due to the average carrier spin . we derive the rate equations for their dynamics due to spin - flip scattering with the carriers spins . the transition rates depend on the instantaneous state of the carrier system at a given time . this derivation generalizes to the non - stationary case the theory from ref . , where the heating of mn spins by electrons excited by cw light was considered in a ( ii , mn)vi based quantum well . apart from the localized spin dynamics , we consider the energy and spin relaxation of carriers by means of phenomenological equations . the energy relaxation time of the carriers sets an upper bound for the time - scale of the ultrafast demagnetization process . if the spin relaxation rate of carriers is smaller than the rate at which the angular momentum is injected into the carrier system by sp - d scattering , the demagnetization becomes suppressed . below we show that this `` spin bottleneck '' effect does not affect qualitatively the results in p - type ( iii , mn)v semiconductors . the general results of this article are directly applicable to any system described by analogous s(p)-d(f ) model . however , when the non - carrier - mediated d - d exchange coupling is strong ( e.g. in the europium chalcogenides @xcite ) , the starting point of the calculation should not be the interaction of a single spin with the carriers ( which is our approach here ) , but the enhancement of the carrier - magnon scattering . a similar treatment should be applied to a recent measurement@xcite of the ultrafast demagnetization in gamnas excited with the pump fluence 3 orders of magnitude smaller than in ref . . in this case , our assumption of complete obliteration of the carrier - mediated exchange coupling by excitation of carriers might not hold , and spin - wave modes of coupled mn spins should be the starting point of the calculation . the article is organized as follows : in section [ sec : sp - d ] we introduce the sp - d model . section [ sec : excitation ] contains a discussion of the photoexcitation process , which is followed in section [ sec : bath ] by the description of the model of the carrier bath heated up by absorption of light . section [ sec : derivation ] contains the formalism and the derivations of equations governing the dynamics of localized spins interacting with hot itinerant spins . in section [ sec:1band ] we calculate the process of ultrafast demagnetization using a simplified band structure ( a single spin - split band ) , introduce the equations governing the carrier dynamics , and discuss how the energy and spin relaxation of carriers influences the demagnetization process . complications introduced by valence band - structure of a ferromagnetic semiconductor are discussed in section [ sec : valence ] , where we use a 6 band luttinger hamiltonian to calculate the hole - mn spin - flip transition rate . finally , we discuss the connection to the experiments in section [ sec : comparison ] .

a prominent example of a class of materials falling into this category are ferromagnetic ( iii , mn)v semiconductors , in which ultrafast demagnetization has been recently observed . in the proposed model light excitation this triggers the process of energy and angular momentum exchange between the two spin systems , which lasts for the duration of the energy relaxation of the carriers . we develop a general theory within the sp - d model and we apply it to the ferromagnetic semiconductors , taking into account the valence band structure of these materials .

we propose and analyze a theoretical model of ultrafast light - induced magnetization dynamics in systems of localized spins that are coupled to carriers spins by sp - d exchange interaction . a prominent example of a class of materials falling into this category are ferromagnetic ( iii , mn)v semiconductors , in which ultrafast demagnetization has been recently observed . in the proposed model light excitation heats up the population of carriers , taking it out of equilibrium with the localized spins . this triggers the process of energy and angular momentum exchange between the two spin systems , which lasts for the duration of the energy relaxation of the carriers . we derive the master equation for the density matrix of a localized spin interacting with the hot carriers and couple it with a phenomenological treatment of the carrier dynamics . we develop a general theory within the sp - d model and we apply it to the ferromagnetic semiconductors , taking into account the valence band structure of these materials . we show that the fast spin relaxation of the carriers can sustain the flow of polarization between the localized and itinerant spins leading to significant demagnetization of the localized spin system , observed in ( iii , mn)v materials .

cond-mat0605198

i

ultracold atoms stored in optical lattices can be controlled and manipulated with a very high degree of precision and flexibility . this places them among the most promising candidates for implementing quantum computations @xcite and quantum simulations of certain classes of quantum many body systems @xcite . quantum simulation would allow us to understand physical properties of certain materials at low temperatures that so far have eluded a theoretical description or numerical simulation . however , both quantum simulation and quantum computation with this system face a crucial problem : the temperature in current experiments is too high . in this paper we propose and analyze several methods to decrease the temperature of atoms in optical lattices and thus to reach the interesting regimes in quantum simulations , as well as to prepare defect free registers for quantum computation . so far , several experimental groups have been able to load bosonic or fermionic atoms in optical lattices and reach the strong interaction regime @xcite . the analysis of experiments in the tonks gas regime indicates a temperature of the order of the width of the lowest bloch band @xcite , and for a mott insulator ( mi ) a temperature of the order of the on - site interaction energy has been reported @xcite . for fermions one observes temperatures of the order of the fermi energy @xcite . those temperatures severely restrict the physical phenomena that can be observed and the quantum information tasks that can be carried out with these lattices . one may think of several ways of cooling atoms in optical lattices . since the process of loading atoms into the lattice may lead to additional heating @xcite we focus here on methods that operate once the lattice potential has been raised . for example , one may sympathetically cool the atoms in the lattice using a second bose einstein condensate @xcite . a completely different approach is the _ filtering _ scheme of rabl _ et al . it operates in the no - tunnelling regime , transferring atoms between optical lattices so as to create a configuration with one atom per site . such a loading scheme can , however , originate holes due to imperfections in the original cloud . our analysis of filtering in the presence of a harmonic trap has shown that these holes , which are preferably located at the borders of the cloud , result in a considerable amount of entropy @xcite . here we propose and investigate several cooling schemes which overcome the limitations of filtering . the first set of schemes uses discrete operations to make atoms in different sites interact , thus concentrating the entropy on some atoms which are then expelled from the lattice . due to the similarity with quantum information processing , we term this kind of methods _ algorithmic cooling_. the second set of cooling methods combine filtering with either particle hopping or evaporative cooling techniques . all our cooling protocols are based on translation invariant operations ( i.e. do not require single site addressing ) and consider the residual harmonic confinement present in current experiments . although we will be mostly analyzing their effects on bosonic atoms , they can also be trivially generalized to fermions . this work has several spin - offs . first of all , we have designed algorithms that very efficiently remove all residual defects from a mott insulator , thus producing an ensemble of perfect registers for quantum computing @xcite . second , we propose how to create pointer atoms at the endpoints of a perfect quantum registers and show how these pointers can be used to tailor the register to a specific length . finally , since filtering is an important ingredient of all our algorithms , we have also designed a new incoherent version of filtering procedure which is better adapted to our protocols than the adiabatic scheme from ref . @xcite . the paper is organized as follows . we start in sect . [ init ] describing our system in terms of the bose - hubbard model and discussing the properties of current experimental states , such as densities , temperature and entropy . we also summarize the basic tools and figures of merit which underlie our cooling schemes . [ sect_filtering ] is devoted to a particular tool , filtering . we describe the effect of filtering on the entropy and temperature for realistic initial states and study the optimal choice of experimental parameters . in the last part we propose an implementation of filtering which is similar to a radio - frequency knife . once we have described all tools , in sect . [ sect_gscool ] we introduce several protocols for cooling to the ground state . this includes the algorithmic cooling in subsect . [ algo - cool ] and two other protocols in the following subsections . based on similar ideas , sect . [ sect_qrcool ] presents a quantum protocol that produces an ensemble of defect - free quantum registers and shows how to create pointer atoms on these registers . we conclude this work with some remarks concerning possible variants and combinations of our cooling schemes . in appendix a we present a detailed description of the numerical method that we use to simulate classically correlated states .

we propose and analyze several schemes for cooling bosonic and fermionic atoms in an optical lattice potential close to the ground state of the no tunnelling regime . we also design algorithms that create an ensemble of defect - free quantum registers . we study the efficiency of our protocols for realistic temperatures and in the presence of a harmonic confinement . k = 10000

we propose and analyze several schemes for cooling bosonic and fermionic atoms in an optical lattice potential close to the ground state of the no tunnelling regime . some of the protocols rely on the concept of algorithmic cooling , which combines occupation number filtering with ideas from ensemble quantum computation . we also design algorithms that create an ensemble of defect - free quantum registers . we study the efficiency of our protocols for realistic temperatures and in the presence of a harmonic confinement . we also propose an incoherent physical implementation of filtering which can be operated in a continuous way . k = 10000

1204.3806

r

here we present results for prof model considered on the networks of cambridge and oxford universities in year 2006 , taken from @xcite . the properties of pagerank distribution @xmath50 for these networks have been analyzed in @xcite . the total number of nodes @xmath2 and links @xmath51 are : @xmath52 , @xmath53 ( cambridge ) ; @xmath54 , @xmath55 ( oxford ) @xcite . both networks are characterized by an algebraic decay of pagerank probability @xmath56 and approximately usual exponent value @xmath57 , additional results on the scale - free properties of these networks are given in @xcite . we discuss usually the fraction of red nodes since by definition all other nodes are blue . : left / right column is for cambridge / oxford network . the initial fraction of red colors is @xmath28 ( top panel ) and @xmath31 nodes have red color for bottom panels with @xmath36 and @xmath58 for cambridge and oxford network respectively . nodes are ordered by the pagerank index @xmath32 and color plot shows only @xmath59 . [ fig2],title="fig:",scaledwidth=23.0% ] : left / right column is for cambridge / oxford network . the initial fraction of red colors is @xmath28 ( top panel ) and @xmath31 nodes have red color for bottom panels with @xmath36 and @xmath58 for cambridge and oxford network respectively . nodes are ordered by the pagerank index @xmath32 and color plot shows only @xmath59 . [ fig2],title="fig:",scaledwidth=23.0% ] + : left / right column is for cambridge / oxford network . the initial fraction of red colors is @xmath28 ( top panel ) and @xmath31 nodes have red color for bottom panels with @xmath36 and @xmath58 for cambridge and oxford network respectively . nodes are ordered by the pagerank index @xmath32 and color plot shows only @xmath59 . [ fig2],title="fig:",scaledwidth=23.0% ] : left / right column is for cambridge / oxford network . the initial fraction of red colors is @xmath28 ( top panel ) and @xmath31 nodes have red color for bottom panels with @xmath36 and @xmath58 for cambridge and oxford network respectively . nodes are ordered by the pagerank index @xmath32 and color plot shows only @xmath59 . [ fig2],title="fig:",scaledwidth=23.0% ] -0.2 cm the typical examples of time evolution of fraction of red nodes @xmath30 with the number of time iterations @xmath26 are shown in fig . we see the presence of bistability in the opinion formation : two random states with the same initial fraction of red nodes @xmath60 evolve to two different final fractions of red nodes @xmath61 . the process gives an impression of convergence to a fixed state approximately after @xmath62 iterations . a special check shows that all node colors become fixed after this time @xmath63 . the convergence time to a fixed state is similar to those found for opinion formation on regular lattices where @xmath64 @xcite . the corresponding time evolution of colors is shown in fig . [ fig2 ] for first 10% of nodes ordered by the pagerank index @xmath32 . the results of fig . [ fig1 ] show that for a random initial distribution of colors we may have different final states with @xmath65 variation compared to the initial @xmath28 . however , if we consider that @xmath31 nodes with the top @xmath32 index values ( from @xmath23 to @xmath31 ) have the same opinion ( e.g. red nodes ) then we find that even a small fraction of the total number of nodes @xmath2 ( e.g. @xmath31 of about 0.5% or 1% of @xmath2 ) can impose its opinion for a significant fraction of nodes of about @xmath66 . this shows that in the frame of prof model the society elite , corresponding to top @xmath32 nodes , can significantly influence the opinion of the whole society under the condition that the elite members have the fixed opinion between themselves . we also considered the case when the red nodes are placed on @xmath67 top nodes of cheirank index @xmath68 . this ranking is characterized by the cheirank probability @xmath69 for a random surfer moving in the inverted direction of links as described in @xcite . in average @xmath69 is proportional to the number of outgoing links . however , in this case the top nodes with a small @xmath70 values are not able to impose their opinion and the final fraction becomes blue . we attribute this to the fact that the opinion condition ( [ eq1 ] ) is determined by the pagerank probability @xmath50 and that the correlations between cheirank and pagerank are not very strong ( see discussion in @xcite ) . to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] + to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] + to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] to find a final red fraction @xmath61 , shown in @xmath71axis , in dependence on an initial red fraction @xmath70 , shown in @xmath72 axis ; data are shown inside the unit square @xmath73 . the values of @xmath74 are defined as a relative number of realizations found inside each of @xmath75 cells which cover the whole unit square . here @xmath76 realizations of randomly distributed colors are used to obtained @xmath74 values ; for each realization the time evolution is followed up the convergence time with up to @xmath77 iterations ; here @xmath35 . _ left column : _ cambridge network ; _ right column : _ oxford network ; here @xmath78 from top to bottom . the probability @xmath74 is proportional to color changing from zero ( blue / black ) to unity ( red / gray ) . [ fig3],title="fig:",scaledwidth=23.0% ] -0.2 cm to analyze how the final fraction of red nodes @xmath61 depends on its initial fraction @xmath70 we study the time evolution @xmath30 for a large number @xmath79 of initial random realizations of colors following it up to the convergent time for each realization . we find that the final red nodes are homogeneously distributed in @xmath32 . thus there is no specific preference for top society levels for an initial random distribution . the probability distribution @xmath74 of final fractions @xmath61 is shown in fig . [ fig3 ] as a function of initial fraction @xmath70 at three values of parameter @xmath17 . these results show two main features of the model : a small fraction of red opinion is completely suppressed if @xmath80 and its larger fraction dominates completely for @xmath81 ; there is a bistability phase for the initial opinion range @xmath82 . of course , there is a symmetry in respect to exchange of red and blue colors . for small value @xmath83 we have @xmath84 with @xmath85 while for large value @xmath86 we have @xmath87 , @xmath88 . + 0.7 cm on the tenacious parameter @xmath17 ( or conformist parameter @xmath89 ) for initial red nodes in @xmath36 values of pagerank index ( @xmath33 ) ; black and red(gray ) curves show data for cambridge and oxford networks ; here @xmath35 . [ fig4],scaledwidth=44.0% ] -0.2 cm ( middle panels ) at @xmath90 but with uniform condition for spin flip being independent of pagerank probability ( top panels : @xmath91 in eq . ( [ eq1 ] ) ) and pagerank probability @xmath92 replaced by @xmath93 in eq.([eq1 ] ) ( bottom panels ) ; left and right panels correspond to cambridge and oxford networks ; here @xmath35 and @xmath76 realizations are used . [ fig5],title="fig:",scaledwidth=23.0% ] ( middle panels ) at @xmath90 but with uniform condition for spin flip being independent of pagerank probability ( top panels : @xmath91 in eq . ( [ eq1 ] ) ) and pagerank probability @xmath92 replaced by @xmath93 in eq.([eq1 ] ) ( bottom panels ) ; left and right panels correspond to cambridge and oxford networks ; here @xmath35 and @xmath76 realizations are used . [ fig5],title="fig:",scaledwidth=23.0% ] + ( middle panels ) at @xmath90 but with uniform condition for spin flip being independent of pagerank probability ( top panels : @xmath91 in eq . ( [ eq1 ] ) ) and pagerank probability @xmath92 replaced by @xmath93 in eq.([eq1 ] ) ( bottom panels ) ; left and right panels correspond to cambridge and oxford networks ; here @xmath35 and @xmath76 realizations are used . [ fig5],title="fig:",scaledwidth=23.0% ] ( middle panels ) at @xmath90 but with uniform condition for spin flip being independent of pagerank probability ( top panels : @xmath91 in eq . ( [ eq1 ] ) ) and pagerank probability @xmath92 replaced by @xmath93 in eq.([eq1 ] ) ( bottom panels ) ; left and right panels correspond to cambridge and oxford networks ; here @xmath35 and @xmath76 realizations are used . [ fig5],title="fig:",scaledwidth=23.0% ] -0.2 cm our interpretation of these results is the following . for small values of @xmath94 the opinion of a given society member is determined mainly by the pagerank of neighbors _ to whom he points to _ ( outgoing links ) . the pagerank probability @xmath92 of nodes , on which many nodes point to , is usually high since @xmath92 is proportional to the number of ingoing links @xcite . thus , at @xmath94 a society is composed of members who form their opinion listening an elite opinion . in such a society its elite with one color opinion can impose this opinion to a large fraction of the society . this is illustrated on fig . [ fig4 ] which shows a dependence of final fraction of red @xmath61 nodes on parameter @xmath17 for a small initial fraction of red nodes in the top values of pagerank index ( @xmath36 ) . we see that @xmath95 corresponds to a conformist society which follows in its great majority the opinion of its elite . for @xmath96 this fraction @xmath61 drops significantly showing that this corresponds to a regime of tenacious society . it is somewhat surprising that the tenacious society ( @xmath97 ) has well defined and relatively large fixed opinion phase with a relatively small region of bistability phase . this is in a contrast to the conformist society at @xmath94 when the opinion is strongly influenced by the society elite . we attribute this to the fact that in fig . [ fig3 ] we start with a randomly distributed opinion , due to that the opinion of elite has two fractions of two colors that create a bistable situation since two fractions of society follows opinion of this divided elite that makes the situation bistable on a larger interval of @xmath70 compared to the case of tenacious society at @xmath97 . to stress the important role of pagerank in the dependence of @xmath61 on @xmath70 presented in fig . [ fig3 ] we show in fig . [ fig5 ] the same analysis at @xmath90 but for the case when in eq.([eq1 ] ) for the spin flip we take all @xmath91 ( equal weight for all nodes ) . the data of fig . [ fig5 ] clearly demonstrate that in this case the bistability of opinion disappears . thus the prof model is qualitatively different from the case when only the links without their pagerank weight are counted for the spin flip condition . we also test the sensitivity in respect to pagerank probability replacing @xmath92 by @xmath93 in eq.([eq1 ] ) as it is shown in fig . [ fig5 ] ( bottom panels ) . we see that compared to the case @xmath91 we start to have some signs of bistability but still they remain rather weak compared to the case of fig . [ fig3 ] . ( middle panel ) at @xmath90 but at finite temperature @xmath47 during the relaxation process with @xmath98 ( top panels ) and @xmath99 ( bottom panels ) ; the number of random initial realizations is @xmath100 , the relaxation is done during @xmath101 iterations . left and right columns correspond to cambridge and oxford networks . [ fig6],title="fig:",scaledwidth=23.0% ] ( middle panel ) at @xmath90 but at finite temperature @xmath47 during the relaxation process with @xmath98 ( top panels ) and @xmath99 ( bottom panels ) ; the number of random initial realizations is @xmath100 , the relaxation is done during @xmath101 iterations . left and right columns correspond to cambridge and oxford networks . [ fig6],title="fig:",scaledwidth=23.0% ] + ( middle panel ) at @xmath90 but at finite temperature @xmath47 during the relaxation process with @xmath98 ( top panels ) and @xmath99 ( bottom panels ) ; the number of random initial realizations is @xmath100 , the relaxation is done during @xmath101 iterations . left and right columns correspond to cambridge and oxford networks . [ fig6],title="fig:",scaledwidth=23.0% ] ( middle panel ) at @xmath90 but at finite temperature @xmath47 during the relaxation process with @xmath98 ( top panels ) and @xmath99 ( bottom panels ) ; the number of random initial realizations is @xmath100 , the relaxation is done during @xmath101 iterations . left and right columns correspond to cambridge and oxford networks . [ fig6],title="fig:",scaledwidth=23.0% ] -0.2 cm in fact the spin flip condition ( [ eq1 ] ) can be viewed as a relaxation process in a disordered ferromagnet ( since all @xmath102 in ( [ eq2 ] ) , ( [ eq3 ] ) ) at zero temperature . such type of analysis of voter model relaxation process on regular lattices is analyzed in @xcite . from this view point it is natural to consider the effect of finite temperature @xmath47 on this relaxation . at finite @xmath47 the flip condition is determined by the thermal metropolis probability @xmath103 as described in previous section . we follow this thermodynamic relaxation process at finite temperature up to @xmath101 iterations and in this way obtain the probability distribution of final @xmath61 fraction of red nodes obtained from initial @xmath70 fraction of red nodes randomly distributed over the network at @xmath29 . the results obtained at finite temperatures are shown at fig . they show that a finite temperature @xmath47 allows to have a finite fraction of red nodes @xmath61 when for their small initial fraction @xmath70 all final @xmath61 were equal to zero . also the bistability splitting is reduced and it disappears at larger values of @xmath47 . thus finite @xmath47 introduce a certain smoothing in @xmath74 distribution . over local energies @xmath45 obtained from the relaxation process during @xmath104 time iterations at temperatures @xmath99 ( black curve ) and @xmath105 ( red / gray curve ) ; average is done over @xmath106 random initial realizations . the insets show the distributions on a large scale including all local energies @xmath45 . left and right panels show cambridge and oxford networks . [ fig7],title="fig:",scaledwidth=23.0% ] 0.2 cm over local energies @xmath45 obtained from the relaxation process during @xmath104 time iterations at temperatures @xmath99 ( black curve ) and @xmath105 ( red / gray curve ) ; average is done over @xmath106 random initial realizations . the insets show the distributions on a large scale including all local energies @xmath45 . left and right panels show cambridge and oxford networks . [ fig7],title="fig:",scaledwidth=23.0% ] -0.2 cm however , the relaxation process at finite temperatures does not lead to the thermal boltzmann distribution . indeed , in fig . [ fig7 ] we show the probability distribution @xmath107 as a function of local energies @xmath45 defined in ( [ eq2 ] ) , ( [ eq3 ] ) . the distribution @xmath107 is obtained from the relaxation process with many initial random spin realizations @xmath79 . even if the temperature @xmath47 is comparable with typical values of local energies @xmath45 we still obtain a rather peaked distribution at @xmath108 being very different from the boltzmann distribution . , coded by color from @xmath109 ( black ) to @xmath110 ( blue / dark gray ) , as a function of initial fraction of red nodes @xmath70 and the total initial energy @xmath111 ; each of @xmath112 random realizations is shown by color point ; data are shown after @xmath77 time iterations at @xmath35 . the energy @xmath113 is the modulus of total energy with all spin up ; here @xmath90 . left and right panels show data for cambridge ( @xmath114 ) and oxford ( @xmath115 ) networks ; bars show color attribution to final probability @xmath61 . [ fig8],title="fig:",scaledwidth=23.0% ] , coded by color from @xmath109 ( black ) to @xmath110 ( blue / dark gray ) , as a function of initial fraction of red nodes @xmath70 and the total initial energy @xmath111 ; each of @xmath112 random realizations is shown by color point ; data are shown after @xmath77 time iterations at @xmath35 . the energy @xmath113 is the modulus of total energy with all spin up ; here @xmath90 . left and right panels show data for cambridge ( @xmath114 ) and oxford ( @xmath115 ) networks ; bars show color attribution to final probability @xmath61 . [ fig8],title="fig:",scaledwidth=23.0% ] -0.2 cm we argue that a physical reason of significantly non - boltzmann distribution is related to the local nature of spin flip condition which does not allow to produce a good thermalization on a scale of the whole system . indeed , there are various energetic branches and probably nonlocal thermalization flips of group of spins are required for a better thermalization . however , the voting is a local process that involves only direct neighbors that seems to be not sufficient for emergence of the global thermal distribution . the presence of a few energy branches is well visible from the data of fig . [ fig8 ] obtained at @xmath35 . this figure shows the diagram of final fraction @xmath61 of red nodes in dependence on their initial fraction @xmath70 and the total initial energy @xmath116 of the whole system corresponding to a chosen initial random configuration of spins . most probably , these different branches prevent efficient thermalization of the system with only local spin flip procedure . in addition to the above points the asymmetric form of @xmath40 couplings plays an important role generating more complicated picture compared to the usual image of thermal relaxation ( see e.g. @xcite ) . we also note that the thermalization is absent in voter models on regular lattices @xcite .

we find that the society elite , corresponding to the top pagerank nodes , can impose its opinion to a significant fraction of the society . however , for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation . we find that livejournal and twitter networks have a stronger tendency to a totalitar opinion formation .

we propose the pagerank model of opinion formation and investigate its rich properties on real directed networks of universities of cambridge and oxford , livejournal and twitter . in this model the opinion formation of linked electors is weighted with their pagerank probability . we find that the society elite , corresponding to the top pagerank nodes , can impose its opinion to a significant fraction of the society . however , for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation . we find that livejournal and twitter networks have a stronger tendency to a totalitar opinion formation . we also analyze the sznajd model generalized for scale - free networks with the weighted pagerank vote of electors .

1204.3806

c

in this work we proposed the pagerank model of opinion formation of social networks and analyzed its properties on example of four different networks . for two university networks we find rather similar properties of opinion formation . it is characterized by the important feature according to which the society elite with a fixed opinion can impose it to a significant fraction of the society members which is much larger than the initial elite fraction . however , when the initial opinions of society members , including the elite , are presented by two options then we find a significant range of opinion fraction within a bistability regime . this range depends on the conformist parameter which characterizes the local aspects of opinion formation of linked society members . the generalization of the sznajd model for the scale - free social networks gives interesting examples of opinion formation where finite small size groups can keep their own opinion being different from the main opinion of the majority . in this way the proposed prof - sznajd model shows that the totalitar opinions can be escaped by small sub - communities . we find that the properties of opinion formation are rather similar for the two university networks of cambridge and oxford . however , the results obtained for networks of livejournal and twitter show that the range of bistability practically disappears for these networks . our data indicate that this is related to a slower algebraic decay of pagerank in these cases compared to the university networks . however , the deep reasons of such a difference require a more detailed analysis . indeed , livejournal and twitter networks demonstrate rather different behavior for the @xmath150-weighted function of opinion formation . the studies performed for regular networks @xcite show existence of stable or bistable fixed points for opinion formation models that have certain similarities with the opinion formation properties found in our studies . at the same time the results obtained in @xcite show that three - body spin coupling can generate a chaotic renormalization dynamics . some our results ( fig . [ fig15 ] , right panel ) give indications on a possible existence of such chaotic phase on the social networks . the enormous development of social networks in a few last years @xcite definitely shows that the analysis of opinion formation on such networks requires further investigations . this research can find also various other applications . one of them can be a neuronal network of brain which represents itself a directed scale - free network @xcite . the applications of network science to brain networks is now under a rapid development ( see e.g. @xcite ) and the google matrix methods can find useful applications in this field @xcite . this work is supported in part by the ec fet open project `` new tools and algorithms for directed network analysis '' ( nadine @xmath174 288956 ) . we thank a.benczr and s.vigna for providing us a friendly access to the livejournal database @xcite and the twitter dataset @xcite . zaller , _ the nature and origins of mass opinion _ , cambridge university press , cambridge uk ( 1999 ) . wikipedia , _ livejournal _ , march 9 , 2012 ` http://en.wikipedia.org/wiki/livejournal ` . wikipedia , _ facebook _ , march 9 , 2012 ` http://en.wikipedia.org/wiki/facebook ` . wikipedia , _ twitter _ , march 9 , 2012 ` http://en.wikipedia.org/wiki/twitter ` . wikipedia , _ vk ( social network ) _ , march 9 , 2012 ` http://en.wikipedia.org/wiki/vk\_(social\_network ) ` . s.n . dorogovtsev and j.f.f . mendes , _ evolution of networks _ , oxford univ . press ( 2003 ) . g. caldarelli , _ scale - free networks _ , oxford univ . press ( 2007 ) . s. galam , j. math . psychology * 30 * , 426 ( 1986 ) . liggett , _ stochastic interacting systems : contact , voter and exclusion processes _ , springer , berlin ( 1999 ) . s. galam , europhys . lett . * 70 * , 705 ( 2005 ) . watts and p.s . dodds , j. consumer research * 34(4 ) * , 441 ( 2007 ) . s. galam , int . c * 19 * , 409 ( 2008 ) . c. castellano , s. fortunato , and v. loreto , rev . 81 * , 591 ( 2009 ) p. l. krapivsky , s. redner and e. ben - naim , _ a kinetic view of statistical physics _ , cambridge university press , cambridge uk ( 2010 ) . b. schmittmann and a. mukhopadhyay , phys . e * 82 * , 066104 ( 2010 ) academic web link database project ` http://cybermetrics.wlv.ac.uk/database/ ` m. kurucz , a.a . benczur , a. pereszlenyi , _ large - scale principal component analysis on livejournal friends network _ , . _ workshop on social network mining and analysis _ held in conjunction with _ 13th acm sigkdd international conference on knowledge discovery and data mining ( kdd 2008 ) _ , las vegas nv , august 24 - 27 ( 2008 ) ; ` http://dms.sztaki.hu/en/letoltes/livejournal-data ` h. kwak , c.lee , h. park and s. moon , _ what is twitter , a social network or a news media ? www2010 , p.591 , acm , new york , n.y . ( 2010 ) ; the web data are downloaded from the web site maintained by s.vigna http://law.dsi.unimi.it/webdata/twitter-2010/ s.brin and l.page , _ computer networks and isdn systems _ * 30 * , 107 ( 1998 ) a.m. langville and c.d . meyer c d 2006 _ google s pagerank and beyond : the science of search engine rankings _ , princeton university press , princeton ( 2006 ) s. redner , phys . today * 58(6 ) * , 49 ( 2005 ) . f. radicchi , s. fortunato , b. markines , and a. vespignani , phys . e * 80 * , 056103 ( 2009 ) . west , t.c . bergstrom , and c.t . bergstrom , coll . * 71 * , 236 ( 2010 ) ; ` http://www.eigenfactor.org/ ` f. radicchi , plos one * 6 * , e17249 ( 2011 ) . zhirov , o.v . zhirov and d.l . shepelyansky , eur . j. b * 77 * , 523 ( 2010 ) l. ermann and d.l . shepelyansky , acta phys . polonica a * 120(6a ) * , a158 ( 2011 ) ; `` k. sznajd - weron and j. sznajd , int . j. mod c * 11 * , 1157 ( 2000 ) . frahm , b. georgeot and d.l . shepelyansky , j. phys , a : math . theor . * 44 * , 465101 ( 2011 ) l.ermann , a.d.chepelianskii and d.l.shepelyansky , _ towards two - dimensional search engines _ , arxiv:1106.6215[cs.ir ] ( 2011 ) ; ` http://www.quantware.ups-tlse.fr/qwlib/dvvadi/ ` s. galam and b. walliser , physica a * 389 * , 481 ( 2010 ) . n. metropolis , a.w . rosenbluth , m.n . rosenbluth , a.h.teller , and e. teller , j. chem . * 21 * , 1087 ( 1953 ) . v. sood and s. redner , phys . lett . * 94 * , 178701 ( 2005 ) . ananikian and s.k . dallakian , physica d * 107 * , 75 ( 1997 ) . zipf , _ human behavior and the principle of least effort _ , addison - wesley , boston ( 1949 ) . eguiluz , d.r . chialvo , g.a . cecchi , m. baliki , and a.v . apkarian , phys . lett . * 94 * , 018102 ( 2005 ) . x .- zuo , r. ehmke , m. mennes , d. imperati , f.x . castellanos , o. sporns and m.p . milham , cereb . cortex doi:10.1093/cercor / bhr269 ( 2011 ) . shepelyansky and o.v . zhirov , phys . a * 374 * , 3206 ( 2010 ) .

we propose the pagerank model of opinion formation and investigate its rich properties on real directed networks of universities of cambridge and oxford , livejournal and twitter . in this model we also analyze the sznajd model generalized for scale - free networks with the weighted pagerank vote of electors .

we propose the pagerank model of opinion formation and investigate its rich properties on real directed networks of universities of cambridge and oxford , livejournal and twitter . in this model the opinion formation of linked electors is weighted with their pagerank probability . we find that the society elite , corresponding to the top pagerank nodes , can impose its opinion to a significant fraction of the society . however , for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation . we find that livejournal and twitter networks have a stronger tendency to a totalitar opinion formation . we also analyze the sznajd model generalized for scale - free networks with the weighted pagerank vote of electors .

1504.00547

i

we denote by @xmath0 the space of symmetric tensors on @xmath4 ; such tensors can be identified with homogeneous polynomials of degree @xmath5 in @xmath6 variables , which are also referred to as _ forms_. in this symmetric setting , the most natural tensor rank decomposition is the classical waring decomposition , which expresses a symmetric tensor as a sum of powers of linear forms . precisely , every form @xmath7 has a minimal expression @xmath8 where @xmath9 are linear forms @xcite ; the minimal number of summands @xmath1 is called the symmetric rank of @xmath10 , since in the correspondence between forms and symmetric tensors , powers of linear forms correspond to tensors of rank @xmath11 . a natural question concerns the number of summands required for representing a general form in @xmath12 . this problem is elementary for @xmath13 , which corresponds to the case of symmetric matrices . for @xmath14 , the question was answered by alexander and hirschowitz in @xcite . letting @xmath15 they proved that the general @xmath7 with @xmath16 has rank @xmath17 , which is called the _ generic rank _ , unless the space @xmath12 is one of the so - called defective cases @xmath18 for @xmath19 and @xmath20 , where the generic rank is @xmath21 . when the rank of a waring decomposition is strictly smaller than @xmath22 , we say that this decomposition is of _ subgeneric rank_. it is worth noting that , in our notation , being of _ subgeneric rank _ is not always equivalent to being of _ rank smaller than the one of a general tensor _ , because in the defective cases above a general tensor has rank strictly bigger than @xmath22 . the alexander hirschowitz theorem implies that the generic tensor of subgeneric rank admits only a finite number of alternative waring decompositions @xcite . in this paper , we shall be concerned with proving that the is an element of the @xmath1-secant variety of the veronese variety @xmath23 , which is an irreducible variety @xcite , this terminology is warranted . ] generic tensor of fixed subgeneric rank admits precisely one waring decomposition , modulo permutations of the summands and scaling by @xmath5-roots of unity . more precisely , the main result of this paper is the following theorem . [ thm_main ] let @xmath16 . the general tensor in @xmath0 of subgeneric rank @xmath24 with @xmath22 as in ( [ eqn_exp_rank ] ) has a _ unique _ waring decomposition , i.e. , it is _ identifiable _ , unless it is one of the following cases : 1 . @xmath25 , @xmath26 , and @xmath27 ; 2 . @xmath28 , @xmath29 , and @xmath30 ; 3 . @xmath2 , @xmath31 , and @xmath27 . in all of these exceptional cases , there are exactly two waring decompositions . the three exceptional cases were already known in the literature . the first two cases are classical ; see remark 4.4 in @xcite and remark 6.5 in @xcite . the third case was recently found by ranestad and voisin ; see the proof of lemma 4.3 in @xcite . a uniform treatment of these cases is presented in proposition [ prop : n235 ] . our original contribution establishes that there are no more exceptions to identifiability for cubics . the proof of theorem [ thm_main ] is based on the study of the geometric concepts of _ weak defectivity _ , developed in @xcite , and _ tangentially weak defectivity _ , developed in @xcite . indeed , from this point of view , the theorem can be reformulated in the following way , which is a result of independent interest . [ thm_main2 ] let @xmath16 , @xmath22 as in ( [ eqn_exp_rank ] ) , and @xmath24 . then , the common singular locus of the space of hypersurfaces of degree @xmath5 in @xmath32 that are singular at @xmath1 general points , consists of exactly these @xmath1 points , except in the following cases : 1 . @xmath25 , @xmath26 , and @xmath27 . the unique sextic plane curve singular at @xmath33 general points is a double cubic , so that its singular locus is an elliptic cubic curve ; 2 . @xmath28 , @xmath29 , and @xmath30 . the net of quartic surfaces singular at @xmath34 points consists of reducible quadrics , so that the common singular locus is the base locus of the pencil of quadrics through @xmath34 general points , which is an elliptic normal curve of degree @xmath35 ; 3 . @xmath2 , @xmath31 , and @xmath27 . the common singular locus of the pencil of cubic 4-folds singular at @xmath33 general points is the unique elliptic normal curve of degree @xmath36 through these @xmath33 points . furthermore , the above exceptional cases are the only instances where there exists a unique elliptic normal curve of degree @xmath6 in @xmath32 through @xmath1 general points . in this formulation , the theorem was already partially proved : the case @xmath37 was proved by chiantini and ciliberto @xcite ; for @xmath3 it was proved by ballico ( * ? ? ? * theorem 1.1 ) ; and for @xmath38 with @xmath39 it was proved by mella ( * ? ? ? * theorem 4.1 ) . consequently , the original contribution of this paper concerns the case of cubics , i.e. , @xmath2 , which we solve completely in the subgeneric case . this answers the question posed in remark 4.4 in @xcite . we notice that ballico @xcite proved an even stronger result for @xmath3 . namely , he showed that a general hypersurface of degree @xmath3 in @xmath32 that is singular in @xmath1 general points , is singular only at these @xmath1 points ( except for the exceptional cases ( 1 ) and ( 2 ) of theorem [ thm_main2 ] ) . this is equivalent to showing that the veronese variety @xmath23 is not @xmath1-weakly defective , while our result only says that it is not _ @xmath1-tangentially _ weakly defective . we wonder whether the above list also gives the classification of all @xmath1-weakly defective veronese varieties @xmath23 , even for @xmath2 . symmetric tensors of general rank are not expected to admit only a finite number of waring decompositions , because the expected dimension @xmath40 of the @xmath17-secant variety of the veronese variety @xmath23 may exceed the dimension @xmath41 of the embedding space @xmath12 . therefore , at least a curve s worth of alternative waring decompositions of a general symmetric tensor is anticipated in these cases . however , if @xmath42 is integer , then a general symmetric tensor is still expected to admit only a finite number of waring decompositions . the approach pursued in this paper , i.e. , proving not tangential weak defectivity , can not handle tensors of the generic rank . other approaches need to be considered in this setting . in fact , mella @xcite formulated a conjecture about the cases where the expression in ( [ eq : waring ] ) is still expected to be unique even for general symmetric tensors . in @xcite , further evidence for this conjecture was given ; in addition , the analogous problem for nonsymmetric tensors was also considered . even though the general symmetric tensor is not of subgeneric rank , the setting considered in this paper is nevertheless important in applications where one is mostly interested in the identifiability of symmetric tensors of subgeneric rank . for instance , anandkumar , ge , hsu , kakade , and telgarsky @xcite consider statistical parameter inference algorithms based on decomposing symmetric tensors for a wide class of latent variable models . the identifiability of the waring decomposition then ensures that the recovered parameters , which correspond with the individual symmetric rank-@xmath11 terms in waring s decomposition , are unique , and , thus , admit an interpretation in the application domain . the rank of the waring decomposition , in these applications , is invariably much smaller than the generic rank . as general sources on tensor decomposition , we refer to @xcite . in analogy to theorem [ thm_main ] , we mention that the results in @xcite give broad evidence to the analogous problem in the setting of nonsymmetric tensors , i.e. , that a general nonsymmetric tensor of subgeneric rank admits a unique tensor rank decomposition , unless it is one of the exceptional cases that have already been proved in @xcite . in the proofs by induction of several theorems , we rely on the software macaulay2 @xcite for proving the base cases . the two scripts we used are available as ancillary files in the arxiv submission of this paper . the content of the paper is the following . in section [ sec : newexample ] , we present a uniform treatment of the exceptional cases appearing in theorems [ thm_main ] and [ thm_main2 ] . remark [ rem : genesis ] also discusses our initial motivation for studying the topic of this paper . section [ sec : cubics ] contains the proof of the main theorem . thereafter , the connection between weakly defective varieties and the dual varieties to secant varieties , including a description of the dual varieties of all weakly defective examples appearing in theorem [ thm_main2 ] , is explored in section [ sec : dual ] . in particular , theorem [ thm : dualveronese ] contains the description of cubic hypersurfaces in @xmath43 that can be written as the determinant of a @xmath44 matrix with linear entries . in section [ sec : algorithm ] , we give an explicit criterion allowing to check if a given waring decomposition is unique . this algorithm is an extension to the symmetric case of the one provided in @xcite for general tensors . [ [ acknowledgements ] ] * acknowledgements * + + + + + + + + + + + + + + + + + + we want to thank c. ciliberto , i. domanov , j.m . landsberg , m. mella , l. oeding , k. ranestad and f. russo for useful discussions . in particular , k. ranestad pointed out the use of gale transforms to prove proposition [ prop : n235 ] and informed us about lemma 4.3 of @xcite which contains a proof of the third exceptional case in theorems [ thm_main ] and [ thm_main2 ] . we thank i. domanov for pointing out that improved specific identifiability results can be obtained by considering reshapings of the tensor . the first and second author wish to thank the simons institute for the theory of computing in berkeley , ca for generous support .

we prove that the general symmetric tensor in of rank is identifiable , provided that is smaller than the generic rank . that is , its waring decomposition as a sum of powers of linear forms is unique . only three exceptional cases arise , all of which were known in the literature .

we prove that the general symmetric tensor in of rank is identifiable , provided that is smaller than the generic rank . that is , its waring decomposition as a sum of powers of linear forms is unique . only three exceptional cases arise , all of which were known in the literature . our original contribution regards the case of cubics ( ) , while for we rely on known results on weak defectivity by ballico , ciliberto , chiantini , and mella .

0708.0616

i

potts models on hierarchical lattices have been introduced in 1979 by berker and ostlund @xcite as an interpretation of migdal - kadanoff models , defined in 1975 @xcite in order to approximate classical spin models on @xmath0 . later , in 1981 , griffiths and kaufman @xcite provided a rigorous definition of hierarchical lattices and studied some examples in detail . one of such examples , the diamond hierarchical lattice , was later considered in a paper by derrida , de seze and itzykson @xcite , who showed that the generator of the renormalization group ( see e.g. @xcite ) could be written as a rational map acting on the riemann sphere ; as a consequence , the fisher set of the model coincides with the julia ( i.e. unstable ) set of the renormalization group map . later , similar results were established to study other specific lattices ( e.g @xcite ) or to introduce coupling with an external magnetic field in a similar dynamical framework ( e.g. @xcite ) . + in this paper we generalize the result of @xcite to all hierarchical lattices , i.e. we prove that the generator of the renormalization group of a potts model on a hierarchical lattice can be represented by a rational map acting on a complex multiprojective space ( sections [ hierarchical ] and [ dynproj ] ) . the general approach that we introduce , not only allows to describe all models on hierarchical lattice that have already been studied , but it also provides an extremely natural way to deal with an external magnetic field ( ) . the study of the dynamics obtained by iteration of a rational map in several complex variables is a quite recent research subject and , as such , it is still quite incomplete . nevertheless , recent results by dinh - sibony @xcite allow us to prove that , at least for some class of hierarchical lattices , lee - yang and fisher sets are a subset of the julia set of the renormalization map ( ) . this paper features two technical appendices that give the basic mathematical background needed to understand the statements in the main part and provide references for the interested reader . a number of examples of potts models on hierarchical lattices are presented in @xcite , where it is shown how to obtain both exact and numerical results by using the general methods developed in this paper .

we prove that the generator of the renormalization group of potts models on hierarchical lattices can be represented by a rational map acting on a finite - dimensional product of complex projective spaces . in this framework we can also consider models with an applied external magnetic field and multiple - spin interactions . we use recent results regarding iteration of rational maps in several complex variables to show that , for some class of hierarchical lattices , lee - yang and fisher zeros belong to the unstable set of the renormalization map .

we prove that the generator of the renormalization group of potts models on hierarchical lattices can be represented by a rational map acting on a finite - dimensional product of complex projective spaces . in this framework we can also consider models with an applied external magnetic field and multiple - spin interactions . we use recent results regarding iteration of rational maps in several complex variables to show that , for some class of hierarchical lattices , lee - yang and fisher zeros belong to the unstable set of the renormalization map .

1412.8399

i

a matroid captures the notion of a discrete collection of points in space . sometimes these points can be assigned coordinates in a consistent way , and sometimes they can not . the problem of characterising when a matroid is _ representable _ has been the prime motivating force in matroid research since whitney s founding paper @xcite . plenty of effort has been invested in characterising matroid representability via excluded minors . less attention has been paid to the prospect of characterisating representability via axioms . perhaps this is because of vmos s well - known article @xcite , which has been interpreted as stating that no such characterisation is possible ( see @xcite ) . in @xcite , we pointed out that the possibility of characterising representable matroids in the language of whitney s axioms was still open ; that , in other words , it was still not proved that the missing axiom of matroid theory is lost forever " , _ contra _ vmos s title . we conjectured that in fact there was no such characterisation , and we made some partial progress towards resolving the conjecture by showing that it was impossible to characterise the class of representable matroids , or the class of matroids representable over an infinite field , using a logical language based on the rank function . however , that language imposed quite strong constraints on the form of quantification . in this article , we present a language with no such constraints , and we prove that it is impossible to characterise representability , or representability over an infinite field , in this more natural language . the language that we develop is a form of monadic second - order logic , @xmath0 . as we show in , @xmath0 is expressive enough to state the matroid axioms , and to state when a matroid contains an isomorphic copy of a fixed minor . this means that any minor - closed class of matroids can be characterised with a sentence in @xmath0 , as long as it has a finite number of excluded minors . in particular , since rota s conjecture has been positively resolved by geelen , gerards , and whittle ( see @xcite ) , it follows that the class of @xmath2-representable matroids can be characterised by a sentence in @xmath0 , whenever @xmath2 is a finite field . our main results show that this is not the case for the class of matroids that are representable over at least one field , nor for the class of @xmath1-representable matroids , when @xmath1 is any infinite field . we say that a matroid is _ representable _ if it is representable over at least one field . [ jungle ] there is no sentence , @xmath3 , in @xmath0 , such that a matroid is representable if and only if it satisfies @xmath3 . [ proton ] let @xmath1 be any infinite field . there is no sentence , @xmath4 , in @xmath0 , such that a matroid is @xmath1-representable if and only if it satisfies @xmath4 . these theorems may seem stronger than those in @xcite , but in fact the results are independent of each other . the logical language used in @xcite had constraints on quantification , unlike @xmath0 , but it also had access to the rank function , and to the arithmetic of the integers , while @xmath0 does not . follow easily from the next two lemmas . let @xmath5 be a positive integer . define @xmath6 to be @xmath7 and recursively define @xmath8 to be @xmath9 . let @xmath10 be @xmath11 . thus @xmath10 is @xmath12 where the tower of exponents has height @xmath13 . recall that if @xmath14 and @xmath15 are matroids with disjoint ground sets , then @xmath16 is the _ direct sum _ of @xmath14 and @xmath15 . [ iguana ] let @xmath5 be a positive integer . there is a partition of the set of matroids into blocks , @xmath17 , such that @xmath18 and the following property holds : for any sentence , @xmath3 , in @xmath19 with @xmath5 variables , whenever @xmath14 and @xmath15 are matroids that belong to the same block , then , for any matroid , @xmath20 , either @xmath21 and @xmath22 both satisfy @xmath3 , or neither satisfies @xmath3 . by using , we can easily deduce . assume that there is a sentence , @xmath3 , in @xmath0 , that characterises representable matroids . let @xmath5 be the number of variables in @xmath3 , and let @xmath17 be the partition provided by . because there are infinitely many prime numbers , we can let @xmath23 and @xmath24 be distinct primes such that the projective planes @xmath25 and @xmath26 belong to the same block . now , setting @xmath20 to be @xmath14 , we see that either @xmath27 and @xmath28 both satisfy @xmath3 , or neither satisfies @xmath3 . in either case we have a contradiction , since the first of these direct sums is a representable matroid , and the second is not . let @xmath5 be a positive integer . we say that matroids @xmath14 and @xmath15 are _ equivalent _ if , for any sentence @xmath3 with @xmath5 variables , and any matroid @xmath20 , either both @xmath21 and @xmath22 satisfy @xmath3 , or neither do . shows that this equivalence relation has finite index for any @xmath5 . in this way , the proof of is reminiscent of the myhill - nerode characterisation of regular languages ( see @xcite or ( * ? ? ? * section 6.1 ) ) . by way of contrast , the theorem in @xcite used a proof technique that was essentially an ehrenfeucht - frass game ( see ( * ? ? ? * section 2.2 ) ) . for every @xmath5 , there is a partition of matroids into finitely many blocks , such that two matroids from the same block satisfy exactly the same @xmath5-variable sentences . this follows from by letting @xmath20 be the empty matroid @xmath29 , or from the fact that there are only finitely many _ rank-@xmath5 @xmath30-types _ ( see ( * ? ? ? * section 3.4 ) for an explanation ) . for the next lemma , we construct families of matroids by using gain graphs . loosely , a gain graph is a graph equipped with edge labels that come from a group . for each such graph , there is a gain - graphic matroid , whose ground set is the edge set of the graph . in , we introduce two families of gain graphs . hoop matroid _ is the gain - graphic matroid that corresponds to a gain graph of the form @xmath31 . here @xmath1 is a field , @xmath32 is an integer , and @xmath33 is a non - zero element of @xmath1 with order greater than @xmath34 . the edge labels of the gain graph @xmath31 come from the multiplicative group of @xmath1 . we also introduce a family of gain graphs , @xmath35 . in this case @xmath36 is a field , @xmath37 is an integer , and @xmath38 is a non - zero element with order greater than @xmath39 . loop matroid _ is gain - graphic , corresponding to a gain graph of the form @xmath35 . if @xmath14 is a hoop matroid , corresponding to the gain graph @xmath31 , and @xmath20 is the loop matroid of @xmath35 , then @xmath14 and @xmath20 can be glued together along a rank-@xmath40 flat , to form an amalgam of the two matroids . the resulting matroid is denoted @xmath41 . in the case that @xmath42 and @xmath43 , where the order of @xmath33 is greater than @xmath44 , then both @xmath14 and @xmath20 can be represented over @xmath1 , but @xmath41 can be represented over @xmath1 if and only if @xmath45 . this means that the following quickly leads to a proof of , with hoop matroids playing the same role that projective planes did in the proof of . details of the proof will be left until the end of the paper . if @xmath5 is a positive integer , then @xmath46 is @xmath47 , and @xmath48 is @xmath49 . define @xmath50 to be @xmath51 [ sentry ] let @xmath5 be a positive integer . there is a partition of the set of hoop matroids into blocks , @xmath52 , such that @xmath53 and the following property holds : for any sentence , @xmath3 , in @xmath19 with @xmath5 variables , whenever @xmath14 and @xmath15 are hoop matroids that belong to the same block and @xmath20 is a loop matroid , when @xmath41 and @xmath54 are defined , either both satisfy @xmath3 , or neither satisfies @xmath3 . also implies the following ( unsurprising ) fact : using @xmath0 to characterise increasingly large finite fields requires increasingly large sentences . [ casava ] there is no integer , @xmath55 , such that , for every finite field , @xmath2 , there is a sentence , @xmath56 , in @xmath0containing at most @xmath55 variables , with the property that a matroid is @xmath2-representable if and only if it satisfies @xmath56 . in fact is sufficient to prove both and , since , if @xmath41 is not representable over the field @xmath1 , then it is not representable over any field ( ) . however , we feel that is more intuitive , and also interesting in its own right , so we prefer to prove that lemma , and then note the easy changes required to produce a proof of . for all matroid essentials we refer to oxley @xcite .

we prove there is no sentence in the monadic second - order language that characterises when a matroid is representable over at least one field , and no sentence that characterises when a matroid is-representable , for any infinite field . by way of contrast , because rota s conjecture is true , there is a sentence that characterises-representable matroids , for any finite field .

we prove there is no sentence in the monadic second - order language that characterises when a matroid is representable over at least one field , and no sentence that characterises when a matroid is-representable , for any infinite field . by way of contrast , because rota s conjecture is true , there is a sentence that characterises-representable matroids , for any finite field .

0802.1137

i

with the recent success of model building in the framework of the heterotic @xmath0 string theory @xcite it becomes important to reconsider the questions of moduli stabilization and supersymmetry breakdown . early attempts considered fluxes and gaugino condensates @xcite , race track superpotentials @xcite and/or khler stabilization @xcite . more recently , these questions have been studied in the framework of type iib string theory . while explicit model building towards the mssm ( the minimal supersymmetric extension of the standard model ) is more difficult in this framework , it is usually argued that the stabilization of moduli can be achieved quite easily . the reason is the appearance of two types of fluxes [ neveu - schwarz neveu - schwarz ( ns - ns ) and ramond ramond ( r - r ) ] @xcite while only one of them is present in the heterotic theory . with the inclusion of nonperturbative effects like gaugino condensation one might then stabilize all moduli @xcite . still , there is a problem with the adjustment of the vacuum energy @xmath1 to a small positive value . one has to postulate a so - called `` up - lifting '' sector that adjusts @xmath1 to the desired value @xcite . it turns out that this up - lifting sector has important consequences for the explicit pattern of supersymmetry breakdown @xcite . instead of modulus mediation one is led to a hybrid mediation scheme and a so - called `` mirage pattern '' of the soft breaking terms emerges @xcite . within the framework of the heterotic string , the importance of this up - lifting sector has not been fully appreciated so far . the present paper is an attempt to fill this gap . to illustrate the importance of this sector , we consider a simple example : a gaugino condensate in the absence of a flux background . this is known to lead to a so - called run - away potential with a supersymmetric vacuum at @xmath2 ( where @xmath3 denotes the dilaton field ) . attempts to stabilize the dilaton at a finite value include the consideration of nonperturbative correction to the khler potential @xcite . the resulting scheme is believed to provide a mediation of supersymmetry breakdown that is dominated by the dilaton . still the question of the fine - tuning of the vacuum energy has to be addressed . in the existing examples it seems again that an additional sector is needed to adjust the vacuum energy to the desired value @xcite , just like the up - lifting sector in the type iib case . to be explicit , we consider the model of barreiro , carlos and copeland ( bcc ) ref . @xcite that appears to be particularly suited for a class of realistic heterotic models @xcite . a stabilization of the dilaton can be achieved , but the actual value of @xmath1 turns out to be large and positive so that the desired `` up - lifting '' mechanism should provide a `` down - lift '' of @xmath1 . we here consider the mechanism of lebedev , nilles and ratz ( lnr ) @xcite to adjust @xmath1 . in the framework of type iib theory this is known as @xmath4-term uplifting @xcite and could be originated in dynamical schemes as considered in @xcite or schemes that might require the existence of additional branes and/or anti - branes @xcite . an explicit discussion of supersymmetry breakdown leads to similar conclusions as in the type iib case , the uplifting sector is important for the mechanism of supersymmetry ( susy ) breakdown and its mediation such that a variant of a mirage pattern emerges @xcite . there are , however , some quantitative differences between the heterotic and the type iib case that will be discussed in detail . so far it seems that the stabilization of the dilaton requires sizeable nonperturbative corrections to the khler potential while the uplifting sector adjusts @xmath1 . a closer inspection , however , reveals the surprising fact that one can switch off the corrections to the khler potential and still remain with a stabilized dilaton ! _ the uplifting sector alone is responsible for both , modulus stabilization and adjustment of the vacuum energy . _ stabilization of the dilaton neither requires nonvanishing flux nor corrections to the khler potential . the appearance of a gaugino condensate , however , remains crucial . this remarkable fact shows that modulus stabilization in heterotic string theory is not as difficult as usually assumed . one just needs a suitable uplifting sector very similar to the one postulated in the framework of type iib string theory . it also shows the importance of this uplifting sector for moduli stabilization and supersymmetry breakdown . moreover it leads to a hybrid mediation scheme and its signature is a mirage pattern of the soft supersymmetry breaking terms . the paper is organized as follows . in section 2 we shall discuss the model of ref @xcite with a gaugino condensate and nonperturbative corrections to the khler potential . we present the heterotic analogy of uplifting in the spirit of lnr @xcite , the adjustment of the vacuum energy of the metastable vacuum and the discussion of supersymmetry breakdown . this will be followed by a discussion of the soft supersymmetry breaking parameters , the appearance of a mirage pattern and the phenomenological properties of the set - up . section 4 will contain some concluding remarks .

it requires a gaugino condensate and an up - lifting sector similar to the one postulated in type iib string theory . its signature is a hybrid mediation of supersymmetry breakdown with a variant of a mirage pattern for the soft breaking terms . the set - up is suited for the discussion of heterotic mssm candidates .

we provide a simple example of dilaton stabilization in the framework of heterotic string theory . it requires a gaugino condensate and an up - lifting sector similar to the one postulated in type iib string theory . its signature is a hybrid mediation of supersymmetry breakdown with a variant of a mirage pattern for the soft breaking terms . the set - up is suited for the discussion of heterotic mssm candidates .

astro-ph0211267

c

it has been known for some time that agns comprise a fraction of the submm source population . indeed , the first identified source in a blank - field survey was found to be an agn ( smm j023990136 ; ivison 1998 ) , and at least three of the 15 submm - detected sources in the -lens survey are agns ( smail 2002 ) . in all these cases the evidence for agn activity was found via optical spectroscopy of optically bright sources . the advantage of searching for agns with x - ray observations is that the limitations of optical spectroscopy are removed , allowing optically faint agns and agns without strong emission lines to be identified ( e.g. , vignati 1999 ; mushotzky 2000 ; alexander 2001 ; hornschemeier 2001 ) . however , obviously the lack of optical spectroscopy for the majority of our sources leads to considerable uncertainties in their source redshifts . in this final section , we discuss the dependence of our results on the assumed source redshifts , the fraction and properties of agns in the submm source population , and the agn contribution to the submm emission in sources . the redshifts for the majority of the submm sources are derived from the radio - to - submm spectral slope and are uncertain . as mentioned in 4.1 these uncertainties should not change our main result ( i.e. , that the average agn contribution to the submm emission is of the order of @xmath18 1.4% ) so long as the sources lie at @xmath52 . however , we note here that since the redshift tracks for the template galaxies rise to lower values of @xmath101 at @xmath110 ( see figure 7 ) , the case for star formation dominating the submm emission is even stronger for sources at lower redshifts ( as may be the case for ; see 3.3.1 ) . finally , we also note that although the implied column densities and x - ray luminosities of the agn - classified sources will be lower if they lie at @xmath110 , since @xmath10 power - law emission is only likely to be produced by obscured agn activity , their classification as agns is insensitive to redshift . in this study we have shown that five of the seven x - ray detected submm sources appear to be obscured agns , placing a lower limit on the source density of obscured agns with @xmath0 5 mjy of @xmath111 deg@xmath7 . under the same assumptions as those used in determining the fraction of the bright submm source population with x - ray counterparts ( see 2.4.2 ) , this suggests that @xmath8 26% of the bright submm source population host agns ( in reasonable agreement with model predictions ; e.g. , almaini , lawrence , & boyle 1999 ; fabian & iwasawa 1999 ) . ivison ( 2002 ) found a similar agn fraction to that derived here using the moderately deep observations of the lockman hole east region ( e.g. , hasinger 2001 ) . however , their submm - detected agn source density is @xmath18 2 times smaller ( i.e. , @xmath59 deg@xmath7 versus @xmath111 deg@xmath7 ) . the difference in the submm - detected agn source densities is mostly due to the higher sensitivity of our x - ray observations . hence the similarity between the agn fraction found by ivison ( 2002 ) and our lower limit may indicate that our estimated agn fraction is conservative . the unabsorbed rest - frame full - band luminosities of the agn - classified sources are @xmath11@xmath12 erg s@xmath5 . this range of x - ray luminosity is typical of luminous seyfert galaxies . therefore , although the majority of the submm sources are likely to be extremely luminous infrared galaxies ( e.g. , ivison 1998 ; smail 2002 ) , their agns are comparitively weak . for example , typical qsos of similar infrared luminosity ( e.g. , isaak 2002 ; page 2001 ) are @xmath18 10100 times more luminous at x - ray energies ( e.g. , page 2001 ; vignali 2001 , 2003 ) . under the assumption that bright submm sources are massive proto galaxies ( e.g. , blain 1999 ; lilly 1999 ) , the luminosities of these agns are consistent with those expected for growing supermassive black holes ( e.g. , archibald 2002 ) . the current constraints suggest that the total contribution to the submm emission from agn activity is unlikely to be more than @xmath18 1.4% ; however , as noted in 2.2 , there are likely to be further bright submm sources in our region that have not yet been detected by . in addition , we have not considered the possible contribution from optically bright submm - detected qsos . although optically bright submm - detected qsos may comprise only @xmath18 510% of the bright submm source population ( see footnote 1 ) , their submm emission could have a large agn component ( perhaps of the order of @xmath18 50% ; frayer 1998 ; bautz 2000 ) . hence , although optically bright submm - detected qsos may not be numerically significant , they may provide the bulk of the agn emission at submm wavelengths .

we provide x - ray constraints and perform the first x - ray spectral analyses for bright sources ( 5 mjy ; s / n ) in an area of the 2 ms deep field - north survey containing the hubble deep field - north . x - ray emission is detected from seven of the ten bright submm sources in this region down to 0.58.0 kev fluxes of erg s , corresponding to an x - ray detected submm source density of deg ; our analyses suggest that this equates to an x - ray detected fraction of the bright submm source population of 36% , although systematic effects may be present .

we provide x - ray constraints and perform the first x - ray spectral analyses for bright sources ( 5 mjy ; s / n ) in an area of the 2 ms deep field - north survey containing the hubble deep field - north . x - ray emission is detected from seven of the ten bright submm sources in this region down to 0.58.0 kev fluxes of erg s , corresponding to an x - ray detected submm source density of deg ; our analyses suggest that this equates to an x - ray detected fraction of the bright submm source population of 36% , although systematic effects may be present . two of the x - ray detected sources have nearby ( within 3 ) x - ray companions , suggesting merging / interacting sources or gravitational lensing effects , and three of the x - ray detected sources lie within the approximate extent of the proto - cluster candidate . five of the x - ray detected sources have flat effective x - ray spectral slopes ( ) , suggesting obscured agn activity . x - ray spectral analyses suggest that one of these agns may be a compton - thick source ; of the other four agns , three appear to be compton - thin sources and one has poor constraints . the rest - frame unabsorbed x - ray luminosities of these agns are more consistent with those of seyfert galaxies than qsos ( i.e. , erg s ) . thus , the low x - ray detection rate of bright submm sources by moderately deep x - ray surveys appears to be due to the relatively low luminosities of the agns in these sources rather than compton - thick absorption . a comparison of these sources to the well - studied heavily obscured agn ngc 6240 shows that the average agn contribution is negligible at submm wavelengths . the x - ray properties of the other two x - ray detected sources are consistent with those expected from luminous star formation ; however , we can not rule out the possibility that low - luminosity agns are present . the three x - ray undetected sources appear to lie at high redshift ( ) and could be either agns or starbust galaxies .

astro-ph0211267

c

we have used the 2 ms exposure of the cdf - n to constrain the x - ray properties of bright sources ( @xmath0 5 mjy ; s / n@xmath1 ) . in this study we have focused on the x - ray spectral properties of the x - ray detected submm sources to determine whether the agn - classified sources are compton thick or compton thin . we have used these results to constrain the contribution to the submm emission from agn activity . our main results are the following : * seven of the ten bright submm sources are detected with x - ray emission . the corresponding source density of bright submm sources with x - ray counterparts ( @xmath6 deg@xmath7 ) suggests that @xmath8 36% of bright submm sources have x - ray counterparts at this x - ray depth ; however we note that this fraction is somewhat uncertain since this region does not have complete coverage down to @xmath32 5 mjy . see 2 . * five of the x - ray detected submm sources have flat x - ray spectral slopes ( @xmath10 ) and luminous x - ray emission ( @xmath11@xmath12 erg s@xmath5 ) , suggesting obscured agn activity with @xmath112 @xmath4 . one source is possibly a compton - thick agn since it has an extremely flat x - ray spectral slope ( @xmath113 0.7 ) and shows possible evidence ( @xmath18 2.3 @xmath50 ) for a redshifted 6.4 kev iron k@xmath64 emission line ; however , the inferred redshift ( @xmath49 0.46@xmath88 ) is in considerable disagreement with the millimetric redshift ( @xmath114 ) . see 3 . * a comparison of the five agn - classified sources to the well - studied heavily obscured agn ngc 6240 suggests that the agns in these sources contribute , on average , a negligible fraction ( i.e. , @xmath18 1.4% ) of the submm emission . hence , the submm emission from these sources appears to be dominated by star formation . this result is relatively insensitive to redshift . see 4 . * the x - ray constraints are weak for the other five submm sources . we find that the x - ray properties for the two sources with millimetric redshifts of @xmath109 are consistent with those expected from luminous star - formation activity ( @xmath77@xmath78 erg s@xmath5 ) . the submm - to - x - ray spectral slopes of these sources are also similar to those expected from arp 220 ( the archetypal ultra - luminous dusty starburst galaxy ) at @xmath52 ; however , we can not rule out the possibility that low - luminosity agns are present in these sources . the three @xmath13 sources could be either agns or starbust galaxies . see 3 and 4 . * the fraction of the bright submm source population with agn activity ( i.e. , @xmath8 26% ) is in reasonable agreement with model predictions . the comparitively low x - ray luminosities of the agn - classified sources are more consistent with seyfert galaxies than qsos . we suggest that optically bright submm - detected qsos ( i.e. , luminous type 1 agns ) , although possibly not numerically significant , may provide the bulk of the agn emission at submm wavelengths . see 5 . these results show that the low x - ray detection rate of bright submm sources by moderately deep x - ray surveys is probably due to the relatively low luminosities of the agns in these sources rather than compton - thick absorption . the current constraints therefore suggest that the total contribution from agns to the submm emission in the bright submm source population is negligible . hence , the submm emission of bright submm sources appears to be predominantly powered by star - formation activity , and therefore can be used to determine star - formation rates .

five of the x - ray detected sources have flat effective x - ray spectral slopes ( ) , suggesting obscured agn activity . the rest - frame unabsorbed x - ray luminosities of these agns are more consistent with those of seyfert galaxies than qsos ( i.e. , erg s ) . thus , the low x - ray detection rate of bright submm sources by moderately deep x - ray surveys appears to be due to the relatively low luminosities of the agns in these sources rather than compton - thick absorption . a comparison of these sources to the well - studied heavily obscured agn ngc 6240 shows that the average agn contribution is negligible at submm wavelengths . the x - ray properties of the other two x - ray detected sources are consistent with those expected from luminous star formation ; however , we can not rule out the possibility that low - luminosity agns are present . the three x - ray undetected sources appear to lie at high redshift ( ) and could be either agns or starbust galaxies .

we provide x - ray constraints and perform the first x - ray spectral analyses for bright sources ( 5 mjy ; s / n ) in an area of the 2 ms deep field - north survey containing the hubble deep field - north . x - ray emission is detected from seven of the ten bright submm sources in this region down to 0.58.0 kev fluxes of erg s , corresponding to an x - ray detected submm source density of deg ; our analyses suggest that this equates to an x - ray detected fraction of the bright submm source population of 36% , although systematic effects may be present . two of the x - ray detected sources have nearby ( within 3 ) x - ray companions , suggesting merging / interacting sources or gravitational lensing effects , and three of the x - ray detected sources lie within the approximate extent of the proto - cluster candidate . five of the x - ray detected sources have flat effective x - ray spectral slopes ( ) , suggesting obscured agn activity . x - ray spectral analyses suggest that one of these agns may be a compton - thick source ; of the other four agns , three appear to be compton - thin sources and one has poor constraints . the rest - frame unabsorbed x - ray luminosities of these agns are more consistent with those of seyfert galaxies than qsos ( i.e. , erg s ) . thus , the low x - ray detection rate of bright submm sources by moderately deep x - ray surveys appears to be due to the relatively low luminosities of the agns in these sources rather than compton - thick absorption . a comparison of these sources to the well - studied heavily obscured agn ngc 6240 shows that the average agn contribution is negligible at submm wavelengths . the x - ray properties of the other two x - ray detected sources are consistent with those expected from luminous star formation ; however , we can not rule out the possibility that low - luminosity agns are present . the three x - ray undetected sources appear to lie at high redshift ( ) and could be either agns or starbust galaxies .

1103.1932

i

quasar absorption lines ( qals ) provide us a unique tool to study abundances , physical conditions and kinematics of gas in a wide variety of astrophysical environments . many of the early detected qals are associated systems with redshifts close to the quasar emission redshifts ( e.g. , burbidge et al . 1966 ; schmidt 1966 ) . the discovery of intervening qals was first reported by bahcall et al . bahcall ( 1968 ) developed the first systematic method for identifying absorption systems on quasar spectra . to date , thousands of qals have been detected ( e.g. , nestor et al . 2005 ; prochter et al . 2006 ) thanks to the huge quasar database from sdss ( york et al . 2000 ) . the existence of dust content in quasar damped ly@xmath4 absorbers ( dlas ) was first detected through reddening measurements of quasar continuum spectra ( fall et al . 1989 ; pei et al . it was later confirmed by measurements of depletion of different metal elements in the gas phase onto dust grains ( e.g. , pettini et al . 1994 , 1997 , 1999 ; lu et al . 1996 ) . murphy & liske ( 2004 ) further investigated dust reddening of dlas on background quasars by comparing the spectral index distribution of a sample of 70 dlas at @xmath6 to that of a large control sample , but they found no evidence for dust reddening . vladilo et al . ( 2008 ) revisited dust reddening of dlas by deriving the color excess of background quasars , and they found significant color excess caused by the foreground absorbers in their sample of 248 dlas at @xmath7 . by studying the average extinction curves on quasar spectra with mg ii absorption lines , york et al . ( 2006 ) found clear evidence for presence of dust in intervening absorption systems with @xmath8 . recently , mnard et al . ( 2008 ) confirmed dust reddening in a much larger absorber sample with nearly 7000 strong mg ii absorption systems at @xmath9 . all these dust reddening studies show that , on average , the dust grain size distribution of quasar absorption systems is similar to that of the small magellanic cloud ( smc ; pei 1992 ) . the extinction curve does not show presence of the broad bump around 2175- found in the milky way ( mw ) interstellar clouds ( e.g. , stecher 1965 ; savage & mathis 1979 ; fitzpatrick 1989 ) . the 2175- dust feature has been found in a handful of local galaxies , where the reddening law of their inter - stellar medium ( ism ) can be studied spatially ( keel et al . the 2175- bumps in the mw extinction curves appear to be the strongest among all of the known galaxies . the strength of the bump in the extinction curves from the large magellanic clouds 2 ( lmc2 ) supershell ( near the 30 dor star formation region ; gordon et al . 2003 ) is quite moderate while the bumps are nearly absent in the smc extinction curves . it is very likely that the mw - like dust is a minor population among ism dust in the universe . therefore , the 2175- dust extinction bumps can not be recovered by using any average extinction curves method . the detections of the 2175- extinction bump in individual quasar absorption systems were well reviewed by wang et al . ( 2004 ) . recently , several new detections have been reported ( e.g. , srianand et al . 2008 ; noterdaeme et al . 2009 ; zhou et al . all the recent ones were detected on sdss spectra by comparing the reddened quasar spectrum with the sdss composite quasar spectrum ( vanden berk et al . 2001 ) . in nearly parallel efforts , the analysis of gamma - ray bursts ( grb ) afterglow spectra has also revealed several positive detections of 2175- dust feature from intervening absorbers and from gas in the grb host galaxies ( e.g. , ellison et al . 2006 ; elasdttir et al . 2009 ; prochaska et al . in this paper , we report detections of 39 2175- dust extinction bump candidates associated with strong mg ii absorption line systems on quasar spectra in sdss dr3 based on the fm90 parameterization modeling of optical / uv extinction curves . this paper is organized as follows : in 2 we describe the parameterization of optical / uv extinction curves ; in 3 we introduce the procedures of searching for 2175- absorbers in a strong mg ii absorber sample from sdss dr3 and report 39 candidates ; in 4 further investigations and follow - up observations in future are discussed ; more relevant discussions and a short summary are given in 5 .

we report detections of 39 2175- dust extinction bump candidates associated with strong mg ii absorption lines at z 11.8 on quasar spectra in sloan digital sky survey ( sdss ) dr3 . ( 2006 ) . most of the candidate bumps in this work are similar to the relatively weak 2175- bumps observed in the large magellanic clouds ( lmc ) lmc2 supershell rather than the strong ones observed in the milky way ( mw ) .

we report detections of 39 2175- dust extinction bump candidates associated with strong mg ii absorption lines at z 11.8 on quasar spectra in sloan digital sky survey ( sdss ) dr3 . these strong mg ii absorption line systems are detected among 2,951 strong mg ii absorbers with the rest equivalent width 1.0 at , which is part of a full sample of 7,421 strong mg ii absorbers compiled by prochter et al . ( 2006 ) . the redshift range of the absorbers is chosen to allow the 2175- extinction features to be completely covered within the sdss spectrograph operation wavelength range . an upper limit of the background quasar emission redshift at z.1 is set to prevent the ly forest lines from contaminating the sensitive spectral region for the 2175- bump measurements . the fm90 ( fitzpatrick & massa 1990 ) parameterization is applied to model the optical / uv extinction curve in the rest frame of mg ii absorbers of the 2175- bump candidates . the simulation technique developed by jiang et al . ( 2010a , b ) is used to derive the statistical significance of the candidate 2175- bumps . a total of 12 absorbers are detected with 2175- bumps at a 5 level of statistical significance , 10 are detected at a 4 level and 17 are detected at a 3 level . most of the candidate bumps in this work are similar to the relatively weak 2175- bumps observed in the large magellanic clouds ( lmc ) lmc2 supershell rather than the strong ones observed in the milky way ( mw ) . this sample has greatly increased the total number of 2175- extinction bumps measured on sdss quasar spectra . follow - up observations may rule out some of possible false detections and reveal the physical and chemical natures of 2175- quasar absorbers .

1103.1932

c

the sdss dr7 database contains 105,783 quasar spectra ( schneider et al . 2010 ) . we expect to find more than 50 significant 2175- bumps associated with mg ii absorption line systems by implementing the same searching strategy in this paper . another possible approach of searching for the 2175- extinction bump on quasar spectra is to compare the reddened quasar with a blue quasar template ( j. wang et al . , 2011 , in preparation ) . the blue quasar template is defined as the spectrum of an observed sdss blue quasar with similar width and strength of broad emission lines ( including the broad feii emission lines ) with the reddened quasar of interest . the only difference between the reddened quasar and its blue template is considered to be dust reddening . this idea is very similar to the method used to extract the extinction curves by comparing the spectrum of a reddened hot early - type star with a unreddened star having the same stellar type in the mw ( e.g. trunpler 1930 ; welty & fowler 1992 ) . this method may measure the 2175- bump on quasar spectrum more precisely when compared with the composite spectrum method since the emission lines are matched . however , the selection of blue quasar template needs to be studied carefully . dust extinction and reddening effects can change the magnitude and color of background quasars . it is very likely that some dust reddened quasars can not be recovered by the sdss quasar target selection algorithm ( richards et al . 2002 ) , which is mainly based on the sdss imaging magnitudes and colors . in addition to searching for 2175- absorbers in the current sdss quasar spectra database , we also plan to select the 2175- quasar absorber candidates in the sdss image database for follow - up spectroscopic observations in future . the wavelength coverage of sdss spectrum is from 3800 to 9200 . it allows us to detect galactic 2175- extinction feature up to redshift @xmath6 . the highest redshift for identified 2175- bump to date is @xmath45 , which was detected by prochaska et al . ( 2009 ) using the afterglow optical / ir photometry of gamma - ray burst grb 080607 . another high redshift 2175- bump was detected by elasdttir et al . ( 2009 ) on the afterglow optical spectrum of grb 070802 at @xmath46 . we are also studying the feasibility of using our method to search for high redshift 2175- bumps . the main difficulty to implement our method to high redshift bumps is that the random ly@xmath4 limit absorptions are present blueward of the ly@xmath4 emission line on the spectrum of quasar beyond @xmath47 . they make the spectrum fitting procedure more complicated . however , a further developed detection method for high redshift bumps would be very helpful for us to search for 2175- dust extinction bumps on the spectra of @xmath0160,000 quasars at redshifts @xmath48 from the sdss - iii s baryon oscillation spectroscopic survey ( boss ; eisenstein et al . 2011 ) in future . in this paper , we searched for 2175- dust extinction bumps associated with strong mg ii absorption lines on quasar spectra in sdss dr3 . the search results in 12 high confidence candidates with a 5@xmath5 level of statistical significance , 10 median confidence candidates with a 4@xmath5 level and 17 low confidence candidates with a 3@xmath5 level . the total number of 2175- bump detections have been largely increased by this work . follow - up observations may rule out some of possible false detections and reveal the physical and chemical natures of 2175- quasar absorbers . the authors appreciate the enlightening suggestions from the anonymous referee , which help to improve the quality of this paper largely . this work was partially supported by nsf with grant nsf ast-0451407 , ast-0451408 & ast-0705139 , and a china nsf grant ( nsf-10973012 ) and the university of florida . pj acknowledges support from china scholarship council . this research has also been partially supported by the cas / safea international partnership program for creative research teams . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new 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y. , ge , j. , lu , h. l. , wang , t. g. , yuan , w. m. , jiang , p. , and shan , h. g. 2010 , , 708 , 742 ccc 800.0 & 14.634 & 1.009 + 801.0 & 17.037 & 1.156 + 802.0 & 17.622 & 1.128 + 803.0 & 15.667 & 0.989 + 804.0 & 15.867 & 1.040 + 805.0 & 15.461 & 1.005 + 806.0 & 17.926 & 1.130 + 807.0 & 17.598 & 1.128 + 808.0 & 16.062 & 0.994 + 809.0 & 16.326 & 0.993 + 810.0 & 17.917 & 1.105 + 811.0 & 18.795 & 1.008 + 812.0 & 15.443 & 0.833 + 813.0 & 15.608 & 0.857 + 814.0 & 16.658 & 0.962 + 815.0 & 16.303 & 0.887 + lcccrccc j000221.80 + 151454.5 & 1.825 & 1.435 & 1.29 & @xmath490.01@xmath500.02 & 2.40@xmath500.28 & 0.82@xmath500.26 & a + j000748.29 + 151746.0 & 1.237 & 1.044 & 1.83 & 0.25@xmath500.02 & 2.13@xmath500.40 & 1.15@xmath500.72 & a + j001410.98@xmath49084429.2 & 1.772 & 1.292 & 2.32 & 0.59@xmath500.03 & 0.68@xmath500.09 & 0.35@xmath500.10 & b + j002355.15 + 141900.9 & 1.116 & 1.012 & 1.46 & 0.19@xmath500.02 & 0.70@xmath500.14 & 0.17@xmath500.08 & a + j003545.13 + 011441.2 & 1.541 & 1.550 & 1.54 & 0.39@xmath500.04 & 0.55@xmath500.07 & 0.13@xmath500.03 & a + j003550.66@xmath49004301.8 & 1.681 & 1.344 & 1.19 & @xmath490.06@xmath500.03 & 1.22@xmath500.34 & 0.25@xmath500.16 & a + j004324.47@xmath49103922.3 & 1.681 & 1.454 & 1.01 & @xmath490.10@xmath500.03 & 0.97@xmath500.62 & @xmath510.11 & a + j011705.18 + 152931.8 & 1.845 & 1.518 & 1.18 & @xmath490.12@xmath500.02 & 2.00@xmath500.53 & 0.48@xmath500.32 & a + lccccrrccccc j074744.16 + 330941.0 & 1.916 & 1.549 & 5.48 & 0.88@xmath500.03 & 0.14@xmath500.03 & 0.40@xmath500.01 & 0.26@xmath500.05 & 4.61@xmath500.01 & 0.61@xmath500.08 & 1.42 & 6.0@xmath5 + j085042.24 + 515911.6 & 1.893 & 1.327 & 4.12 & 0.99@xmath500.03 & @xmath490.95@xmath500.02 & 0.45@xmath500.01 & 0.62@xmath500.08 & 4.52@xmath500.01 & 1.22@xmath500.06 & 1.14 & 5.0@xmath5 + j090016.67 + 021445.8 & 1.992 & 1.051 & 4.06 & 1.04@xmath500.04 & 0.09@xmath500.08 & 0.47@xmath500.03 & 1.46@xmath500.44 & 4.66@xmath500.04 & 1.11@xmath500.16 & 1.16 & 9.2@xmath5 + j095631.05 + 404628.2 & 1.510 & 1.323 & 3.79 & 0.86@xmath500.05 & 0.56@xmath500.04 & 0.35@xmath500.01 & 0.24@xmath500.07 & 4.60@xmath500.03 & 0.64@xmath500.09 & 1.28 & 8.4@xmath5 + j101751.15 + 474940.0 & 1.220 & 1.118 & 2.75 & 0.32@xmath500.03 & 0.16@xmath500.03 & @xmath490.02@xmath500.02 & 1.65@xmath500.42 & 4.55@xmath500.03 & 1.85@xmath500.16 & 1.11 & 5.2@xmath5 + j103718.77 + 014430.7 & 1.482 & 1.126 & 1.72 & 0.06@xmath500.02 & 1.04@xmath500.03 & @xmath490.10@xmath500.01 & 1.18@xmath500.17 & 4.49@xmath500.01 & 1.26@xmath500.07 & 1.29 & 6.3@xmath5 + j105748.63 + 610910.8 & 1.276 & 1.203 & 3.60 & 0.78@xmath500.04 & 0.51@xmath500.04 & 0.27@xmath500.02 & 0.20@xmath500.07 & 4.54@xmath500.03 & 0.78@xmath500.13 & 1.32 & 6.1@xmath5 + j120935.80 + 671715.7 & 2.030 & 1.843 & 3.19 & 0.01@xmath500.03 & 0.69@xmath500.02 & 0.13@xmath500.01 & 0.26@xmath500.03 & 4.44@xmath500.01 & 0.86@xmath500.05 & 1.51 & 6.7@xmath5 + j143108.98 + 000725.1 & 1.842 & 1.153 & 1.79 & 0.74@xmath500.03 & @xmath490.25@xmath500.03 & 0.36@xmath500.01 & 0.51@xmath500.01 & 4.65@xmath500.02 & 1.01@xmath500.09 & 1.10 & 8.1@xmath5 + j144612.97 + 035154.4 & 1.945 & 1.511 & 2.89 & 0.89@xmath500.03 & @xmath490.02@xmath500.04 & 0.57@xmath500.01 & 0.68@xmath500.12 & 4.52@xmath500.02 & 1.00@xmath500.09 & 1.22 & 6.7@xmath5 + j153020.05 + 592217.0 & 1.689 & 1.405 & 2.68 & 0.09@xmath500.04 & 2.05@xmath500.06 & 0.10@xmath500.02 & 0.49@xmath500.16 & 4.79@xmath500.03 & 0.87@xmath500.16 & 1.10 & 6.1@xmath5 + j214811.57@xmath49085904.6 & 1.642 & 1.643 & 2.79 & 0.76@xmath500.05 & @xmath490.12@xmath500.03 & 0.46@xmath500.01 & 0.68@xmath500.22 & 4.56@xmath500.04 & 1.46@xmath500.21 & 1.40 & 5.0@xmath5 + lccccrrccccc j081540.60 + 264021.6 & 1.936 & 1.680 & 2.88 & 0.38@xmath500.03 & 0.72@xmath500.02 & 0.16@xmath500.01 & 0.15@xmath500.03 & 4.53@xmath500.02 & 0.72@xmath500.07 & 1.24 & 4.3@xmath5 + j091927.61 + 014603.0 & 1.277 & 1.274 & 2.18 & 0.76@xmath500.04 & 0.05@xmath500.03 & 0.43@xmath500.01 & 0.07@xmath500.03 & 4.80@xmath500.03 & 0.55@xmath500.11 & 1.33 & 4.8@xmath5 + j102832.58 + 042354.1 & 1.725 & 1.461 & 1.70 & 0.09@xmath500.03 & 1.28@xmath500.02 & @xmath490.02@xmath500.01 & 0.71@xmath500.14 & 4.72@xmath500.02 & 1.25@xmath500.11 & 1.10 & 4.3@xmath5 + j105049.73 + 071554.8 & 1.913 & 1.262 & 2.33 & 0.54@xmath500.03 & 0.40@xmath500.02 & 0.17@xmath500.01 & 0.18@xmath500.05 & 4.69@xmath500.02 & 0.85@xmath500.11 & 1.13 & 4.5@xmath5 + j110747.04 + 631607.1 & 1.952 & 1.250 & 3.87 & 0.40@xmath500.02 & 0.10@xmath500.01 & 0.07@xmath500.01 & 0.25@xmath500.05 & 4.60@xmath500.02 & 0.99@xmath500.08 & 1.08 & 4.3@xmath5 + j111857.03 + 484750.1 & 1.993 & 1.639 & 1.17 & 0.20@xmath500.04 & 0.88@xmath500.02 & 0.13@xmath500.01 & 0.58@xmath500.10 & 4.71@xmath500.02 & 1.18@xmath500.10 & 1.28 & 4.3@xmath5 + j124715.26 + 520801.0 & 1.812 & 1.050 & 3.58 & 0.59@xmath500.05 & 0.57@xmath500.04 & 0.19@xmath500.01 & 0.19@xmath500.06 & 4.57@xmath500.02 & 0.68@xmath500.08 & 1.13 & 4.5@xmath5 + j133125.93 + 004414.0 & 2.021 & 1.310 & 1.77 & 0.17@xmath500.02 & 0.50@xmath500.01 & 0.07@xmath500.01 & 0.05@xmath500.01 & 4.64@xmath500.01 & 0.50@xmath500.04 & 1.25 & 4.2@xmath5 + j145953.23 + 012944.2 & 1.659 & 1.623 & 2.00 & 0.53@xmath500.03 & 0.33@xmath500.02 & 0.21@xmath500.01 & 0.13@xmath500.03 & 4.68@xmath500.02 & 0.73@xmath500.08 & 1.25 & 4.0@xmath5 + j233131.90@xmath49001940.1 & 1.845 & 1.391 & 1.46 & 0.71@xmath500.04 & 0.29@xmath500.03 & 0.26@xmath500.01 & 0.43@xmath500.08 & 4.43@xmath500.02 & 1.00@xmath500.10 & 1.26 & 4.1@xmath5 + lccccrrccccc j074259.57 + 225003.2 & 1.182 & 1.181 & 2.19 & 0.60@xmath500.02 & @xmath490.56@xmath500.03 & 0.29@xmath500.01 & 0.34@xmath500.12 & 4.68@xmath500.04 & 1.22@xmath500.17 & 1.17 & 3.3@xmath5 + j092201.86 + 494010.6 & 1.488 & 1.068 & 1.04 & 0.39@xmath500.03 & 0.28@xmath500.04 & 0.10@xmath500.02 & 0.93@xmath500.30 & 4.70@xmath500.03 & 1.50@xmath500.18 & 1.83 & 3.9@xmath5 + j092923.67 + 443343.2 & 1.296 & 1.072 & 1.63 & 0.23@xmath500.03 & 0.30@xmath500.04 & 0.11@xmath500.02 & 0.38@xmath500.17 & 4.55@xmath500.04 & 1.16@xmath500.19 & 1.00 & 3.4@xmath5 + j094933.34 + 020657.0 & 1.531 & 1.215 & 4.41 & 0.03@xmath500.03 & 2.13@xmath500.04 & @xmath490.12@xmath500.02 & 0.51@xmath500.18 & 4.53@xmath500.03 & 1.22@xmath500.18 & 1.60 & 3.1@xmath5 + j102725.91 + 060505.8 & 1.219 & 1.002 & 1.71 & 0.16@xmath500.03 & 0.77@xmath500.11 & @xmath490.10@xmath500.05 & 2.66@xmath501.67 & 4.72@xmath500.09 & 2.19@xmath500.41 & 1.08 & 3.0@xmath5 + j104934.08 + 022118.9 & 1.831 & 1.594 & 2.60 & 0.34@xmath500.03 & 0.85@xmath500.02 & 0.12@xmath500.01 & 0.40@xmath500.08 & 4.61@xmath500.02 & 1.11@xmath500.10 & 1.06 & 3.8@xmath5 + j105122.23 + 032300.6 & 2.015 & 1.527 & 2.62 & 0.46@xmath500.03 & 0.45@xmath500.02 & 0.30@xmath500.01 & 0.22@xmath500.05 & 4.43@xmath500.02 & 0.74@xmath500.09 & 1.10 & 3.9@xmath5 + j113448.13 + 593945.7 & 1.345 & 1.335 & 3.56 & 0.37@xmath500.03 & 0.48@xmath500.01 & 0.13@xmath500.01 & 0.08@xmath500.02 & 4.55@xmath500.02 & 0.64@xmath500.07 & 1.33 & 3.8@xmath5 + j121312.08 + 542748.0 & 1.703 & 1.070 & 1.44 & 0.21@xmath500.03 & 1.05@xmath500.04 & 0.06@xmath500.01 & 0.11@xmath500.07 & 4.54@xmath500.04 & 0.81@xmath500.22 & 1.09 & 3.7@xmath5 + j135731.06 + 022726.5 & 1.773 & 1.368 & 2.31 & 0.10@xmath500.04 & 1.37@xmath500.03 & 0.17@xmath500.01 & 0.16@xmath500.04 & 4.40@xmath500.03 & 0.65@xmath500.10 & 1.19 & 3.9@xmath5 + j142820.59@xmath49005348.3 & 1.533 & 1.517 & 2.04 & 0.54@xmath500.03 & @xmath490.01@xmath500.02 & 0.27@xmath500.01 & 0.17@xmath500.04 & 4.51@xmath500.03 & 0.96@xmath500.12 & 1.24 & 3.2@xmath5 + j143512.94 + 042036.9 & 1.944 & 1.657 & 3.41 & 0.22@xmath500.03 & 0.24@xmath500.01 & 0.13@xmath500.01 & 0.17@xmath500.02 & 4.58@xmath500.02 & 0.83@xmath500.06 & 1.23 & 3.0@xmath5 + j144046.93 + 012041.0 & 1.397 & 1.030 & 1.58 & 0.10@xmath500.02 & 0.87@xmath500.06 & @xmath490.11@xmath500.03 & 1.42@xmath500.49 & 4.59@xmath500.04 & 1.67@xmath500.20 & 1.35 & 3.5@xmath5 + j154734.12 + 033314.4 & 1.369 & 1.007 & 1.19 & 0.34@xmath500.03 & 0.55@xmath500.06 & 0.07@xmath500.03 & 1.04@xmath500.42 & 4.48@xmath500.04 & 1.48@xmath500.22 & 1.19 & 3.6@xmath5 + j203926.15 + 005444.9 & 1.256 & 1.118 & 1.49 & 0.41@xmath500.03 & 0.24@xmath500.04 & 0.24@xmath500.01 & 0.06@xmath500.05 & 4.70@xmath500.08 & 0.61@xmath500.26 & 1.07 & 3.1@xmath5 + j214324.36 + 003502.8 & 2.037 & 1.604 & 1.99 & 0.14@xmath500.02 & 0.48@xmath500.01 & 0.17@xmath500.01 & 0.23@xmath500.03 & 4.43@xmath500.01 & 0.92@xmath500.07 & 1.33 & 3.0@xmath5 + j232713.03@xmath49100027.7 & 1.981 & 1.266 & 1.67 & 0.22@xmath500.03 & 0.65@xmath500.02 & 0.14@xmath500.01 & 0.06@xmath500.02 & 4.50@xmath500.02 & 0.62@xmath500.10 & 1.30 & 3.0@xmath5 + lcccccccc 2180 & 0.25 & 0.37 & 0.53 & 1.01 & 0.41 & 0.60 & 0.85 & 1.62 + 2130 & 0.27 & 0.40 & 0.56 & 1.06 & 0.44 & 0.64 & 0.90 & 1.70 + 2080 & 0.29 & 0.43 & 0.60 & 1.13 & 0.47 & 0.70 & 0.97 & 1.81 + 2030 & 0.31 & 0.47 & 0.66 & 1.22 & 0.51 & 0.77 & 1.10 & 1.96 + 1980 & 0.35 & 0.53 & 0.73 & 1.35 & 0.58 & 0.86 & 1.20 & 2.17 + 1930 & 0.41 & 0.60 & 0.83 & 1.49 & 0.69 & 0.98 & 1.35 & 2.41 + 1880 & 0.43 & 0.64 & 0.89 & 1.61 & 0.72 & 1.06 & 1.47 & 2.62 + 1830 & 0.36 & 0.59 & 0.87 & 1.68 & 0.61 & 0.99 & 1.45 & 2.75 + 1780 & 0.29 & 0.50 & 0.78 & 1.68 & 0.49 & 0.83 & 1.29 & 2.76 + 1730 & 0.25 & 0.41 & 0.66 & 1.59 & 0.41 & 0.68 & 1.08 & 2.61 + 1680 & 0.22 & 0.35 & 0.54 & 1.41 & 0.37 & 0.57 & 0.89 & 2.30 + 1630 & 0.28 & 0.39 & 0.55 & 1.26 & 0.47 & 0.65 & 0.89 & 2.04 + 1580 & 0.40 & 0.55 & 0.71 & 1.28 & 0.67 & 0.91 & 1.16 & 2.06 + 1530 & 0.55 & 0.73 & 0.91 & 1.51 & 0.91 & 1.20 & 1.48 & 2.43 +

a total of 12 absorbers are detected with 2175- bumps at a 5 level of statistical significance , 10 are detected at a 4 level and 17 are detected at a 3 level . follow - up observations may rule out some of possible false detections and reveal the physical and chemical natures of 2175- quasar absorbers .

we report detections of 39 2175- dust extinction bump candidates associated with strong mg ii absorption lines at z 11.8 on quasar spectra in sloan digital sky survey ( sdss ) dr3 . these strong mg ii absorption line systems are detected among 2,951 strong mg ii absorbers with the rest equivalent width 1.0 at , which is part of a full sample of 7,421 strong mg ii absorbers compiled by prochter et al . ( 2006 ) . the redshift range of the absorbers is chosen to allow the 2175- extinction features to be completely covered within the sdss spectrograph operation wavelength range . an upper limit of the background quasar emission redshift at z.1 is set to prevent the ly forest lines from contaminating the sensitive spectral region for the 2175- bump measurements . the fm90 ( fitzpatrick & massa 1990 ) parameterization is applied to model the optical / uv extinction curve in the rest frame of mg ii absorbers of the 2175- bump candidates . the simulation technique developed by jiang et al . ( 2010a , b ) is used to derive the statistical significance of the candidate 2175- bumps . a total of 12 absorbers are detected with 2175- bumps at a 5 level of statistical significance , 10 are detected at a 4 level and 17 are detected at a 3 level . most of the candidate bumps in this work are similar to the relatively weak 2175- bumps observed in the large magellanic clouds ( lmc ) lmc2 supershell rather than the strong ones observed in the milky way ( mw ) . this sample has greatly increased the total number of 2175- extinction bumps measured on sdss quasar spectra . follow - up observations may rule out some of possible false detections and reveal the physical and chemical natures of 2175- quasar absorbers .

astro-ph0701710

r

the 25 orionis group stands out as a concentration of tts stars in the ori ob1a sub - association ( figure [ fig1 ] ) , roughly surrounding the b1vpe star 25 ori ( @xmath52 ) . this star has been classified as a classical be object @xcite ; more recently @xcite determined a spectral type b2 . in @xcite we already pointed out the existence of this stellar aggregate as a distinct feature in the spatial distribution of the brighter ( v@xmath29 ) members , albeit with lower number statistics . @xcite classify the region around 25 ori as a new cluster ( ascc 16 ) , based on parallaxes , proper motions and v , b - v data for _ hipparcos _ and tycho-2 stars . they place the cluster center coordinates at @xmath53 , @xmath54 south - west of 25 ori , and derive a cluster radius of @xmath55 ( figure [ fig1 ] ) . the parallaxes of the _ hipparcos _ stars yield a mean distance of 323 pc ; we assume here a value of 330 pc ( see * ? ? ? we are aware we are missing the northernmost region of the 25 ori cluster , as can be seen in figure [ fig1 ] . however , because our continuing survey ultimately will span orion up to @xmath56 we will be in a position to study whether the cluster extends further north . for the present analysis we defined a circle of @xmath30 radius around 25 ori as the 25 orionis group . though this is larger than the cluster radius derived by @xcite , it allows us to improve our member statistics , and at the same time is not large enough to expect contamination from the younger stars in the orion ob1b region . the @xcite catalog lists 143 stars within this circle and south of our @xmath57 declination limit ( figure [ fig1 ] ) : 12 are b - type stars , including 25 ori , 18 are a - type stars , one of which is the herbig ae / be star v346 ori ( spectral type a8 ; @xcite ) , and 21 are f - type stars . a number of these early type stars show ir emission properties consistent with membership in this young stellar group . @xcite used spitzer data to look for circumstellar disks in a subset of the @xcite stars . they studied 7 of the 12 _ hipparcos _ b - type stars , and found one with 24@xmath58 m excess emission and lack of near - ir excesses indicative of a debris disk . their sample also included 13 a - type stars , out of which 7 had debris disks , and 1 ( v346 ori ) had an optically thick disk , for a disk fraction among a - stars of 62% ; of the 5 f - type stars in their sample 3 ( 60% ) had debris disks . in our subsequent discussion we adopt these sources as early type members of the 25 ori group . if a standard initial mass function ( imf ; e.g. @xcite ) is assumed , one would expect that a cluster formed with 12 b - type stars will produce roughly 12 a - stars , 12 f - stars , 18-g stars , 48-k stars and 336-m stars ( down to @xmath59m6 ) . within this area we identify 197 tts from our low - resolution follow up spectroscopy ( 124 inside our 25 ori hectochelle field - field 1 ) , all of them k and m - type ; 21 objects were reported in @xcite and 176 are new identifications , whose detailed properties will be discussed in @xcite . the magnitude limit of our spectroscopic follow - up effectively places our completeness at a spectral type of roughly m4 ( we discuss this with better number statistics in @xcite ) ; therefore , our sample is missing a number of the later type m - stars . still , the number of low - mass young stars we have identified within this region is in agreement , within a factor of @xmath60 , to expectations from a typical imf . figure [ fig2 ] shows the velocity distribution of stars in table [ ttsdata ] . because in our sample @xmath61 the typical velocity errors are @xmath62 . the two regions show clearly distinct kinematics , with well defined peaks located at @xmath63 for the 25 ori field and @xmath64 for the ori ob1b field . the narrow cores @xmath65 of both distributions are not much larger than the estimated errors , and consistent with velocity dispersions in typical regions of star formation . the peak of the velocity distribution in ori ob1a is consistent with the majority of radial velocity measurements for 25 ori ( @xmath66 , @xcite ; @xmath67 , @xcite ; @xmath68 , @xcite ; @xmath69 , @xcite ) , suggesting that the bulk of the tts are indeed related to the star 25 ori . the presence of a @xmath70 shift between the cores of the velocity distributions in ob1a/25 ori region and ob1b qualitatively supports the findings that these two sub - associations are at very different distances , though nearly along the line of sight @xcite . in a recent study , @xcite found two distinct velocity components when analyzing velocity data toward four fields around @xmath4 ori , located in the sub - association ori ob1b . their kinematic _ group 1 _ has velocities @xmath71 . taking the average value of @xmath72 determined by @xcite for ori ob1a , derived for each ori ob1 sub - association are the error of the mean , @xmath73 . from their ob1a and ob1b measurements , the actual mean internal error is @xmath74 and their mean external error is @xmath75 . ] they relate stars in _ group 1 _ with this sub - association ; this is consistent with suggestions that the closer ori ob1a region in fact extends in front of ori ob1b @xcite . the velocities of _ group 1 _ roughly overlap our distribution for 25 ori . however , it is interesting to highlight that the peak of the distribution for the _ group 2 _ of @xcite is located at @xmath76 , @xmath77 off the @xmath78 peak of our 25 ori @xmath79 distribution . with errors in both studies in the range @xmath80 , this is a statistically robust difference . if the kinematics of the `` field '' population of ori ob1a is indeed characterized by the velocity distribution of _ group 1 _ in the @xcite sample , then our results strongly argue in favor of 25 ori cluster being a a distinct entity in velocity space , different from the general population of ob1a , which is widely spread with a low spatial density ( c.f . figs . 5 and 6 of * ? ? ? the distribution of velocities in 25 ori ( field 1 ) looks somewhat skewed to higher velocities ( @xmath81 ; figure [ fig2 ] ) , though with few objects . this is what would be expected from the presence of a few interloper pms stars from the widespread population of ob1a . if this degree of contamination ( 5/47 ) is taken as representative of the field pms population of ori ob1a in the 25 ori area , we would expect that of the 124 tts within our hectochelle field , @xmath82 could be `` contaminants '' from ob1a . the ob1b stars in our sample lie to the west of the main distribution of molecular gas , corresponding to the respective ends of the orion a and b clouds ( figure [ fig1 ] ) . the gas nearest the stars has a heliocentric radial velocity @xmath83 ( e.g. , figure 5 of * ? ? ? * ) , velocity as the stars in our hectochelle field . there is also a degree of asymmetry in the velocity distribution for ori ob1b ( right panel in figure [ fig2 ] ) , this time extending to lower @xmath79 , toward the same velocity range expected of ob1a stars and of 25 ori . this is not surprising if we recall that ori ob1a is closer than ob1b , and much more spatially extended , such that along any line of sight in the direction of ob1b there probably will be some pms members of the general population of ori ob1a , that will contribute at these velocities . another fact worth pointing out is that the gas is present over a range of several @xmath84 , which could also account for this asymmetry . the orion belt star nearest to our hectochelle field 2 , in ori ob1b , is @xmath35 ori , with estimated velocities that range from @xmath85 @xcite to @xmath86 @xcite , though most measurements cluster around @xmath87 . @xcite classify @xmath35 ori as a member of ob1b . the _ hipparcos _ parallax is @xmath88 @xcite , which corresponds to a distance of 412 pc , consistent with our assumed distance of 440 pc . the tts in our southern hectochelle field share the same velocity as the nearby gas and @xmath35 ori , indicating that these objects indeed belong to what is called the ob1b sub - association . in their study @xcite found for their _ group 2 _ velocities in the range @xmath89 , peaking at @xmath90 . they identify this group as the `` @xmath4 ori cluster '' , with an age of @xmath45 myr and at a distance of 440 pc , similar to ori ob1b ; however , they argue it is kinematically distinct to ob1b , because they assume the value of @xmath91 from @xcite for this sub - association . our findings do not support their claim . first , the @xmath92 peak velocity we find for ob1b , and the small width of the distribution shown in figure [ fig2 ] , strongly suggest that ob1b and the @xmath4 ori cluster share similar kinematics . ori appears to be younger than the general population of ori ob1b , and with a higher disk fraction ( their figure 13 ) . ] second , if we recompute the average group velocity for the ob1b stars in @xcite , but considering only objects with reliable membership , that are not spectroscopic binaries , and flagged as having constant @xmath79 , we find @xmath93 with a @xmath94 dispersion of @xmath95 . therefore , the peak velocity of the @xcite _ group 2 _ is consistent with the radial velocity of both our sample of spectroscopically confirmed low - mass members , and samples of early type stars in ori ob1b . in contrast to the strongly peaked velocity distributions for the young stars , field stars ( objects showing strong h@xmath22 absorption in our hectochelle spectra ) exhibit an almost flat distribution , with stars at all velocity bins ( lower panels in figure [ fig2 ] ) . other objects recognized as part of the field population are dme stars , which look very similar to wtts in that they have weak h@xmath22 emission , but lack the strong li i 6707 absorption feature characteristic of m stars younger than @xmath96 myr . however , the velocity distribution of dme stars in both fields shows a small excess of objects at the velocity peak for each region . a few of these objects could actually be wtts , but the snr of their low resolution spectra does not allow detection of the li i line . but even if this were the case , we expect to be missing no more than 1 - 2 objects in 25 ori and 2 - 4 in orion ob1b . as mentioned in [ lowres ] and above , the presence of the li i 6707 line strongly in absorption is a clear indicator of youth in k and m - type stars . in figure [ fig3 ] , we show the distribution of li i equivalent widths , @xmath97 , measured in our low - resolution spectra , plotted as a function of the effective temperature for each star , derived from the adopted spectral type and the temperature scale in table a5 of @xcite . in order to compare with our sample , we show the lithium equivalent width measurements by @xcite and @xcite of taurus tts , representative of @xmath98 myr old , low - mass stars . the dotted line indicates the lower boundary of w(li i ) for the majority of taurus tts . we also plot the upper envelopes for the pleiades cluster ( age @xmath99 myr ; @xcite ) using data from @xcite and @xcite , and for the ic 2602 cluster ( age @xmath100 myr ; @xcite ) , from the dataset of @xcite . all the 25 ori and ori ob1b members fall above the upper cluster envelopes ; however , an important fraction of the m - stars in each field fall below the lower boundary of the taurus tts . also , in both orion fields the observed @xmath101 is lower than in taurus . the large spread toward lower values of @xmath97 for the m - type stars has also been observed by @xcite in @xmath4 ori . comparison of the @xmath97 in 25 ori and ob1b members shows that while 40% of all the ori ob1b members in table [ ttsdata ] fall within the taurus tts locus only 22% of the tts in the 25 ori group share this region of the diagram ( see figure [ fig3 ] ) . this analysis includes all stars with velocities within @xmath102 of the peak @xmath79 in each field . in figure [ fig3 ] we have also plotted the line separating wtts from post - t tauri stars ( ptts ) . @xcite used the term ptts for pms stars which have lost their t tauri properties ; @xcite identify as ptts those pms stars with essentially wtts properties , except they fall below the the lithium isoabundance line plotted in figure [ fig3 ] . in general , ptts are expected to be slightly more evolved tts . in the ori ob1b field , the wtts / ptts fraction is 0.48 ; in the 25 ori field it is 0.25 . in contrast , the wtts / ptts fraction for taurus members is 5.57 . we argue that the lower @xmath103 , the increasing fraction of tts with @xmath97 values below the taurus lower boundary as a function of age , and the decreasing wtts / ptts fraction , suggest we are looking at the effects of li depletion over the age range spanned by these three regions . in figure [ fig4 ] we show the color - magnitude diagrams ( cmds ) , of _ all _ tts within our two hectochelle fields ( open and solid circles ) , and for the subset of members for which high - resolution spectra were obtained ( hc - only , listed in table [ ttsdata ] ; open and solid diamonds ) . as in @xcite we adopted distances of 330 pc for the 25 ori group and 440 pc for the ori ob1b field . we also show two sets of isochrones for 1 , 3 , 30 , and 100 myr from @xcite and @xcite . the tts in the 25 ori field follow a relatively well defined band in the cmd . the spread observed is largely consistent with the upper limit of 0.75 magnitudes expected from unresolved binaries ( the dashed - lined isochrone in figure [ fig4 ] ) , plus a small spread introduced if we assume the stars follow some distance distribution along the line of sight ( @xmath104 at 400 pc corresponds to @xmath105 pc , or 0.04 magnitudes ) . variability should not affect in an important way our cmds because we use for each object the mean magnitudes derived from our multi - epoch optical survey ( see * ? ? ? * ) . from our photometry and spectral types for the tts members , assuming the intrinsic colors in table a5 of @xcite , and the extinction law of @xcite with @xmath106 , we compute an overall mean @xmath107 mags for the 25 ori cluster , in good agreement with the e(b - v)= 0.09 obtained by @xcite . for the 25 ori group we also plot the v and @xmath108 values for _ hipparcos _ stars ( including 25 ori ; * ? ? ? * ) , v346 ori and the excess ir emission early type stars from @xcite ; the v , b photometry for these later objects is from @xcite , transformed to @xmath108 assuming a mean @xmath107 and the appropriate colors for their spectral types from @xcite . similarly , we show the location of the _ hipparcos _ b - type stars and the belt star @xmath35 ori in the cmd diagram of ori ob1b . all these early type stars fall on or close to the the zams , consistent with them being the higher mass members of these stellar populations . the band of tts in the 25 ori field is roughly encompassed by the 3 - 10 myr isochrones . at the bright end of our tts sample ( v@xmath109 ) the stars seem to cross over to the left , towards the 30 myr isochrone ; this could be due to the photometry for some of these stars being affected by saturation ( the bright limit for our photometry varies with each ccd in the quest camera , but is roughly between v@xmath110 ) . alternatively , this could be due to uncertainties in the location of the birthline at these range of masses @xcite . at the faint end we note a deviation from the theoretical models that we attribute to limitations in the currently available pms isochrones . at v@xmath111 , @xmath112 the bulk of our stars in the cmd seems to deviate slightly downwards from the @xcite isochrones . with the baraffe tracks , which are considered to be more appropriate for low mass stars ( e.g. * * ; * ? ? ? * ) , the behavior is opposite , the lower mass stars seem systematically younger ( or the tracks bend down too steeply ) . a similar discrepancy is found in the ori ob1b field . overall , the baraffe models produce mean ages with are @xmath113 younger than those derived from the the siess isochrones . for the larger sample we derive an average age of @xmath7 myr from the @xcite isochrones , and of @xmath105 myr from the @xcite isochrones , in agreement with our determination in @xcite with smaller number of objects . for the hc - only sample in 25 ori the resulting average ages are similar . for both tts samples within the orion ob1b field , the resulting average ages are @xmath114 myr from the siess et al . isochrones and @xmath115 myr from the baraffe et al . models . in the ob1b field we find an average @xmath116 mags . within the uncertainties , the age derived here for 25 ori is the same as for the general ori ob1a sub - association in @xcite , though for this larger region the spread in ages for the individual stars is larger , probably caused in some measure by the increase in distance depth along the line of sight as one encompasses much wider areas . with a well defined , spatially confined , numerous sample in ori ob1b , resulting in a smaller spread in the cmd , the age difference between this younger region and the older ori ob1a is now firmly established . this age difference of a factor @xmath117 is consistent with the indications of li i depletion we discuss in [ lithium ] , and with the decay in accretion indicators shown by @xcite and considered here in the following section . + our finding of slightly different kinematics between the 25 ori cluster and what can be interpreted as the widely spread pms low - mass population of ori ob1a , suggest that although both stellar populations probably share a common origin , a previously unrecognized degree of substructure is present in this region . the fraction of ctts , or stars thought to be accreting from their circumstellar disks , can be derived by comparing the value of w(h@xmath22 ) for each spectral type in our low resolution spectroscopy , with the criteria in @xcite : a star is considered to be a ctts if @xmath118 in the range k0-k5 , @xmath119 for k7-m2.5 , @xmath120 for m3-m5.5 , and @xmath121 for m6-m7.5 . inside each 0.5 deg radius hectochelle field , and considering _ all _ tts , the ctts fraction in the 25 ori field is 5.6% ( 7 out of 124 stars ) , while in the ori ob1b field the ctts fraction is 12.6% ( 15 out of 119 stars , @xmath6 higher ) . these values are almost a factor of @xmath122 lower than those reported in @xcite . however , this apparent discrepancy can be easily explained by considering the following : first , in @xcite our sample for ori ob1b included regions like the very young ngc 2024 cluster ( @xmath123 myr ) which has a large number of ctts , and is nominally located within ori ob1b if one uses the @xcite boundaries . second , as one increases the census of pms stars in older regions like ori ob1a , the most frequent type of members are wtts , which tends to lower the accretor fraction . if we assume that our present ctts fraction in 25 ori is more representative of this region , then we find it is a factor of @xmath124 larger than what @xcite obtained in the @xmath7 myr old ngc 7160 ( 1 accretor in their sample of 55 members ) , but much smaller than the @xmath125% they report for the @xmath115 myr old cluster tr 37 . the higher ctts fraction in 25 ori when compared to ngc 7160 could be because this region is indeed younger , or due to the small number statistics in the @xcite sample . in order to provide a first look at the spatial distribution of young stars in this aggregate , we computed a spatial density map by counting the number of tts in squares @xmath126 in side ; because the spectroscopic followup is most spatially uniform for the brighter stars , we only considered tts with v@xmath127 ( the non - overlapping hectospec circular fields produce circular `` imprints '' on the spatial distribution for the fainter members , as can be seen in figure [ fig1 ] ) . the result is shown in figure [ fig5 ] . the largest starred symbol marks the location of 25 ori , and the belt stars @xmath128 and @xmath35 ori ; the small solid starred symbols correspond to b - type stars included as probable members of the 25 ori cluster in the list of @xcite , and _ hipparcos _ b - stars classified as members of ori ob1b by @xcite . there is a peak in the spatial distribution of low - mass young stars in the 25 ori region , containing 8 tts ( an implied density of 128 @xmath129 ) , at @xmath130 , @xmath131 south - east of 25 ori . @xcite place their cluster center at @xmath132 , @xmath133 , which given our bin size agrees with our determination . the density of stars falls off to @xmath123/bin at a radius of @xmath134 , which corresponds to 7 pc at the assumed distance of 330 pc . this value is slightly larger than what @xcite found for the younger @xmath4 ori cluster ( @xmath135 pc ) . at a velocity dispersion of @xmath62 , an unbound stellar aggregate would expand roughly 1 pc every 1 myr . if the 25 ori group resembled the @xmath4 ori cluster at an age of @xmath115 myr , a naive dynamical picture would have it evolve to a cluster radius of @xmath136 pc at @xmath137 myr . however , we must caution that the detailed spatial structure can not yet be fully investigated from our present data . first , because of gaps between the ccd detectors in the quest ccd mosaic camera , artifacts appear such as the e - w gap apparent at @xmath138 ( figure [ fig1 ] ) . second , we have not yet completed follow - up spectroscopy of the photometric candidates located north of @xmath57 ( figures [ fig1 ] and [ fig2 ] ) . therefore , if more young stars turn up northward of that line , the actual membership and spatial extent of the 25 ori group may be larger than shown here , and the point with the highest density of members could well shift somewhat . to illustrate this point we have plotted as small magenta stars the tts with @xmath79 within 1@xmath4 of the peak velocity for the 25 ori cluster ( 34 objects ) . it can be seen that these stars concentrate in the northern half of the hectochelle field , with 74% located in this area . the highest density is in the ne quadrant of the field , mostly within the highest contour of the spatial density map . we conclude that the spatial distribution of the kinematical members within the hectochelle field suggests the cluster may extend further north ( the apparent dearth of members close at the northernmost part of the field could well be an incompleteness effect ) . @xcite used sloan digital sky survey data ( sdss ) to look for tts in a @xmath139 wide equatorial strip between @xmath140 and @xmath141 . in his fig.8 he shows an excess of candidate pms stars at @xmath142 and @xmath143 , which he identifies as the south tip of the 25 ori cluster . because of this he derives a larger cluster radius of 8 - 11 pc . though his sample does not overlap the 25 ori nor the ori ob1b fields discussed here , we can compare with the larger scale distribution of stars in our orion ob1 survey . the feature identified by mcgehee as part of 25 ori can be seen as an elongated density enhancement in our spatial density map , roughly @xmath144 south of 25 ori ; additionally , we find a number of faint tts at this location ( figure [ fig1 ] ) . even taking into account this group of young objects , there is an apparent paucity of stars beyond @xmath134 south from 25 ori ; radial velocities need to be obtained before these objects can be interpreted as related to the 25 ori cluster . at present we are obtaining additional hectochelle fields north and south of the 25 ori field discussed here , and also in nearby regions of ori ob1a . these observations will not only help us constrain the spatial extent and refine the kinematics of this unique sample of young , low - mass stars , but will also provide for the first time important information on the actual velocity distribution of the sparse pms population of the orion ob1a sub - association .

we report here on the photometric and kinematic properties of a well defined group of nearly 200 low - mass pre - main sequence stars , concentrated within of the early - b star 25 ori , in the orion ob1a sub - association . the group also harbors the herbig ae / be star v346 ori and a dozen other early type stars with photometry , parallaxes , and some with ir excess emission , consistent with group membership . the number of high and low - mass stars is in agreement with expectations from a standard initial mass function . the velocity distribution for the young stars in 25 ori shows a narrow peak centered at , very close to the velocity of the star 25 ori . this velocity peak is offset from the velocity characterizing the younger stars of the ori ob1b sub - association , and from the velocity of more widely spread young stars of the ori ob1a population near the ori cluster ; this result provides new and compelling evidence that the 25 ori group is a distinct kinematic entity , and that considerable space and velocity structure is present in the ori ob1a sub - association . + the highest density of members is located near the star 25 ori , but the actual extent of the cluster can not be well constrained with our present data . in a simple - minded kinematic evolution scenario ,

we report here on the photometric and kinematic properties of a well defined group of nearly 200 low - mass pre - main sequence stars , concentrated within of the early - b star 25 ori , in the orion ob1a sub - association . we refer to this stellar aggregate as the 25 orionis group . the group also harbors the herbig ae / be star v346 ori and a dozen other early type stars with photometry , parallaxes , and some with ir excess emission , consistent with group membership . the number of high and low - mass stars is in agreement with expectations from a standard initial mass function . the velocity distribution for the young stars in 25 ori shows a narrow peak centered at , very close to the velocity of the star 25 ori . this velocity peak is offset from the velocity characterizing the younger stars of the ori ob1b sub - association , and from the velocity of more widely spread young stars of the ori ob1a population near the ori cluster ; this result provides new and compelling evidence that the 25 ori group is a distinct kinematic entity , and that considerable space and velocity structure is present in the ori ob1a sub - association . the low - mass members follow a well defined band in the color - magnitude diagram , consistent with an isochronal age of myr , depending on the assumed evolutionary model . the drop in the overall li i equivalent widths and accretion fraction between the younger ori ob1b and the 25 ori group , is consistent with the later being significantly older , independent of the absolute age calibration . + the highest density of members is located near the star 25 ori , but the actual extent of the cluster can not be well constrained with our present data . in a simple - minded kinematic evolution scenario , the 25 ori group may represent the evolved counterpart of a younger aggregate like the ori cluster . + the 25 ori stellar aggregate is the most populous myr sample yet known within 500 pc , setting it as an excellent laboratory to study the evolution of solar - like stars and protoplanetary disks .

astro-ph0701710

i

we have used the hectochelle spectrograph on the 6.5 m mmt to obtain high resolution spectra of 149 low - mass pms stars distributed in two fields located in the orion ob1 association , one field placed on the 25 ori group originally identified by @xcite , the other near the belt star @xmath35 ori , in the ori ob1b sub - association . we determined radial velocities with errors @xmath145 for 78 stars ( 47 in the 25 ori field and 31 in the ori ob1b field ) . the pms members of the 25 ori group have radial velocities in a narrow range , peaking at @xmath1 ; this value is very close to that of 25 ori itself , suggesting this may be indeed the most massive star in this stellar aggregate . the stars belonging to the ori ob1b sub - association peak at @xmath146 , and also show a very narrow distribution . these two differing values clearly show that these are two separate populations , and give strength to findings of a significant distance difference between these two groups . however , the 25 ori group not only is distinct in velocity space from the ori ob1b sub - association . the cluster peak @xmath79 is @xmath77 off from the peak velocity found by @xcite for stars they identify as belonging to the orion ob1a sub - association . therefore the 25 ori group constitutes a distinct kinematic group , clearly differentiated in velocity space from both the younger and more distant ob1b , and from what seems to be the general , widely spread population of ori ob1a . the color - magnitude diagrams yield ages of 7 - 10 myr for the 25 ori group , and of 4 - 5 myr for ori ob1 , depending on the assumed set of isochrones . the observed spread in each sample is roughly consistent with the upper limit expected for a population of unresolved binaries , combined with the distance depth estimated for each region . our finding of a similar age but slightly different kinematics between the 25 ori cluster and what can be interpreted as the widely spread pms low - mass population of ori ob1a , suggest that both stellar populations probably share a common origin , but also that a previously unrecognized degree of spatial and kinematic substructure is present in this region . the overall behavior of the li i equivalent widths from one region to the other , and the decline of a factor @xmath122 in the fractions of ctts are consistent with the 25 ori group being significantly older than ori ob1b , independent of the absolute age calibration . a first approach to the spatial structure of the 25 orionis group , with the caveat of an incomplete census , suggests that the low - mass pms stars peak at @xmath130 , @xmath131 south - east of the star 25 ori , with a maximum surface density of @xmath147 . however , the pms stars with @xmath79 values within @xmath94 of the cluster peak velocity concentrate slightly north of the density maximum . we argue that this may indicate that the cluster does indeed extend further north . + we derive a cluster radius of @xmath105 pc . in a simple - minded kinematic evolution scenario , this value is consistent with the 25 ori group representing the evolved counterpart of a @xmath115 myr old aggregate like the @xmath4 ori cluster . c. briceo acknowledges support from grant s1 - 2001001144 of fonacit , venezuela . this work has been supported by nsf grant ast-9987367 and nasa grant nag5 - 10545 . we are grateful to susan tokarz at cfa , who is in charge of the reduction and processing of fast , hectospec and hectochelle spectra . we thank the invaluable assistance of the observers and night assistants , in particular freddy moreno , orlando contreras , ubaldo sanchez and gregory rojas , at the venezuela schmidt telescope that made possible obtaining the data over these past years . we also acknowledge the support from the cida technical staff , and in particular of gerardo snchez . briceo , c. , preibisch , t. , sherry , w. h. , mamajek , e. e. , mathieu , r. d. , walter , f. m. , zinnecker , h. 2006 , in protostars & planets v. , b. reipurth , d. jewitt , and k. keil ( eds ) , university of arizona press , tucson . fabricant , d.g . , hertz , e.n . , szentgyorgyi , a.h . , fata , r.g . , roll , j.b . , & zajac , j.m . 1998 , construction of the hectospec : 300 optical fiber - fed spectrograph for the converted mmt , proc . spie , 3355 , 285 szentgyorgyi , a.h . , cheimets , p. , eng , r. , fabricant , d.g . , geary , j.c . , hartmann , l. , pieri , m.r . , roll , j.b . 1998 , proc . spie , vol . 3355 , p. 242 - 252 , optical astronomical instrumentation , sandro dodorico , ed . rcccclrrrrrrcc 19 & 05:23:30.93 & + 01:45:49.3 & 15.87 & 2.44 & m3 & -5.4 & 0.4 & -4.70 & 17.6 & 1.5 & 5.9 & w & 25ori + 198 & 05:23:46.57 & + 01:45:15.8 & 13.97 & 1.27 & k4 & -0.1 & 0.5 & -0.08 & 19.1 & 0.5 & 17.8 & w & 25ori + 199 & 05:23:55.36 & + 01:34:18.7 & 16.92 & 2.40 & m3 & -4.4 & 0.3 & -5.21 & 20.1 & 1.4 & 5.8 & w & 25ori + 200 & 05:24:02.30 & + 01:53:21.5 & 16.54 & 2.36 & & -5.1 & & -5.12 & 19.1 & 1.2 & 5.7 & w & 25ori + 24 & 05:24:04.26 & + 01:48:30.5 & 16.34 & 2.22 & m2 & -6.1 & 0.3 & -5.67 & 19.3 & 0.9 & 9.1 & w & 25ori + 201 & 05:24:07.56 & + 01:38:41.7 & 16.28 & 2.17 & m3 & -3.2 & 0.2 & -6.07 & 19.9 & 1.7 & 3.4 & w & 25ori + 25 & 05:24:10.36 & + 01:44:07.6 & 15.42 & 1.88 & m0 & -2.6 & 0.3 & -1.42 & 19.6 & 0.7 & 13.4 & w & 25ori + 202 & 05:24:18.14 & + 01:39:22.9 & 17.41 & 2.61 & m3 & -4.7 & 0.5 & -4.44 & 18.8 & 1.8 & 3.1 & w & 25ori + 203 & 05:24:20.27 & + 01:40:54.8 & 16.66 & 2.37 & m3 & -5.6 & 0.4 & -3.37 & 19.0 & 1.4 & 5.9 & w & 25ori + 204 & 05:24:25.45 & + 01:48:14.3 & 17.45 & 2.72 & m4 & -6.6 & 0.6 & -6.37 & 18.0 & 1.7 & 3.2 & w & 25ori + 205 & 05:24:26.64 & + 01:18:13.9 & 14.77 & 1.99 & m2 & -2.1 & 0.3 & -2.08 & 25.1 & 0.7 & 12.0 & w & 25ori + 206 & 05:24:41.04 & + 01:54:38.6 & 14.93 & 1.54 & k5 & -53.5 & 0.5 & -43.42 & 18.8 & 0.9 & 11.4 & c & 25ori + 207 & 05:24:52.27 & + 01:38:43.9 & 13.63 & 1.16 & k4 & -0.8 & 0.5 & -0.61 & 24.2 & 0.8 & 15.0 & w & 25ori + 208 & 05:24:54.18 & + 01:34:02.1 & 18.08 & 3.22 & m5 & -10.0 & 0.6 & -3.51 & 19.9 & 1.8 & 3.1 & w & 25ori + 209 & 05:25:01.92 & + 01:34:56.4 & 16.87 & 2.56 & m3 & -5.8 & 0.5 & -4.74 & 18.5 & 1.2 & 5.6 & w & 25ori + 29 & 05:25:02.07 & + 01:37:21.2 & 16.19 & 2.49 & m3 & -7.6 & 0.5 & -7.13 & 22.1 & 1.1 & 7.1 & w & 25ori + 210 & 05:25:03.61 & + 01:44:12.1 & 16.92 & 2.46 & m3 & -5.9 & 0.3 & -4.15 & 19.6 & 1.6 & 5.2 & w & 25ori + 211 & 05:25:08.76 & + 01:45:54.3 & 13.98 & 1.24 & k5 & -0.1 & 0.5 & -0.13 & 19.4 & 0.5 & 17.6 & w & 25ori + 212 & 05:25:13.55 & + 01:16:20.6 & 17.55 & 2.72 & m3 & -6.9 & 0.5 & -3.64 & 21.4 & 2.1 & 3.5 & w & 25ori + 213 & 05:25:16.72 & + 01:16:15.9 & 16.08 & 2.53 & m3 & -4.4 & 0.2 & -4.07 & -0.1 & 2.1 & 5.2 & w & 25ori + 214 & 05:25:17.04 & + 01:48:22.4 & 13.42 & 1.04 & k2 & -0.2 & 0.5 & -0.06 & 19.1 & 0.5 & 17.6 & w & 25ori + 215 & 05:25:27.70 & + 01:41:46.9 & 17.54 & 2.63 & m3.5 & -8.0 & 0.2 & -4.28 & 17.4 & 2.0 & 4.0 & w & 25ori + 216 & 05:25:34.25 & + 01:34:05.7 & 18.45 & 2.95 & m4.5 & -7.1 & 0.3 & -7.02 & 17.5 & 1.6 & 4.1 & w & 25ori + 217 & 05:25:34.39 & + 01:52:19.8 & 15.29 & 1.92 & m1 & -2.1 & 0.3 & -1.70 & 19.2 & 0.7 & 13.2 & w & 25ori + 218 & 05:25:35.18 & + 01:43:40.6 & 17.29 & 2.62 & m4 & -7.7 & 0.3 & -4.31 & 19.0 & 1.7 & 4.2 & w & 25ori + 219 & 05:25:35.65 & + 01:28:23.2 & 15.05 & 1.82 & m0 & -1.3 & 0.5 & -0.13 & 21.0 & 0.6 & 13.4 & w & 25ori + 220 & 05:25:38.89 & + 02:01:29.9 & 14.01 & 1.19 & k4 & -0.7 & 0.4 & -0.40 & 19.0 & 0.7 & 15.8 & w & 25ori + 221 & 05:25:39.57 & + 01:42:53.7 & 15.10 & 1.94 & m0 & -1.8 & 0.5 & -1.53 & 20.6 & 0.7 & 12.4 & w & 25ori + 222 & 05:25:39.72 & + 01:25:46.9 & 16.03 & 2.49 & m3 & -9.9 & 0.3 & -7.47 & 15.5 & 1.9 & 6.1 & w & 25ori + 223 & 05:25:39.94 & + 01:40:21.1 & 16.50 & 2.41 & m3 & -5.3 & 0.4 & -4.35 & 21.2 & 1.1 & 6.7 & w & 25ori + 35 & 05:25:45.91 & + 01:45:50.2 & 14.72 & 1.91 & k7 & -10.3 & 0.4 & -15.72 & 18.8 & 1.0 & 11.0 & c & 25ori + 224 & 05:25:46.74 & + 01:43:30.4 & 17.21 & 2.60 & m3 & -20.3 & 0.3 & -13.67 & 18.4 & 1.7 & 3.1 & w & 25ori + 36 & 05:25:50.37 & + 01:49:37.3 & 16.00 & 2.22 & m3 & -8.9 & 0.5 & -3.92 & 17.9 & 0.8 & 10.7 & w & 25ori + 225 & 05:25:51.82 & + 01:47:36.1 & 16.17 & 2.58 & m4 & -4.9 & 0.2 & -3.45 & 18.5 & 1.3 & 5.8 & w & 25ori + 226 & 05:25:52.61 & + 01:34:44.2 & 17.75 & 2.73 & m4 & -4.9 & 0.3 & -3.98 & 20.4 & 1.3 & 4.5 & w & 25 ori + 227 & 05:25:59.05 & + 01:23:34.7 & 16.30 & 2.60 & m4 & -4.8 & 0.2 & -4.99 & 20.2 & 1.2 & 6.0 & w & 25ori + 228 & 05:26:06.36 & + 01:45:46.7 & 16.30 & 2.26 & m2 & -3.4 & 0.2 & -3.84 & 20.6 & 0.9 & 8.8 & w & 25ori + 38 & 05:26:06.41 & + 01:37:11.8 & 16.18 & 2.26 & m2 & -7.5 & 0.5 & -4.04 & 20.8 & 1.1 & 9.1 & w & 25ori + 229 & 05:26:07.84 & + 01:23:08.3 & 15.95 & 2.43 & m3 & -4.3 & 0.2 & -3.71 & 24.1 & 1.6 & 5.5 & w & 25ori + 230 & 05:26:08.02 & + 01:41:15.2 & 15.44 & 1.94 & m2 & -4.9 & 0.5 & -2.90 & 19.9 & 1.1 & 11.6 & w & 25ori + 231 & 05:26:10.10 & + 01:18:44.3 & 16.42 & 2.69 & m4 & -9.0 & 0.2 & -7.28 & 21.4 & 1.7 & 3.9 & w & 25ori + 232 & 05:26:11.18 & + 01:54:52.3 & 14.70 & 1.94 & m2 & -3.7 & 0.3 & -3.22 & 19.1 & 1.2 & 10.5 & w & 25ori + 233 & 05:26:21.98 & + 01:47:57.6 & 16.30 & 2.46 & m3 & -5.0 & 0.3 & -4.46 & 18.3 & 1.2 & 6.8 & w & 25ori + 234 & 05:26:38.04 & + 01:21:45.5 & 15.35 & 2.08 & m2 & -4.0 & 0.4 & -3.77 & 24.0 & 0.8 & 10.4 & w & 25ori + 235 & 05:26:42.65 & + 01:39:47.3 & 16.65 & 2.33 & m2.5 & -5.7 & 0.3 & -7.69 & 20.3 & 1.3 & 5.5 & w & 25ori + 42 & 05:26:50.43 & + 01:55:03.6 & 15.99 & 2.16 & m2 & -3.8 & 0.3 & -2.15 & 20.7 & 0.9 & 8.7 & w & 25ori + 236 & 05:27:00.52 & + 01:49:27.2 & 16.51 & 2.36 & m3.5 & -7.7 & 0.3 & -5.45 & 29.6 & 1.1 & 8.2 & w & 25ori + 89 & 05:31:19.99 & -01:46:53.3 & 15.47 & 1.57 & k7 & -1.6 & 0.4 & -1.18 & 30.5 & 0.7 & 13.3 & w & ob1b + 92 & 05:31:31.75 & -01:47:05.6 & 16.90 & 2.21 & m2 & -3.6 & 0.2 & -5.53 & 23.6 & 1.9 & 3.7 & w & ob1b + 97 & 05:31:42.80 & -01:39:48.3 & 16.79 & 2.41 & m2 & -5.4 & 0.2 & -6.46 & 30.4 & 1.8 & 4.8 & w & ob1b + 237 & 05:31:48.29 & -01:47:59.2 & 16.36 & 2.36 & m3 & -4.3 & 0.4 & -3.78 & 30.8 & 0.8 & 10.5 & w & ob1b + 99 & 05:31:50.79 & -01:55:17.5 & 17.37 & 2.44 & m2 & -5.5 & 0.2 & -5.06 & 30.9 & 1.1 & 8.2 & w & ob1b + 238 & 05:32:00.42 & -01:40:11.0 & 15.85 & 1.88 & & -47.5 & & -47.46 & 32.4 & 0.8 & 13.1 & c & ob1b + 239 & 05:32:03.47 & -01:56:32.0 & 14.91 & 1.56 & k5 & -1.2 & 0.3 & -1.31 & 4.6 & 0.6 & 16.3 & w & ob1b + 240 & 05:32:05.41 & -01:46:31.8 & 17.42 & 2.47 & & -5.7 & 0.2 & -4.16 & 29.9 & 1.7 & 4.0 & w & ob1b + 106 & 05:32:21.51 & -01:43:45.6 & 16.80 & 2.44 & m2 & -7.0 & 0.3 & -8.39 & 31.0 & 2.1 & 3.4 & w & ob1b + 241 & 05:32:25.69 & -01:33:11.8 & 14.92 & 1.67 & k6 & -3.8 & 0.6 & -3.23 & 29.9 & 0.8 & 13.0 & c & ob1b + 242 & 05:32:28.93 & -01:27:34.6 & 17.85 & 2.06 & m1 & -0.2 & 0.2 & -2.03 & 55.6 & 2.1 & 3.2 & w & ob1b + 243 & 05:32:29.90 & -01:52:40.0 & 15.37 & 1.69 & k6 & -0.9 & 0.5 & -0.61 & 31.5 & 0.6 & 16.7 & w & ob1b + 110 & 05:32:34.35 & -01:50:46.3 & 15.41 & 1.60 & m0 & -2.0 & 0.6 & -1.72 & 31.7 & 0.7 & 12.5 & w & ob1b + 244 & 05:32:59.21 & -02:00:38.1 & 16.00 & 2.47 & m1 & -4.8 & 0.5 & -4.45 & 20.5 & 0.8 & 9.8 & w & ob1b + 245 & 05:33:06.62 & -01:47:03.2 & 17.60 & 2.79 & m3 & -6.6 & 0.3 & -5.01 & 33.0 & 1.7 & 5.1 & w & ob1b + 246 & 05:33:10.69 & -01:31:35.8 & 15.06 & 2.17 & & -2.5 & & -2.54 & 25.5 & 0.9 & 11.6 & w & ob1b + 247 & 05:33:19.87 & -01:56:28.9 & 17.57 & 2.37 & m2 & -2.8 & 0.2 & -2.63 & 32.3 & 1.1 & 7.7 & w & ob1b + 248 & 05:33:22.72 & -01:43:42.2 & 16.04 & 1.91 & k7 & -3.3 & 0.6 & -2.12 & 27.6 & 0.8 & 11.8 & w & ob1b + 118 & 05:33:25.76 & -01:32:18.7 & 14.70 & 1.26 & k5 & -1.0 & 0.5 & -0.72 & 31.6 & 0.6 & 15.9 & w & ob1b + 249 & 05:33:29.30 & -01:30:28.2 & 17.00 & 2.69 & m3 & -5.5 & 0.3 & -6.05 & 32.9 & 1.9 & 4.2 & w & ob1b + 250 & 05:33:36.11 & -01:28:52.6 & 15.00 & 1.69 & k6 & -1.3 & 0.5 & -1.30 & 29.8 & 0.7 & 15.8 & w & ob1b + 251 & 05:33:41.87 & -01:47:40.7 & 16.14 & 1.94 & m0 & -3.3 & 0.5 & -8.35 & 29.7 & 0.8 & 11.5 & w & ob1b + 252 & 05:33:43.63 & -01:13:36.2 & 17.29 & 2.48 & m3 & -3.2 & 0.3 & -3.11 & 27.9 & 1.8 & 4.0 & w & ob1b + 253 & 05:33:46.84 & -01:56:55.1 & 15.01 & 1.49 & k3 & -0.5 & 0.4 & -0.63 & 31.5 & 0.6 & 17.2 & w & ob1b + 122 & 05:33:47.29 & -01:20:27.3 & 15.85 & 1.85 & m1 & -1.9 & 0.5 & -1.66 & 29.8 & 0.8 & 11.6 & w & ob1b + 254 & 05:34:00.70 & -01:50:08.4 & 15.70 & 1.78 & k6 & -2.4 & 0.5 & -2.06 & 31.2 & 0.8 & 12.4 & w & ob1b + 255 & 05:34:06.17 & -01:58:55.9 & 16.75 & 2.39 & m3 & -4.4 & 0.2 & -2.98 & 26.7 & 2.2 & 5.1 & w & ob1b + 256 & 05:34:15.31 & -01:15:19.6 & 16.57 & 2.46 & m3 & -3.8 & 0.4 & -3.82 & 30.2 & 1.7 & 5.6 & w & ob1b + 257 & 05:34:15.46 & -01:34:29.8 & 17.77 & 2.80 & m4 & -7.3 & 0.5 & -7.35 & 27.6 & 2.1 & 3.3 & w & ob1b + 258 & 05:34:17.87 & -01:41:08.0 & 14.57 & 1.50 & k4 & -1.6 & 0.5 & -0.56 & 27.2 & 0.7 & 14.1 & w & ob1b + 134 & 05:34:38.98 & -01:46:56.4 & 15.25 & 1.71 & m0 & -4.6 & 0.5 & -2.84 & 29.0 & 0.6 & 14.9 & w & ob1b + ) wtts , and small stars to bright ctts . plus symbols indicate the faint ( v@xmath154 ) wtts , and plus symbols enclosed in open squares the faint ctts . the belt stars , 25 ori and @xmath4 ori are indicated with large starred symbols . the solid circles indicate the location of the hectochelle fields ( field 1 and field 2 ) . the smaller dashed - lined circle around 25 ori corresponds to the kharchenko et al . ( 2005 ) cluster radius . the grey scale image shows the dust extinction map from schlegel et al . ( 1998 ) ; the countours represent @xmath155 values of 0.1 to 1.5 magnitudes . the thick dashed line outlines the boundaries between ori ob1a and ob1b from @xcite . the horizontal dashed lines mark the limits of the survey region where most of our spectroscopic follow - up has been carried out so far.[fig1 ] ] measurements . these values have later been rounded off to one decimal place for their presentations in table [ ttsdata ] , more representative of our actual error . data for taurus pms stars ( age @xmath98 myr ) are shown as @xmath156 s @xcite . the dotted line traces the lower boundary to the majority of taurus tts . the long dash - dot line corresponds to the lithium isoabundance line from @xcite , which separates wtts from ptts . we show as a short - dash line the upper envelope for the pleiades cluster ( age @xmath99 myr ; @xcite . data from @xcite and @xcite ) , and in the long - dash line the upper envelope of the ic 2602 cluster ( age @xmath100 myr ; @xcite . data from @xcite ) . our typical error bar is also indicated in each panel.[fig3 ] ] ) t tauri stars in the orion ob1a and ob1b sub - associations . the contours correspond to stellar densities of 2 , 4 , 6 , 8 , and 10 stars per 0.25 deg square bin . the largest starred symbol marks the location of 25 ori ( @xmath52 ) . the smaller stars around 25 ori indicate the b - type stars from the list of kharchenko et al . ( 2005 ) in their ascc 16 cluster . the orion belt stars @xmath128 and @xmath35 , in the ori ob1b region , are also indicated with large starred symbols . the short dashed line around the belt stars indicates the ori ob1b boundaries of @xcite . the two light circles show the 1 deg wide hectochelle fields . the small open stars in the 25 ori hectochelle field indicate tts with velocities within 1@xmath4 of the @xmath79 peak for the cluster ( @xmath157).[fig5 ] ]

the low - mass members follow a well defined band in the color - magnitude diagram , consistent with an isochronal age of myr , depending on the assumed evolutionary model . the drop in the overall li i equivalent widths and accretion fraction between the younger ori ob1b and the 25 ori group , is consistent with the later being significantly older , independent of the absolute age calibration . the 25 ori group may represent the evolved counterpart of a younger aggregate like the ori cluster . + the 25 ori stellar aggregate is the most populous myr sample yet known within 500 pc , setting it as an excellent laboratory to study the evolution of solar - like stars and protoplanetary disks .

we report here on the photometric and kinematic properties of a well defined group of nearly 200 low - mass pre - main sequence stars , concentrated within of the early - b star 25 ori , in the orion ob1a sub - association . we refer to this stellar aggregate as the 25 orionis group . the group also harbors the herbig ae / be star v346 ori and a dozen other early type stars with photometry , parallaxes , and some with ir excess emission , consistent with group membership . the number of high and low - mass stars is in agreement with expectations from a standard initial mass function . the velocity distribution for the young stars in 25 ori shows a narrow peak centered at , very close to the velocity of the star 25 ori . this velocity peak is offset from the velocity characterizing the younger stars of the ori ob1b sub - association , and from the velocity of more widely spread young stars of the ori ob1a population near the ori cluster ; this result provides new and compelling evidence that the 25 ori group is a distinct kinematic entity , and that considerable space and velocity structure is present in the ori ob1a sub - association . the low - mass members follow a well defined band in the color - magnitude diagram , consistent with an isochronal age of myr , depending on the assumed evolutionary model . the drop in the overall li i equivalent widths and accretion fraction between the younger ori ob1b and the 25 ori group , is consistent with the later being significantly older , independent of the absolute age calibration . + the highest density of members is located near the star 25 ori , but the actual extent of the cluster can not be well constrained with our present data . in a simple - minded kinematic evolution scenario , the 25 ori group may represent the evolved counterpart of a younger aggregate like the ori cluster . + the 25 ori stellar aggregate is the most populous myr sample yet known within 500 pc , setting it as an excellent laboratory to study the evolution of solar - like stars and protoplanetary disks .

0704.1450

i

it is a continuous topic of study how a galaxy evolves with time @xcite . integrated photometry of star clusters and star associations in a galaxy can provide fundamental insight on the star - formation history @xcite . @xmath5 colors of galaxies depend mainly on their history of star formation @xcite . the fact that morphologically peculiar galaxies show bluer @xmath6 colors in the two color diagram suggests that galaxies with peculiar appearance have experienced anomalous star formation histories characterized by recent burst . models with recent bursts of star formation ( sfr ) predict colors that in general lie off the normal relation for models with monotonically decreasing sfr @xcite , for example , a very recent strong burst results in an excessively blue @xmath6 for a given @xmath7 @xcite . integrated photometry of star clusters and star associations in a galaxy would provide fundamental insight on the star - formation history @xcite . ngc 3367 , the disk galaxy with a stellar bar of our study , is noteworthy because of observational characteristics , some of them are : * 1 ) * it shows a bipolar synchrotron outflow from the nucleus with a compact unresolved source with deconvolved diameter less than 65 pc , and two large lobes straddling the nucleus with a total , projected extent on the sky , from the north - east to the south - west lobe of about 12 kpc ( an image like a radio galaxy , but from , a nearby late disk galaxy ) ; only the south - west lobe shows polarized emission , suggesting that this lobe is out of the plane of the disk and is closer to the observer than the other lobe @xcite ; * 2 ) * the axis of the ejected outflow is highly inclined with respect to the axis of rotation of the disk of the galaxy @xcite ; * 3 ) * there is a lot of molecular gas mostly concentrated in the central 9@xmath8 with an unresolved source with m(h@xmath9 m@xmath10 ; this molecular mass suggests an optical extinction value a@xmath11 magnitudes toward the nucleus @xcite ( as it has been detected through its co(j=1 - 0 ) emission with the ovro mm array@xmath12 ) ; its total molecular ( h@xmath13 ) mass within 11.4 kpc diameter is m(h@xmath14 m@xmath10 @xcite ; * 4 ) * it shows a bright southwest optical structure ( resembling a `` bow shock '' ) with a collection of h@xmath15 knots at a galactocentric radius of about 10 kpc from the nucleus @xcite , * 5 ) * it has _ crooked _ arms in its northwest side , and * 6 ) * it seems to be isolated with no similar - diameter galaxy in its proximity ; ngc 3367 lies , behind the leo group of galaxies , at a distance of 43.6 mpc , with a closest companion lying at a projected distance of @xmath16 563 kpc or 18 optical diameters away @xcite . ngc 3367 is an sbc(s ) barred spiral galaxy with a stellar bar structure of diameter @xmath17 kpc oriented at a position angle ( p.a . ) @xmath18 . the disk is inclined with respect to the plane of the sky at @xmath19 @xcite . ngc3367 has an x ray luminosity much larger than any normal spiral galaxy @xcite . its radio continuum emission at a @xmath20 angular resolution shows weak radio continuum emission extended throughout the disk @xcite . from fabry perot observations of the h@xmath15 emission it is deduced that the kinematic major axis lies projected on the disk at a p.a . of 51@xmath21 @xcite . its optical spectrum shows moderately broad h@xmath15+[nii ] lines with fwhm@xmath22 km s@xmath23 , but its emission of h@xmath24 is stronger than its emission of [ oiii]@xmath25 and there is weak emission of he ii @xmath26 suggesting the existence of wr stars @xcite . ngc 3367 has been clasiffied as an hii nucleus ( from the optical line ratios ; see @xcite and normal content of atomic hydrogen with m@xmath27 m@xmath10 @xcite . table 1 lists relevant information for ngc 3367 coming from the literature . previous @xmath28 phometry of ngc 3367 has been obtained for the whole galaxy with magnitudes reported in rc3 @xcite and compiled in the nasa extragalactic data base ( ned)@xmath29 as listed in table 1 ; previously reported colors are as follows : @xmath30 = 1.45 . larson & tinsley ( 1978 ) have discussed different factors that would affect the @xmath5 colors , among them are _ reddening _ ( galactic and intrinsic ) , _ gaseous emission lines and nonthermal emission _ , _ chemical composition _ and _ initial mass function _ ( imf ) . the color @xmath7 of ngc 3367 agrees with the color expected from a late type disk galaxy @xcite ; however the @xmath6 color of ngc 3367 certainly lie above the _ mean _ value of normal disk galaxies and the position in the @xmath6 vs @xmath7 @xcite is more in agreement with the statistical colors of galaxies from the arp atlas of peculiar galaxies @xmath31 . these colors of ngc 3367 suggest that this late type barred galaxy is currently having many regions with recent star formation . although galactic reddening is a major source of uncertainity in the @xmath5 colors , for this galaxy it is not a major concern given its lalitude , @xmath32 . we report our magnitude estimates for the different structures corrected for galactic extinction . gaseous emission lines , different chemical composition and different initial mass function may contribute to the uncertainities of the expected colors @xcite . this paper reports new @xmath33 photometry of 81 individual structures throughout ngc 3367 using the 84 cm optical telescope in san pedro mrtir , baja california , mxico @xcite . for the data reduction and analysis we used the iraf@xmath34 task _ phot _ with an aperture radius of 8 pixels ( @xmath35 pc ) . the existence of a close connection between violent galactic dynamical phenomena is consistent with theoretical expectations that high velocity collisions and shock fronts should be effective in compressing gas to high densities and triggering rapid star formation . section 2 reports the observations , 3 reports the results and 4 gives the discussion and finally 5 describes the conclusions .

the images show many different structures indicating that star formation is going on in the most part of the disk . ngc 3367 is known to have a very high concentration of molecular gas distribution in the central regions of the galaxy and bipolar synchrotron emission from the nucleus with two lobes ( at 6 kpc ) forming a triple structure similar to a radio galaxy .

we report new detailed surface and photometry of 81 stellar structures in the disk of the barred galaxy ngc 3367 . the images show many different structures indicating that star formation is going on in the most part of the disk . ngc 3367 is known to have a very high concentration of molecular gas distribution in the central regions of the galaxy and bipolar synchrotron emission from the nucleus with two lobes ( at 6 kpc ) forming a triple structure similar to a radio galaxy . we have determined the and magnitudes and and colors for the central region ( nucleus ) , a region which includes supernovae 2003 aa , and 79 star associations throughout ngc 3367 . estimation of ages of star associations is very difficult due to several factors , among them : filling factor , metallicity , spatial distribution of each structure and the fact that we estimated the magnitudes with a circular aperture of 16 pixels in diameter , equivalent to kpc . however , if the colors derived for ngc 3367 were similar to the colors expected of star clusters with theoretical evolutionary star tracks developed for the lmc and had a similar metallicity , ngc 3367 show 51% of the observed structures with age type swb i ( few tens of myrs ) , with seven sources outside the bright surface brightness visible disk of ngc 3367 .

0704.1450

c

to conclude , we have obtained several images in the broadband filters @xmath0 and @xmath1 in order to estimate the optical magnitudes and colors of 81 different stellar structures throughout the disk of ngc 3367 . the structures were chosen from the images in the @xmath1 and @xmath61 filters by eye at different locations of the disk of the galaxy in order to have enough of them as to be able to compare their colors as a function of their spatial location . it included structures to the north - east , south and west , well outside of the semicircle structure with bright surface brightness . our estimated magnitudes for the ngc 3367 , after correcting for galactic extinction are @xmath66 , @xmath67,@xmath68 , @xmath69 , and @xmath70 . ngc 3367 global colors , after being corrected for galactic extinction are @xmath71 = 1.48 . all images except the image in @xmath42 were convolved with an appropiate two dimensional gaussian function in order to have a final of 2@xmath111 full width at half maximum , since the seeing was different for each filter and was about 1@xmath112 to @xmath113 . the 81 stellar structures reported in this paper were selected mainly from the @xmath61 and the @xmath1 images based on the location in the disk in order to have as many as possible from different positions in ngc 3367 . we have made careful analysis of the calibration methods to estimate magnitudes and have compared different iraf tasks , in particular , _ qphot _ and _ phot _ utilizing different apertures in order to estimate the uncertainities in the final magnitudes at different filters with 9 stars in m 67 as our standards . in the case of estimating the magnitudes for the structures throughout the disk in ngc 3367 , we have made careful analysis utilizing different iraf tasks , in particular , _ qphot _ and _ phot _ using different aperture diameters for the bright stars in the field of ngc 3367 in order to estimate the uncertainities in the final magnitudes at different filters before estimating the final magnitudes reported for the different structures in ngc 3367 . the magnitudes reported here for the structures in ngc 3367 were estimated using an aperture radius of 8 pixels ( @xmath38 pc ) . we were able to estimate the optical magnitudes @xmath0 and @xmath1 and colors @xmath114 and @xmath3 for 81 different stellar structures throughout the disk in ngc 3367 . it is difficult to estimated the ages of the structures in ngc 3367 given our circular aperture diameter , equivalent to @xmath4 kpc . however if their colors were taken as representative as the colors of star clusters ( studied by many other authors with better angular resolution , appropiate chemical abundance and current theoretical star evolutionary tracks ) in the lmc many have colors equivalent to cluster types swb i , and swb ii suggesting that many are young associations with only tens of millions of years of age . we found 41 structures out of 81 ( 50% ) with age type swb i. several of those structures lie near or in spiral arms ; some lie outside of the bright surface brightness visible disk ( for example the poss image ) . in order to understand better the large scale environment of ngc 3367 it would also be very important to determine the large scale spatial distribution and kinematics of atomic hydrogen ( hi ) and new observations with high angular resolution of the emission of the molecular gas ( co , h@xmath13 ) in the center of ngc 3367 .

we report new detailed surface and photometry of 81 stellar structures in the disk of the barred galaxy ngc 3367 . we have determined the and magnitudes and and colors for the central region ( nucleus ) , a region which includes supernovae 2003 aa , and 79 star associations throughout ngc 3367 . however , if the colors derived for ngc 3367 were similar to the colors expected of star clusters with theoretical evolutionary star tracks developed for the lmc and had a similar metallicity , ngc 3367 show 51% of the observed structures with age type swb i ( few tens of myrs ) , with seven sources outside the bright surface brightness visible disk of ngc 3367 .

we report new detailed surface and photometry of 81 stellar structures in the disk of the barred galaxy ngc 3367 . the images show many different structures indicating that star formation is going on in the most part of the disk . ngc 3367 is known to have a very high concentration of molecular gas distribution in the central regions of the galaxy and bipolar synchrotron emission from the nucleus with two lobes ( at 6 kpc ) forming a triple structure similar to a radio galaxy . we have determined the and magnitudes and and colors for the central region ( nucleus ) , a region which includes supernovae 2003 aa , and 79 star associations throughout ngc 3367 . estimation of ages of star associations is very difficult due to several factors , among them : filling factor , metallicity , spatial distribution of each structure and the fact that we estimated the magnitudes with a circular aperture of 16 pixels in diameter , equivalent to kpc . however , if the colors derived for ngc 3367 were similar to the colors expected of star clusters with theoretical evolutionary star tracks developed for the lmc and had a similar metallicity , ngc 3367 show 51% of the observed structures with age type swb i ( few tens of myrs ) , with seven sources outside the bright surface brightness visible disk of ngc 3367 .

astro-ph0502376

c

the detection limit estimates also permit us to calculate an upper limit of the projected separation between a star and a potential planet , as follows . we consider a typical @xmath3m@xmath4 planet , we calculate the theoretical value ( retrieved by the models ) of the star / planet contrast , we then place this value on the ordinates of the detection limit curve ( see for example fig.[det_lim1 ] ) and finally we retrieve ( on the abscissae ) the distance beyond which we can affirm that such a planet should not exist ( because it was not detected ) . table [ tab4 ] shows , for each target , such upper limits for the star / exo - planet distance . table [ tab5 ] shows the frequency at which we would be able to detect a @xmath3m@xmath4 planet at different distances from the parent star . by analysing these results from a statistical point of view , we can calculate ( fig.[prob ] ) the cumulative distribution of the upper limit of the distance star / exo - planet for our sample of targets . the thin line represents the cumulative distribution obtained for @xmath3m@xmath4 planets . we find that ( fig.[prob ] ) , with respect to our sample of targets , in @xmath119 of cases ( median value ) , there are not planets at distances larger than @xmath5 au and , in @xmath120 of cases , there are no planets at distances larger than @xmath10 au . we underline that we are considering a @xmath3m@xmath4 planet just as a reference , but the same calculation could be done for more and/or less massive planets in the range @xmath22-@xmath6 m@xmath4 . in the case of more massive planets , the cumulative distribution should have a median value ( @xmath119 ) associated with an angular separation smaller than @xmath5 au . in the case of less massive planets , the cumulative distribution should have a median value ( 50 @xmath2 ) associated with an angular separation larger than @xmath5 au . to better appreciate the sensitivity with respect to the mass of the planets we also calculated the cumulative distribution for @xmath6m@xmath4 planets ( fig.[prob ] - bold line ) . we find that , in @xmath119 of the cases ( median value ) there are no planets at distances larger than @xmath7 au and in @xmath120 of the cases there are not planets at distances larger than @xmath9 au . table [ tab4 ] and table [ tab5 ] show the upper limit of the projected star / planet separation and statistical results also for @xmath6m@xmath4 planets . the numbers given in these tables illustrate that it is relatively unlikely that a massive planet exists beyond a certain distance from the star . for example the fact that no @xmath3m@xmath4 planet was found for @xmath118 of our targets beyond @xmath60 au ( see table[tab4 ] ) means that the likelood for the existance of such planets beyond this distance is @xmath12 @xmath121 @xmath2 i.e. @xmath12 @xmath122@xmath2 . this last estimation is useful for the reader to have an idea of how much the size of the sample affects the statistical results . we recall that we are using the term _ probability _ in a less conventional way . a precise ( statistically speaking ) definition of _ probability _ should need some positive detection that we obviously do not have . which are the implications of these results with respect to models such as those cited in section [ intr ] ( gravitational scattering model and outward migration ) , explaining the transfer of planets to large distances ( some tens of au ) from the central star ? our results indicate that the frequency of planet jumps or outward migration is quite low . more precisely , it seems difficult for @xmath6m@xmath4 planets to find a stable orbit at distances larger than @xmath88 au , and that @xmath3m@xmath4 planets at distances larger than @xmath123 au , at least in the range of early ages that we considered . we note that the statistical analysis presented in fig.[prob ] related to the @xmath6m@xmath4 planets is particularly interesting because , due to a steeper cumulative distribution concentrated at small projected separations from the central star , it permits us to better constrain the probability of location of planets . we also recall that such massive planets are rarely detected at distances smaller than @xmath30 au using radial velocity measurements . as described in the introduction , the radial velocity technique is sensitive only to planets orbiting at closer distances ( @xmath73 @xmath30 au ) from the central star . it is interesting to analyse what the direct imaging technique reveals about @xmath6m@xmath4 planets at distances larger than @xmath30 au . looking at our results , we can state that , for most of the targets ( @xmath12 @xmath124 of cases ) , there are no @xmath6m@xmath4 planets at distances larger than @xmath12 @xmath88 au . we find that the probability to find planets equal or more massive than @xmath6m@xmath4 at large distances is low as well as the probability to find them at close distances ( @xmath42 @xmath30 au ) as appears from radial velocity surveys ( marcy et al . massive planets are expected to form beyond the so called _ line _ distance ( @xmath12 @xmath3 au for the solar - like stars au for typical solar - like star . this distance is calculated for simple thermal equilibrium and is estimated equal to @xmath19-@xmath29 au for late type stars ( black 1980 ) ] ) ( lissauer , 1993 ) and from this distance they might migrate inward . our study shows that , at least for late spectral type ( k and m ) stars , if such massive ( @xmath12 @xmath6m@xmath4 ) planets form beyond the snow line , we can envisage the following possibilities : * ( 1 ) * massive planets form and can be found in the narrow range of distances _ snow line _ - @xmath88 au from the central star , * ( 2 ) * at distances larger than @xmath88 au only planets having masses smaller than @xmath6m@xmath4 can form and can be found , * ( 3 ) * if any @xmath6m@xmath4 planet would have formed beyond the _ snow line _ , the formation and inward migration necessarily happen on a time scale @xmath42 @xmath6myr . to test the hypotheses ( 1 ) and ( 2 ) one should improve the contrast at small angular separations . to test the hypothesis ( 3 ) one should select a sample of stars younger than ours . unfortunately , stars having this property are placed preferably at distances @xmath38 @xmath8 pc from the observer . even future ground - based planet finders will be able to detect planets only at larger separations ( a few tens of au ) from the central star if the targets are placed at such distances ( @xmath38 @xmath8 pc ) . for this reason , it would be probably more efficient and appropriate to observe them from space . in this way , one could by - pass the limitations imposed by the atmosphere on the attainable angular resolution and to probe the same projected separations ( as those analysed in this paper ) from these distant stars . the resolution reachable in space by the hubble space telescope ( hst ) is not good enough to probe such small physical distances . in a previous study ( brandner et al . 2000 ) , a set of pre - main sequence t tauri stars in the chamaleon t ( @xmath19-@xmath3 myr at @xmath125 pc ) and scorpius - centaurus ob ( @xmath3-@xmath14 myr at @xmath125 pc ) associations were observed . results showed that at @xmath46 au it would be possible to detect only more massive planets ( @xmath12 @xmath60m@xmath4 ) than those we would detect with naco ( this paper ) . we should thus wait for a new generation of space telescope to probe such close distances at so early ages . other interesting issues can be retrieved by our analysis concerning the core - accretion model . our results provide interesting information concerning mechanisms to explain planet formation . we are considering here the core - accretion model originally proposed by pollack ( 1996 ) since it provides an explanation for the formation of all gaseous as well as solid planets . it claims that a growing solid core , after reaching a critical mass , accretes a massive atmosphere . according to our results , this model could work , assuming that massive planets ( @xmath38 @xmath6m@xmath4 ) form in a narrow @xmath3-@xmath14 au distance from the central star in a time scale of @xmath12@xmath25 yr ( typical time scale of disk lifetime ) . one of the critical aspects of the core - accretion model has always been that it can not explain the presence of planets observed with the radial velocity technique at close distances from the central star . the time necessary for the formation plus the migration should be longer than the typical disk lifetime ( @xmath12@xmath25 yr , haisch et al . 2001 ) . the modified version of the pollack model , recently proposed by alibert et al . ( 2004 ) , seems to solve this problem . using a detailed description of the composition ( gas plus solid ) of the disk this model reduces the time necessary for a planet to form and migrate by a factor of @xmath6 . with such a modification , the process of formation and migration might need a time shorter than the typical disk lifetime . following the predictions of alibert s model , it would be possible that we did not detect massive planets simply because they formed at ages ( @xmath42 @xmath6myr ) earlier than those of our selected sample . this means that our results are consistent with the core - accretion model in the alibert formulation . this model seems thus promising due to the fact that it matches with both observational issues coming from radial velocity measurements and also from direct imaging observations . we finally mention that our results indicate that a sort of _ exo - planet desert _ for massive ( @xmath12 @xmath6m@xmath4 ) planets is observed at distances larger than @xmath14 au from the stars of our survey . this desert seems to extend to quite large distances from the central star . a recent survey ( mccarthy @xmath31 zuckerman , 2004 ) carried out with the near - infrared camera nirc and a coronograph at keck did not detect any @xmath3-@xmath13 m@xmath4 exo - planet in the range @xmath126-@xmath127 au around @xmath12 @xmath128 stars having a mean age of @xmath127 myr . we would like to mention the relevant improvement in terms of sensitivity reached by our study ( using naco at the vlt ) with respect to previous published results . a recent analysis of massive planet detection ( neuhuser et al . 2003 ) , carried out with the mpe speckle camera at the eso s @xmath129 m ntt telescope , put an upper limit of @xmath16 au on the distance between the star and @xmath6m@xmath4 exo - planets in the case of targets belonging to @xmath11 pictoris ( @xmath12@xmath13 myr ) . results from our study show that we can exclude any @xmath6m@xmath4 planets at distances larger than @xmath14 au ( a physical distance @xmath15 times smaller ) for targets belonging to the same moving group . our results show a better sensititity also with respect to previous observations made with hst ( neuhuser et al . estimates provided by this study give an upper limit distance between the star and @xmath3m@xmath4 planets of @xmath12 @xmath1 au . stars observed by neuhuser et al . ( 2002 ) belong to a @xmath12@xmath29myr old systems ( well younger than our sample - @xmath6-@xmath23 myr ) . models predict a mean difference in h and k band of the order of at least @xmath22 mag between the age of stars in neuhuser et al . study and ours . we thus deduce that the same instrument ( hst ) would have an upper limit for the star / planet distance quite a bit larger than @xmath1 au for @xmath3m@xmath4 planets in the @xmath6-@xmath23 myr age range . how can we improve our results to better constrain planet - formation models ? it is evident that an increase of the achievable contrast at smaller angular separations shifts the median value of the cumulative distributions to smaller angular separations ( fig.[prob ] ) . this means that the upper limit of the projected star / exo - planet separation decreases . however , we note that , using the observational strategy employed in our survey , we can hardly improve the sensitivity at subarcsecond distances using a @xmath21 meter class telescope as illustrated in fig.[sdi_pot ] . this figure shows the detection limit obtained for one of our targets for an integration time of @xmath3 , @xmath6 and @xmath130 minutes . the deep image was filtered from low spatial frequencies before we calculated the detection limit . we observe that , beyond @xmath19@xmath48 , the reachable contrast increases with increasing the integration time ( @xmath12 @xmath19 mag in @xmath14 min ) . at distances smaller than @xmath19@xmath48 , on the contrary , a longer integration time does not increase the contrast because we are strongly limited by the speckle noise . the differential imaging technique proposed by racine et al . ( 1999 ) is a rather efficient method to reduce the speckle noise at small angular separations from the central star . images taken simultaneously at slightly different wavelengths are subtracted from each other . since the speckle noise of both images is nearly the same/@xmath131 factor . ] , the speckle noise is eliminated in the resulting image providing one can sufficiently limit static aberrations . the differential technique finds a useful application in detecting cool methane - rich faint objects . rosenthal et al . ( 1996 ) first proposed observations of the same star done simultaneously in two different wavelengths which are located _ `` on '' _ and _ `` off '' _ the methane ( ch@xmath70 ) absorption band . if one subtracts the image taken in the absorption band from the one taken outside the absorption band , planet / brown dwarf features appear in the continuum . the absorption at @xmath132 @xmath71 m , in the ch@xmath70 band , is a clear signature of any object having temperature t @xmath27 @xmath133 k ( giant exo - planets and t - type brown dwarfs ) . we can thus increase the sensitivity ( contrast ) at subarcsecond distances using the recently implemented naco / sdi ( simultaneous differential imager ) instrument . this instrument employs the differential technique in @xmath39 band . preliminary results ( close et al . 2004 , lenzen et al . 2004 ) indicate a @xmath26 @xmath12 @xmath134 mag at @xmath110 from the central star . considering our averaged estimate of @xmath26 @xmath91 @xmath114 mag in the @xmath39 band ( see section [ sensit ] ) , we should gain @xmath12 @xmath29 mag in contrast using naco / sdi at @xmath110 ( see fig.[sdi_pot ] ) . a further and fundamental improvement in contrast should be attained by future ground - based `` planet finders '' , i.e. instruments supported by ao systems providing a better strehl ratio . the contrast reachable by such an instrument at @xmath110 should be @xmath26 @xmath12 @xmath135 mag in @xmath136-@xmath39 bands ( see fig.[sdi_pot ] ) . we refer in particular to the top level requirements of cheops , a second generation instrument for the vlt conceived for planet detection ( gratton et al . we think that the principal goals of these instruments ( naco / sdi and ground - based planet finders ) in the context of the detection of massive and young exo - planets and the understanding of mechanisms responsible for exo - planet formation are the following : * ( a ) * they will permit us to provide answers to the hypothesis ( 1 ) and ( 2 ) ( see section [ dist ] ) . * ( b ) * they will be rather appropriate to do studies similar to the one proposed in this paper but applied to a sample of targets characterized by an earlier spectral type ( i.e. solar - like type ) in the same range of ages . this is due to the better contrast reachable at subarcsecond distances ( see fig.[sdi_pot ] ) . * ( c ) * they will be appropriate instruments to detect even fainter exo - planets ( i.e. in the @xmath19-@xmath3 m@xmath4 range ) at subarcsecond angular separations from the central star .

for example , for the pictoris group , ( myr ) , we did not detect anym planet at distances larger than au . a previous study carried out with m class telescopes put an upper limit form planets at au . for our closest target ( v oph - d = pc ) our results are discussed with respect to mechanisms explaining planet formation and migration and to forthcoming observational strategies and future planet finder observations from the ground .

we report on a survey devoted for the search of exo - planets around young and nearby stars carried out with naco at the vlt . the detection limit for among the best available targets vs. the angular separation from the star is presented . the non - detection of any planetary mass companion in our survey is used to derive , for the first time , the frequency of the upper limit of the projected separation planet - stars . in particular , we find that in of cases , nom planet ( or more massive ) has been detected at projected separations larger than au and nom planet ( or more massive ) has been detected at projected separations larger than au . in of cases , these values increase to au and au respectively . the excellent sensitivity reached by our study leads to a much lower upper limit of the projected planet - star separation compared with previous studies . for example , for the pictoris group , ( myr ) , we did not detect anym planet at distances larger than au . a previous study carried out with m class telescopes put an upper limit form planets at au . for our closest target ( v oph - d = pc ) it is shown that it would be possible to detect am planet at a minimum projected separation from the star of au and am planet at a minimum projected separation of au . our results are discussed with respect to mechanisms explaining planet formation and migration and to forthcoming observational strategies and future planet finder observations from the ground .

1606.01138

i

( genzel et al . 2010 ) , the supermassive black hole ( bh ) at the galactic center ( gc ) , generates a deep gravitational potential that is expected to bind tens of thousands of stellar remnants , such as neutron stars ( ns ) or bh that have settled dynamically into the central parsec of the milky way ( morris 1993 ; lee 1995 ; miranda - escud & gould 2000 ; muno et al . deep radio surveys were so far unsuccessful in detecting either ordinary or millisecond pulsars , leading to the `` missing pulsar problem '' ( wharton et al . 2012 ; dexter & oleary 2014 ) . surprisingly a few years ago the magnetar sgrj1745 - 2900 was discovered via its outburst activity ( mori et al . 2013 ; rea et al . 2013 ; eatough et al . 2013 ; kaspi et al . 2014 ; coti zelati et al . 2015 ) , representing the first radio and x - ray pulsar discovered in the galatic center region ( at less than a few parsecs from ) . many millisecond radio pulsars are expected in the region , but currently not a single one has been detected . due to the three body interaction between this concentration of degenerate stars and multiple stellar systems , a large population of x - ray binaries is also expected . the monitoring of x - ray transients allows us to study this population ( pfahl & loeb 2004 ; muno et al . 2005 ; hopman 2009 ; faucher - giguere & loeb 2011 ) . the majority of accreting x - ray binaries spend most of their time in a quiescent state ( below the detection limit ) , sporadically interrupted by outbursts during which the x - ray luminosity rises by many orders of magnitudes ( fender & belloni 2012 ) . pioneering works on monitoring of gc x - ray sources have been performed with and ( muno et al . 2005 ; wijnands et al . 2006 ; campana et al . 2009 ; degenaar et al . 2012 ; 2015 ) . was discovered by the satellite on feb . 6@xmath3 2016 ( reynolds et al . 2016 ) during the first x - ray observation after the gc exited the solar constraint window . the x - ray telescope ( xrt ) data showed a bright ( @xmath4 erg @xmath5 s@xmath6 , in the @xmath7 kev range ) transient located at less than 16 arcsec from ( reynolds et al . 2016 ) . was detected also in the 20 - 80 kev energy range ( esposito et al . 2016 ) , while observations with the karl g. jansky very large array ( vla ) and giant metrewave radio telescope ( gmrt ) did not detect the radio counterpart ( however the limits still leave open the possibility of a hard state accreting bh or ns ) or any pulsation ( maan et al . 2016 ; bower et al . 2016 ) . within a week from this discovery , observed the field and refined the transient position to : ra@xmath817:45:40.66@xmath90.34 , dec@xmath8 - 29:00:15.61@xmath90.33 , where no previous x - ray sources were ever detected ( baganoff et al . therefore , is a new transient source . in this paper we report the identification of the source as a low - inclination x - ray binary hosting a neutron star or a black hole , most probably with a low mass companion . we discuss the temporal and spectral characteristics of the transient using the long - term daily x - ray monitoring of the field performed by the satellite , the high energy long term monitoring provided by the satellite , a 35 ks observation obtained in director s discretionary time ( to study the dust scattering halo ) performed about 20 days after the onset of the outburst as well as vla observations . finally , we report on the search for the near - ir counterpart within vlt/ and grond data .

we report on the identification of the new galactic center ( gc ) transient as a likely low mass x - ray binary ( lmxb ) located at only 16 arcsec from . we observed the field with on february for 35 ks , detecting the source in the soft state , characterised by a low level of variability and a soft x - ray thermal spectrum with a high energy tail ( detected by up to kev ) , typical of either accreting neutron stars or black holes .

we report on the identification of the new galactic center ( gc ) transient as a likely low mass x - ray binary ( lmxb ) located at only 16 arcsec from . this transient was detected on 2016 february during the gc monitoring , and it showed long - term spectral variations compatible with a hard to soft state transition . we observed the field with on february for 35 ks , detecting the source in the soft state , characterised by a low level of variability and a soft x - ray thermal spectrum with a high energy tail ( detected by up to kev ) , typical of either accreting neutron stars or black holes . we observed : i ) a high column density of neutral absorbing material , suggesting that is located near or beyond the gc and ; ii ) a sub - solar iron abundance , therefore we argue that iron is depleted into dust grains . the lack of detection of fe k absorption lines , eclipses or dipping suggests that the accretion disc is observed at a low inclination angle . radio ( vla ) observations did not detect any radio counterpart to . no evidence for x - ray or radio periodicity is found . the location of the transient was observed also in the near - ir with grond at mpg / eso la silla 2.2 m telescope and vlt/ pre- and post - outburst . within the error region we find multiple objects that display no significant variations . [ firstpage ] x - rays : binaries , methods : observational , techniques : spectroscopic

1201.5056

i

using our deep _ chandra _ observation , we detect metal - rich ejecta features in snr n49 . these ejecta features include a `` bullet '' that is most likely a stellar fragment travelling beyond the southwestern boundary of the snr . we also find an ejecta feature in the eastern part of the snr , nearly in the opposite side of the snr to the bullet . both of these ejecta features show highly enhanced si and s abundances by an order of magnitude above the lmc values . we do not find compelling evidence for overabundant o and/or fe in these ejecta features . if n49 is a remnant of a core - collapse explosion of a massive progenitor , the si - rich nature of ejecta may be considered to be nucleosynthesis products of explosive o - burning or incomplete si - burning from deep inside of the sn . on the other hand , the estimated si- and s - rich ejecta mass ratio appears to favor a type ia origin for n49 . if n49 was the remnant of a type ia sn , the suggested physical association between n49 and sgr 052666 would be unambiguously ruled out . however , we note that our sn ejecta study is limited because we used only some small localized ejecta features rather than the integrated ejecta composition from the entire snr to represent the true sn nucleosynthesis . follow - up studies to reveal the comprehensive ejecta composition in n49 are required to unveil the true origin of this snr . our new _ chandra _ observation allows us to detect the blast wave forming the swept - up shell in the southern boundary with significant photon statistics . since this part of the shell is not affected by spectral complications due to the snr s interaction with dense clumpy clouds , it provides a useful opportunity to reveal the dynamics of the snr more accurately than previous works . we estimate the sedov age of @xmath71 @xmath9 4800 yr and the explosion energy @xmath72 @xmath9 1.8 @xmath3 10@xmath4 erg for n49 . our spectral analysis of the quiescent x - ray emission from sgr 052666 using the deep exposure clearly reveals the presence of a bb emission ( @xmath53 @xmath9 0.44 kev ) in addition to a pl component . the implied bb emitting area is relatively small ( @xmath74 @xmath9 56 km ) compared to the canonical size of neutron stars . the estimated pl photon index ( @xmath54 @xmath9 2.5 ) is identical to that of axp 1e 1048.15937 , the well - known candidate transition object between axps and sgrs . alternatively , the observed x - ray spectrum of 052666 can be equally fitted by a two - component bb model . this model indicates that x - ray emission originates from a small ( @xmath74 @xmath9 1 km ) , hot ( @xmath35 @xmath9 1 kev ) spot(s ) in addition to a cooler ( @xmath35 @xmath9 0.4 kev ) surface of the neutron star ( @xmath74 @xmath9 10 km ) . we find marginal evidence for a slow decay in the observed x - ray flux of 052666 ( @xmath92030% for the last @xmath917 yr ) . continuous x - ray monitoring of 052666 is needed to clarify the nature of its long - term light curve . we find a considerable difference in the foreground column by a factor of @xmath93 between two modelings ( bb+pl vs. bb+bb ) of the x - ray spectrum of 052666 . while such a model - dependent discrepancy has been noticed for several other axps , the 052666 case is particularly intriguing because discriminating these competing models may be able to provide some critical clues on the nature of 052666 and n49 : e.g. , their physical association , the origin of x - ray emission of 052666 , and the origin of n49 . this work has been supported in part by the sao under the _ chandra _ grants go9 - 0072a to the university of texas at arlington , and go9 - 0072x to the pennsylvania state university . j.p.h . has been supported in part by the _ grant go0 - 11090x . cccc 10123 & 2009 - 7 - 18 & 26.8 & acis - s3 ( 1/4 subarray ) + 10806 & 2009 - 9 - 19 & 26.5 & acis - s3 ( 1/4 subarray ) + 10807 & 2009 - 9 - 16 & 26.0 & acis - s3 ( 1/4 subarray ) + 10808 & 2009 - 7 - 31 & 28.7 & acis - s3 ( 1/4 subarray ) + 747 & 2000 - 1 - 4 & 39.9 & acis - s3 ( 1/8 subarray ) + 1957 & 2001 - 8 - 31 & 48.4 & acis - s3 ( 1/8 subarray ) + cccccc shell & 0.89@xmath95 & 0.57@xmath96 & 6.35@xmath97 & 6.75@xmath98 & 49.1/68 + sgr_bg & 1.58@xmath43 & 0.56@xmath910.03 & 9.65@xmath99 & 15.45@xmath100 & 258.9/218 + tail & 1.01@xmath101 & 2.02@xmath102 & 0.68@xmath103 & 0.50@xmath104 & 44.9/44 + tail & 1.68@xmath105 & 0.71@xmath106 & 4.02@xmath107 & 1.61@xmath108 & 52.4/49 + head & 1.32@xmath109 & 1.04@xmath110 & @xmath4420.3 & 2.25@xmath111 & 67.0/59 + east & 3.11@xmath112 & 1.09@xmath113 & @xmath4467.0 & 2.68@xmath114 & 144.4/133 + ccccccc shell & 0.32@xmath115 & 0.27@xmath116 & 0.25@xmath910.10 & 0.36@xmath117 & 0.84@xmath118 & 0.21@xmath119 + sgr_bg & 0.24@xmath120 & 0.17@xmath121 & 0.15@xmath122 & 0.24@xmath123 & 0.59@xmath124 & 0.13@xmath125 + tail & 0.28@xmath126 & @xmath881.54 ( 0.58 ) & 0.37@xmath127 & 0.88@xmath128 & @xmath882.30 ( 0.49 ) & 0.28@xmath129 + head & 0.32 & 0.27 & 0.25 & 2.28@xmath130 & 3.22@xmath131 & 0.21 + east & 0.27 & 0.21 & 0.20 & 1.92@xmath132 & 1.39@xmath133 & 0.17 + lccc @xmath35 ( kev ) & 0.44@xmath910.02 & - & - + @xmath54 & - & 2.50@xmath134 & - + @xmath135 ( km ) & 6.0@xmath136 & - & - + @xmath137 ( km ) & 5.5@xmath910.6 & - & - + @xmath138 ( 10@xmath94 erg @xmath32 s@xmath11 ) & 0.40@xmath139 & 0.78@xmath910.13 & 1.18@xmath140 + @xmath141 ( 10@xmath94 erg @xmath32 s@xmath11 ) & 0.33@xmath142 & 0.69@xmath910.11 & 1.01@xmath143 + @xmath144 ( 10@xmath145 erg s@xmath11 ) & 1.68@xmath146 & 3.84@xmath910.65 & 5.52@xmath147 + @xmath148 ( 10@xmath145 erg s@xmath11 ) & 1.37@xmath149 & 3.36@xmath910.54 & 4.74@xmath150 + @xmath33 ( 10@xmath38 @xmath32 ) & - & - & 5.44@xmath151 + @xmath30 ( 10@xmath38 @xmath32 ) & - & - & 0.6 ( fixed ) + @xmath34/n & - & - & 577.4/582 + lccc @xmath35 ( kev ) & 0.39@xmath910.01 & 1.01@xmath120 & - + @xmath135 ( km ) & 9.7@xmath152 & 1.0@xmath910.2 & - + @xmath137 ( km ) & 9.0@xmath910.5 & 0.9@xmath910.2 & - + @xmath138 ( 10@xmath94 erg @xmath32 s@xmath11 ) & 0.73@xmath153 & 0.40@xmath154 & 1.13@xmath155 + @xmath141 ( 10@xmath94 erg @xmath32 s@xmath11 ) & 0.62@xmath156 & 0.35@xmath157 & 0.96@xmath155 + @xmath144 ( 10@xmath145 erg s@xmath11 ) & 0.90@xmath120 & 0.42@xmath158 & 3.96@xmath159 + @xmath148 ( 10@xmath145 erg s@xmath11 ) & 0.77@xmath160 & 0.36@xmath161 & 3.39@xmath162 + @xmath33 ( 10@xmath38 @xmath32 ) & - & - & 1.70@xmath163 + @xmath30 ( 10@xmath38 @xmath32 ) & - & - & 0.6 ( fixed ) + @xmath34/n & - & - & 616.4/582 +

the x - ray spectrum of the bullet is distinguished from that of the main snr shell , showing significantly enhanced si and s abundances . if n49 was produced by a core - collapse explosion of a massive star , the detected si - rich ejecta may represent explosive o - burning or incomplete si - burning products from deep interior of the supernova . on the other hand , the observed si / s abundance ratio in the ejecta may favor type ia origin for n49 . our blackbody ( bb ) + power law ( pl ) model for the quiescent x - ray emission from sgr 052666 indicates that the pl photon index ( 2.5 ) is identical to that of psr 1e1048.15937 , the well - known candidate transition object between anomalous x - ray pulsars and sgrs . alternatively , the two - component bb model implies x - ray emission from a small ( 1 km ) hot spot(s ) ( 1 kev ) in addition to emission from the neutron star s cooler surface ( 10 km , 0.4 kev ) . there is a considerable discrepancy in the estimated column toward 052666 between bb+pl and bb+bb model fits . discriminating these spectral models would be crucial to test the long - debated physical association between n49 and 052666 .

we report on the results from our deep _ chandra _ observation ( 120 ks ) of the supernova remnant ( snr ) n49 and soft-ray repeater ( sgr ) 052666 in the large magellanic cloud . we firmly establish the detection of an ejecta `` bullet '' beyond the southwestern boundary of n49 . the x - ray spectrum of the bullet is distinguished from that of the main snr shell , showing significantly enhanced si and s abundances . we also detect an ejecta feature in the eastern shell , which shows metal overabundances similar to those of the bullet . if n49 was produced by a core - collapse explosion of a massive star , the detected si - rich ejecta may represent explosive o - burning or incomplete si - burning products from deep interior of the supernova . on the other hand , the observed si / s abundance ratio in the ejecta may favor type ia origin for n49 . we refine the sedov age of n49 , 4800 yr , with the explosion energy 1.8 10 erg . our blackbody ( bb ) + power law ( pl ) model for the quiescent x - ray emission from sgr 052666 indicates that the pl photon index ( 2.5 ) is identical to that of psr 1e1048.15937 , the well - known candidate transition object between anomalous x - ray pulsars and sgrs . alternatively , the two - component bb model implies x - ray emission from a small ( 1 km ) hot spot(s ) ( 1 kev ) in addition to emission from the neutron star s cooler surface ( 10 km , 0.4 kev ) . there is a considerable discrepancy in the estimated column toward 052666 between bb+pl and bb+bb model fits . discriminating these spectral models would be crucial to test the long - debated physical association between n49 and 052666 .

astro-ph0509135

i

investigations of multiply imaged high - redshift quasars are important for our basic understanding of the formation and growth of supermassive black holes in galactic centers ( turner 1991 ; haiman & loeb 2001 ) and the ionization state of the universe as a function of time ( madau , haardt , & rees 1999 ; wyithe & loeb 2003a ) . gravitational lensing changes the apparent flux coming from a quasar and thus changes our interpretation of flux - dependent properties ; the discovery that a given quasar is gravitationally lensed means that the naively estimated luminosity is too high . thus , gravitational lensing would modify the expected size of ionized ( ) regions around individual quasars ( cen & haiman 2000 ) and would weaken the lower limits on the neutral fraction in the igm as inferred from the size of regions ( wyithe & loeb 2004 ; mesinger & haiman 2004 ) . this paper concentrates on the effect that gravitational lensing has on the apparent shape of the quasar luminosity function ( comerford , haiman , & schaye 2002 ; wyithe & loeb 2002 ; fan et al . 2003 ) . in a previous paper ( richards et al . 2004 , hereafter paper i ) we investigated whether the known @xmath9 quasars are gravitationally lensed and discussed how the lack of lenses in this sample affects our understanding of the growth of black holes in the early universe ( e.g. , haiman & loeb 2001 ) and the ionization history of the universe at the end of the reionization period ( e.g. , fan et al . 2002 ) . in this paper , we examine the constraints that can be placed on the intrinsic slope of the quasar luminosity function ( qlf ) at @xmath1045 from a search for gravitational lenses in a sample of @xmath1045 quasars ( fan et al . 2001a ; anderson et al . 2001 ; schneider et al . 2001 ; schneider et al . 2005 ) in the sloan digital sky survey ( sdss ; 2000 ) . much theoretical effort has been devoted to placing constraints on the slope of the quasar luminosity function from the fraction of lenses found amongst high-@xmath11 quasars ( e.g. , comerford et al . 2002 ; wyithe & loeb 2002 ) . ( 2002 ) showed that modest constraints could be obtained from a sample of @xmath12 @xmath9 quasars from ground - based imaging ( i.e. , sensitive to @xmath13 splittings ) , and that similar limits could be derived from _ hubble space telescope ( hst ) _ resolution imaging of the ( then ) four known @xmath9 quasars . paper i presented _ hst _ imaging showing that none of those four quasars are strongly gravitationally lensed and derived a limit on the slope of the bright end quasar luminosity function of @xmath14 . ( 2004 ) found even stronger constraints for this sample by including the observation that two quasars appear to be lensed by foreground galaxies but are not multiply imaged . these limits come from magnification bias ( turner , ostriker , & gott 1984 ; narayan 1989 ) , which would be strong if the slope of the qlf were steep and there were many quasars with intrinsic luminosities below the detection threshold . as discussed in paper i , the expected fraction of multiply - imaged quasars at a given redshift depends both on the cosmological model and on the luminosity function of quasars . in the wmap cosmology ( 2003 , using a halo distribution taken from the large n - body simulations of 2001 ) , the fraction of random lines of sight out to @xmath3 that produce multiple images at all splitting angles is of order 0.2% ; this fraction rises to @xmath15% at @xmath16 . if the intrinsic ( unlensed ) qlf has a break in slope , then , in general , the fraction of lensed quasars would increase for apparent fluxes above the break . in a flux - limited survey , there is a strong correlation between luminosity and redshift . if the true qlf possesses a break which moves to fainter luminosities at higher redshift , then the most distant quasars ( which also look through the longest path length ) are expected to be the most likely to be lensed . more explicitly , in the event that no lensing is observed , paper i showed that the tightest constraints on the qlf slope come from @xmath9 quasars , and also that roughly seven @xmath17 quasars have the same statistical power as a single @xmath9 quasar . herein we present the results for a sample of 157 @xmath17 quasars from the sdss that were imaged with _ hst _ ; we find that none of these sources is lensed . as predicted , these quasars provide a constraint on the slope of the qlf that is roughly equivalent to _ hst _ imaging of 22 @xmath9 quasars , limiting the bright end slope of the @xmath35 qlf to @xmath18 . section 2 describes the sample and the data . in 3 we discuss the constraints on the qlf that can be derived from the data . we summarize in 4 . throughout this paper , we adopt the wmap cosmology with @xmath19 , @xmath20 , @xmath21 , an rms mass fluctuation within a sphere of radius @xmath22 mpc of @xmath23 , and power law index @xmath24 for the power spectrum of density fluctuations ( spergel et al . 2003 ) . we also adopt the cosmological transfer function from & hu ( 1999 ) . conversions between @xmath25 and @xmath26 assume @xmath27 ( schmidt , schneider , & gunn 1995 ) with spectral index @xmath28 .

we report on-band snapshot observations of 157 sloan digital sky survey ( sdss ) quasars at using the advanced camera for surveys on the _ hubble space telescope ( hst ) _ to search for evidence of gravitational lensing of these sources . none of the quasars appear to be strongly lensed and multiply imaged at the angular resolution ( ) and sensitivity of _ hst_. the non - detection of strong lensing in these systems constrains the luminosity function to an intrinsic slope of , assuming a break in the quasar luminosity function at . such constraints are important for our understanding of the true space density of high - redshift quasars and the ionization state of the early universe .

we report on-band snapshot observations of 157 sloan digital sky survey ( sdss ) quasars at using the advanced camera for surveys on the _ hubble space telescope ( hst ) _ to search for evidence of gravitational lensing of these sources . none of the quasars appear to be strongly lensed and multiply imaged at the angular resolution ( ) and sensitivity of _ hst_. the non - detection of strong lensing in these systems constrains the luminosity function to an intrinsic slope of , assuming a break in the quasar luminosity function at . this constraint is considerably stronger than the limit of obtained from the absence of lensing in four quasars . such constraints are important for our understanding of the true space density of high - redshift quasars and the ionization state of the early universe .

astro-ph0412110

c

ps2000 drew attention to the relatively long periods and low orbital eccentricities of many of the binary stars they discovered . in combination with the high binary frequency and small fraction of double - lined systems , they argued that their results supported the identification of many of these binary systems as blue stragglers created by mass transfer , a model proposed originally by mccrea ( 1964 ) . cllgm similarly drew attention to the unusual orbital properties of the six field blue stragglers they studied and the ten systems discovered by ps2000 with [ fe / h ] @xmath42 @xmath12 and for which our own software resulted in what we considered compelling orbital solutions . neglecting the three ps2000 systems with periods of less than 20 days ( and whose orbital elements may have been altered by tidal interactions , independent of mass transfer ) , we found that 10 of the 13 binaries had @xmath43 and @xmath44 . for all 13 systems , @xmath45 and @xmath46 . the periods ranged from 167 days up to roughly 1600 days . one should recall that the median orbital eccentricity for normal main sequence , single - lined spectroscopic binaries is about 0.37 , independent of metallicity ( duquennoy & mayor 1991 ; latham et al . 2002 ) . mass transfer appears to be the best explanation for these orbital characteristics , as discussed originally by webbink ( 1986 ) . our earlier paper also discussed stellar systems where mass transfer is likely to have occurred , leaving an overabundance of elements synthesized during the agb evolutionary stage deposited in the outer layers of the receptor . if we confine our attention to the more metal - poor stars , there are three classes of stars to consider . the ch stars are not luminous enough to be agb stars themselves , yet show abundances expected of such stars , implying mass transfer has occurred and also that the companion star is likely to be a white dwarf . mcclure & woodsworth ( 1990 ) found that essentially all ch stars they studied are binaries , and those with orbital solutions showed periods of 328 to 2954 days , and low orbital eccentricities ( @xmath47 ; @xmath48 ) . the subgiant ch " stars discovered by bond ( 1974 ) may be descendents of some blue stragglers , as noted by luck & bond ( 1991 ) . mcclure ( 1997 ) found that 9 of the 10 such stars under long - term radial velocity monitoring are binary systems with long periods . he obtained orbital solutions for six of the sytems , finding orbital periods of 878 to 4140 days , and small orbital eccentricities ( @xmath49 ; @xmath50 , @xmath51 ) . finally , the one well - studied dwarf carbon star , g77 - 61 , has been found to have a nearly circular orbit and a moderately long period of 245 days ( dearborn et al . 1986 ) . one of the primary purposes of the observations reported in this paper was to test the idea that many blue stragglers are binary stars , and that their binary orbital properties confirm this kinship with the more obvious mass transfer systems described above . in figure 4 we update figure 4 from cllgm , which showed the orbital eccentricity vs. log p for the 6 new binary systems reported therein , and the 10 systems fom ps2000 subjected to the same orbital solution analyses . for comparison , we included the 156 orbital solutions for cooler single - lined spectroscopic binaries from latham et al . ( 2002 ) . in this new figure 4 , we highlight the locations of the four new orbital solutions from table 4 using filled circles . ( filled squares are our results from cllgm ; filled diamonds are stars from ps2000 with periods longer than 20 days , and open diamonds are stars from ps2000 with shorter periods . ) as before , the longer orbital period binary stars have unusually low values of the orbital eccentricity . in figure 5 , we take a different perspective , and consider the distribution of orbital eccentricities for stars in figure 4 with periods longer than 20 days . aside from the absence of high orbital eccentricities among the blue stragglers , we note that the orbital eccentricities cluster near zero but have a tail to higher values . this might indicate two different types of mass transfer and orbital evolution , despite the similarity of the orbital periods . alternately , it may reflect the original distribution of orbital eccentricities since binary systems with very high eccentricities evolve more slowly , and so are more likely to preserve a higher - than - average orbital eccentricity . in figure 6 we show the lithium gap " seen among some members of the hyades , using the results of cayrel et al . ( 1984 ) , boesgaard & trippico ( 1986 ) , and boesgaard & budge ( 1988 ) . open circles are measurements and v " symbols represent upper limits . the gap is easily seen between effective temperatures of about 6400 k and 6800 k. the normal lithium abundance for metal - poor dwarfs hotter than about 5400 k ( the spite plateau " ) . is shown as a dashed line . that value is lower than the peak of the hyades dwarfs and is in itself a long - standing puzzle , but beyond the point of this paper . we also show the stars from table 1 , with filled circles for stars that have measured lithium abundances , and which , it turns out , are all also stars with constant velocities . none of the binary stars in table 1 have detectable lithium lines and hence the abundances are only upper limits . these stars are plotted as downward - pointing arrows . note that for hd 142575 , glaspey et al . ( 1994 ) derived @xmath52 = 6550 k , and fulbright ( 2000 ) adopted @xmath52 = 6500 k , but we have adopted the photometric temperature of 6700 k to maintain consistency with the derivation of the temperature for all of our program stars . we have adjusted the lithium abundance derived for the star by fulbright ( 2000 ) as well to account for the change in temperature : log n(li ) rises from 1.45 to 1.58 . ( note as well , however , that glaspey et al . 1994 argued that log n(li ) @xmath3 0.7 . ) the first interesting point is that three of the metal - poor single stars have normal lithium abundances , at least for metal - poor stars . two of the stars , hd 84937 and cs @xmath18 , are very close to our adopted color limits used to identify blue stragglers . small changes in the measured @xmath13 color index or in the reddening estimate could easily shift either star into or out of the blue straggler candidate domain . however , bd+72 94 is considerably bluer and hotter , and in the middle of the hyades lithium gap , yet has a lithium abundance consistent with the spite plateau . conclusions from such a small sample may not be secure , but the results suggest the lithium gap may not exist for single metal - poor stars , or , perhaps , it is shifted to higher temperatures than the stars in our sample . a survey of the metal - poor single stars identified by ps2000 would answer this question . related to this point , hd 142575 , which appears to be single and slightly hotter than the other three single stars , has a reduced lithium abundance according to fulbright ( 2000 ) . is this star distinguishable in any way from the three constant velocity , normal - lithium stars ? if our photometric temperature estimate is correct , the star is slightly hotter than the other single stars , and so might be in the metal - poor equivalent to the hyades lithium gap . table 3 may provide another clue : hd 142575 has a relatively large value for . is rotation a factor in either the formation of the lithium gap or the depletion of lithium more generally ? we need more observations of lithium absorption line strengths in blue metal - poor stars , especially those studied by ps2000 . we conclude that our use of low lithium abundances as a selection criterion is supported by the ( admittedly limited ) data available . we note also that the relation between blue stragglers and lithium depletion has been discussed extensively by ryan et al . ( 2001 ) . ryan et al . ( 2002 ) have noted the modest but significant levels of rotation in three of the blue stragglers discussed in our previous paper ( cllgm ) . for bd+51 1817 , g66 - 30 , and g202 - 65 , they found @xmath22 sin @xmath23 values of @xmath53 , @xmath54,and @xmath55 kms@xmath20 , all of which are larger than values derived for cooler metal - poor dwarfs with normal lithium abundances . ( note that our method obtains somewhat higher values of 9.0 , 8.1 , and 11.6 kms@xmath20 , respectively . ) ryan et al . ( 2002 ) suggested that the likely origin of the rotation was the mass transfer process itself , and discussed the mechanisms by which such a process would lead to lithium depletion . these include mass transfer - induced deep mixing or transfer of lithium - depleted material from the donor star . regarding the latter point , pilachowski et al . ( 1993 ) found that surface lithium depletion in post - main sequence metal - poor stars begins before the stars reach the base of the red giant branch , so mass transfer from a more highly evolved red giant would deposit lithium - depleted material on the recipient main sequence star . we explore here the available rotational velocity information for the stars of table 3 . as described above , we are able to estimate using our grid of synthetic spectra . because different approaches appear to derive different values of , we proceed differentially by comparing values of constant velocity and binary stars only within a particular methodology . thus we make comparisons only between stars we have studied , or among the stars studied by ps2000 , but we do not intermingle those results . for the stars for which we have estimated , we must first explore the results for a control sample " . in figure 7 we show the histograms of the derived values using data taken from latham et al . we include only single stars judged to be main sequence dwarfs , and single - lined spectroscopic binary stars with periods exceeding 25 days . tidal circularization effects are clearly present for metal - poor dwarfs with orbital periods of 20 days or less , but should not be significant for the longer period systems we consider here . none of these three different groups were found to have different distributions of . however , metallicity does seem to have a small influence on the values we derive , as may be seen in figure 7 . we do not claim that figure 7 represents the true distribution of rotational velocities of metal - poor dwarfs because our instrumental resolution ( @xmath56 kms@xmath20 ) prevents accurate determinations for values much smaller than that . on the other hand , we are confident of our results for rotational velocities at or above that of our instrumental resolution . the fraction of stars with @xmath57 8.0 kms@xmath20 in the combined sample is only 4.0% ( 7.7% for the more metal - poor stars and 0.3% for the more metal - rich stars ) . note that we do not believe these results imply that metal - poor dwarfs rotate somewhat faster than metal - rich dwarfs . the differences may be artificial in the sense that the synthetic spectrum templates may introduce metallicity - dependent differences in the derived rotational velocities . in figure 8 we show the rotational velocities we have derived ( open and filled circles ) for the stars of table 3 , plus values from ps2000 ( open and filled squares ) . while the observations of ps2000 were obtained using a system with velocity resolution comparable to ours , they derived values using a different method than have we , which is why we distinguish the two sets of results graphically . the key question is whether mass transfer is a major cause of the blue straggler phenomenon and whether evidence for it exists in higher rotational velocities for the binary systems . because tidal interactions will spin up short - period binary systems , independent of mass transfer , we have excluded binary systems with orbital periods of less than 20 days from the figure or from further consideration here . we consider the results from ps2000 first . there are 14 stars in their study that appear to have constant velocity and have [ fe / h ] @xmath42 @xmath58 . recall that they have interpreted ( correctly , we believe ) these stars to be bona fide young metal - poor main sequence stars . note that all of them have @xmath42 12 kms@xmath20 , and @xmath3@xmath4 = 10.1 kms@xmath20 ( @xmath59 = 1.7 kms@xmath20 ) . cs @xmath18 , which is a binary system but which we do not consider to be a blue straggler candidate , has = 10 kms@xmath20 . [ we have assigned cs @xmath60 a temperature of 6925 k rather than 6900 k so it would not be overplotted on another star . ] if we restrict the sample to those stars from ps2000 for which we could obtain an independent orbital solution that agrees with their results ( cllgm , table 4 ) , we find that none of the seven binary stars with orbital periods longer than 20 days have values as small as the largest value found for the single stars , and that @xmath3@xmath4 = 17.3 kms@xmath20(@xmath59 = 3.5 kms@xmath20 ) . [ here we have altered the temperature for cs @xmath61 from 7050 k to 7000 k to inhibit it being overplotted on another star . ] if we further consider the 11 more binary stars for which ps2000 presented only one orbital solution , but which are not plotted in figure 8 , only two have values of 12 kms@xmath20 or less , while the remaining nine stars have values reaching as high as 160 kms@xmath20 . our own results , from our previous work ( cllgm ) and this paper , confirm this picture . we consider bd+25 1981 an uncertain case and have plotted it in figure 8 as an open triangle . the other four constant velocity stars ( bd+72 94 , bd+40 1166 , hd 84937 , hd 142575 ) have @xmath3@xmath4 = 7.8 kms@xmath20(@xmath59 = 3.8 kms@xmath20 ) , while the ten binary stars in table 3 have @xmath3@xmath4 = 18.7 kms@xmath20(@xmath59 = 10.0 kms@xmath20 ) . in summary , our own studies and the results of ps2000 show that blue straggler candidates which are binaries show significantly enhanced surface rotation compared to constant velocity stars . because the orbital periods imply separations far too great for tidal interactions to _ currently _ have any significant effects on the stars rotational periods , we believe the enhanced rotation indicates mass transfer has occurred and is the cause of the spin - up . the mass transfer model predicts that the originally more massive star transfers mass to the lower mass secondary , diminishing the orbital period and separation , until the original secondary star becomes the more massive component . at that point , the stars begin the separate , but mass transfer has transformed orbital angular momentum into rotational angular momentum , and tidal interactions or some mechanism has reduced the orbital eccentricities . as noted above , luck & bond ( 1991 ) suggested that some blue stragglers may be progenitors of the subgiant ch stars . until recently , there has been little information regarding abundances of carbon and @xmath7-process abundances in blue stragglers that would indicate mass transfer from an agb star , but such data are now beginning to appear , and so we have summarized in table 1 the abundances of the @xmath7-process elements strontium and barium . the available data for most candidate blue straggler stars are consistent with the normal abundances of these elements in metal - poor main sequence and red giant branch stars ( see mcwilliam 1997 ) . recently , spc2003 have found strong enhancements of these elements in three of the blue metal - poor stars discussed previously by ps2000 . thus for these stars the evidence favors mass transfer from an evolving agb star , supporting the hypothesis of luck & bond ( 1991 ) . if mass transfer from a highly - evolved agb star is responsible for the @xmath7-process enhancements , whereas the stars without such enhancements experienced mass transfer from a normal red giant , we might expect to see some differences in the orbital properties of the two samples . mass transfer from an agb star could imply , for example , that mass transfer did not occur during the preceding red giant evolutionary phase , and , therefore , the original orbital periods of binary systems destined to experience mass transfer from an agb star should be longer than those which undergo mass transfer from a first ascent red giant . one might expect , then , that blue stragglers showing signs of agb mass transfer ( @xmath7-process enhancements ) should have longer minimum orbital periods than those that ( presumably ) arose from mass transfer from a red giant ( no such enhancements ) . qualitatively , table 1 confirms this view . excluding cs @xmath62 , the eight stars with normal strontium and barium abundances have orbital periods as low as 167 days , and none exceed 500 days . the six subgiant ch stars with orbital solutions obtained by mcclure ( 1997 ) have periods only as short as 878 days , and extend up to 4140 days . the eight ( giant ) ch stars studied by mcclure & woodsworth ( 1990 ) have orbital periods ranging from 328 and 2954 days , roughly consistent with this simple picture . cs @xmath62 is consistent with this trend , with an orbital period of 1307 days ( spc2003 ) . its orbital eccentricity is also on the high side ( 0.21 ) for the ensemble of field halo blue stragglers , as figure 4 shows . however , the other two stars with @xmath7-process enhancements , cs @xmath8 and cs @xmath9 , show rather short periods , according to spc2003 , with 342 days ( and e @xmath63 ) and 194 days ( and e @xmath64 ) , respectively . we have not included these stars in table 1 because our orbital solutions using the data available to spc2003 indicated that alternative periods and eccentricities were possible , although less likely . preston ( private communication ) has continued to observe these stars and these orbital periods are increasingly robust . in particular , we have been able to confirm to our own satisfaction the orbital period for cs @xmath8 has cost the first author payment of a wager with dr . preston that longer periods would be preferred . ] . additional velocity data are needed , however , for cs @xmath9 . we are therefore confronted with the results that mass transfer from red giant and agb stars yield similar ranges in orbital periods and eccentricities . we can only speculate that diversity in the masses of the original primary stars and their original orbital periods contribute to this splendid if confusing variety . a point stressed by mcclure & woodsworth ( 1990 ) and mcclure ( 1997 ) was that the mass functions of the ch and subgiant ch stars , respectively , were small and indicative of a uniform secondary mass , roughly that of a white dwarf with 0.6@xmath0 . we undertook a similar analysis in our previous paper , which we revisit here . we begin by comparing the distribution of the mass functions of the blue stragglers and the somewhat lower masses of the primary stars in the single - lined spectroscopic binaries of latham et al . ( 2002 ) for stars with orbital periods longer than 20 days . the mass function for a spectroscopic binary is defined to be @xmath65 where the numerical value of @xmath66 is derived from the parameters of the orbital solution . figure 9 shows that the two mass function distributions are quite different , with the steeper one for the blue stragglers indicative of a narrower range of secondary masses , as in the cases of the ch and subgiant ch stars . so what is that secondary mass ? we must begin with an estimate of the masses of the primary stars , then exploit the mass functions to get some idea of the secondary masses of the ensemble . as we have noted , the lack of a detectable secondary spectrum in any of the blue straggler binary systems is suggestive of underluminous secondaries , and we explore here the idea that all the secondaries are stellar remnants with similar masses . in cllgm , we estimated the mass of each primary star using the derived effective temperatures and chemical compositions , plus the isochrones of girardi et al.(2000 ) . the isochrone ages were relatively young , generally 1.7 to 2.0 gyrs , to accomodate the high temperatures and apparent high masses of the primaries . the isochrones were computed using elemental abundances consistent with solar values and , to allow for enhanced abundances of the @xmath15 " elements ( [ @xmath15/fe ] @xmath67 ) , we employed the scaling relation of salaris , chieffi , & straniero ( 1993 ) to calculate @xmath68 for each primary . here we exploit the yonsei - yale " ( y@xmath14 ) isochrones of yi , kim , & demarque ( 2003 ) , which were computed using @xmath15-enhanced abundances and somewhat more appropriate ( and variable ) helium mass fractions . we used isochrones with an age of 2.0 gyrs in all cases . table 5 shows the results . we have also compared these new primary mass estimates with those computed using the girardi et al . ( 2000 ) isochrones . the maximum difference in derived primary mass was 0.04 @xmath0 , and the mean difference , in the sense of y@xmath14 minus girardi et al . ( 2000 ) , was @xmath69 @xmath0 , with @xmath70 @xmath0 . [ tab5 ] from the estimated value of @xmath71 , we can estimate the mass of the undetected companion ; i.e. for @xmath72 , using a revised version of equation [ eq : massfunction ] : @xmath73 these are also provided in table 5 . all of the minimum masses lie below the expected mass of a metal - poor white dwarf , @xmath74@xmath0 . they also lie far below those expected for a metal - poor main sequence turn - off star ( @xmath75@xmath0 ) or that of a neutron star ( @xmath76@xmath0 ) . the mean difference in secondary masses derived using the two sets of isochrones is only @xmath77 @xmath0 , with @xmath78 @xmath0 . if all the secondaries have roughly the same mass , is it closer to that of a white dwarf or a neutron star ? if we _ assume _ that all the secondaries have the same mass of @xmath79 , and calculate the orbital inclinations that this would imply , we obtain the @xmath80 values listed in table 5 . the average @xmath80 for the 17 stars in table 5 is @xmath81 ( @xmath82 ) , which is not far from the value of @xmath83 expected for randomly oriented orbits . ( use of the isochrones of girardi et al . 2000 leads to an identical result . ) increasing the assumed secondary mass to 0.65 @xmath0 , results in @xmath84 ( @xmath85 ) , which is inconsistent with the expectation by a significant amount , although we must recognize that our results suffer some observational bias in that very low values of sin @xmath23 result in smaller observed radial velocity variations and such systems are more likely to elude detection . if we further assume the secondaries are all neutron stars , with @xmath86@xmath0 , we find @xmath87 ( @xmath88 ) , and we rule out that class of secondaries , at least in the general case . we conclude that our orbital solutions are consistent with all the unseen companions in our low - eccentricity long - period orbits being white dwarfs viewed at random orbital orientations , which supports the mass - transfer model for the formation of field blue stragglers . if all the secondaries are white dwarfs with the same mass , then that mass can not be much smaller than @xmath89 , because the three largest minimum masses are @xmath90 ( cs @xmath62 ) , @xmath91 ( cs @xmath61 ) , and @xmath92 ( g202 - 65 ) , where the quoted errors include only the contribution from the mass functions and not from possible systematic errors in our estimates of the primary masses . on the other hand , the secondary masses can not be larger than about @xmath93 , because then the average value for the orbital inclinations would become seriously inconsistent with random orientations of the orbits . ryan et al . ( 2002 ) have discussed the mechanism for the mass transfer that might have increased the rotational velocities of the stars we see now as blue stragglers . one of the questions they raised was whether the mass transfer mechanism could have involved stable roche lobe overflow or whether the mass transfer process was unstable . sudden mass loss via a supernova , for example , would be such an unstable process , although we have essentially ruled out neutron star companions among this sample of field blue stragglers . rappaport et al . ( 1995 ) modelled the results of roche lobe overflow . they considered the evolution of binaries undergoing stable mass transfer , but for the case where the recipient is a neutron star . the same physics should also apply to systems where the recipient is a main - sequence star . the essence of the model is that short - period systems are so close that mass transfer begins early , when the expanding red giant core has not yet grown to a mature " size . therefore , the resultant white dwarf will appear with a small , premature " mass . in figure 10 , we plot the minimum white dwarf mass as a function of the orbital period and eccentricity , log [ @xmath94 . we also show the model predictions of rappaport et al . ( 1995 ) using their coefficient @xmath95 to be 3300 @xmath96 , consistent with the population ii case that they discussed . if all the secondary stars were white dwarfs and had evolved via stable mass transfer , their minimum masses , plotted in figure 10 , should all lie to the left of the theoretical curve , and we find that the data do so , more or less , except for g202 - 65 . thus almost all of the blue stragglers in table 5 , with orbital periods longer than 20 days , have orbital periods and eccentricities consistent with stable mass transfer . this includes cs @xmath62 , the star that shows signs of @xmath7-process enhancements and an implied agb donor star . we show in figure 10 the locations of the other two such stars from sp2003 , cs @xmath8 and cs @xmath9 . all three stars lie well within the regime of stable mass transfer .

this suggests that the lithium gap " for hot metal - poor main sequence stars may not exist or lies at higher temperatures than found in the hyades . our results and those of preston & sneden ( 2000 ) show higher values of for the binary stars than those of comparable temperature constant velocity stars . the orbital periods are too long for tidal effects to be important , implying that spin - up during mass transfer when the orbital separations and periods were smaller is the cause of the enhanced rotation . the mass function distribution is steeper for the blue straggler binary stars than that of lower mass single - lined spectroscopic binaries , indicating a narrower range in secondary masses . we argue that if all secondaries are white dwarfs with the same mass , it is probably around 0.55 . the models of rappaport et al . ( 1995 ) , applied to white dwarf secondaries , suggest that the orbital elements of all metal - poor binary blue stragglers are consistent with stable mass transfer , with the possible exception of g202 - 65 .

we report radial velocity studies of five candidate metal - poor field blue stragglers , all known to be deficient in lithium . four of the five stars are single - lined spectroscopic binaries , with periods ranging from 302 to 840 days , and low orbital eccentricities , in agreement with similar behavior found for other blue straggler candidates by preston & sneden ( 2000 ) and carney et al . ( 2001 ) . the limited data available for lithium abundances indicate that all blue straggler binaries have depleted lithium , but that constant velocity stars generally have normal lithium abundances . this suggests that the lithium gap " for hot metal - poor main sequence stars may not exist or lies at higher temperatures than found in the hyades . our results and those of preston & sneden ( 2000 ) show higher values of for the binary stars than those of comparable temperature constant velocity stars . the orbital periods are too long for tidal effects to be important , implying that spin - up during mass transfer when the orbital separations and periods were smaller is the cause of the enhanced rotation . the mass function distribution is steeper for the blue straggler binary stars than that of lower mass single - lined spectroscopic binaries , indicating a narrower range in secondary masses . we argue that if all secondaries are white dwarfs with the same mass , it is probably around 0.55 . the models of rappaport et al . ( 1995 ) , applied to white dwarf secondaries , suggest that the orbital elements of all metal - poor binary blue stragglers are consistent with stable mass transfer , with the possible exception of g202 - 65 .

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in dwarf novae , mass is transferred from a late - type star ( the secondary ) to a companion white dwarf ( wd ) via an accretion disc . they show recurrent outbursts on timescales of days - months , in which the disc brightens by factors 20 - 100 for @xmath2 days . outbursts are explained in terms of either a thermal - viscous disc - instability model ( dim , e.g. , * ? ? ? * ; * ? ? ? * ) or a mass - transfer instability model ( mtim , e.g. , * ? ? ? dim predicts matter accumulates in a low viscosity , where @xmath3 is the non - dimensional viscosity parameter , @xmath4 is the local sound speed and @xmath5 is the disc scaleheight . ] disc during quiescence ( @xmath6 ) which switches to a high - viscosity regime during outbursts , whereas in mtim the disc viscosity is always the same ( @xmath7 , from the decline timescale of outbursting dwarf novae , e.g. , * ? ? ? therefore , estimating @xmath3 of a quiescent disc is key to gauge which model is at work in a given dwarf nova . aside of the normal outbursts , the short - period dwarf novae of the suuma type show longer , slightly brighter and more regular superoutbursts , during which a hump - shaped brightness modulation ( named _ superhump _ ) with period slightly longer than the orbital period @xmath8 is seen in their light curves @xcite . the most promising explanation for superhumps is given by the tidal resonance instability model @xcite : during a superoutburst , the accretion disc expands beyond the 3:1 resonance radius , @xmath9 , and a tidal instability sets in , giving rise to an elliptical , slowly precessing disc . superhump modulation then arises from the periodic tidal interaction between the outer elliptical disc and the mass - donor star ( normal superhumps ) or by the varying release of gravitational energy at the point where the gas stream hits the precessing elliptical disc outer edge ( late superhumps ) , at the beat period between the orbital and the disc precession period , @xmath10 . eclipse mapping @xcite is a powerful tool to test for the presence of elliptical discs in outbursting dwarf novae as well as to check whether the orientation of the ellipse is according to the expectation of the tidal instability model ( e.g. , * ? ? ? * ; * ? ? ? flickering is the intrinsic brightness fluctuation of 0.01 - 1 mag on timescales of seconds to dozens of minutes seen in dwarf novae light curves . optical studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) suggest there may be three different sources of flickering in dwarf novae and novalike systems , the relative importance of which varies from system to system : ( i ) the stream - disc impact region ( possibly because of unsteady mass transfer or post - shock turbulence , * ? ? ? * ; * ? ? ? * ) , ( ii ) the innermost disc regions around the wd [ ] ej82,bruch92 , and ( iii ) the accretion disc itself ( probably as a consequence of magneto - hydrodynamic ( mhd ) turbulence or events of magnetic reconnection at the disc atmosphere , * ? ? ? * ; * ? ? ? * ; * ? ? ? the power density spectrum ( pds ) of the flickering is characterized by a continuum power - law , @xmath11 , with @xmath12 @xcite , which flattens below a given cut - off frequency @xmath13 . currently , the most promising explanation for the anomalously large viscosity of accretion discs is related to mhd turbulence in the differentially rotating disc gas ( driven by the magnetorotational instability , mri , see * ? ? ? * ; * ? ? ? most of the studies on this subject over the last two decades focused on confirming that mri leads to self - sustained , turbulent and efficient outward flow of angular momentum and inward flow of disc matter ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) , and on the comparison of the numerically derived values of @xmath3 with those inferred by the decline timescale of outbursting dwarf novae ( e.g. , * ? ? ? * ; * ? ? ? on the other hand , the study of @xcite focused on the time variability of the viscous energy release in a mhd turbulent disc . they found that mhd turbulence leads to large fluctuations in the energy dissipation rate per unit area at the disc surface , @xmath14 , which they suggested could be a source of flickering in mass - exchanging binaries . indeed , the pds of the fluctuations in their study resemble those of flickering sources , with a power - law dependency of similar index range and a flat slope at low - frequencies . the interpretation of the fluctuations in @xmath14 as the stochastic and statistically independent release of energy from a large number of turbulent eddies leads to a direct relation between the relative amplitude of the energy fluctuations @xmath15 and the disc viscosity parameter , @xmath16 , providing an interesting observational way to estimate the local accretion disc viscosity parameter ( see , e.g. , * ? ? ? * ) . for a thin accretion disc ( @xmath17 ) , the above relation predicts that low - viscosity discs ( @xmath18 ) should show low - amplitude disc flickering ( hardly detectable at a level @xmath19 per cent ) , whereas high - viscosity discs ( @xmath20 0.1 - 1 ) should display detectable flickering with relative amplitudes in the range 2.5 - 7.5 per cent . there is observational support for this prediction : e.g. , the accretion disc seems the dominant source of flickering in the high - viscosity discs of the novalike systems rwtri @xcite and uxuma @xcite , whereas there is no evidence of disc - related flickering in the low - viscosity accretion discs of the dwarf novae ugem @xcite and ippeg @xcite in quiescence . v4140 sgr is an 88-min period eclipsing su uma type dwarf nova @xcite showing low - amplitude ( @xmath21 mag ) , 5 - 10d long outbursts recurring every 80 - 90d and longer , brighter superoutbursts where superhumps appear in its light curve @xcite . here we report the analysis of a sample of light curves of v4140 sgr with eclipse mapping techniques to trace the evolution of the surface brightness of its accretion disc during decline from a superoutbursts , to locate the sources of flickering in the binary and to estimate the radial run of the quiescent disc viscosity parameter . section[observa ] reports the observations and data reduction procedures . data analysis and results are presented in section[analysis ] , discussed in section[discuss ] , and summarized in section[conclusions ] .

we report the analysis of 22 b - band light curves of the dwarf nova v4140 sgr obtained with soi / soar during two nights along the decline of a superoutburst in 2006 sep 12 - 24 and in quiescence over 50 days following the superoutburst . accretion , accretion discs binaries : eclipsing novae , cataclysmic variables stars : dwarf novae

we report the analysis of 22 b - band light curves of the dwarf nova v4140 sgr obtained with soi / soar during two nights along the decline of a superoutburst in 2006 sep 12 - 24 and in quiescence over 50 days following the superoutburst . three - dimensional eclipse mapping of the outburst light curves indicates that the accretion disc is elliptical ( eccentricity ) and that superhump maximum occurs when the mass donor star is aligned with the bulge of the elliptical disc . the accretion disc is geometrically thin both in outburst and in quiescence ; it fills the primary roche lobe in outburst and shrinks to about half this size in quiescence . the stability of the eclipse shape , width and depth along quiescence and the derived disc surface brightness distribution indicate that the quiescent accretion disc is in a high - viscosity , steady - state . flickering mapping of the quiescent data reveal that the low - frequency flickering arises from an azimuthally - extended stream - disc impact region at disc rim and from the innermost disc region , whereas the high - frequency flickering originates in the accretion disc . assuming the disc - related flickering to be caused by fluctuations in the energy dissipation rate induced by magneto - hydrodynamic turbulence , we find that the quiescent disc viscosity parameter is large at all radii . the high - viscosity quiescent disc and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc - instability model , and lead to the conclusion that the outbursts of v4140 sgr are powered by mass transfer bursts from its donor star . [ firstpage ] accretion , accretion discs binaries : eclipsing novae , cataclysmic variables stars : dwarf novae stars : individual ( v4140 sagitarii )

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we applied 3d eclipse mapping techniques to follow the evolution of the surface brightness of the accretion disc of v4140 sgr in a superoutburst . we find that the disc is elliptical in outburst and decline , with an eccentricity @xmath0 . in both outburst stages , the disc orientation is such that superhump maximum occurs when the secondary star is aligned with the bulge of the elliptical disc . this lends observational support for the tidal resonance instability model of superhumps . the accretion disc fills the primary roche lobe at outburst ( @xmath126 ) , shrinks to @xmath229 during decline and reaches a lower value of @xmath178 in quiescence . there is marginal evidence that the disc half - opening angle is larger in outburst ( @xmath95 ) than in quiescence ( @xmath96 ) , but the disc is geometrically thin in all three cases . the superoutburst occurs at disc temperatures too low to be accounted for by the disc - instability model even at the upper @xmath230 limit on the inferred distance to the binary . the stability of the eclipse shape , width and depth along 50d in the quiescent period following the superoutburst and the derived disc surface brightness distribution ( outshining any contribution from the white dwarf ) indicate that the quiescent accretion disc of v4140 sgr is in a high - viscosity , steady - state regime . flickering mapping of the quiescent data reveal three different sources of flickering in v4140 sgr : an azimuthally - extended stream - disc impact region at disc rim ( statistically significant at the @xmath113 level ) and the innermost disc region ( statistically significant at the @xmath188 level ) , responsible for the low - frequency flickering , and an extended , high - frequency disc component responsible for 2/3 of the total optical flickering in v4140sgr . assuming that the disc - related flickering is caused by fluctuations in the energy dissipation rate induced by mhd turbulence according to the model of @xcite , we find that the quiescent disc viscosity parameter in v4140 sgr is large ( @xmath231 ) at all disc radii , in agreement with mtim predictions and in marked contrast with dim predictions . the discrepancy between the inferred @xmath3 values and dim predictions is statistically significant at the @xmath227 confidence level outside the region @xmath226 . the high - viscosity , steady - state quiescent disc of v4140 sgr and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc - instability model , and lead to the conclusion that the outbursts of v4140 sgr are powered by the only other mechanism considered so far , namely , bursts of enhanced mass transfer rate from its donor star . the dominant source of uncertainty in the computed @xmath222 distribution are the errors in the relative amplitude of the high - frequency , disc - related flickering component . these errors can be reduced by increasing the @xmath232 of the flickering curves , i.e. , by increasing the statistics and/or the @xmath232 of the individual light curves included in the data sample . the benefits of this observational effort are double : it will allow a more meaningful and statistically robust estimate of the magnitude of the disc viscosity parameter and it will open the possibility to properly probe changes in @xmath3 with radius .

three - dimensional eclipse mapping of the outburst light curves indicates that the accretion disc is elliptical ( eccentricity ) and that superhump maximum occurs when the mass donor star is aligned with the bulge of the elliptical disc . the accretion disc is geometrically thin both in outburst and in quiescence ; it fills the primary roche lobe in outburst and shrinks to about half this size in quiescence . the stability of the eclipse shape , width and depth along quiescence and the derived disc surface brightness distribution indicate that the quiescent accretion disc is in a high - viscosity , steady - state . flickering mapping of the quiescent data reveal that the low - frequency flickering arises from an azimuthally - extended stream - disc impact region at disc rim and from the innermost disc region , whereas the high - frequency flickering originates in the accretion disc . assuming the disc - related flickering to be caused by fluctuations in the energy dissipation rate induced by magneto - hydrodynamic turbulence , we find that the quiescent disc viscosity parameter is large at all radii . the high - viscosity quiescent disc and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc - instability model , and lead to the conclusion that the outbursts of v4140 sgr are powered by mass transfer bursts from its donor star . [ firstpage ]

we report the analysis of 22 b - band light curves of the dwarf nova v4140 sgr obtained with soi / soar during two nights along the decline of a superoutburst in 2006 sep 12 - 24 and in quiescence over 50 days following the superoutburst . three - dimensional eclipse mapping of the outburst light curves indicates that the accretion disc is elliptical ( eccentricity ) and that superhump maximum occurs when the mass donor star is aligned with the bulge of the elliptical disc . the accretion disc is geometrically thin both in outburst and in quiescence ; it fills the primary roche lobe in outburst and shrinks to about half this size in quiescence . the stability of the eclipse shape , width and depth along quiescence and the derived disc surface brightness distribution indicate that the quiescent accretion disc is in a high - viscosity , steady - state . flickering mapping of the quiescent data reveal that the low - frequency flickering arises from an azimuthally - extended stream - disc impact region at disc rim and from the innermost disc region , whereas the high - frequency flickering originates in the accretion disc . assuming the disc - related flickering to be caused by fluctuations in the energy dissipation rate induced by magneto - hydrodynamic turbulence , we find that the quiescent disc viscosity parameter is large at all radii . the high - viscosity quiescent disc and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc - instability model , and lead to the conclusion that the outbursts of v4140 sgr are powered by mass transfer bursts from its donor star . [ firstpage ] accretion , accretion discs binaries : eclipsing novae , cataclysmic variables stars : dwarf novae stars : individual ( v4140 sagitarii )

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[ sec : discussion ] empirical sequences of substellar isochrones in color - magnitude diagrams are important tools to chart the physical and spectral properties of brown dwarfs and giant planets at a given age , map their entire cooling history at a given mass , and jointly test low - temperature atmospheric and evolutionary models . the positions of young ( @xmath110200 myr ) substellar objects in near - infrared color - magnitude diagrams have progressively come into focus with programs searching for low - mass members of young moving groups ( @xcite ; @xcite ) and gas giant planets with high - contrast imaging ( @xcite ) together with follow - up parallax programs to measure distances ( @xcite ; liu et al . 2016 ) . this is particularly true for the young late - m through mid - l dwarf populations , whose numbers and trigonometric distances have swelled in recent years , but the location of young late - l , l / t , and t dwarfs have largely remained elusive owing to the relative dearth of discoveries in this regime and their intrinsic scarcity . the ab dor moving group is among the oldest of the nearby ( @xmath47100 pc ) young ( @xmath47200 myr ) comoving associations in the solar neighborhood ( e.g. , @xcite ; @xcite ) . with an age of @xmath1120 @xmath3 10 myr , it straddles younger well - characterized moving groups like @xmath38 pic and tuc - hor at 2050 myr and older , more heavily populated clusters at 500800 myr like ursa majoris , the hydes , and coma ber ( @xcite ) , thereby serving as an important benchmark for stellar and substellar evolution . the population of confirmed or suspected free - floating brown dwarfs in ab dor now includes over a dozen objects spanning the entire l dwarf sequence down to @xmath1t1 ( e.g. , @xcite ; @xcite ) as well as the single mid - t dwarf candidate sdss j1110 + 0116 ( @xcite ) . many brown dwarf and planetary - mass companions have also been identified with masses ranging from roughly 9 to 40 ( figure [ fig : abdorcomp ] ) : 1rxs j2351 + 3127 b ( l0 ; @xcite ) , cd35 2722 b ( l3 ; @xcite ) , 2m01222439 b ( l4 ; @xcite ) , and gu psc b ( t3.5 ; @xcite ) . altogether , this is the largest set of substellar companions for any young moving group . with a mass of 1114 , 2m2236 + 4751b is the second lowest - mass companion discovered in ab dor after gu psc b ( 11 @xmath3 2 ; figure [ fig : abdorcomp ] ) . 2m2236 + 4751b is also the reddest known member of this group and resides in a prominent position at the `` elbow '' of its substellar isochrone ( figure [ fig : abdoriso ] ) . it has an even more extreme color than two red free - floating brown dwarfs in ab dor , wise j0047 + 6803 ( ( @xmath5@xmath4)@xmath6= 2.48 @xmath3 0.08 mag ) and 2m2244 + 2043 ( ( @xmath5@xmath4)@xmath6 = 2.43 @xmath3 0.04 mag ) , demonstrating that the tip of the l dwarf sequence extends to at least ( @xmath5@xmath4)@xmath6 = 2.7 mag even at the relatively old age of this cluster . -1.2 in -.2 in -.6 in .1 in -.1 in 0 in -0.1 in .6 in 0 in the shape of the ab dor substellar isochrone has important implications for other clusters with similar ages . the pleiades is an especially interesting example with a comparable age of about 125 myr ( @xcite ) and possible dynamical relationship with the ab dor group ( @xcite ) . although it is one of the best - characterized nearby open clusters with a population of over one thousand stars ( e.g. , @xcite ) , its very low - mass substellar members have been difficult to explore owing to their intrinsic faintness . nevertheless , several deep near - infrared imaging surveys have identified l dwarfs down to the planetary - mass regime ( e.g. , @xcite ; @xcite ) . @xcite show the pleiades l dwarf sequence in the @xmath5/@xmath5@xmath4 diagram generally resembles ab dor , progressively reddening to @xmath5@xmath4 values of @xmath12.5 mag , but then appears to turn over to bluer colors beyond @xmath5@xmath120.3 mag ( @xmath7@xmath114.7 mag ) and @xmath13@xmath117.8 mag ( @xmath100@xmath112.2 mag ; @xcite ) . the absolute magnitudes of 2m2236 + 4751b ( @xmath7=15.97 @xmath3 0.2 mag ; @xmath100=13.35 @xmath3 0.18 mag ) are over one magnitude _ fainter _ than the location of this apparent turnover . similarly , the two aforementioned red l dwarfs wise j0047 + 6803 and 2m2244 + 2043 in ab dor have absolute magnitudes nearly half a magnitude fainter than this possible l / t turnover , suggesting that there is either an age discrepancy between ab dor and the pleiades , a dramatic level of photospheric diversity exists among brown dwarfs with similar absolute magnitudes at this age , or that some of the faint blue planetary - mass candidates identified by @xcite are contaminants . compared to other companions , 2m2236 + 4751b appears to have even more extreme photospheric properties than all previously known objects except the @xmath05 object 2m12073932 b ( ( @xmath5@xmath4)@xmath6 = 3.0 @xmath3 0.2 mag ; figure [ fig : cmd ] ) . however , all isolated objects and companions in this region of the color - magnitude diagram show qualitatively similar atmospheric properties : red colors , faint absolute magnitudes , strong co absorption , and no signs of methane absorption despite having effective temperatures below the traditional l / t transition of @xmath012001400 k for the older field population ( e.g. , @xcite ) . @xcite and @xcite find that very thick clouds and rapid vertical mixing are required to reproduce the red colors and lack of methane absorption in 2m12073932 b , the most extreme object at the tip of the l dwarf sequence , and these traits are likely to apply to 2m2236 + 4751b as well . however , liu et al . ( 2016 ) show that another population of red l dwarfs like 2m2148 + 4003 ( @xcite ) and wise j2335 + 4511 ( @xcite ) which do not appear to be young can also reside in this part of the color - magnitude diagram , indicating that surface gravity is not the sole underlying explanation for the shared atmospheric traits of these objects . 2m2236 + 4751b reinforces the impression that there do not appear to be any obvious differences between the red , faint objects being discovered as companions and the analogous population of isolated free - floating objects . with a projected separation of 230 au , 2m2236 + 4751b is the latest example of a growing population of planetary - mass companions on wide orbits of several hundred au ( e.g. , @xcite ; @xcite ; @xcite ) . the origin of these objects is unclear ; planet - planet scattering ( @xcite ) , the tail end of disk instability ( @xcite ) , and turbulent fragmentation of molecular clouds ( @xcite ) have all been invoked to explain their origin . @xcite argue against scattering as the dominant origin of this population due to the lack of additional close - in companions in these systems and the dearth of multiple massive ( @xmath110 ) planets uncovered at small separations in radial velocity surveys . in fact , because of their low numbers and lack of robust statistics , it is unclear whether these objects make up their own population or are part of a broader distribution of giant planets or low - mass brown dwarfs spanning small separations ( tens of au ) out to extremely wide separations ( thousands of au ) . unlike most of the wide planetary - mass companions currently known , 2m2236 + 4751b is part of a well - defined survey ( to be discussed in more detail in a future publication ) and will help clarify the statistical properties of planetary - mass companions on wide orbits around low - mass stars .

follow - up keck / osiris-band spectroscopy of the companion reveals strong co absorption similar to other faint red l dwarfs and lacks signs of methane absorption despite having an effective temperature of k. with a () color of 2.69 0.12 mag , the near - infrared slope of 2m2236 + 4751b is redder than all of the hr 8799 planets and instead resembles the myr isolated planetary - mass object pso j318.522 , implying that similarly thick photospheric clouds can persist in the atmospheres of giant planets at ages beyond 100 myr . in near - infrared color - magnitude diagrams , 2m2236 + 4751b

we report the discovery of an extremely red planetary - mass companion to 2mass j22362452 + 4751425 , a.6 late - k dwarf likely belonging to the myr ab doradus moving group . 2m2236 + 4751b was identified in multi - epoch nirc2 adaptive optics imaging at keck observatory at a separation of 3.7 , or 230 20 au in projection at the kinematic distance of 63 5 pc to its host star . assuming membership in the ab dor group , as suggested from its kinematics , the inferred mass of 2m2236 + 4751b is 1114 . follow - up keck / osiris-band spectroscopy of the companion reveals strong co absorption similar to other faint red l dwarfs and lacks signs of methane absorption despite having an effective temperature of k. with a () color of 2.69 0.12 mag , the near - infrared slope of 2m2236 + 4751b is redder than all of the hr 8799 planets and instead resembles the myr isolated planetary - mass object pso j318.522 , implying that similarly thick photospheric clouds can persist in the atmospheres of giant planets at ages beyond 100 myr . in near - infrared color - magnitude diagrams , 2m2236 + 4751b is located at the tip of the red l dwarf sequence and appears to define the `` elbow '' of the ab dor substellar isochrone separating low - gravity l dwarfs from the cooler young t dwarf track . 2m2236 + 4751b is the reddest substellar companion to a star and will be a valuable benchmark to study the shared atmospheric properties of young low - mass brown dwarfs and extrasolar giant planets .

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[ sec : conclusions ] we have presented the discovery of a faint red l dwarf companion to the late k dwarf 2mass j22362452 + 4751425 . the radial velocity and proper motion of the host star are consistent with the 120 myr ab dor young moving group . 2m2236 + 4751a is relatively inactive , showing partly - filled h@xmath61 absorption but no x - ray emission or uv excess , suggesting that it is either in the tail end of the ab dor activity distribution or it is an older kinematic interloper in that group . the unusually red colors of the companion are similar to ( but more extreme than ) other mid- to late - l dwarfs in ab dor , possibly bolstering membership likelihood , but the existence of high - gravity brown dwarfs in this part of the color - magnitude diagram means that this trait is not uniquely a sign of younth and low surface gravity . assuming the pair is indeed a member of ab dor , the mass of 2m2236 + 4751b is 1114 from hot start evolutionary models and resides at a projected separation of @xmath0230 au at the kinematic distance of @xmath065 pc to the host star . if the system is a older kinematic interloper then the implied mass of the companion can be as high as @xmath174 at 10 gyr . the near - infrared colors of 2m2236 + 4751b are among the reddest known of any brown dwarf or giant planet . in near - infrared color - magnitude diagrams , it appears to mark the elbow of the ab dor substellar isochrone between other faint red l dwarfs like wise j0047 + 6803 and 2m2244 + 2043 and the two t dwarfs gu psc b and sdss j1110 + 0116 . this implies that the transition from red l dwarfs to dust - free t dwarfs occurs between a narrow mass range of about 1113 at an age of @xmath0120 myr . the colors of 2m2236 + 4751b are redder than hr 8799 b but slightly bluer than 2m12073932 b , demonstrating that even intermediate - age giant planets can possess similarly extreme atmospheric properties beyond 100 myr . the 2m2236 + 4751ab system is well - suited for a broad range of follow - up studies . the age and mass of 2m2236 + 4751b will eventually be clarified with a parallax measurement of the host star from @xmath48 to establish whether the system is a member of ab dor . follow - up photometry of the companion at both shorter and longer wavelengths will better constrain its luminosity , spectral type , and atmospheric properties . both low- and high - resolution near - infrared spectroscopy of 2m2236 + 4751b can be used to derive spectral and gravity classifications , independently age - date the system through gravity - dependent absorption line depths , measure its projected rotational velocity , and determine its composition and abundance ratios . finally , 2m2236 + 4751b is also an excellent target for variability studies to measure its rotational period and search for signatures of heterogeneity and patchiness in its unusually thick clouds . we thank a. kraus for helpful discussions about the age of the host star and the entire keck observatory staff for their exceptional support . i.t . was supported by the department of astronomy at the university of texas at austin though the cox endowment and board of visitors funds , as well as a nasa wiyn pi data award administered by the nasa exoplanet science institute as part of nn - explore through the scientific partnership of the national aeronautics and space administration , the national science foundation , and the national optical astronomy observatory . this paper includes data taken at the mcdonald observatory of the university of texas at austin . based on observations obtained with espadons , located at the canada - france - hawaii telescope ( cfht ) . cfht is operated by the national research council of canada , the institut national des sciences de lunivers of the centre national de la recherche scientique of france , and the university of hawaii . espadons is a collaborative project funded by france ( cnrs , menesr , omp , latt ) , canada ( nserc ) , cfht and esa . we utilized data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . nasa s astrophysics data system bibliographic services together with the vizier catalogue access tool and simbad database operated at cds , strasbourg , france , were invaluable resources for this work . this work used the immersion grating infrared spectrometer ( igrins ) that was developed under a collaboration between the university of texas at austin and the korea astronomy and space science institute ( kasi ) with the financial support of the us national science foundation under grant ast- 1229522 , to the university of texas at austin , and of the korean gmt project of kasi . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . finally , mahalo nui loa to the kamaina of hawaii for their support of keck and the mauna kea observatories . we are grateful to conduct observations from this mountain . cutri , r. m. , skrutskie , m. f. , van dyk , s. , et al . 2003 , the 2mass all - sky catalog of point sources , university of massachusetts and infrared processing and analysis center ; ipac / california institute of technology

we report the discovery of an extremely red planetary - mass companion to 2mass j22362452 + 4751425 , a.6 late - k dwarf likely belonging to the myr ab doradus moving group . 2m2236 + 4751b was identified in multi - epoch nirc2 adaptive optics imaging at keck observatory at a separation of 3.7 , or 230 20 au in projection at the kinematic distance of 63 5 pc to its host star . assuming membership in the ab dor group , as suggested from its kinematics , the inferred mass of 2m2236 + 4751b is 1114 . is located at the tip of the red l dwarf sequence and appears to define the `` elbow '' of the ab dor substellar isochrone separating low - gravity l dwarfs from the cooler young t dwarf track .

we report the discovery of an extremely red planetary - mass companion to 2mass j22362452 + 4751425 , a.6 late - k dwarf likely belonging to the myr ab doradus moving group . 2m2236 + 4751b was identified in multi - epoch nirc2 adaptive optics imaging at keck observatory at a separation of 3.7 , or 230 20 au in projection at the kinematic distance of 63 5 pc to its host star . assuming membership in the ab dor group , as suggested from its kinematics , the inferred mass of 2m2236 + 4751b is 1114 . follow - up keck / osiris-band spectroscopy of the companion reveals strong co absorption similar to other faint red l dwarfs and lacks signs of methane absorption despite having an effective temperature of k. with a () color of 2.69 0.12 mag , the near - infrared slope of 2m2236 + 4751b is redder than all of the hr 8799 planets and instead resembles the myr isolated planetary - mass object pso j318.522 , implying that similarly thick photospheric clouds can persist in the atmospheres of giant planets at ages beyond 100 myr . in near - infrared color - magnitude diagrams , 2m2236 + 4751b is located at the tip of the red l dwarf sequence and appears to define the `` elbow '' of the ab dor substellar isochrone separating low - gravity l dwarfs from the cooler young t dwarf track . 2m2236 + 4751b is the reddest substellar companion to a star and will be a valuable benchmark to study the shared atmospheric properties of young low - mass brown dwarfs and extrasolar giant planets .

0811.1562

c

observations at various wavelengths suggest that irasf001837111 derives a substantial fraction of its bolometric power from accretion onto a central black hole . especially important in this respect is the detection by @xcite of a 6.7kev fek@xmath11 line ( fe xxv ) with a large equivalent width , indicating the presence of a compton - thick agn in irasf001837111 . another clear indication is a higher than expected radio power based on the radio - far - infrared correlation for starburst galaxies @xcite , as well as unpublished radio interferometric data showing the nucleus to be unresolved on the 200pc scale ( r.p . norris , 2004 , private communication ) . the non - detection of several common mid - infrared agn tracers in our _ spitzer_-irs high resolution spectrum may hence indicate that the agn coronal line region ( clr ) is small or absent or , alternatively , that our line of sight to the agn clr is strongly obscured . the latter would be in agreement with the detection of a deep 9.7@xmath0 m silicate absorption feature ( * ? ? ? * fig[fig4 ] ) , which is unusual for classical seyfert galaxies and quasars @xcite . even stronger obscuration , along all lines of sight , is suggested by @xcite , who concluded from a study of the 4.7@xmath0 m co gas absorption band that the strong detection of this feature in irasf001837111 @xcite and its non - detection in local agns observed with iso indicates that the central power source in irasf001837111 must be fully covered rather than blocked by an edge - on torus . to gain insight into the processes responsible for the presence of high velocity gas in irasf001837111 we compare irasf001837111 to the only other two ulirgs in our sample that show pronounced blue wings in their 12.81@xmath0 m [ ne ii ] and 15.56@xmath0 m [ ne iii ] line profiles : iras12127 - 1412ne ( fig.[fig9 ] ) and iras13451 + 1232 ( fig.[fig10 ] ) . clear evidence for unusual excitation conditions in irasf001837111 emerge if we compare the pah emission and low - ionization neon line emission for agns , ulirgs and starburst galaxies from the various _ spitzer_-irs gto programs , ( u)lirgs from _ spitzer _ program 1096 and iras121271412ne . the pah luminosity should track the low - ionization neon line luminosity to within a factor two , if predominantly excited in star forming regions . this was indeed found to be the case for the sample of ulirgs published by @xcite . in fig.[fig5 ] we plot the ratio of these two quantities ( the combined [ ne ii]+[ne iii ] luminosity and the combined luminosity of the 6.2 and 11.2@xmath0 m pah features ) as a function of increasing apparent depth of the 9.7@xmath0 m silicate feature ( i.e. the negative of the silicate strength , s@xmath42 ; * ? ? ? the symbol size scales linearly with the [ ne v]/[ne ii ] ratio above a threshold value of 0.4 . this distinguishes ulirgs with a strong agn contribution to the [ ne ii]+[ne iii ] luminosity ( e.g. mrk463 ; * ? ? ? * ) from those without . as expected , for the sources lacking a strong agn signature the average value of neon / pah has a reasonably low scatter of a factor 1.4 , in agreement with the scaling relation between neon and pah flux for ulirgs found by @xcite . the notable exception is irasf001837111 , which appears to be at least 8 times overluminous in the neon lines compared to its combined pah luminosity . another exception in the s@xmath42@xmath171.5 regime is iras121271412ne , which is overluminous in neon / pah by a factor of 3 . at s@xmath42@xmath251.5 , the situation is less straightforward . in this regime there are several sources with large [ ne v]/[ne ii ] ratios for which the agn contributes significantly to the [ ne ii]+[ne iii ] luminosity , thereby raising the neon / pah ratio ( fig.[fig5 ] ) . the only ulirg in this regime which has an elevated neon / pah ratio despite a low [ ne v]/[ne ii ] ratio of 0.28 is iras13451 + 1232 , at @xmath256 times the average neon / pah ratio ( fig.[fig5 ] ) . this brings the number of ulirgs with unusual excitation conditions to three . since these same three ulirgs are also the only ulirgs in our sample that show pronounced blue wings in their 12.81@xmath0 m [ ne ii ] and 15.56@xmath0 m [ ne iii ] line profiles , it seems plausible that the high neon / pah ratios for these sources could be the result of additional neon line emission contributed by these blue wings rather than unusually weak pah emission in these three sources . m [ ne iii]/12.81@xmath0 m [ ne ii ] versus 14.32@xmath0 m [ ne v]/12.81@xmath0 m [ ne ii ] . plotted are predicted line ratios as computed by mappings version iiiq @xcite for combined precursor+shock models at solar metallicity at a gas density n=100@xmath43 ( upper panel ) and n=10@xmath43 ( lower panel ) . different colors ( ranging from _ purple _ to _ red _ ) denote different magnetic field strengths , ranging from 10@xmath44 to 100@xmath0 g . shock velocities range from 200 to 1000 km s@xmath1 and are labeled along the _ red _ curve . overlaid are the positions of irasf001837111 , iras12127 - 1412ne and iras13451 + 1232 for the integrated fluxes ( _ gray disks _ ) and for just the blue shifted component ( _ black disks _ ) . _ gray squares _ mark the positions of the nuclear spectra of the classical agns ngc1068 and ngc4151 @xcite [ fig11],width=321 ] in fig.[fig11 ] we show a mid - infrared diagnostic diagram based on the 12.81@xmath0 m [ ne ii ] , 15.56@xmath0 m [ ne iii ] and 14.32@xmath0 m [ ne v ] lines . in the diagram we plot shock excitation models from the mappings iiiq library @xcite for solar metallicity gas with densities n=100@xmath43 ( upper panel ) and n=10@xmath43 ( lower panel ) . the model tracks plotted include the ionizing effects from uv and soft x - ray photons in the shock cooling zone on the gas ahead of the shock front . overplotted are the positions of irasf001837111 , iras12127 + 1412ne and iras13451 + 1232 from our spitzer observations . black filled circles indicate the results for just the broad blue - shifted emission line components , the gray versions denote the results based on the velocity - integrated line fluxes ( i.e. the narrow and broad components combined ) . for irasf001837111 and iras12127 + 1412ne the low observed [ ne iii]/[ne ii ] line ratios are consistent with high - velocity shocks ( v@xmath25500 km s@xmath1 ) in high - density environments ( n@xmath25100@xmath43 ) with low magnetic field strengths ( @xmath171@xmath0 g ) . at lower gas densities ( n@xmath4510@xmath43 ) , only the highest velocity shocks ( v=1000 km s@xmath1 ) at the lowest magnetic field strengths ( @xmath170.1@xmath0 g ) are consistent with the observed [ ne iii]/[ne ii ] line ratios . below this density the observed line ratios can not have an origin in shock emission . given the absence of density measurements we can not rule out either scenario . however , as we will argue later , if the neon line emission originates at the base of the optical outflow , gas densities of n@xmath25100@xmath43 may not be unreasonable . in iras13451 + 1232 it is the high observed [ ne v]/[ne ii ] ratio which appears to rule out shocks of any velocity and density as the source of excitation for the neon lines . for the latter source , exposure of the blue shifted gas to direct radiation from the agn seems a likely explanation for the presence of [ ne v ] emission at the observed ratio to [ ne ii ] . this explanation is supported by the proximity of the blue shifted component of iras13451 + 1232 to the positions of the classical agns ngc1068 and ngc4151 in fig.[fig11 ] . in sect.3.3 we analyzed the velocity structure of the 12.81@xmath0 m [ ne ii ] and 15.56@xmath0 m [ ne iii ] lines in irasf001837111 and compared the results to those of studies of its optical and near - infrared forbidden lines . this revealed that the mid - infrared neon emission lines have strongly blue shifted components not detected in both the optical 5007 [ o iii ] and near - infrared 1.644@xmath0 m [ fe ii ] line profiles . given the mid - infrared spectral evidence for strong obscuration in the nucleus of irasf001837111 @xcite , the simplest explanation for the absence of strongly blue shifted gas components in the optical and near - infrared emission lines is extinction . we estimate the required extinction by assuming line emission at any wavelength @xmath46 to be effectively suppressed by a specific extinction a(@xmath46)@xmath392 . the level of screen extinction required to obscure the high - velocity components of the 5007 [ o iii ] line then amounts to a@xmath47 = a@xmath2@xmath252 . if the same screen is responsible for obscuring the high - velocity components of the 1.644@xmath0 m [ fe ii ] line , the required extinction increases to a@xmath2@xmath2510 ( a@xmath48@xmath252 ) . then to still be able to see the strongly blue shifted 12.81@xmath0 m [ ne ii ] emission through this screen , the maximum extinction is constrained to a@xmath2@xmath1750 ( a@xmath49@xmath171 ) . this implies a column density of the obscuring screen of n@xmath50 = 210 @xmath9 10@xmath51 @xmath37 , assuming n@xmath50 = 1.9 @xmath9 10@xmath52 @xmath9 a@xmath2 . in the absence of spatial information for the mid - infrared neon line emission , the location of the screen blocking the optical and near - infrared line emission can not be determined with any certainty . however , it is plausible for the screen to be situated at the base of the outflow traced in 5007 [ o iii ] . the observed strong decrease in blueshift of the 5007 [ o iii ] line from 3@xmath22 to 0@xmath22 east of the nucleus ( fig.12 of * ? * ) may hence indicate that the material that obscures the most highly disturbed optical ( but not mid - infrared ) line emission is located within the inner 10kpc . irasf001837111 is a clear outlier in a mid - infrared diagnostic diagram which combines the equivalent width of the 6.2@xmath0 m pah emission feature and the silicate strength in the so - called ` fork ' diagram @xcite . in this diagram most ulirgs are found along one of two branches . one branch connects starburst - dominated mid - infrared spectra ( e.g. ngc7714 and m82 ) to spectra of deeply buried central sources , characterized by very deep silicate features and the ( virtual ) absence of pah emission ( e.g. iras08572 + 3915 ) . the other branch connects starburst - dominated sources with featureless hot dust - dominated sources , which are mostly agn dominated . irasf001837111 is located in the scarcely populated region in between the tips of the two branches and has iras12127 + 1412ne as its nearest neighbor . their location , away from other deeply obscured sources , either implies a more than 10 times lower 6.2@xmath0 m pah equivalent width than other ulirgs with similar silicate strength , or a less pronounced silicate feature than other deeply obscured ulirgs . @xcite have proposed that sources in between the two branches may be agn evolving from a fully covered obscuring geometry to an incomplete or clumpy obscuring geometry , with a decrease in apparent depth of the silicate feature as a result . in this scenario , the detection of strongly blue shifted neon line emission would then trace a unique phase in the ( partial ) disruption of the obscuring medium around the powerful agn . alternatively , the isolated positions of irasf001837111 and iras12127 + 1412ne in the fork diagram may be the result of unusual lines of sight into these systems . the unusual mid - infrared excitation conditions and kinematics may then be associated to that . if sources with mid - infrared kinematic properties and neon / pah ratios similar to irasf001837111 and iras12127 + 1412ne are indeed agn evolving from full to incomplete or clumpy obscuration , there should be observational characteristics linking them . however , the only ulirg in our sample with these same mid - infrared properties , iras13451 + 1232 , has a mid - infrared continuum spectrum which is very different from the other two sources , displaying only a weak silicate absorption feature on an otherwise featureless power law spectrum . this places it firmly on the agn branch in the fork diagram , far off from the other two sources . evidence supporting an unusual evolutionary stage is presented by @xcite . based on the shape of its radio sed and a kinematic study of its optical emission line spectrum , they conclude that iras13451 + 1232 must be a young compact radio source whose radio jets are expanding through a dense nuclear dust shell , entraining gas and dust from this shell . they infer the reddening to be highest toward the broadest ( most disturbed ) most blue shifted kinematic component in their optical line study , reminiscent of our findings for irasf001837111 using optical , near and mid - infrared line profiles .

we report the first mid - infrared detection of highly disturbed ionized gas in the ultraluminous infrared galaxy ( ulirg ) irasf001837111 . for irasf001837111 , the neon / pah ratio is 8 times higher than the average ratio . similar mid - infrared kinematic and excitation characteristics are found for only two other ulirgs in our sample : iras121271412ne and iras13451 + 1232 .

we report the first mid - infrared detection of highly disturbed ionized gas in the ultraluminous infrared galaxy ( ulirg ) irasf001837111 . the gas , traced by the 12.81 m [ ne ii ] and 15.56 m [ ne iii ] lines , spans a velocity range of 3500 to + 3000 km s with respect to systemic velocity . optical and near - infrared spectroscopic studies show no evidence for similarly high velocity gas components in forbidden lines at shorter wavelengths . we interpret this as the result of strong extinction ( a=1050 ) on the high - velocity gas , which identifies the base of the outflow traced in 5007 [ o iii ] as a plausible origin . unusual excitation conditions are implied by a comparison of the mid - infrared low - excitation neon line emission and the polycyclic aromatic hydrocarbon ( pah ) emission for a sample of 56 ulirgs . for irasf001837111 , the neon / pah ratio is 8 times higher than the average ratio . similar mid - infrared kinematic and excitation characteristics are found for only two other ulirgs in our sample : iras121271412ne and iras13451 + 1232 . both sources have an elevated neon / pah ratio and exhibit pronounced blue wings in their 15.56 m [ ne iii ] line profiles . iras13451 + 1232 even shows a strongly blue shifted and broad 14.32 m [ ne v ] line . while for iras13451 + 1232 the observed [ ne iii]/[ne ii ] and [ ne v]/[ne ii ] line ratios indicate exposure of the blue shifted gas to direct radiation from the agn , for irasf001837111 and iras121271412ne the neon line ratios are consistent with an origin in fast shocks in a high - density environment , and with an evolutionary scenario in which strongly blue shifted [ ne ii ] and [ ne iii ] emission trace the ( partial ) disruption of the obscuring medium around a buried agn . the detection of strongly blue shifted [ ne v ] emission in iras13451 + 1232 would then indicate this process to be much further advanced in this ulirg than in irasf001837111 and iras121271412ne , where this line is undetected .

0811.1562

c

we have discovered high - velocity ionized gas with velocities ranging from -3500 to + 3000 km s@xmath1 as part of a nuclear outflow from the ulirg irasf001837111 . the gas is traced by the mid - infrared 12.81@xmath0 m [ ne ii ] and 15.51@xmath0 m [ ne iii ] lines , which are dominated by blue shifted components . optical and near - infrared spectroscopic studies show no evidence for similar high - velocity gas components in forbidden lines at shorter wavelengths . we interpret this as the result of strong extinction ( a@xmath2=1050 ; a@xmath49@xmath171 ) on the blue shifted gas , identifying the base of the optical outflow ( @xmath173@xmath22 east ) as its most likely origin . unusual excitation conditions in irasf001837111 are further implied by a comparison of the combined [ ne ii ] and [ ne iii ] luminosity and the combined 6.2 and 11.2@xmath0 m pah luminosity for a large sample of agns , ulirgs and starburst galaxies . this reveals the neon line emission in irasf001837111 to be at least 8 times stronger compared to its pah emission than the typical ratio for the sample . two other ulirgs in our sample of 56 display mid - infrared excitation and kinematic properties similar to irasf001837111 : iras121271412ne and iras13451 + 1232 . both sources have elevated neon / pah ratios and exhibit pronounced blue wings in their 15.56@xmath0 m [ ne iii ] line profiles . wings are also present in their 12.81@xmath0 m [ ne ii ] profiles , but are less pronounced , indicating blue shifted gas to have a higher [ ne iii]/[ne ii ] ratio than gas closer to systemic velocity . iras13451 + 1232 even shows strongly blue shifted 14.32@xmath0 m [ ne v ] emission . while for iras13451 + 1232 the observed [ ne iii]/[ne ii ] and [ ne v]/[ne ii ] ratios indicate exposure of the blue shifted gas to direct radiation from the agn , for irasf001837111 and iras121271412ne the observed ratios are consistent with an origin in fast shocks ( v@xmath25500 km s@xmath1 ) in an environment with gas densities n@xmath2510@xmath43 . irasf001837111 and iras121271412ne are clear outliers in the mid - infrared diagnostic diagram of silicate strength and 6.2@xmath0 m pah equivalent width , the so - called ` fork ' diagram @xcite . the sources are found in between the two branches which separate deeply buried nuclei and sources with incomplete or clumpy obscuring geometries . @xcite have proposed that ulirgs in between the tips of these branches may be agn in the process of disrupting their fully covered geometry before settling on the agn branch . iras13451 + 1232 would then already be there , given its nearly featureless mid - infrared power law spectrum . the results from our mid - infrared kinematic and excitation study are consistent with the above evolutionary scenario in that the strongly blue shifted [ ne ii ] and [ ne iii ] emission ( from shocks ) may trace the ( partial ) disruption of the obscuring medium around buried agns in irasf001837111 and iras121271412ne . the detection of strongly blue shifted [ ne v ] emission in iras13451 + 1232 may then indicate the lifting of the obscuration around the agn coronal line region to be further advanced in this ulirg than in irasf001837111 and iras121271412ne , where this line is undetected . our measurements of the s(1 ) , s(2 ) , s(3 ) and s(4 ) pure rotational molecular hydrogen lines allow us to investigate the properties of warm molecular hydrogen in irasf001837111 . unfortunately , a measurement of the important s(0 ) line is lacking as it is outside the irs - lh bandpass . in fig.[fig6 ] we show the excitation diagram for molecular hydrogen for the four measured lines . given the placement of the s(3 ) line at the peak of the silicate absorption feature , we can attempt an extinction correction on the four data points under the assumption that a ) the excitation temperature should be constant or increase monotonically with increasing upper level energy e@xmath53(@xmath54,j ) , b ) that the ortho - to - para ratio is 3 ( i.e. assuming lte ) , and c ) that the cooler gas probed by the s(1 ) and s(2 ) lines is more or less co - spatial with the warmer gas probed by the s(3 ) and s(4 ) lines . adopting the local ism extinction law of @xcite , we then find that the extinction on the h@xmath18 lines ranges between a@xmath2=15 and 25 . this is far lower than the extinction on the continuum source , which is a@xmath2@xmath2554 based on the apparent depth of the 9.7@xmath0 m silicate feature ( @xmath55=3.0 ; * ? ? ? * ) and a@xmath2/@xmath55=18 @xcite . based on the two detected ortho - h@xmath18 lines , it is possible to infer an excitation temperature for the warm molecular hydrogen . the value ranges from 330 to 390k for extinction corrections ranging from a@xmath2=0 to 25 . assuming all h@xmath18 levels to be in lte at 330390k , we derive a total warm molecular hydrogen mass of 820@xmath910@xmath57 m@xmath7 . this value becomes a lower limit if the excitation temperature based on the upper level populations of the s(0 ) and s(1 ) lines is lower than those based on the s(1 ) and s(3 ) lines which is usually the case ( e.g. * ? ? ? unfortunately , we can not determine the warm to total molecular hydrogen fraction and compare this to other ulirgs , as no millimeter co line measurement exists for irasf001837111 from which to infer the cold molecular hydrogen mass . [ [ non - detection - of - absorption - bands - of - c_2h_2-and - hcn - gas ] ] non - detection of absorption bands of c@xmath18h@xmath18 and hcn gas ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ several ulirgs show absorption bands of c@xmath18h@xmath18 and hcn gas in their 13.714.1@xmath0 m _ spitzer _ irs - sh spectra @xcite . detections are especially strong among ulirgs with pronounced silicate absorption features , like iras201004156 and iras15250 + 3609 . far weaker detections are reported for ulirgs with agn - like spectra , like iras051892524 , iras010032238 and mrk231 @xcite . detections at these levels require spectra to have signal - to - noise ratios of at least 100 in their continua . the irs - sh spectrum of irasf001837111 does not show any indication for the presence of either feature , despite a continuum s / n of 70 . this translates into upper limits on the c@xmath18h@xmath18 and hcn gas column densities of n(c@xmath18h@xmath18)@xmath171.2@xmath910@xmath58@xmath37 and n(hcn)@xmath173.0@xmath910@xmath58@xmath37 for an adopted excitation temperature of 300k ( f. lahuis , private communication ) . the authors thank jan cami , helmut dannerbauer , brent groves , lei hao , timothy heckman , lisa kewley , dieter lutz and xander tielens for discussions , catherine buchanan , joanna holt and sylvain veilleux for sharing their published spectra , and mark g. allen for providing mappings shock models ahead of publication . we also would like to thank the slow but dilligent referee for comments which helped to strengthen the paper . support for this work was provided by nasa . this research has made extensive use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa . spoon , h.w.w . , keane , j.v . , cami , j. , lahuis , f. , tielens , a.g.g.m . , armus , l. , charmandaris , v. , 2005 , in iau symp . 231 , astrochemistry : recent successes and current challenges , eds . lis , g.a . blake & e. herbst , ( cambridge : cambridge univ .

optical and near - infrared spectroscopic studies show no evidence for similarly high velocity gas components in forbidden lines at shorter wavelengths . we interpret this as the result of strong extinction ( a=1050 ) on the high - velocity gas , which identifies the base of the outflow traced in 5007 [ o iii ] as a plausible origin . unusual excitation conditions are implied by a comparison of the mid - infrared low - excitation neon line emission and the polycyclic aromatic hydrocarbon ( pah ) emission for a sample of 56 ulirgs . both sources have an elevated neon / pah ratio and exhibit pronounced blue wings in their 15.56 m [ ne iii ] line profiles . iras13451 + 1232 even shows a strongly blue shifted and broad 14.32 m [ ne v ] line . while for iras13451 + 1232 the observed [ ne iii]/[ne ii ] and [ ne v]/[ne ii ] line ratios indicate exposure of the blue shifted gas to direct radiation from the agn , for irasf001837111 and iras121271412ne the neon line ratios are consistent with an origin in fast shocks in a high - density environment , and with an evolutionary scenario in which strongly blue shifted [ ne ii ] and [ ne iii ] emission trace the ( partial ) disruption of the obscuring medium around a buried agn . the detection of strongly blue shifted [ ne v ] emission in iras13451 + 1232 would then indicate this process to be much further advanced in this ulirg than in irasf001837111 and iras121271412ne , where this line is undetected .

we report the first mid - infrared detection of highly disturbed ionized gas in the ultraluminous infrared galaxy ( ulirg ) irasf001837111 . the gas , traced by the 12.81 m [ ne ii ] and 15.56 m [ ne iii ] lines , spans a velocity range of 3500 to + 3000 km s with respect to systemic velocity . optical and near - infrared spectroscopic studies show no evidence for similarly high velocity gas components in forbidden lines at shorter wavelengths . we interpret this as the result of strong extinction ( a=1050 ) on the high - velocity gas , which identifies the base of the outflow traced in 5007 [ o iii ] as a plausible origin . unusual excitation conditions are implied by a comparison of the mid - infrared low - excitation neon line emission and the polycyclic aromatic hydrocarbon ( pah ) emission for a sample of 56 ulirgs . for irasf001837111 , the neon / pah ratio is 8 times higher than the average ratio . similar mid - infrared kinematic and excitation characteristics are found for only two other ulirgs in our sample : iras121271412ne and iras13451 + 1232 . both sources have an elevated neon / pah ratio and exhibit pronounced blue wings in their 15.56 m [ ne iii ] line profiles . iras13451 + 1232 even shows a strongly blue shifted and broad 14.32 m [ ne v ] line . while for iras13451 + 1232 the observed [ ne iii]/[ne ii ] and [ ne v]/[ne ii ] line ratios indicate exposure of the blue shifted gas to direct radiation from the agn , for irasf001837111 and iras121271412ne the neon line ratios are consistent with an origin in fast shocks in a high - density environment , and with an evolutionary scenario in which strongly blue shifted [ ne ii ] and [ ne iii ] emission trace the ( partial ) disruption of the obscuring medium around a buried agn . the detection of strongly blue shifted [ ne v ] emission in iras13451 + 1232 would then indicate this process to be much further advanced in this ulirg than in irasf001837111 and iras121271412ne , where this line is undetected .

1701.03536

i

quantum entanglement - a direct consequence of linearity of quantum mechanics and the superposition principle - is one of the most intriguing phenomena distinguishing quantum and classical description of physical systems . quantum correlated ( e.g. , entangled ) states of composite systems possess features unknown in the classical world , like the seemingly paradoxical nonlocal properties exhibited by the famous einstein - podolsky - rosen analysis of completeness of the quantum theory . recently , with the development of quantum information theory they came to prominence as the main resource for several applications aiming at speeding up and making more secure information transfers ( see , e.g. , @xcite ) . a novel kind of quantum correlations , called _ quantum discord _ , different from entanglement , but also absent in the macroscopic world , was discovered @xcite , @xcite adding one more element to `` mysteries of quantum mechanics '' as seen from the classical point of view . although typically a quantum system , as , e.g. , a harmonic oscillator or a hydrogen atom , is described in terms of an infinitely dimensional hilbert space , for most quantum - information applications the restriction to finite dimensions suffices , since usually the active role in information processing play only spin degrees of freedom or only few energy levels are excited during the evolution . from the mathematical point of view such finite - dimensional quantum mechanics seems to mount a smaller challenge than in the infinite - dimensional case - the tool of choice is here linear algebra rather than functional analysis . nevertheless , understanding of correlations in multipartite finite dimensional quantum systems is still incomplete , especially for systems with many components or consisting of particles governed by quantum statistics ( bosons , fermions ) @xcite . the statistical interpretation of quantum mechanics disturbs a bit the simple linear - algebraic approach to quantum mechanics - vectors of state ( elements of a finite - dimensional hilbert space @xmath2 ) should be of the unit norm . obviously , physicist are accustomed to cope with this problem in a natural way by `` normalizing the vector and neglecting the global phase '' . nevertheless , it is often expedient to implement this prescription by adopting a suitable mathematical structure , the projective space @xmath3 , already from the start . the projective space is obtained from the original hilbert space @xmath2 by identifying vectors , etc . , and the short one @xmath4 etc . for elements ( vectors ) of @xmath2 . ] differing by a scalar , complex , non - zero factor , @xmath5 . we will denote elements ( points ) of @xmath3 by @xmath6 , etc . and , if we want to identify a particular equivalence class of e vector @xmath7 , by @xmath8 $ ] , etc . obviously , both approaches , the linear - algebraic ( plus normalization and neglecting the global case ) picture and the projective one are equivalent . following the former we loose linearity , so which advantages we could expect instead ? we answered this question in our paper @xcite , where we propose , by working in the projective space , to apply completely new ( in this context ) techniques to analyze the phenomenon of entanglement . the approach has given a deeper insight into the unexpectedly rich geometric structure of the space of states and enabled the use of recently developed advanced methods of complex differential , algebraic and symplectic geometry . the most efficient characterization of quantum correlations is achieved by identifying states that are ` equally correlated ' or , in other words , states that can be mutually transformed _ via _ methods allowed by rules of quantum mechanics without destroying quantum correlations . this is the case of pure quantum operations that are _ local _ , i.e. restricted to act independently on each subsystem . as required by quantum mechanics , such operations are unitary in the relevant hilbert space @xmath2 , but form only a subgroup of the whole group @xmath9 as limited by the restriction to subsystems . for these reasons they are called _ local unitary _ ( lu ) operations . a complementary insight is provided by adding more operations , like measurements performed locally , i.e. , each restricted to a single subsystem , and possible communication among subsystems _ via _ classical means of communication . such operations are dubbed locc - _ local operations with classical communication_. they usually destroy purely quantum correlations , but in any case do not increase them , so if one state can be transformed to another one _ via _ locc transformation , the latter is not more ( and usually less ) correlated than the former . this allows quantifying correlations by constructing _ entanglement measures _ , quantities characterizing states that remain unchanged under lu operations and do not increase under locc ones . technically it is convenient to group together states related to each other by invertible stochastic local operations and classical communication ( slocc ) two states , @xmath10 and @xmath7 belong to the same slocc class if both transformations , @xmath11 and @xmath12 can be achieved by means of locc with non - zero probability . hence , in general , if two states belong to two distinct slocc classes , they have different correlation properties and might be not exchangeable for achieving the same quantum informational tasks . as mentioned above the lu operations form a subgroup @xmath13 of the whole unitary group @xmath9 of the relevant hilbert space @xmath2 ( since the global phase of a state is irrelevant , we can use the special unitary group @xmath14 instead ) . the slocc also form a group @xmath15 that happens to be the complexification of @xmath13 , i.e. , @xmath16 . in contrast to @xmath13 , which is compact as a subgroup of the unitary group , @xmath15 is not compact . the exact forms of @xmath13 and , consequently , @xmath15 depend on the problem in question ( number and dimensionality of subsystems , distinguishability of particles constituting them ) . the actions of @xmath13 and @xmath15 on @xmath2 are naturally and easily transferred to the projective space @xmath3 _ via _ @xmath17=[u\psi]$ ] . the projective space has a reach geometrical structure . in particular , in a natural way , it is a khler manifold , i.e. , a complex symplectic riemannian manifold on which all three structures are compatible . symplecticity means that it can be treated as a kind of a classical phase space for a hamiltonian system . the action of a group on such a manifold reflects symmetries of the dynamical system , and the methods of analysis of such systems can be borrowed from classical mechanics . in modern formulation of classical mechanics ( see , e.g. , @xcite , @xcite ) one employs the full power of symplectic geometry . so far the above outlined geometric treatment of correlations was restricted to pure states . there exists , however , its natural extension to mixed states . instead of the projective space @xmath3 one considers another manifold - an orbit of the whole @xmath14 group through a chosen mixed state ( i.e. , the set of all mixed density matrices obtained for the chosen one @xmath18 _ via _ by unitary conjugations , @xmath19 , @xmath20 ) , in other words all density matrices with the same spectrum . such an orbit posses a natural khlerian structure given by the so called kirillov - kostant - souriau form . this observation allows to apply the same geometric techniques as in the pure - state case .

we review a geometric approach to classification and examination of quantum correlations in composite systems . since quantum information tasks are usually achieved by manipulating spin and alike systems or , in general , systems with a finite number of energy levels , classification problems are usually treated in frames of linear algebra . such classifications are interpreted as identification of states with ` the same correlations properties ' i.e. ones that can be used for the same information purposes , or , from yet another point of view , states that can be mutually transformed one to another by specific , experimentally accessible operations . it is clear that the latter characterization answers the fundamental question ` what can be transformed into what _ via _ available means ? ' . center for theoretical physics , polish academy of sciences , al . lotnikw 32/46 , 02 - 668 warszawa , poland icfo - institut de ciencies fotoniques , the barcelona institute of science and technology , 08860 castelldefels ( barcelona ) , spain

we review a geometric approach to classification and examination of quantum correlations in composite systems . since quantum information tasks are usually achieved by manipulating spin and alike systems or , in general , systems with a finite number of energy levels , classification problems are usually treated in frames of linear algebra . we proposed to shift the attention to a geometric description . treating consistently quantum states as points of a projective space rather than as vectors in a hilbert space we were able to apply powerful methods of differential , symplectic and algebraic geometry to attack the problem of equivalence of states with respect to the strength of correlations , or , in other words , to classify them from this point of view . such classifications are interpreted as identification of states with ` the same correlations properties ' i.e. ones that can be used for the same information purposes , or , from yet another point of view , states that can be mutually transformed one to another by specific , experimentally accessible operations . it is clear that the latter characterization answers the fundamental question ` what can be transformed into what _ via _ available means ? ' . exactly such an interpretations , i.e , in terms of mutual transformability can be clearly formulated in terms of actions of specific groups on the space of states and is the starting point for the proposed methods . center for theoretical physics , polish academy of sciences , al . lotnikw 32/46 , 02 - 668 warszawa , poland icfo - institut de ciencies fotoniques , the barcelona institute of science and technology , 08860 castelldefels ( barcelona ) , spain

cond-mat0205321

i

it is often noted that nonequilibrium statistical mechanics lacks the comprehensive formalism of ensembles that has proved so useful in equilibrium . the reason is that equilibrium statistical mechanics treats stationary states for a special subclass of systems , that possess detailed balance . this allows one to bypass the dynamics , and study stationary properties directly . for systems out of equilibrium , we generally do not have such a shortcut , and must deal with the full dynamical problem , even if our goal is only to obtain stationary properties . in the case of stochastic systems with a discrete state space , the fundamental description is given by the master equation , which governs the evolution of the probability distribution . this class of problems includes a wide range of systems of current interest , that exhibit phase transitions or scale invariance far from equilibrium : driven lattice gases , birth - and - death processes such as directed percolation or the contact process , sandpile models , and interface growth models . one of the more powerful tools for studying stochastic models is a formalism that maps the process to a path - integral representation @xcite . the mapping generates an _ effective action _ that can be studied using the tools of equilibrium statistical physics , for example , the renormalization group . several methods for mapping a stochastic process to an equilibrium - like action have been proposed @xcite . in these notes we review the method developed by peliti @xcite , and apply it to some simple stochastic processes . this method has several advantages . with it , one can map any birth - and - death type process to a path - integral representation without ambiguity . in particular , the step of writing a langevin equation , and of postulating noise autocorrelations , does not arise in this formalism . thus it provides a direct path from the model of interest to an effective action , and ( in the continuum limit ) , to its field theory , without the uncertainties that often attend the specification of the noise term @xcite . a second advantage , which we explore in some examples , is that it leads to a systematic perturbative analysis for markov processes . the principal aim of this article is to acquaint the reader with the formalism and provide a set of worked examples whose mastery will allow one to apply the method to problems at the frontier of research . while peliti s article @xcite provides an excellent exposition of the mapping , we include , for completeness , a derivation of the central formulas . our development of the perturbation theory differs somewhat from peliti s . most of the applications discussed are also new . the balance of this article is structured as follows . in sec . ii we derive the path - integral representation , starting from the master equation . sec . iii presents an application to the simple decay process , and expressions for two - time joint probabilities . in sec . iv we begin our discussion of diagrammatic perturbation theory for the probability generating function , which is illustrated with a pedagogical example . this is extended in sec . v where we analyze the birth - and - death process using perturbation theory . in sec . vi a perturbation expansion for moments of the distribution is developed , which turns out to be much simpler than that for the full generating function . this method is applied to the malthus - verhulst process in sec . vii . in sec . viii we illustrate another application of the formalism , showing how the path - integral description for a lattice of coupled malthus - verhulst processes leads , in the continuum limit , to a field theory for directed percolation . sec . ix presents a brief summary .

we show how to implement a diagrammatic perturbation theory for processes that do not admit an exact solution . analysis of a set of coupled malthus - verhulst processes on a lattice leads , in the continuum limit , to a field theory for directed percolation and allied models . 1em email : dickman@fisica.ufmg.br

we review and extend the formalism introduced by peliti , that maps a markov process to a path - integral representation . after developing the mapping , we apply it to some illustrative examples : the simple decay process , the birth - and - death process , and the malthus - verhulst process . in the first two cases we show how to obtain the exact probability generating function using the path integral . we show how to implement a diagrammatic perturbation theory for processes that do not admit an exact solution . analysis of a set of coupled malthus - verhulst processes on a lattice leads , in the continuum limit , to a field theory for directed percolation and allied models . 1em email : dickman@fisica.ufmg.br

1507.06054

i

spintronics invokes the spin degree of freedom of the electron to improve the efficiency of and add functionalities to electronic devices @xcite . here the generation , propagation , processing , and detection of spin currents form central themes @xcite . the spin - orbit coupling ( soc ) provides a mechanism to couple the charge and spin of electrons . a prominent example is the spin hall effect ( she ) , i.e. the soc - induced pure spin current transverse to an applied charge current @xcite . in bilayers of a normal metal ( n : a non - magnetically ordered metal ) and a ferromagnet ( f , which includes in the present context ) , the magnetization dynamics is affected by the she spin current via the spin - transfer torque @xcite that can be strong enough to switch the magnetization @xcite . on the other hand , the inverse of the she ( ishe ) , i.e. , the pure spin current - driven transverse charge current , is a convenient tool to detect spin currents generated by spin pumping ( sp ) @xcite and the spin seebeck effect ( sse ) @xcite . quite some attention has been recently focused on ferromagnetic insulators ( fi ) such as yttrium iron garnet ( yig : y@xmath0fe@xmath1o@xmath2 ) that can be activated electrically and thermally by attached normal metal contacts . yig s very low magnetization damping makes it an attractive material for low - power spin - wave based interconnects and heat - harvesting devices @xcite . the magnetoresistance ( mr ) is the ratio of the electrical resistance of a material with and without an applied magnetic field @xcite . in ferromagnetic conductors the mr is often dominated by effects that are not caused directly by the applied magnetic field , but rather by the magnetization orientation as controlled by the applied field . the anisotropic magnetoresistance ( amr ) , for example , refers to the phenomenon that the electrical resistance of ferromagnets depends on the angle between the current and magnetization directions @xcite . for applications in magnetic field sensors and data storage devices , the amr has been superseded by the giant magnetoresistance ( gmr ) @xcite and tunneling magnetoresistance @xcite . this review addresses a new type of mr discovered in a bilayer made of a metal n with strong soc ( usually platinum ) and an fi ( usually yig ) , where the electrical resistance was found to depend on the magnetization of the fi @xcite . since it can be explained by the simultaneous action of the she and ishe @xcite , it has been dubbed spin hall magnetoresistance ( smr ) . this mechanism is similar to that of the predicted magnetoresistance of the two - dimensional electron gas induced by magnetic field - induced decoherence of an edge spin accumulation @xcite ( the related hanle effect was observed recently in pt films under large magnetic fields @xcite ) . the smr can be used to electrically measure the magnetization direction of an insulator @xcite and helps to non - invasively access fundamental transport parameters such as the spin hall angle , spin diffusion length , and spin - transfer torque ( spin - mixing conductance ) at an n@xmath3fi interface @xcite . the smr originates from the simultaneous action of two effects , viz . the she and ishe , that both made an impact on modern spintronics . the she causes current - induced spin - transfer torques without a polarizing ferromagnet ( spin - orbit torques ) while the ishe has become a standard method of detecting spin currents . however , controversial issues remain , such as the magnetic proximity effect and the rashba soc at the n@xmath3fi interface , challenging the applications mentioned above , but also our understanding of phenomena such as the spin seebeck effect . the smr in n@xmath3fi bilayers is arguably the most simple observable to detect socs : it exists in bilayers of well - studied and characterized materials , and is a strictly linear response effect . hence , it is essential to understand the smr before more complicated ones that involve complex devices , difficult materials , magnetization dynamics , noise or non - linearitis . many groups have theoretically and experimentally studied the smr since its discovery . hence we believe that the time has come to consolidate the existing knowledge . this review is organized as follows : in section [ materials ] , we introduce the basic concepts and prevalent materials necessary to understand and observe the smr . in section [ theory ] , we describe the diffusion theory for the ( i)she with quantum mechanical boundary conditions at interfaces . experiments by various groups are discussed in section [ comparison ] as well as the parameters obtained by fitting the theory . in section [ issues ] , we address controversial issues such as magnetic proximity and rashba soc at interfaces . smr - related new developments are reviewed in section [ developments ] . we present conclusions and an outlook in section [ conclusions ] .

the associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction . the smr provides a convenient tool to non - invasively measure the magnetization direction and spin - transfer torque to an insulator . we introduce the minimal theoretical instruments to calculate the smr , i.e. spin diffusion theory and quantum mechanical boundary conditions . we discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and rashba spin - orbit torques , and point out new developments . _ keywords _ : spintronics , spin currents , spin hall effect

we review the so - called spin hall magnetoresistance ( smr ) in bilayers of a magnetic insulator and a metal , in which spin currents are generated in the normal metal by the spin hall effect . the associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction . the smr provides a convenient tool to non - invasively measure the magnetization direction and spin - transfer torque to an insulator . we introduce the minimal theoretical instruments to calculate the smr , i.e. spin diffusion theory and quantum mechanical boundary conditions . this leads to a small set of parameters that can be fitted to experiments . we discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and rashba spin - orbit torques , and point out new developments . _ keywords _ : spintronics , spin currents , spin hall effect

1103.0276

i

supermassive black holes ( smbhs ) are now known to be ubiquitous in the centers of all massive galaxies @xcite . smbhs grow in an `` active '' phase of accretion , during which they are observed as active galactic nuclei ( agn ) . agn growth is intimately tied to galaxy evolution , as evident in the well - studied correlations between smbh mass ( @xmath3 ) and properties of the host galaxy bulge ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the agn phase is also hypothesized to regulate star formation in its host galaxy , with the galaxy feeding the black hole in turn ( e.g. * ? ? ? * ; * ? ? ? all massive galaxies are thought to experience episodic agn behavior in their lifetime @xcite . agns are generally classified by differences in their optical spectra . type 1 or broad - line agns have broad ( @xmath4 km s@xmath5 ) emission lines superimposed on blue unobscured continua in the uv / optical ( e.g. , * ? ? ? * ) , and are the most luminous persistent sources in the sky . type 2 or narrow - line agns lack broad emission lines and have weaker continua ( frequently dominated by their host galaxies ) , but have strong narrow emission lines , especially from forbidden transitions . narrow emission lines associated with nuclear activity can be distinguished from lines caused by star formation by studying the line ratios @xcite . the line ratio diagnostics work because the `` harder '' emission of an agn is more efficient at ionizing the surrounding gas and dust than star formation , and thus agns have stronger lines from high - energy forbidden transitions ( e.g. , @xmath65007 and @xmath66583 ) relative to the lower - energy hydrogen transitions ( e.g. , @xmath64861 and @xmath66563 ) . the subclass of `` low - ionization nuclear emission region '' agns ( liners , * ? ? ? * ) have narrow emission lines that are probably excited by some combination of ionization from both star formation and an agn @xcite . deep x - ray surveys have additionally revealed `` optically dull '' agns @xcite , which have bright x - ray emission but none of the broad or narrow emission line signatures of agn accretion . while many optically dull agns can be explained as type 2 agns diluted by prominent host galaxies @xcite , at least @xmath71/3 are undiluted but intrinsically optically weaker than other agns @xcite . the inferred x - ray column density @xmath8 can also be used to classify agns , with type 2 ( narrow - line ) agns typically more x - ray absorbed than type 1 ( broad - line ) agns . however x - ray and optical classifications differ for @xmath720% of objects @xcite . historically , type 2 and optically dull agns have been described as obscured versions of type 1 agn , with the broad emission line region ( blr ) hidden behind a partially opaque `` torus '' of gas and dust , while the narrow emission lines lie outside the torus ( e.g. , * ? ? ? the best evidence for this scenario is the observation that some type 2 agns have a `` hidden '' blr revealed by spectropolarimetry @xcite . however , recent observations have revealed several serious limitations of a simple unified model based solely on geometric obscuration . even in very deep spectropolarimetric observations , many type 2 agns show no hidden blr @xcite . observations suggest a lower @xmath9 limit in accretion rate for broad - line agns @xcite , although they remain incomplete at low accretion rates and low masses @xcite . the x - ray spectra are unabsorbed ( @xmath10 @xmath11 ) for 30 - 40% of type 2 agns @xcite , as well as most local liners ( * ? ? ? * and references therein ) and distant optically dull agns @xcite . several well - studied liners additionally lack the narrow fe k@xmath12 emission signature of a dusty torus @xcite . many type 2 agns and most optically dull agns have mid - ir colors like normal galaxies @xcite , in contrast to hot mid - ir colors of type 1 agns described by torus models @xcite . toroidal obscuration is additionally ruled out for some strongly varying type 2 @xcite and optically dull agns @xcite , since these objects have continua which vary on year timescales , well within the inferred light travel time dimension of any torus . several authors have proposed models which use different accretion rates as a cause of the differences between observed agns . @xcite suggest that the blr and `` torus '' are inner ( ionized ) and outer ( clumpy and dusty ) parts of the same disk - driven wind , and that this wind is no longer supported at low accretion rate ( see also * ? ? ? * ; * ? ? ? similarly , @xcite suggested that low accretion rates actually drive the disk wind within the last stable orbit of the smbh , meaning that the blr can not form . models for radiatively inefficient accretion ( e.g. , * ? ? ? * ) suggest that at @xmath13 , the accretion disk becomes truncated near the smbh , with a geometrically thick and optically thin disk at low radii , and a normal thin disk ( e.g. , * ? ? ? * ) at higher radii . such objects are predicted to lack strong emission lines ( both broad and narrow ) and have weak uv / optical emission , as observed in many optically weak low - luminosity agns @xcite and x - ray bright , optically dull agns @xcite . @xcite additionally show that x - ray hardness , generally attributed to x - ray absorption , may also result from the naturally x - ray hard spectrum expected from radiatively inefficient accretion . in this work we directly measure eddington ratios for a large , x - ray selected sample of broad - line , narrow - line , and lineless agns . the eddington ratio is a unitless measure of accretion power , defined as @xmath14 . ( with @xmath0 the intrinsic accretion luminosity ) . the sample is drawn from the cosmic evolution survey ( cosmos , * ? ? ? * ) x - ray agn sample @xcite , as described in section 2 . estimates of specific accretion rates are described in section 3 , with intrinsic accretion luminosity @xmath0 measured directly from fits to the multiwavelength continuum ( avoiding uncertain bolometric corrections ) and black hole masses from the broad line scaling relations ( for broad - line agns ) or the @xmath15 relations ( for narrow - line and lineless agns ) . in section 4 we show that broad emission lines are present at only high accretion rates ( @xmath16 ) , while narrow - line and lineless agns at lower accretion rates have cooler disks , stronger radio jets , and no torus ir signature . we present a `` cartoon '' model which summarizes our results in section 5 , with predictions for future observations in section 6 . we adopt a cosmology with @xmath17 , @xmath18 , @xmath19 throughout .

we avoid the systematic errors plaguing previous studies of agn accretion rate by using accurate accretion luminosities ( ) from well - sampled multiwavelength seds from the cosmic evolution survey ( cosmos ) , and accurate black hole masses derived from virial scaling relations ( for broad - line agns ) or host - agn relations ( for narrow - line and lineless agns ) . in general , broad emission lines are present only at the highest accretion rates ( ) , and these rapidly accreting agns are observed as broad - line agns or possibly as obscured narrow - line agns . narrow - line and lineless agns at lower specific accretion rates ( ) are unobscured and yet lack a broad line region .

we show how accretion rate governs the physical properties of a sample of unobscured broad - line , narrow - line , and lineless active galactic nuclei ( agns ) . we avoid the systematic errors plaguing previous studies of agn accretion rate by using accurate accretion luminosities ( ) from well - sampled multiwavelength seds from the cosmic evolution survey ( cosmos ) , and accurate black hole masses derived from virial scaling relations ( for broad - line agns ) or host - agn relations ( for narrow - line and lineless agns ) . in general , broad emission lines are present only at the highest accretion rates ( ) , and these rapidly accreting agns are observed as broad - line agns or possibly as obscured narrow - line agns . narrow - line and lineless agns at lower specific accretion rates ( ) are unobscured and yet lack a broad line region . the disappearance of the broad emission lines is caused by an expanding radiatively inefficient accretion flow ( riaf ) at the inner radius of the accretion disk . the presence of the riaf also drives narrow - line and lineless agns to 10 times higher ratios of radio to optical / uv emission than broad - line agns , since the unbound nature of the riaf means it is easier to form a radio outflow . the ir torus signature also tends to become weaker or disappear from agns , although there may be additional mid - ir synchrotron emission associated with the riaf . together these results suggest that specific accretion rate is an important physical `` axis '' of agn unification , described by a simple model .

0804.1505

i

there has been a renewed interest in higher dimensional solutions to einstein field equations . several interesting vacuum static / stationary solutions @xcite , the methods of their generations @xcite and study @xcite , as well as some general results on uniqueness of higher dimensional static vacuum black holes @xcite,@xcite , @xcite in @xmath2 dimensions have appeared recently . in the case of time - dependent geometries , the main interest is to study higher dimensional spacetimes as backgrounds for string propagation @xcite . in cosmology @xcite , the new trends impose lifting " the cosmological models to higher dimensions . another , and probably the most relevant reason to study the higher dimensional generalizations of the einstein equations stems from the fact that we live in a four dimensional world . it would be important then , if we were able to convince ourselves , by studying the higher dimensional solutions , that there is something special , unique and deep about four dimensions . this could only be done if we study the alternatives . much work has been done previously @xcite , yet , since the interests move with time , the motivation , and with it the boundary / initial conditions imposed on the solutions change as well . in solving einstein equations , one usually imposes some sort of symmetry . what we are good at is the situation where the spacetime does not depend on more than two , preferably non - null variables . in four dimensions these are known as the so - called @xmath3 solutions . almost all known interesting four - dimensional solutions of einstein equations in vacuum , electrovacuum or with some fundamental matter fields belong to this class and contain at least two commuting killing directions . once we are confronted with the situation where the line element _ does _ depends on at most two coordinates , we are in business " : whether these are stationary solutions with axial symmetry , boost - symmetric spacetimes , anisotropic ( isotropic ) and inhomogeneous ( homogeneous ) cosmologies , cylindrical , or plane gravity and matter waves - there are dozens of generating techniques , algorithms etc . to construct new solutions of ever increasing complexity @xcite starting from more simple seeds . because of their generality , on one hand , and applicability , on the other , the known @xmath3 solutions provide a perfect seed " or a building block to construct further new solutions . the construction of families of higher dimensional solutions is not an exception : one can efficiently use the known @xmath3 solutions as the seeds in order to construct their higher dimensional generalizations and analogues . as usual , the physics enters via the boundary and initial conditions ( asymptotic flatness , clean horizons and singularities in the case of compact objects ; singularity structure , inflation , late / early - time acceleration - for cosmological models etc . ) obtaining sufficiently general solutions , of course , does not necessarily mean alleviating the search for specialty and physical meaningfulness , nevertheless , the understanding of the sufficiently general class of solutions may shed some light on a problem . the above considerations lead us to the main purpose of this paper : the construction , in a possibly most simple and controllable way of higher dimensional vacuum solutions to einstein equations which depend , at most , on two variables . our starting point would be the @xmath4-dimensional vacuum seed metrics with the @xmath3 symmetry . the vacuum seed spacetime will be generalized to include massless dilatons , which will serve to lift the solutions to higher dimensions . to include the scalar field , the vacuum line element would be written in the coordinates especially adopted for this matter . it happens so , that in these coordinates the scalar dilaton coupled to gravity in the @xmath3 case satisfies a linear differential equation . this equation can be easily solved with the general solution representing a linear combination of some elementary solutions . any term , as well as , any linear combination of these solutions , may serve to lift the dilaton spacetime to higher dimensions , obtaining in such a way a new vacuum solution in any dimension greater than @xmath4 . to get interesting solutions , one must choose the right " @xmath3 seed as well as the right combination of elementary scalar solutions ( dilatons ) . the scheme works both , in the case when the two commuting killing vectors of the seed " are spacelike ( cosmologies , cylindrical waves , colliding waves etc . ) as well as , when one of the killing vectors is timelike . it is important to mention that there is no need in imposing the hypersurface orthogonality of the two killing directions ( diagonality of the metric ) and therefore , the solutions obtained this way generalize , in the case when one of the killing directions is timelike , for example , the static higher dimensional solutions due to @xcite , enabling to obtain the generalized stationary solutions , in fact , an infinite dimensional family of such solutions . in the following section we briefly review the generating technique for the case where the two killing directions of the seed solution are both spacelike . in sec . iii the case with one timelike killing vector is addressed . in sec . iv the method is specialized to the 5-d case ; aspects such as asymptotic flatness and the interpretation of the method as the insertion of rod sources are as well included in this section . in sec . v , we analyze the trapping of surfaces , horizons and singularities of the generated solutions . in secs . vi and vii some 5-d static and stationary solutions are generated . finally , some conclusions are drawn in the last section .

. the construction uses einstein - scalar field seed solutions in 4 dimensions and is performed both for the case when all the killing directions are spacelike , as well as when one of the killing vectors is timelike . some examples representing generalizations of known higher dimensional stationary solutions are discussed in terms of their rod structure and horizon locations and deformations .

we show how one can systematically construct vacuum solutions to einstein field equations with commuting killing vectors in dimensions . the construction uses einstein - scalar field seed solutions in 4 dimensions and is performed both for the case when all the killing directions are spacelike , as well as when one of the killing vectors is timelike . the later case corresponds to generalizations of stationary axially symmetric solutions to higher dimensions . some examples representing generalizations of known higher dimensional stationary solutions are discussed in terms of their rod structure and horizon locations and deformations .

1011.4864

i

a branching random walk is a collection of points which , starting from a single point , diffuse and branch independently of the time , of their positions or of the other points , as in figure [ fig : brw ] . branching random walks appear in many contexts ranging from mathematics @xcite to biology @xcite . they can for example be used to describe how a growing population invades a new environment . in the one dimensional case , see figure [ fig : brw ] , there is , at a given time @xmath0 , a rightmost individual at position @xmath1 , a second rightmost at @xmath2 and so on . ( note that the rightmost @xmath3 at a time @xmath4 is not necessarily a descendant of the rightmost @xmath1 at time @xmath0 . ) the expected position @xmath5 of the rightmost individual as well as the probability distribution of its position @xmath1 around @xmath6 are well understood @xcite ; the goal of the present paper is to describe the statistical properties of the positions of all the rightmost points in the system , in particular the distribution of the distances between the two rightmost points , the average density of points at some fixed distance from the rightmost @xmath1 , etc . one motivation for studying these distances is that the problem belongs to the broader context of extreme value statistics @xcite : trying to understand the statistical properties of the rightmost points in a random set of points on the line is a problem common to the studies of the largest eigenvalues of random matrices @xcite , of the extrema of random signals @xcite , or of the low lying states of some disordered systems such as spin glasses @xcite . in fact , the points generated after some time @xmath0 by a branching random walk can be viewed as the energies of the configurations of a directed polymer in a random medium @xcite , and the distances between the rightmost points as the gaps between the low lying energy states . the most studied example of branching random walk is the branching brownian motion : one starts with a single point at the origin which performs a brownian motion and branches at a given fixed rate ( right part of figure [ fig : brw ] ) . whenever a branching event occurs , the point is replaced by two new points which evolve themselves as two independent branching brownian motions . while the number of points generated after some time @xmath0 grows exponentially with time , the expected position @xmath6 of the rightmost point increases only linearly with time @xcite . in one dimension , mc kean @xcite and bramson @xcite have shown that the probability distribution of the rightmost point is given by the traveling wave solution of the fisher - kpp equation , with a step initial condition . here we will see that all the statistical properties of the rightmost points can be understood in terms of solutions to the fisher - kpp equation with appropriate initial conditions @xcite . we will also show that the distribution of the distances between these rightmost points has a long time limit which exhibits the striking property of superposability : the distances between the rightmost points of the union of two realizations of the branching brownian motion have the same statistics as those of a single realization . this paper is organized as follows : in section [ statistics ] we introduce some generating functions useful to study random sets of points on the line and show how one can use them to obtain all the properties of these random sets . in section [ sec : bbmfkpp ] we show that , for the branching brownian motion , all these generating functions are solutions of the fisher - kpp equation . we also show that the distribution of all the rightmost points as seen from @xmath6 or , alternatively , as seen from @xmath1 , has a long time limit which can be computed as the delay of fisher - kpp traveling waves . this distribution has the property of superposability . in section [ quantitative ] , we present results , mostly numerical , on some specific aspects of the limiting distribution of points in the branching brownian motion , namely the distribution of the distance between the two rightmost points and the average density seen from the rightmost point . in section [ sec : disc ] we explain how the results on the branching brownian motion can be extended to more general branching random walks . finally , we study in section [ statmeas ] the distribution of all the rightmost points in a specific frame which depends on the realization and which was introduced by lalley and sellke @xcite .

we show that the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher - kpp traveling waves when the initial condition is modified . the limiting measure exhibits the surprising property of superposability : the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization . we discuss the extension of our results to more general branching random walks .

we show that all the time - dependent statistical properties of the rightmost points of a branching brownian motion can be extracted from the traveling wave solutions of the fisher - kpp equation . we show that the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher - kpp traveling waves when the initial condition is modified . the limiting measure exhibits the surprising property of superposability : the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization . we discuss the extension of our results to more general branching random walks .

1406.2722

i

the aim of this article is to relate two generalizations of the burau representation of the braid groups to certain types of tangles . consider the standard presentation of the braid group in @xmath1 strands @xmath2 the _ unreduced _ burau representation @xmath3 is defined on the free @xmath4$]-module of rank @xmath1 , given by the homomorphism @xmath5^n):\,\sigma_i\mapsto { { \mathcal b}_{n } } ( \sigma_i)=\beta_i\,.\ ] ] here the burau matrices @xmath6 and their inverses , denoting @xmath7 , are defined as @xmath8\oplus { \mathbbm{1}}_{n - i - 1 } \quad \mbox{,}\quad \beta_i^{-1}={\mathbbm{1}}_{i - 1}\oplus \left[\begin{array}{cc } 0 & \overline t\\ 1&(1 - \overline t)\\ \end{array}\right]\oplus { \mathbbm{1}}_{n - i - 1}\,.\ ] ] r45 mm there are various generalizations of the burau representation from braids to tangles . to explain these recall first the usual category of oriented tangles , denoted by @xmath9 , whose objects are tuples of signs @xmath10 writing @xmath11 . a morphisms @xmath12 is an equivalence classes of oriented tangle diagrams in @xmath13 $ ] with endpoints @xmath14 at the bottom of the diagram and @xmath15 at the top so that the orientation is upwards at the @xmath16-th positions if @xmath17 and downwards if @xmath18 . the equivalences are given by isotopies and the usual reidemeister moves . we denote by @xmath19 the array of length @xmath1 with all + entries , which implies that the orientations of all strands at this objects ( either as source or target ) must be pointing upwards . a string link is a tangle class @xmath20 with precisely @xmath1 interval components each of which has one endpoint @xmath21 at the bottom and the other endpoint @xmath22 at the top of the diagram . see figure [ fig : ex_strlk ] for an example of a string link @xmath23 on two strands . string links form a monoid @xmath24 with respect to the composition in @xmath9 so that we have the following inclusions of monoids : @xmath25 in @xcite lin , tian , and wang consider a generalization of @xmath26 to @xmath24 which is inspired by a remark vaughan jones in his seminal paper @xcite , where he offers a probabilistic interpretation of the burau representation . the description there is in terms of a bowling ball that runs along an arc in a braid diagram following its orientation . at positive crossings the ball drops from an overcrossing strand to an undercrossing strand with probability @xmath27 and remains on the overcrossing strand with probability @xmath28 . r38 mm the situation is illustrated in figure [ fig : cross_jump ] . an analogous rule is used for negative crossings in which @xmath28 is replaced by @xmath7 , see figure [ fig : x_opp_jump ] , so that `` probabilities '' should rather be understood as weights whose values are allowed to be outside of the unit interval . assuming the pictured strands are the @xmath29-th and @xmath30-st strands in a braid presentation on @xmath1 strands the markov transition matrix from the array of probabilities just above the crossing to one just below is given by the unreduced burau matrices in ( [ eq - buraum ] ) . the construction in @xcite extends the idea of weighted paths along an oriented string link diagram with the same rule as in figure [ fig : cross_jump ] . as opposed to braid diagrams it is possible to encounter loops and thus infinite numbers of paths between two endpoints . it is shown that for @xmath28 sufficiently close to 1 the resulting series of weights converge . for example , the diagram in figure [ fig : ex_strlk ] contains a loop of combined weight @xmath31 and associated geometric series @xmath32 . the combined transition matrix in this example is given as @xmath33\,.\ ] ] it is shown in @xcite that the resulting transition matrix will always have rational functions in @xmath28 as entries . the functorial nature of the construction , see lemma [ lm - basicsltw ] below , further implies a homomorphism of monoids @xmath34 which restricts to @xmath26 on the braid group @xmath3 . the main result of this paper will also extend to the exterior powers of this representation @xmath35 the construction of the random walk invariant in @xcite has been applied to studies of the jones polynomial and its relation to the alexander polynomial in @xcite and has been generalized in @xcite . a second generalization to the entire category of oriented tangles is given in section 3.3 of ohtsuki s book @xcite as operator invariants a tangles associated to the alexander polynomial . the matrices assigned to generating tangles there have entries in the ring of laurent polynomials in @xmath36 for suitable basis . the construction can thus be summarizes as a functor @xmath37-{\rm fmod}\ ] ] from the tangle category to the category of free @xmath38$]-modules . the assignment on objects is given by @xmath39 where @xmath40 is the free @xmath38 $ ] module of rank 2 generated by elements @xmath41 and @xmath42 , and @xmath43 is the dual module with dual basis @xmath44 . in fact , @xmath45 is easily seen to be a tensor functor with respect to the tensor product on @xmath9 defined by the usual juxtaposition . as described in section 4.5 of @xcite the tangle functor may be derived from the representation theory of the quantum group @xmath46 following the methods originally introduced by reshetikhin and turaev @xcite . one implication of this observation , which can also be checked directly , is that for a tangle @xmath47 the operator @xmath48 preserves a natural grading on the the modules induced , for example , by @xmath49 , @xmath50 , and @xmath51 . for example , the module assigned to the object of length @xmath1 with all positive orientations decomposes , as free @xmath38$]-modules , into its invariant graded components as follows : @xmath52 a consequence of this decomposition is that the representation of @xmath24 on @xmath53 implied by the inclusion in ( [ eq - incls ] ) yields a series of representations as follows : @xmath54 we note that @xmath55 is of rank one so that we may write @xmath56 as a well - defined polynomial - valued invariant . we will see in lemma [ lm - t=1of ] that its specialization at @xmath57 is one for all string links so that @xmath58 also as an element in @xmath59 . we can therefore define representations of the string monoid as follows . @xmath60 it is shown in @xcite that the restriction of @xmath1-dimensional representation @xmath61 to the braid group is , up to a universal rescaling of generators , equivalent to the unreduced burau representation @xmath26 from ( [ eq - buraur ] ) . an closely related approach of constructing tangles invariants associated to the burau representation and alexander polynomial makes use of the quantum groups @xmath62 , see for example @xcite . in view of the dominance of algebraically constructed functorial invariants it is natural to ask whether the representation @xmath63 is really a special case of these . among the obstacles in an identification is the peculiar analytic flavor of the construction involving geometric series . particularly , the role of the denominators that are obtained by summing these series is , as for example @xmath64 in ( [ eq - ltwstr - exs ] ) , are not obvious and their algebraic or topological meaning are not at all immediate from the construction . the main result of this article is to provide such algebraic interpretations in terms of an equivalence of string link representations as stated in the following theorem . [ thm - main ] the representations @xmath65 and @xmath66 of the string link monoid @xmath24 are isomorphic to each other . we note that the isomorphism will consist only of rescaling or reordering of basis vectors . in the case of @xmath67 we obtain a direct formula for the string link invariant : @xmath68 where @xmath69 is given as a bijection of canonical basis vectors up to multiplication with units of @xmath59 . the denominator occurring in the random walk construction can thus also be interpreted as the zero - graded part of ohtsuki s functor . additional interpretations are suggested in section [ ss - comm ] . an immediate implication of theorem [ thm - main ] is that @xmath63 is dominated by finite type invariants since it is dominated by @xmath45 . this fact has been proved by more indirect means in @xcite . another consequence of theorem [ thm - main ] is the following . [ corr - main ] suppose @xmath70 . then @xmath71 divides all @xmath72 minors of @xmath73 in @xmath59 . the original random walk construction of @xmath74 @xcite is reviewed and formalized in section [ s - rwi ] , where it is also applied to the situation of a string link @xmath47 given as the closure of a braid @xmath75 . particularly , we obtain in proposition [ prop - blfrm ] an expression for @xmath76 in terms of blocks of the burau matrix for @xmath75 . a consequence , stated in corollary [ corr - ltweigen ] , is that @xmath76 admits an equilibrium state that is independent of @xmath47 ( and thus contains no information about @xmath47 ) . in section [ s - rmat ] we review ohtsuki s construction of the tangle functor @xmath45 as well as the equivalence given in @xcite of the implied braid representation with the exterior algebra extension of the unreduced burau representation . the quantum trace , relevant to evaluating braid closures , is related to the natural supertrace on exterior algebras in section [ ss - trrel ] . in addition various grading and equivariance properties are discussed . section [ ss - proof ] contains the proofs for theorem [ thm - main ] and corollary [ corr - main ] after introducing several technical lemmas on relating traces , evaluations on top forms , and schur complements of block matrices in sections [ ss - strviatop ] and [ ss - trschur ] . finally , we present additional points of view and possible further questions of study in section [ ss - comm ] . * acknowledgment : * the first author thanks craig jackson for discussions and calculations on an early version of the conjecture that are documented in @xcite .

we show that the exterior powers of the matrix valued random walk invariant of string links , introduced by lin , tian , and wang , are isomorphic to the graded components of the tangle functor associated to the alexander polynomial by ohtsuki divided by the zero graded invariant of the functor . several resulting properties of these representations of the string link monoids are discussed .

we show that the exterior powers of the matrix valued random walk invariant of string links , introduced by lin , tian , and wang , are isomorphic to the graded components of the tangle functor associated to the alexander polynomial by ohtsuki divided by the zero graded invariant of the functor . several resulting properties of these representations of the string link monoids are discussed .

1111.3509

i

the general aim in quantum tomography is to identify quantum states from measurement outcome statistics . a collection of observables with this property is called _ informationally complete _ @xcite . even a single observable can be informationally complete , but then it must be a noncommutative positive operator valued measure ( povm ) @xcite . we will study a class of informationally complete povms in dimension @xmath0 with the minimal number of @xmath1 outcomes and we will explain how they can be implemented as sequential measurements of two @xmath0-outcome measurements . one can interpret the generated joint observable as a phase space measurement in the discrete phase space @xmath2 @xcite . there are some particularly interesting approaches to finite dimensional quantum tomography , and one of them is based on complete collections of mutually unbiased bases ( mubs ) @xcite . in a @xmath0-dimensional hilbert space one needs @xmath3 mubs in order to be able to identify all quantum states , but it is not known if a complete set of mubs exists in all dimensions . in fact , there is evidence that for @xmath4 there is no complete set of mubs @xcite . in our scheme we start from two mutually unbiased bases connected by the finite fourier transform . they define a pair of complementary observables , which can not be measured jointly . however , it is possible to realize their joint measurement if some additional noise is allowed . we show that their joint measurement can be chosen to be informationally complete , and that this can be realized as a sequential measurement where we first perform a ` weak measurement ' in one basis and then another successive measurement in the other basis . compared to the fact that one would need @xmath3 complementary observables in order to reach informational completeness in separate measurements , it is remarkable that in the sequential scheme only two observables suffice . the price to have a joint measurement is that the marginal observables are not the original complementary observables but their unsharp versions . we will analyze the required additional noise and characterize the optimal joint observable from this point of view . the qubit case has been first studied in @xcite , and our work generalizes those results to arbitrary finite dimension . the covariant phase space observables , i.e. , povms covariant under the finite weyl - heisenberg group , play a special role in our investigation . we prove that if a pair of conjugate observables have a joint measurement , then they also have a joint measurement which is a covariant phase space observable . since every covariant phase space observable arises from a sequential measurement of two conjugate observables @xcite , the covariant phase space observables are an outstanding choice for finite dimensional quantum tomography . the weyl - heisenberg group has also a pivotal role in the investigations of symmetric informationally complete ( sic ) observables @xcite . it is generally believed that a weyl - heisenberg covariant sic observable exists in every finite dimension and their existence is numerically tested in all dimensions up to 67 @xcite . our results show that any such observable has a neat sequential realization scheme . there is an interesting difference between the even and odd dimensional hilbert spaces . if we require minimal noise in both marginal observables , then their joint observable is unique . if @xmath0 is odd , then this observable is informationally complete . but if @xmath0 is even , then the joint observable is not informationally complete . this result gives an additional aspect to the common observation that quantum tomography is different in even and odd dimensions @xcite .

if we require minimal noise in the joint measurement , then the joint observable is unique . if the dimension is odd , then this observable is informationally complete . but if is even , then the joint observable is not informationally complete and one has to allow more noise in order to obtain informational completeness .

we show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system , meaning that they enable to identify all quantum states from their measurement outcome statistics . we further demonstrate that it is possible to implement a joint observable as a sequential measurement . if we require minimal noise in the joint measurement , then the joint observable is unique . if the dimension is odd , then this observable is informationally complete . but if is even , then the joint observable is not informationally complete and one has to allow more noise in order to obtain informational completeness .

astro-ph0701856

c

we have performed a comprehensive calculation of the neutrino and @xmath0-ray flux distributions which are expected to be originated by the interaction of cr nuclei with the interstellar gas . our computation improves and updates previous analyses under several aspects . + modelling the spatial distribution of cr in the galaxy , we accounted for a spatial dependence of the diffusion coefficients . that approach allowed us to test how different models of the turbulent component of the gmf affect the cr distribution and the secondary @xmath0-ray flux and to choose our preferred model as that which best reproduces egret @xmath0-ray observations above few gevs . interestingly , we found that such a model gives also the best agreement with the hard @xmath0-ray spectra observed for several snrs . + having assumed that cr sources are distributed like snrs , we adopted a detailed model of the spatial distribution of those objects . + concerning the gas distribution , we considered two models , both for the hi and @xmath70 , which we applied for the first time in this framework . although these models have significant differences in some regions , we showed that they give rise to neutrino and @xmath0-ray fluxes which , when averaged over windows larger than few degrees squared , coincide within a factor of a 2 . we also found that the column density profile across the gp is almost the same for those two models , while it differs significantly from that adopted in previous works @xcite . as a consequence , we predict the neutrino and @xmath0-ray emissions to be more narrowly peaked along the gp . this improves significantly the perspectives to disentangle the signal from the almost isotropic background if the experimental angular resolution will be better than @xmath210 . we compared our predictions with the available observations . + concerning the @xmath0-rays , we found that above the tev our predicted fluxes are below the experimental limits by less than an order of magnitude . since our analysis does not account for a possible ic contribution , which may be not negligible above the tev , it is possible that those experiments will get a positive signal in the next few years . the comparison of the experimental results with our predictions , as well as with those of previous works ( see e.g. @xcite ) , will help to understand which fraction of that emission is of leptonic origin . + concerning the signal observed by milagro in the cygnus region @xcite , we confirm that it can not be explained without invoking a significant cr overdensity , or a large ic contribution , which may be due to a local concentration of sources . a similar effect takes place in the gc region . we found that in order to explain the excess observed by hess from the gc ridge @xcite the cr flux must exceed our prediction by a factor of about 10 . this is not unexpected since the distribution of star forming regions , hence of cr sources , is known to be quite clumpy . it is understood that the kind of simulation performed in this work , as well as in previous ones @xcite , can only model the mean cr distribution smoothed on scale of several hundred parsecs . we also extrapolated our results down to few gevs , where the ic scattering emission is expected to be subdominant . we found that in the most dense regions the flux distribution agrees reasonably well with egret observations . this result encourages us to improve the accuracy of our analysis by using , for example , more detailed models of the gas distribution , so to be able to simulate what glast may observe above the gev at least in some limited regions of the sky . going back to neutrinos , we compared our predictions for the muon neutrino flux from the gp with the experimental limit recently established by amanda - ii @xcite . we found that our predicted flux is almost two orders of magnitude below that limit . unfortunately , also icecube @xcite will hardly be able to get a positive signal . + since a neutrino telescope placed in the north hemisphere may have better changes , we investigated this possibility in some details . assuming that such an instrument will be placed at the same position of antares @xcite and have a 40 times larger effective area we estimated the expected signal and the background along the galactic equator . we found that the detection of the smooth component of the diffuse emission may require more than 10 years of data taking . it should be noted , however , that our analysis provides only a lower limit to the expected emission from the galactic plane . as we mentioned in the above , several observations suggest that the cr and gas distributions may be more clumpy than what considered in this work . furthermore , fluctuations of those quantities are likely to be spatially correlated . this may lead to a significant enhancement of the neutrino flux from some regions as may be the case for the gc ridge @xcite and the cygnus region @xcite . in a forthcoming paper we will try to develop our analysis in order to model at least some of these effects .

we simulate the neutrino and-ray emissions of the galaxy which are originated from the hadronic scattering of cosmic rays ( cr ) with the interstellar medium ( ism ) . rather than assuming a uniform cr density , we estimate the spatial distribution of cr nuclei by means of numerical simulations . we confirm that the excesses observed by milagro in the cygnus region and by hess in the galactic centre ridge can not be explained without invoking significant cr over - densities in those regions .

we simulate the neutrino and-ray emissions of the galaxy which are originated from the hadronic scattering of cosmic rays ( cr ) with the interstellar medium ( ism ) . rather than assuming a uniform cr density , we estimate the spatial distribution of cr nuclei by means of numerical simulations . we consider several models of the galactic magnetic field and of the ism distribution finding only a weak dependence of our results on their choice . we found that by extrapolating the predicted-ray spectra down to few gev we get a good agreement with egret measurements . then , we can reliably compare our predictions with available observations above the tev both for the-rays and the neutrinos . we confirm that the excesses observed by milagro in the cygnus region and by hess in the galactic centre ridge can not be explained without invoking significant cr over - densities in those regions . finally , we discuss the perspectives that a km neutrino telescope based in the north hemisphere has to measure the diffuse emission from the inner galaxy .

1309.3709

i

since half a century ago , the hubbard model has been widely studied as a simple model accounting for several nontrivial phenomena in electronic systems , such as the mott insulator , ( anti)ferromagnetism , and novel superconductivity@xcite . its bosonic version , the bose - hubbard ( bh ) model , has been appreciably investigated for more than two decades@xcite . the bh model not only aptly describes the many - body behavior of bosons in lattices , but also serves as a good and simple example for understanding how competition between two common mechanisms , localization and itineracy , can drive matter toward extremely different phases , namely mott - insulator ( mi ) or superfluid . the mi phase , characterized by commensurate occupations , gapped excitations and incompressibility , undergoes a transition to a superfluid , characterized by bose - einstein condensation , gapless excitations and finite compressibility , as the ratio of tunneling to interaction energy increases beyond a density - dependent critical value . differently from the fermionic case , the bosonic nature allows the bh phase diagram of multiple mi regions for all possible integer occupations , surrounded by the superfluid region . various realizations of the bh model have been early suggested in granular systems with an embedded condensate , such as a josephson junction array@xcite or liquid helium in porous media@xcite , and later in lattice bosons , such as bosonic atoms in optical lattices@xcite or exciton - polaritons in an array of microcavities@xcite . recent achievements in cold - atom experiments have successfully created inhomogeneous bh systems and realized the mi - superfluid transition@xcite as well as a spatially separated structure of multiple mis@xcite . these multiple applications have stimulated a broad interest in the bh physics and lead to an active study of a great variety of bh models @xcite . recently , a theoretical investigation we carried out on imbalanced fermionic superfluids in a two - dimensional ( 2d ) array of coupled tubes@xcite [ a setup which has been experimentally realized@xcite in the search for the elusive fulde - ferrell - larkin - ovchinnikov ( fflo ) state@xcite ] has shown an exotic compressible - incompressible quantum phase transition of the tube occupation of unpaired majority fermions ( umfs ) in the system . the phase diagram obtained from the microscopic model of fermions exhibits similarities and contrasts to the structure as a bh phase diagram . on the one hand there is a phase with well defined umf occupation numbers in each tube . on the other hand , the occupations of the incompressible ( mi ) regions are either all even or all odd . the similarities reflect the competition between the ontube energy and cross - tube kinetics of the umfs and hence suggests an effective description of the ( projected ) system by a 2d bh model , while the contrasts suggest the need for an additional term in the effective model that `` orients '' the occupation parities ( see sec . [ sec : model ] below for a detailed discussion ) . motivated by this previous work , we study an extended bh model having a ferromagneticlike coupling between occupation parities of nearest - neighbor sites . this proposed coupling can be pictured as domain - wall energies between nearest - neighbor sites of opposite occupation parities , reminiscent of local magnetization kinks in the ferromagnetic ising model@xcite , resulting in a ground state that favors all the sites having the same occupation parity . the parity coupling shows interesting interplays with the other two original bh ingredients , single - particle tunneling and onsite repulsion . first , it is antagonistic toward the single - particle tunneling process , during which two involved neighbor sites flip the parity and form domain walls between themselves and the surrounding sites [ see illustration in figs . [ fig : f01](a ) and [ fig : f01](b ) ] . second , it is different from the onsite repulsion in that it drives the system to accept additional doping as pairs rather than single particles , to avoid the domain wall energy , while the onsite repulsion does the opposite as a way to reduce the interaction energy [ see fig . [ fig : f01](c ) and [ fig : f01](d ) ] . in this paper , we analyze the system and characterize the effects of the occupation - parity coupling . we will suggest two possible experimental realizations for exploring the model in cold atomic and condensed matter systems . we shall find a rich phase diagram for the uniform case in the zero - tunneling limit , reflecting different doping preferences driven by the parity coupling and onsite repulsion . for the finite - tunneling case , we apply two commonly used treatments , quantum monte carlo@xcite ( qmc ) and gutzwiller mean - field@xcite ( gmf ) methods , on trapped systems , thus successfully describing the state of the system as the parity coupling increases for finite tunneling . in the large - tunneling regime , we identify an exotic pair superfluid state , which emerges with a different mechanism from previously studied ones@xcite . , interaction @xmath0 , and parity coupling @xmath1 of the system . ( a ) a reference state of each site occupied by @xmath2 particles . ( b ) after a single particle tunneling , the change in number of two neighbor sites alters the interaction energy by @xmath3 , while the change in parity of them results in a domain - wall formation ( dashed curve ) of energy cost @xmath4 . ( c ) at small @xmath5 , two doping particles tend to occupy different sites , minimizing the interaction energy . ( d ) at large @xmath5 , the two occupy the same site as a pair doping , avoiding the domain - wall energy.,width=302 ] the paper outline is as follows . in sec . [ sec : model ] , we introduce the model hamiltonian and discuss its possible realizations by studying its emergence in imbalance fermi gases as well as in spin systems . in sec . [ sec : phase ] , we perform a detailed analysis of the competition between the parity coupling and the onsite repulsion , and obtain an exact phase diagram in the zero - tunneling plane . in sec . [ sec : numerical ] , we present results from qmc and gmf calculations that show the evolution of a trapped system and the emergence of the pair superfluid . finally , we summarize our work in sec . [ sec : conclusion ] .

we study a bose - hubbard model having on - site repulsion , nearest - neighbor tunneling , and ferromagneticlike coupling between occupation parities of nearest - neighbor sites . for a uniform system in any dimension at zero tunneling we also identify an exotic pair superfluid at relatively large tunneling strength . our model ought to effectively describe recent findings in imbalanced fermi gases in two - dimensional optical lattices and also potentially apply to an anisotropic version of bilinear - biquadratic spin systems .

we study a bose - hubbard model having on - site repulsion , nearest - neighbor tunneling , and ferromagneticlike coupling between occupation parities of nearest - neighbor sites . for a uniform system in any dimension at zero tunneling , we obtain an exact phase diagram characterized by mott - insulator ( mi ) and pair liquid phases and regions of phase separation of two mis . for a general trapped system in one and two dimensions with finite tunneling , we perform quantum monte carlo and gutzwiller mean - field calculations , both of which show the evolution of the system , as the parity coupling increases , from a superfluid to wedding - cake - structure mis with their occupations jumping by 2 . we also identify an exotic pair superfluid at relatively large tunneling strength . our model ought to effectively describe recent findings in imbalanced fermi gases in two - dimensional optical lattices and also potentially apply to an anisotropic version of bilinear - biquadratic spin systems .

1309.3709

c

in this paper , we studied an extended bose - hubbard model incorporating a ferromagneticlike coupling between the nearest - neighbor site - occupation parities . this parity coupling generates domain - wall energies that compete with the single - particle tunneling and favors pair doping rather than the single - particle one that is favored instead by the on - site repulsion . the interplay between the parity coupling and on - site repulsion leads to a rich phase diagram of a uniform system at zero tunneling , characterized by ( 1 ) mott - insulator ( mi ) phases at each commensurate filling and ( 2 ) phase separation of two mis when the on - site interaction dominates or ( 3 ) pair - liquid phases when the parity coupling dominates at incommensurate fillings . in the finite - tunneling inhomogeneous case , we have obtained both quantum monte carlo and gutzwiller mean - field results that agreeably show an evolution of a trapped system from a superfluid to a wedding - cake - structure of mis with the same parity ( or the occupation jumping by 2 ) , as the parity coupling increases . in a relatively large tunneling and large - parity coupling regime , the trapped system exhibits a structure with the inner bulk being a single - particle superfluid as usual and the outer shell being an exotic pair superfluid . considering the realization of our model , we have shown that it effectively describes the behavior of the umfs in a system of imbalanced fermionic superfluids in 2d optical lattices of tubes , which has been realized@xcite and is being studied in ongoing experiments@xcite . the transition between a superfluid and mis of the same parity in our model corresponds to that between compressible and incompressible states of umfs in the tubular system with a strong oscillatory pairing order@xcite . such transition can be detected by the response of the umfs to optical - lattice modulation@xcite or by the momentum distribution of umfs in a time - of - flight experiment @xcite . the pair - superfluid state in our model corresponds to the compressible state of itinerant umf pairs in the tubular system , reminiscent of a triplet - pair superfluid . in addition , a truncated version of our model can be mapped to an anisotropic bilinear - biquadratic spin model , in which the occupation - parity coupling is associated with biquadratic spin coupling . such mapping provides a potential realization for exploring our model in spin systems and would also stimulate interest in the physics of these two models .

, we obtain an exact phase diagram characterized by mott - insulator ( mi ) and pair liquid phases and regions of phase separation of two mis . for a general trapped system in one and two dimensions with finite tunneling , we perform quantum monte carlo and gutzwiller mean - field calculations , both of which show the evolution of the system , as the parity coupling increases , from a superfluid to wedding - cake - structure mis with their occupations jumping by 2 .

we study a bose - hubbard model having on - site repulsion , nearest - neighbor tunneling , and ferromagneticlike coupling between occupation parities of nearest - neighbor sites . for a uniform system in any dimension at zero tunneling , we obtain an exact phase diagram characterized by mott - insulator ( mi ) and pair liquid phases and regions of phase separation of two mis . for a general trapped system in one and two dimensions with finite tunneling , we perform quantum monte carlo and gutzwiller mean - field calculations , both of which show the evolution of the system , as the parity coupling increases , from a superfluid to wedding - cake - structure mis with their occupations jumping by 2 . we also identify an exotic pair superfluid at relatively large tunneling strength . our model ought to effectively describe recent findings in imbalanced fermi gases in two - dimensional optical lattices and also potentially apply to an anisotropic version of bilinear - biquadratic spin systems .

1412.2914

i

observations of the cosmic microwave background ( cmb ) most recently @xcite have clearly established that scalar perturbations in the early universe were nearly scale - invariant . it is thus necessary for any realistic cosmological model to generate , in some fashion , scale - invariant perturbations . to achieve this , many cosmological models rely on the presence of matter fields ( typically scalar fields ) that have not yet been observed in nature . the new matter fields are necessary in these models as they play an essential role in the generation of scale - invariant perturbations . while it is of course a requirement for any cosmological scenario to predict near scale - invariance in order to be potentially viable , there are some cosmological scenarios where it is possible to avoid the weakness of postulating the existence of unknown matter fields and nonetheless obtain scale - invariance . we shall study one such model in this paper . this cosmological model consists of a spatially flat friedmann - lematre - robertson - walker ( flrw ) universe , with a positive cosmological constant , cold dark matter ( cdm ) , and radiation . these are three ingredients known to be present in our universe , and we will not assume the existence of any other matter fields . we also assume that the initial conditions are such that the space - time curvature is small and the universe is large and contracting . as the universe contracts , the space - time curvature will increase , and quantum gravity effects are expected to become important at some point , likely when the space - time curvature nears the planck scale . in this work , we will assume that loop quantum cosmology ( lqc ) captures the salient non - perturbative quantum gravity effects in the very early universe . lqc , a mini - superspace approach to quantum cosmology motivated by loop quantum gravity , predicts that a bounce occurs near the planck scale and that , once these quantum gravity effects are included , the space - time is free of the singularities that appear in classical general relativity @xcite . thus , this model will be that of a bouncing universe , with a matter content of radiation and cold dark matter and a positive cosmological constant . now , it is well known in cosmological perturbation theory that , for perturbations that are initially in the quantum vacuum state , the fourier modes that reach the long wavelength limit in a contracting space - time whose dynamics are dominated by a pressureless matter field become scale - invariant @xcite . ( note that the long - wavelength limit of a fourier mode does not always coincide with the mode exiting the hubble radius here the relevant length scale is the sound hubble radius , as explained in more detail later . ) furthermore , if the pressure is slightly negative , for example due to the presence of a positive cosmological constant , then the long wavelength perturbation modes will be almost scale - invariant with a slight red tilt . therefore , in the model considered here , we expect the modes that become large during the epoch of the universe that is dominated by cold dark matter to be almost scale - invariant , and those that become large when the effective equation of state is slightly negative to have a small red tilt . various realizations of the matter bounce scenario suggested in @xcite have been considered in the literature , but in most studies the matter content is taken to be scalar fields with specific potentials that can mimic pressureless matter fields for some specific initial conditions . to the best of our knowledge , this is the first study of a matter bounce scenario where the pressureless matter field is taken to be cold dark matter and that the effect of a positive cosmological constant is also included . we will compare the predictions of this scenario with other realizations of the matter bounce scenario in sec . [ s.disc ] . in this paper we calculate the spectrum of the cosmological perturbations for this @xmath0cdm bounce scenario . by the use of some approximations , it is possible to complete the calculations entirely analytically ; we also solve the equations numerically in order to provide a check on the validity of the approximations . in sec . [ s.hom ] we study the dynamics of the background , first analytically and then numerically . then in sec . [ s.scal ] we calculate the evolution of the scalar perturbations , from their initial quantum vacuum state to their final form after the bounce in the background flrw space - time . once again , this calculation is first done analytically with the help of some approximations , and is solved numerically afterwards . we continue in sec . [ s.tens ] by determining the spectrum of the primordial gravitational waves , and end in sec . [ s.disc ] with a discussion . we use units where @xmath1 , but keep @xmath2 and @xmath3 explicit except where stated otherwise , typically in the sections devoted to the numerical studies .

we study a contracting universe composed of cold dark matter and radiation , and with a positive cosmological constant . as is well known from standard cosmological perturbation theory , under the assumption of initial quantum vacuum fluctuations the fourier modes of the comoving curvature perturbation that exit the ( sound ) hubble radius in such a contracting universe at a time of matter - domination will be nearly scale - invariant . furthermore , the modes that exit the ( sound ) hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt , in agreement with observations . we calculate the evolution of the perturbations through the bounce and find that they remain nearly scale - invariant .

we study a contracting universe composed of cold dark matter and radiation , and with a positive cosmological constant . as is well known from standard cosmological perturbation theory , under the assumption of initial quantum vacuum fluctuations the fourier modes of the comoving curvature perturbation that exit the ( sound ) hubble radius in such a contracting universe at a time of matter - domination will be nearly scale - invariant . furthermore , the modes that exit the ( sound ) hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt , in agreement with observations . we assume that loop quantum cosmology captures the correct high - curvature dynamics of the space - time , and this ensures that the big - bang singularity is resolved and is replaced by a bounce . we calculate the evolution of the perturbations through the bounce and find that they remain nearly scale - invariant . we also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter , the hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation , and the curvature scale that the loop quantum cosmology bounce occurs at . importantly , as this scenario predicts a positive running of the scalar index , observations can potentially differentiate between it and inflationary models . finally , for a small sound speed of cold dark matter , this scenario predicts a small tensor - to - scalar ratio .

1412.2914

c

in this paper we have seen how in a contracting universe cosmological perturbations , assumed to be initially in their quantum vacuum state , become scale - invariant if their sound wavelength becomes larger than the hubble radius when the dynamics of the universe is dominated by cold dark matter . a small red tilt is generated when the effective equation of state is negative due to the presence of a positive cosmological constant , and a small tensor - to - scalar ratio is predicted . the scale - invariant perturbations can provide appropriate initial conditions for an expanding universe in order to seed structure formation if there is a bounce to connect the contracting branch of the universe to our current expanding branch . in the realization of the matter bounce scenario studied here , the bounce occurs due to non - perturbative quantum gravity effects , as captured by lqc , that resolve the classical singularity and provide a quantum bridge between the pre - big - bang and post - big - bang epochs . further , the only matter fields present in this model are assumed to be cold dark matter and radiation , together with a positive cosmological constant . the main predictions depend on four parameters : the scalar index @xmath10 is determined by the effective equation of state at the time when the fourier modes @xmath64 exit the sound hubble radius , while the amplitude of the scalar perturbations depend on a combination of the sound speed of cold dark matter @xmath68 , the amount of asymmetry in the universe , which can be parametrized by @xmath109 the hubble rate at matter - radiation equality in the contracting branch , and the matter energy density at the bounce @xmath54 . in particular , a symmetric bounce is ruled out and , in order to match observations , it is necessary for matter - radiation equality to occur at higher space - time curvature scales in the contracting branch than in the expanding branch . this type of asymmetry can be caused by particle production during the bounce , a process which may be important in lqc @xcite . there exist several other realizations of the matter bounce scenario , some where the bounce is caused by matter fields that violate energy conditions @xcite , and others where it is quantum gravity effects that provide the bounce @xcite . there are also some matter bounce scenarios where the gravitational sector is modified not only in the high - curvature regime , but also in the pre - bounce era in order to obtain a matter - like contracting phase without requiring the presence of any matter fields @xcite . of course , there is no _ a priori _ reason to prefer one realization of the matter bounce scenario over another ( other than perhaps the simplicity or the elegance of a particular model ) . instead , it is necessary to determine how these realizations differ in their predictions which can then be compared to observations . for this reason , it is important to point out that the predictions of the different matter bounce realizations vary in some significant aspects , concerning both cmb experiments @xcite as well as dark matter searches @xcite . the recent review @xcite explains the different predictions of many of the various realizations of the matter bounce scenario and in order to complement that paper , here we shall briefly explain how the predictions of the model studied in this paper differ from the other realizations of the matter bounce scenario . first , the @xmath4cdm bounce model studied in this paper gives a slight red tilt in a natural fashion , something which is absent in many other realizations of the matter bounce ( see for example @xcite for specific realizations ) . and second , the predicted tensor - to - scalar ratio is very small . most realizations of the matter bounce typically predict relatively large tensor - to - scalar ratios , and it is often necessary to assume the presence of a large number of fields ( and thus of entropy perturbations as well ) in order to decrease the relative amplitude of the tensor perturbations . this is not necessary here since the tensor - to - scalar ratio is naturally predicted to be small due to the small sound speed of cold dark matter . note that this effect of a small @xmath155 strongly damping the value of @xmath133 has also previously been noticed in a study of the matter bounce scenario in a bohm - de broglie quantum cosmology model @xcite . another important point is that this scenario predicts a positive running of the scalar index , @xmath156 . this result shows that it is possible for observations to differentiate between the @xmath0cdm bounce scenario and inflationary models , where the running of the scalar index is predicted to be negative . the amplitude of this effect in the @xmath0cdm bounce scenario depends on the time evolution of effective equation of state during matter domination @xmath157 , which in turn depends quite sensitively on the parameters @xmath158 , @xmath159 and @xmath160 set as initial conditions for the background in the contracting branch . we leave a detailed study of the relation between these parameters and the amplitude of @xmath107 for future work . there do remain two other important open questions regarding this model that are also left for future work . the first one concerns the importance of particle production effects during the bounce . will there be enough particle production to cause sufficient asymmetry around the bounce point for this model to be viable ? the second , more difficult , open problem is to determine how the presence of anisotropies would modify the predictions of this model . the friedmann equation for the mean scale factor in bianchi models shows that anisotropies dominate the dynamics in the high curvature limit , and we should expect them to typically become important during ( and possibly for some time before and after ) the bounce in lqc . indeed , anisotropies can modify the predictions of a number of cosmological scenarios including inflation @xcite . despite their importance , anisotropies are often neglected as cosmological perturbation theory becomes considerably more complex in their presence @xcite ; in particular , for non - vanishing anisotropies the equations of motion for the scalar , vector and tensor perturbations no longer decouple . note that if there is an ekpyrotic phase in the contracting branch of the space - time , it is possible to avoid the growth of anisotropies generated during matter contraction @xcite and then there is no need to include them in the analysis . however , it is certainly possible ( and outside of ekpyrotic models it appears more natural ) for anisotropies to grow and dominate the dynamics near the bounce . in this case , while the anisotropies will be diluted soon after the bounce ( see , e.g. , sec . iiic of @xcite ) , they may change the spectrum of the cosmological perturbations as they evolve through the anisotropy - dominated bounce , and some of these modifications may ultimately be observable today . for this reason , it is important to allow for anisotropies by generalizing the results obtained here for the case where the background is an anisotropic bianchi i space - time ( rather than flat flrw ) , and determining precisely how anisotropies may affect the predictions of this model . finally , we conclude with some comments regarding the universality and robustness of the predictions of the @xmath4cdm bounce scenario with respect to the physics of the bounce . in this paper we assumed that the bounce is caused by the quantum gravity effects captured by loop quantum cosmology . as mentioned above , it is also possible to generate a bounce via other mechanisms , either with matter fields that violate energy conditions , or by modifications to the gravitational action as occur for example in @xmath161 theories . an important property of the @xmath0cdm bounce scenario is that most of the salient characteristics of the predicted spectra of scalar and tensor perturbations are due to the pre - bounce physics , where quantum gravity and other high energy effects are negligible and therefore the majority of the predictions including the small red tilt for the modes that exit the sound hubble radius when the effective equation of state is slightly negative , as well as the positive running of the scalar index are independent of the high - curvature dynamics of the background space - time at the bounce point . however , there is one effect that is partially due to lqc : the tensor - to - scalar ratio is suppressed by a factor of 1/4 during the bounce by lqc effects ( specifically , due to the modifications that arise in the lqc effective mukhanov - sasaki equation for tensor perturbations ) . thus , while many predictions of the @xmath0cdm bounce are quite robust and are mostly independent of the physics of the bounce , one exception is the predicted value of the tensor - to - scalar ratio which in fact is affected by lqc effects and , if the sound speed of cold dark matter is known , this effect could provide a potentially important observational test for lqc . we would like to thank robert brandenberger , jim cline , parampreet singh , jun - qing xia and wei xue for helpful discussions . the work of yfc is supported in part by an nserc discovery grant and by funds from the canada research chair program . this work is supported in part by a grant from the john templeton foundation . , g. hinshaw _ et al . _ , `` nine - 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we assume that loop quantum cosmology captures the correct high - curvature dynamics of the space - time , and this ensures that the big - bang singularity is resolved and is replaced by a bounce . we also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter , the hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation , and the curvature scale that the loop quantum cosmology bounce occurs at . importantly , as this scenario predicts a positive running of the scalar index , observations can potentially differentiate between it and inflationary models .

we study a contracting universe composed of cold dark matter and radiation , and with a positive cosmological constant . as is well known from standard cosmological perturbation theory , under the assumption of initial quantum vacuum fluctuations the fourier modes of the comoving curvature perturbation that exit the ( sound ) hubble radius in such a contracting universe at a time of matter - domination will be nearly scale - invariant . furthermore , the modes that exit the ( sound ) hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt , in agreement with observations . we assume that loop quantum cosmology captures the correct high - curvature dynamics of the space - time , and this ensures that the big - bang singularity is resolved and is replaced by a bounce . we calculate the evolution of the perturbations through the bounce and find that they remain nearly scale - invariant . we also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter , the hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation , and the curvature scale that the loop quantum cosmology bounce occurs at . importantly , as this scenario predicts a positive running of the scalar index , observations can potentially differentiate between it and inflationary models . finally , for a small sound speed of cold dark matter , this scenario predicts a small tensor - to - scalar ratio .

1203.2971

r

, and kinetic and magnetic energies , @xmath128 and @xmath129 , respectively . two dotted vertical lines bound the period of gradually increasing turbulence . the resistivity in this model is set to @xmath130 and the shared component of magnetic field @xmath131 . in this model we inject turbulence in the magnetic field . [ fig : energies],scaledwidth=45.0% ] in figure [ fig : energies ] we present an example of the evolution of total mass , and kinetic and magnetic energies in a model with @xmath132 , @xmath133 , and @xmath134 . we inject turbulence in magnetic field using new forcing method , gradually increasing its strength from @xmath135 to @xmath136 . this period is marked by two dotted vertical lines in figure [ fig : energies ] . we see an increase of kinetic energy during this period due to the injection and saturation after @xmath136 . the kinetic energy preserves constant value during the turbulent stage very well . the magnetic energy increases during this stage , slowly saturating . this increase is attributed to the injection of magnetic eddies . on the contrary , the total mass in the system decays slowly . we emphasize , that since we use open boundary conditions , not perfect conservation of mass and energies is possible in the presence of turbulence . ( black ) for the same model as in fig . [ fig : energies ] . blue line show the evolution of reconnection in a model with the same parameters in which the turbulence were driven using the old method . in this plot we present the measured rates of the sweet - parker reconnection @xmath137 and during the presence of turbulence , @xmath138 . symbol @xmath139 is the time variance . @xmath140 is the estimated uncertainty of the measure . [ fig : rate],scaledwidth=45.0% ] in figure [ fig : rate ] we show the evolution of reconnection rates @xmath0 for two models with the same set of initial conditions , but in the first model we drove turbulence by injecting magnetic eddies using the new method described in this paper ( black line ) , and in the second model we inject velocity fluctuations using the old method described in @xcite ( blue line ) . in this plot we recognize an increase of both rates during the introduction of turbulence . after the transition period between @xmath135 and @xmath136 , when the system adjusts to a new state , both measures coincide and even though they fluctuate , they reach a stationary state characterized by faster reconnection . both types of turbulence bring the reconnection rate to similar level . somewhat higher reconnection rate in the model with new driving could be attributed to the fact that this model was calculated using the 5th order spatial reconstruction and the 3rd order integration in time , in contrast to the old model where we used the second order methods . lower order , especially in the spatial interpolation , introduces additional numerical diffusion decreasing the amplitudes of turbulent fluctuations at scales comparable to the current sheet scale . in figure [ fig : rate ] we also show the way of measuring the reconnection rates , in the sweet - parker and lv99 stages , @xmath137 and @xmath138 , respectively . because the reconnection rates fluctuate in the presence of turbulence we also measure their time variance @xmath139 using the standard deviation . in addition to the time variance of @xmath0 , we measure their errors by splitting the averaging region into two subregions and after averaging the rates @xmath141 and @xmath142 over each subregion ( see fig . [ fig : rate ] ) , we take the absolute value of their difference @xmath143 . this difference corresponds to the error of @xmath0 , i.e. it is different from zero if the rate is not constant in time . in all further analysis and presented plots we use values estimated in this way . these measures correspond exactly to those presented in @xcite . in this section we compare field topologies in two example models run with the same set of parameters , but with different types of driving . both models have been simulated with the uniform resistivity @xmath134 and the resolution 256x512x256 . we injected turbulence with power @xmath144 at the injection scale @xmath145 . the only difference between models is the way we injected turbulence . in the old model we inject velocity fluctuations with random phases in fourier space , and then transform them to real space and shape by a window in order to limit the injection to the specified region near the current sheet . in the new model , we inject magnetic loops with random locations and random orientations in the 3d volume near the current sheet . the way of injecting turbulence is essentially different in both cases . in figure [ fig : top_turb ] we show examples of xy - cuts ( upper row ) and xz - cuts ( lower row ) through the box for the model with old driving . in the left and middle columns we show topologies of the velocity and magnetic field , respectively , with the intensities corresponding to the amplitude of components parallel to the plotted plane . in the right column we show the absolute value of current density with overplotted magnetic vectors . velocity has a very complex and mixed structure near the midplane due to constant injection of fluctuations in this region ( see the left panel in fig . [ fig : top_turb ] ) . the majority of the velocity fluctuations is perpendicular to the mean magnetic field . this is because we are in the nearly incompressible regime of turbulence ( large plasma @xmath146 ) and most of the fluctuations propagate as alfvn waves along the mean magnetic field . slow and fast waves , whose strengths are significantly reduced , are allowed to propagate in directions perpendicular to the mean field as well . as a result , a big fraction of the turbulent kinetic energy leaves the box along magnetic lines . we observe , however , an efficient bending of magnetic lines at the midplane where the field is weaker ( see the upper middle plot in fig . [ fig : top_turb ] ) . this is not result of a driving , but result of reconnection . in general the interface between positively and negatively directed magnetic lines is much more complex than in the case of sweet - parker reconnection . this complexity favors creation of enhanced current density regions , where the local reconnection works faster ( see the right panel of fig . [ fig : top_turb ] ) . since we observe multiple reconnection events happening at the same time , the global reconnection rate should be significantly enhanced . in figure [ fig : top_new ] we show similar examples of xy - cuts ( upper row ) and xz - cuts ( lower row ) through the box but for a model with the new way of driving turbulence . here , a big number of individual eddies is injected in the magnetic field with random locations and random orientations in domain . comparing to plots in figure [ fig : top_turb ] we see differences but also some clear similarities . among the similarities , we note a highly turbulent region near the current sheet seen in all xy - cuts , with the current sheet itself strongly deformed and fragmented into many small scale current sheets ( the right column of figures [ fig : top_turb ] and [ fig : top_new ] ) . we see also some small increase of magnetic field strength near the current sheet ( middle top panels ) resulting from working turbulence in the injection region . among the differences we can list somewhat different distributions of the fragmented current sheets in the new model with clear enhancements in the locations where the magnetic eddies are injected at that moment . these enhancements are clearly seen in the magnetic topology and current density plots ( middle and right columns ) . in order to decrease those strong disturbances of the magnetic lines , we shall reproduce the same model with higher injection rate and reduced amplitudes of individual eddies . another difference is the strength of current density @xmath70 . in the model with old driving we see more volume in which @xmath147 reaches high magnitude and its structure is elongated with the local field . in the model with new driving , the current density with high strength seems to be less correlated with the local field , probably due to the presence of newly injected eddies . in the intermediate strengths , the structure of @xmath147 seems to be better correlated with the local field . we see from this comparison that models with different driving of turbulence demonstrate different topologies of the fields . in the next sections we show , that the averaged reconnection rates do not change significantly , confirming that the way we inject turbulence is of less importance and only its strength and injection scale have influence on @xmath0 . on @xmath1 updated by symbols from new models . blue symbols show models with new driving in which the eddies where injected in magnetic field instead of velocity , as in the previous models ( black symbols ) . the dotted line corresponds to the sweet - parker reconnection rate for models with @xmath148 . a unique red symbol shows the reconnection rates from model with new driving in velocity performed with higher resolution ( 512x1024x512 ) and resistivity coefficient reduced to @xmath149 . error bars represent the time variance of @xmath0 . the size of symbols corresponds to the error of @xmath0 ( the way we calculate errors is described in [ ssec : evolution ] ) . [ fig : pow_dep ] ] models with the new method of turbulence driving are listed in table [ tab : models ] . we run a few models with varying turbulent powers in order to verify if the new driving modifies our previous results . in these models we kept the same parameters as in the previous ones , which allowed to confirm the dependence of the reconnection rate @xmath0 on the power of injected turbulence @xmath1 . figure [ fig : pow_dep ] shows the values of reconnection speed @xmath0 in models with turbulent power @xmath1 varying in the range of values by more than one order of magnitude , from 0.1 to 2.0 , for all previously shown models ( black symbols ) in @xcite and for new models ( blue and red symbols ) in which we drove turbulence using the new method . because the evolution of @xmath0 in new models reaches stationarity after time @xmath150 , we averaged @xmath0 from @xmath150 to @xmath151 in these models . figure [ fig : rate ] shows that the reconnection rates oscillate around their mean values . in figure [ fig : pow_dep ] we plot how the averaged reconnection speed depends on the strength of turbulence . filled symbols represent the averaged reconnection rate in the presence of turbulence . the dotted line corresponds to the reconnection rate during the sweet - parker process , i.e. without turbulence . the error bars show the time variance of @xmath0 . the size of symbols indicates the uncertainty in our estimate of the reconnection speed @xmath152 normalized to the uncertainty in the reconnection speed during the sweet - parker evolution @xmath153 . it is calculated from a formula @xmath154 . if @xmath152 is of the order of @xmath153 their symbols have the same sizes . the reconnection rates for models with new driving , which is described in [ ssec : forcing ] , confirm the theoretical dependence of @xmath0 on the injected power , which scales as @xmath155 . there is no significant difference between models in which turbulence was driven in velocity and in magnetic field . this is in agreement with the lv99 prediction , that the reconnection rate does not depend on the type of turbulence . the reconnection rate @xmath0 in the presence of turbulence depends only on the strength of turbulence and its injection scale @xmath2 , according to equation [ eq : constraint ] , for a fixed magnitude of the antiparallel magnetic field component . in the previous subsection we presented studies on the turbulent power dependence in this subsection we aim to study the injection scale dependence . for this purpose we performed several models with the new way of driving turbulence , as well , in order to verify if they confirm the dependence of the reconnection speed @xmath0 on the scale @xmath2 at which we inject turbulence . the new models are listed in table [ tab : models ] . we inject turbulence at several scales , from @xmath156 to @xmath157 . at the upper end of this range the turbulence barely broadens the sweet - parker current sheet . at the lower end the turbulent eddies are barely contained within the volume in which we excite turbulent motions . in figure [ fig : sca_dep ] we present the reconnection speed dependence on the injection scale . we plot the averaged @xmath0 for old models ( black symbols ) completed by the values from new models with alternative driving ( blue and red symbols ) . from the plot we clearly see a strong dependence of the reconnection rate on the injection scale . the new models very precisely follow the same dependence , confirming again that the type of turbulent driving has no influence on the process of reconnection , and only the power and injection scale of this driving have strong importance . similarly , as in the power dependence plot , the new models have slightly higher reconnection speeds comparing to the old ones . this is due to reduced numerical dissipation of velocity , since in the new models we used higher order methods . dissipation removes energy at small scales . if it is smaller , due to higher order numerical scheme , the turbulent fluctuations reach higher amplitudes at the current sheet scale . this influences the rate of individual reconnection events improving slightly the global reconnection rate @xmath0 . on @xmath2 with additional models in which turbulence was driven in a new way , as described in [ ssec : forcing ] . similarly to fig . [ fig : pow_dep ] , blue symbols show models with perturbed magnetic field , and red symbols correspond to a high resolution model with reduced uniform resistivity in which turbulence was driven in velocity . the dotted line corresponds to the sweet - parker reconnection rate for models with @xmath148 . error bars and the size of symbols have the same meaning as in fig . [ fig : pow_dep ] . [ fig : sca_dep ] ] figure [ fig : sca_dep ] shows a bit weaker scaling with the injection scale than that predicted by lv99 model , i.e. @xmath158 . we see several possible sources for the discrepancy . for instance , the existence of a turbulent inverse cascade can modify the effective @xmath2 . in addition , reconnection can also modify the characteristics of turbulence , such as the power spectrum and anisotropy . we aim to study these problems in the future work . in @xcite we performed studies of the reconnection rate on the resistivity , both the uniform and anomalous ones , and we obtained great agreement with the sweet - parker scaling @xmath159 for the case without turbulence , and no dependence on resistivity in the presence of turbulence , as was predicted in lv99 . in this section we performed additional studies of the reconnection rate dependence on viscosity . the dissipation scale of turbulent cascade is related to the magnitude of viscosity . if the dissipation works at scales larger than the current sheet thickness , the turbulence cascade stops before reaching the current sheet and the global reconnection rate should be reduced . the reconnection will be enhanced still by the broadened ejection region , allowing for more efficient removal of the reconnected magnetic flux . in figure [ fig : vis_dep ] we show reconnection rates for models with varying viscosity coefficient . although there is not prediction for this dependence in the lv99 model , we could test it numerically . in the figure [ fig : vis_dep ] we see a weak dependence @xmath160 . this dependence might be also useful in understanding the reconnection speed differences between models with the same set of parameters but different resolutions , or solved with different orders of the numerical scheme . at low resolutions or low order schemes , the numerical viscosity is expected to be larger , thus we should observe reduced reconnection speeds in those cases . this is confirmed in figures [ fig : pow_dep ] and [ fig : sca_dep ] where we compare old models done with the second order scheme , and new models done with higher order schemes and higher resolutions . in those plots all new models demonstrate slightly higher reconnection rates . on the uniform viscosity coefficient @xmath5 . as explained in the text , the reconnection speed is reduced with increasing value of @xmath5 . the dotted line corresponds to the sweet - parker reconnection rate . error bars and the size of symbols have the same meaning as in fig . [ fig : pow_dep ] . [ fig : vis_dep ] ]

the model has been already successfully tested in confirming the dependencies of the reconnection speed on the turbulence injection power and the injection scale expressed by a constraint and no observed dependency on ohmic resistivity . in , in order to drive turbulence , we injected velocity fluctuations in fourier space with frequencies concentrated around , as described in alvelius ( 1999 ) . in this paper we performed simulations with new forcing in order to study turbulent power and injection scale dependencies . the results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases . this is in agreement with the lazarian & vishniac ( 1999 ) predictions . although lazarian & vishniac ( 1999 ) do not provide any prediction for this dependence , we report a weak relation between the reconnection speed with viscosity , . proposed that slow - mode shocks on either side of the x - point would serve this purpose . more generally estimated that the scale of the reconnection sheet should not exceed about 40 times the electron mean free path . * hereinafter lv99 ) proposed a model for fast reconnection which depends on the presence of turbulence , and its production of weakly stochastic field lines ( also briefly described in section [ sec : lv99model ] ) . * see also review by , and references therein ) , as well as recent studies of emission lines and faraday rotation ( see * ? ? ? lv99 s model uses the properties of turbulence to predict broad outflows from extended current sheets . the main predictions of the model were confirmed . in this paper we provide additional numerical evidence of magnetic reconnection in turbulent environments by testing different mechanisms for injecting turbulence . in [ although the initial setup and boundary conditions are similar to our previous studies , and described in details in , we briefly describe them here for completeness , as well . in [ sec : results ] we present an extensive description of new results obtained from studying our numeric model , which we discuss later in [ sec : discussion ] . in

we study a model of fast magnetic reconnection in the presence of weak turbulence proposed by using three - dimensional direct numerical simulations . the model has been already successfully tested in confirming the dependencies of the reconnection speed on the turbulence injection power and the injection scale expressed by a constraint and no observed dependency on ohmic resistivity . in , in order to drive turbulence , we injected velocity fluctuations in fourier space with frequencies concentrated around , as described in alvelius ( 1999 ) . in this paper we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving . the new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space . we provide exact relations between the eddy parameters and turbulent power and injection scale . we performed simulations with new forcing in order to study turbulent power and injection scale dependencies . the results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases . this is in agreement with the lazarian & vishniac ( 1999 ) predictions . in addition , we performed a series of models with varying viscosity . although lazarian & vishniac ( 1999 ) do not provide any prediction for this dependence , we report a weak relation between the reconnection speed with viscosity , . magnetic fields are observed in many astrophysical objects and usually play an important or even crucial role in their dynamics ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * e.g. ) . they are a key ingredient of astrophysical processes such as magneto - rotational instability , magnetic dynamo , transport and acceleration of cosmic rays , accretion disks , turbulence , solar phenomena , gamma ray bursts , etc . . magnetic fields are solenoidal and evolve only through changes in the curl of the electric field . in the limit of zero resistivity the topology of the field lines is a constant of motion and the magnetic flux threading any fluid element is constant . generating large scale magnetic fields requires some kind of battery effect , like the biermann battery and generating strong large scale magnetic fields requires a dynamo ( see * ? ? ? * for example ) . in the limit of very small resistivity , which is typical for astrophysical objects , the magnetic flux is `` frozen in '' and magnetic field lines will resist passing through one another or changing their topology . due to the presence of plasma motions , in particular turbulence , this would result in a very complex tangle of field lines in real objects , with negligible large scale magnetic flux . however , observations indicate that the mean and turbulent components of magnetic fields in many astrophysical objects are of similar strengths ( see * ? ? ? * for example ) . this implies the existence of a process which can violate the frozen - in condition on dynamical time scales , i.e. fast magnetic field reconnection . the first analytic model for magnetic reconnection was proposed independently by and . sweet - parker reconnection has the virtue that it relies on a robust and straightforward geometry . two regions with uniform magnetic fields are separated by thin current sheet . the speed of reconnection is given roughly by the resistivity divided by the sheet thickness . however , the plasma in the current sheet is constrained to move along the local field lines , and is ejected from the edge of the current sheet at the alfvn speed , . since the width of the current sheet limits the flux of expelled plasma , the overall reconnection speed is reduced from the alfvn speed by the square root of the lundquist number , , where is the resistivity and is the length of the current sheet . in most astrophysical contexts is very large and the sweet - parker reconnection speed , , is negligible . fast reconnection requires that the dependence on be erased . given the simplicity of the sweet - parker setup , this requires that the simple geometry of the current sheet must be broken . the realization that sweet - parker reconnection is inadequate to explain magnetic reconnection in an astrophysical context was immediately apparent , and gave rise to decades of research on models of fast reconnection ( see * ? ? ? * ; * ? ? ? * for reviews ) . the first proposal was to replace the current sheet with an x - point configuration , so that the `` sheet '' thickness and length are comparable . this is the basis for petschek s model of fast reconnection . however , a dynamically self - consistent x - point requires that the outflow prevent a general collapse into a narrow current sheet . otherwise we would expect that the same bulk forces that brought the magnetic field lines together would lead to sweet - parker reconnection . proposed that slow - mode shocks on either side of the x - point would serve this purpose . moreover , those shocks are responsible for converting most of the magnetic energy into the heat and kinetic energy . the x - point in this model has an overall size which depends on resistivity , but since the magnetic field decrease logarithmically when approaching the current sheet ( due to the assumption of the current - free magnetic field in the inflow region ) , the resulting reconnection speed is some fraction of . numerical simulations with uniform resistivity have showed that in the mhd limit the shocks fade away and the contact region expands into a sheet . the only way to make the petschek configuration stable is by introducing the local nonuniform resistivity . this leaves the possibility that x - point reconnection is stable when the plasma is collisionless . numerical simulations have been encouraging . however , there are several important issues that remain unresolved . first , it is not clear that this kind of fast reconnection persists on scales greater than the ion inertial scale ( see * ? ? ? * ) . several numerical studies have found large scale reconnection speeds which depend on resistivity , i.e. are not fast . second , in many circumstances the magnetic field geometry does not allow the formation of x - point reconnection . for example , a saddle - shaped current sheet can not be spontaneously replaced by an x - point . the energy required to do so is comparable to the magnetic energy liberated by reconnection , and must be available beforehand . finally , the requirement that reconnection occur in a collision less plasma restricts this model to a small fraction of astrophysical applications . for example , while reconnection in stellar coronae might be described in this way , stellar chromospheres are not . more generally estimated that the scale of the reconnection sheet should not exceed about 40 times the electron mean free path . this condition is not satisfied in many environments which one might naively consider to be collisionless , among them the interstellar medium . the conclusion that stellar interiors and atmospheres , accretion disks , and the interstellar medium in general does not allow fast reconnection is drastic and unpalatable . an alternative to the x - point geometry is to consider magnetic fields that are chaotic , even if only weakly so . requiring the plasma to flow along the local magnetic field implies a powerful constraint on reconnection only if the field lines themselves are laminar . ( * ? ? ? * hereinafter lv99 ) proposed a model for fast reconnection which depends on the presence of turbulence , and its production of weakly stochastic field lines ( also briefly described in section [ sec : lv99model ] ) . turbulence is a natural consequence of convection in stars and of the magnetorotational instability in accretion disks ( for a review see * ? ? ? * ) . in addition , it is now generally accepted that the `` big power law in the sky '' indicates the presence of turbulence on scales from tens of parsecs to thousands of kilometers . among other sources , evidence for this comes from studies of atomic hydrogen spectra in molecular clouds and galaxies ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * see also review by , and references therein ) , as well as recent studies of emission lines and faraday rotation ( see * ? ? ? * ; * ? ? ? * ) . lv99 s model uses the properties of turbulence to predict broad outflows from extended current sheets . the diffusivity of magnetic field line trajectories in a turbulent plasma implies that flows can follow local magnetic field lines without being confined to the current sheet . when the turbulent diffusivity is less than the ohmic resistivity , this model reduces to the sweet - parker reconnection model . the first test of the lv99 model using three - dimensional ( 3d ) mhd simulations was performed in . the main predictions of the model were confirmed . in this paper we provide additional numerical evidence of magnetic reconnection in turbulent environments by testing different mechanisms for injecting turbulence . in [ sec : lv99model ] we briefly review the lv99 model of reconnection and its theoretical predictions . in [ sec : setup ] we describe in details the numerical model studied in this paper and new method of turbulence driving . although the initial setup and boundary conditions are similar to our previous studies , and described in details in , we briefly describe them here for completeness , as well . in [ sec : results ] we present an extensive description of new results obtained from studying our numeric model , which we discuss later in [ sec : discussion ] . in [ sec : summary ] we present our main conclusions .

1203.2971

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the lv99 model was introduced for both collisional and collisionless media and it claimed that the microphysics of collisionless reconnection events does not change the resulting reconnection rates . this point was subjected to further scrutiny in @xcite who provided a thorough investigation of the problem and concluded that for most of astrophysical collisionless plasmas the lv99 model should be applicable , provided that plasma is turbulent . with turbulence being ubiquitous in astrophysical conditions , this hardly constraints the applicability of the lv99 model . the lv99 model of reconnection is applicable to the collisional medium , such as the ism , which is both turbulent and magnetized , and where the hall - mhd reconnection does not work @xcite . for instance , for hall - mhd reconnection to be applicable , it is required that the sweet - parker current sheet @xmath161 width is smaller than the ion inertial length @xmath162 . thus , the `` reconnection criterion for media to be collisionless '' is @xmath163 , which presents a much severe constraint on the possible rate of collisions . as a result magnetic reconnection happens to be mediated by the hall - mhd only if the extend of the contact region @xmath10 ( see fig . [ fig : lv99model ] ) does not exceed @xmath164 cm . magnetic fields in the ism should interact over much larger scales . the lv99 model works in astrophysical environments to which the hall - mhd reconnection is applicable , as well , like solar corona , interplanetary medium , if the level of turbulence is high enough . the reconnection on microscales can happen fast , i.e. in the hall - mhd fashion . this may not change , however , the global reconnection rate . the lv99 model shows that even with relatively slow sweet - parker reconnection at microscales the global reconnection is limited not by ohmic resistivity , but by the rate of magnetic field wondering . we believe that the hall - mhd _ local _ reconnection of magnetic fields is taking place in the interplanetary medium , which is being tested by local _ in - situ _ measurements , while the _ global _ reconnection rates are determined by magnetic field wandering as prescribed in lv99 . in the absence of quantitative model to be tested , simulations aimed at studying reconnection speed have been done in 2d , both for collisional and collisionless regimes . this allowed to achieve higher resolutions ( compared to those contemporary available in 3d ) but substantially constrained magnetic field dynamics . for instance , the closest study to ours was done by @xcite ( see also * ? ? ? * ) . the authors studied 2d magnetic reconnection in the presence of external turbulence . an enhancement of the reconnection rate was reported , but the numerical setup precluded the calculation of a long term average reconnection rate . a more recent study along the approach in @xcite is one in @xcite , where the effects of small scale turbulence on 2d reconnection were studied and no significant effects of turbulence on reconnection were reported for the setup chosen by the authors . later , @xcite redone the modeling of 2d turbulent reconnection following @xcite with much higher resolutions . they used an advanced technique to detect precisely all x - points in the domain and then performed statistical studies confirming the sweet - parker relation for the reconnection rate as a function of x - point geometry . the development of different techniques to study magnetic reconnection is very important . even though their modeling was limited to one type of highly superalfvnic decaying turbulence ( the initial uniform magnetic field was zero ) , they reported reconnection rates with normalized values @xmath165 and confirmed the importance of turbulence for modifying the character of magnetic reconnection and specifies heating and transport as the effect of particular significance , as well as formation of petschek - type `` x - points '' in 2d turbulence . due to the lack of large scale magnetic field configuration , their model represents a specific case , far from generic situation observed in the astrophysical objects where the mean and turbulent components of magnetic fields have comparable strengths . therefore , these studies can not predict the global reconnection rate , as well . moreover , @xcite interpreted successful numerical confirmation of the lv99 model as a result of strong turbulence , although @xcite addressed this problem carefully showing that the amplitudes of velocity fluctuations , both injected and obtained from spectra of developed and stationary turbulence , are fractions of alfvn speed . the fact that our study is in 3d is essential , as the lv99 model is intrinsically three dimensional . the general picture is of tangled field lines with reconnection taking place via a series of `` y - points '' or modified sweet - parker sheets distributed in some fractal way throughout the turbulence . a large scale sweet - parker sheet will be replaced by a more fractured surface , but the current sheets will occupy a vanishingly small fraction of the total volume and the field reversal will remain relatively well localized . the model predicts that the reconnection speed would be approximately equal to the strong turbulent velocity with a modest dependence on the ratio of the eddy length to the current sheet length . there should be no dependence on resistivity . the major results contained in our figures showing the dependence of the reconnection speed on resistivity , input power and input scale agree with the quantitative predictions of the lv99 model . we are not aware of any competing models to compare our simulations with . the major differences from the present study stem from the fact that we test a 3d model of reconnection , as the lv99 depends on effects , like field wandering , that happen only in 3d . in order to show how different 2d and 3d worlds are , we performed similar studies to those presented in @xcite , but limiting the domain to two dimensions ( see * ? ? ? * ) . in @xcite we demonstrated that 2d magnetic reconnection in the presence of turbulence depends on the ohmic resistivity , therefore , it is not fast . also , the dependencies on the turbulent power and injection scales were significantly weaker than in the lv99 . this dependence of 2d reconnection rate on ohmic resistivity in the presence of turbulence , although weaker than the sweet - parker relation @xmath166 , has been independently confirmed by @xcite studies , performed with very different approach . these differences call for deliberation with simple extension of conclusions coming from the 2d modeling to natural for magnetic field fully three dimensional world . reconnection is one of the most fundamental processes involving magnetic fields in conducting fluids or plasmas . therefore , the identification of a robust process responsible for reconnection has many astrophysically important consequences . below we list a few selected implications of the successful validation of the lv99 model . numerical studies on fermi acceleration in turbulent reconnection have a long history ( e.g. * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in the sweet - parker model , it has been shown that particles can accelerate due to the induced electric field in the reconnection zone @xcite . this @xmath167 acceleration process , however , is constrained by the narrow thickness of the acceleration zone which has to be larger than the particle larmor radius and by the strength of the magnetic field . therefore , the efficiency of this process is rather limited . besides , it also does not predict a power - law spectrum , as generally observed for cosmic rays . observations have always been suggestive that magnetic reconnection can happen at a high speed in some circumstances , in spite of the theoretical difficulties in explaining it . for instance , the phenomenon of solar flares suggests that magnetic reconnection should be first slow in order to ensure the accumulation of magnetic flux and then suddenly become fast in order to explain the observed fast release of energy . the lv99 model can naturally explain this and other observational manifestations of magnetic reconnection . consider a particle entrained on a reconnected magnetic field line ( see fig.[fig : lv99model ] ) . this particle may bounce back and forth between magnetic mirrors formed by oppositely directed magnetic fluxes moving towards each other with the velocity @xmath0 . each bounce will increase the energy of a particle in a way consistent with the requirements of the first - order fermi process @xcite . this is in contrast to the second - order fermi acceleration that is frequently discussed in terms of accelerating particles by turbulence generated by reconnection @xcite . the numerical studies of the particle acceleration supporting these ideas have been already started @xcite . an interesting property of this acceleration mechanism is that it is also potentially testable observationally , since the resulting spectrum of accelerated particles is different from that arising from a shock . @xcite used this mechanism of particle acceleration to explain the synchrotron power - law spectrum arising from the flares of the microquasar grs 1915 + 105 . further applications can be found in the solar physics . following @xcite we note that solar flares inspired much of the earlier research on reconnection ( see * ? ? ? * ; * ? ? ? as the plasma involved is substantially rarefied , the restrictive conditions for the collisionless reconnection are satisfied in this particular environment . @xcite stated that bistable hall reconnection can be important in this case . stochastic reconnection provides an alternative explanation . indeed , an important prediction of the lv99 model is related to the _ reconnection instability _ that arises in the situation when the initial structure of the flux prior to reconnection is laminar . reconnection at the sweet - parker rate is negligible . this allows magnetic flux to accumulate . however , when the degree of stochasticity exceeds a threshold value , the reconnection itself should excite more turbulence , creating a positive feedback resulting in a flare ( see * ? ? ? the instability is a generic property of laminar field reconnection in both collisionless and collisional environments . referring to the sun , one may speculate that the difference between gradual and eruptive flares arises from the original state of magnetic field prior to the flare , at least in some specific situations . in the case when the magnetic field is sufficiently turbulent the accumulation of magnetic flux does not happen and the flare is gradual . similarly , the observed spatial spread of energy release during solar flares may be due to the spread of the region of turbulent fields once reconnection is initiated at one place . recent observations demonstrate that gradual flares occur rather in regions with large scale and weak magnetic fields for which alfvn times are large @xcite . in light of that , the difference in alfvn times may explain different time scales in gradual and impulsive flares . further research is necessary for establishing the role of turbulence in changing the time scale of flare evolution . the lv99 model can find its application in the removal of magnetic flux from the star formation regions . @xcite showed that magnetic field is removed from the star forming core cluster faster than it is allowed by the standard ambipolar diffusion scenario @xcite . @xcite proposed a mechanism using efficient reconnection through `` hyper - resistivity '' . @xcite performed numerical studies of such a concept , replacing the `` hyper - resistivity '' with efficient stochastic reconnection . they reported removal of strong anticorrelations of magnetic field through `` reconnection diffusion '' , which can mimic the effect of enhanced ohmic resistivity . lv99 showed that fast reconnection of stochastic magnetic field makes the models of strong mhd turbulence self - consistent , because the critical balance in the gs95 model requires the existence of eddy - type motions perpendicular to the magnetic field . in the absence of reconnection this would result in unresolved knots that should drain energy from the cascade . the estimates in lv99 showed that the rates of reconnection predicted by the model are sufficient to resolve magnetic knots within one period . the lv99 model of magnetic reconnection in the presence of weakly stochastic magnetic fields was proposed by @xcite in @xcite . however , due to a few objective factors it met less enthusiasm in the community than , for example , the x - point collisionless reconnection . we believe that there were three major factors responsible for this . 1 . the collisionless x - point reconnection was initiated and supported by numerical simulations , while lv99 was a theory . its numerical testing became possible only recently . the reconnection subject had a history of failed theories and models , which without direct numerical support were taken with a grain of salt . the acceptance of the idea of astrophysical fluids generically being in turbulent state had much less observational support at that time compared to the present day . by now we have much more evidence which allows to claim that models not taking the pre - existent turbulence has little relevance to astrophysics . the analytical solutions of lv99 were based on the use of gs95 model of turbulence . the gs95 model of turbulence , in fact , was extended lv99 by introducing the concept of local reference frame for turbulent eddies and by extending the gs95 scalings to the subalfvnic case . the gs95 theory was far from being generally accepted at the time of the lv99 publishing . the situation has changed substantially by now . first of all , gs95 was successfully tested numerically @xcite and their ideas have been extended to describing the alfvnic cascade in compressible mhd turbulence ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? the so - called `` big power law in the sky '' indicating the presence of turbulence on scales from tens of parsecs to thousands of kilometers has been extended @xcite , and the observations of gas and synchrotron emission provided extended number of direct turbulence measurements confirming their presence ( see * ? ? ? * ; * ? ? ? finally , the situation has changed with the numerical testing of the lv99 model . the 3d mhd simulations in @xcite supported the predictions in the lv99 paper and our present work goes further with testing this model , by including different types of energy injection . it is worth noting also , that there is some implicit observational evidence in the favor of the lv99 model , like observations of the thick reconnection current outflow regions observed in the solar flares @xcite . @xcite , explaining quasi - periodic pulsations in observed flaring energy releases at an active region above the sunspot , proposed that the wave packets arising from the sunspots can trigger such pulsations . they established a phenomenological relation between oscillations in a sunspot and pulsations in flaring energy releases . this phenomenon can be naturally explained by the lv99 model . in this article we performed additional testing of the lv99 model of fast reconnection under different types of turbulent driving using 3d numerical simulations . we have introduced a new method of driving turbulence by direct injection of the velocity or magnetic eddies with random locations in the domain . we analyzed the dependence of the reconnection speed on the turbulence injection power , on the injection scale , as well as on the viscosity . we found that : * we observe similar changes of the topology of the magnetic field near the interface of oppositely directed magnetic field lines in models with two different turbulence injection mechanisms . these changes include the fragmentation of the current sheet , favoring multiple simultaneous reconnection events , as well as a substantial increase in the thickness of the outflow of reconnected magnetic flux and matter . * the relation between the reconnection rate @xmath0 and turbulent power @xmath1 remains unchanged under two different mechanisms of energy injection and is confirmed by new models to be @xmath168 , in agreement with the lv99 prediction . moreover , the injection in magnetic field produces similar effects on the reconnection as injection in velocity , remaining the dependence unaltered . * the reconnection rate grows with the size of the injected eddies , which can be directly related to the turbulence injection scale . the rate of growth , for the models with old and new driving mechanism , is approximated by @xmath169 scaling which agrees with the previously obtained scaling . somewhat steeper lv99 prediction , @xmath170 , could results from limitations in the dynamic range available for study . * reconnection in the presence of weak turbulence is only weakly sensitive to viscosity @xmath5 . from performed simulations we obtained a dependence @xmath160 for one set of parameters : @xmath171 , @xmath145 , @xmath134 , @xmath59 . the research of gk is supported by fapesp grant no . 2009/50053 - 8 , al is supported by the center for magnetic self - organization in laboratory and astrophysical plasmas , nsf grant ast-08 - 08118 and nasa grant nnx09ah78 g . the work of etv is supported by the national science and engineering research council of canada . the research of kom is supported by the polish ministry of science and higher education through grants : 92/n - astrosim/2008/0 and 3033/b / h03/2008/35 . this research also was supported by the national science foundation project tg - ast080005n through teragrid resources provided by texas advanced computing center ( tacc : http://www.tacc.utexas.edu ) . part of this work was made possible by the facilities of the shared hierarchical academic research computing network ( sharcnet : http://www.sharcnet.ca ) and the galera supercomputer in the academic computer centre in gdask ( task : http://www.task.gda.pl ) . bhattacharjee , a. , ma , z. w. , and wang , x. : recent developments in collisionless reconnection theory : applications to laboratory and astrophysical plasmas , lec . not . phys . , 614 , 351375 , 2003 . bhattacharjee , a. , huang , y .- m . , yang , h. , and rogers , b. : fast reconnection in high - lundquist - number plasmas due to the plasmoid instability , phys . plas . , 16 , 112102 , 2009 . cho , j. and lazarian , a. : compressible magnetohydrodynamic turbulence : mode coupling , scaling relations , anisotropy , viscosity - damped regime and astrophysical implications , mon . not . r. astron . soc . , 345 , 325339 , 2003 . de gouveia dal pino , e. m. and lazarian , a. : the role of violent magnetic reconnection on the production of the large scale superluminal ejections of the microquasar grs 1915 + 105 , arxiv : astro - ph/0307054 , 2003 . de gouveia dal pino , e. m. and lazarian , a. : production of the large scale superluminal ejections of the microquasar grs 1915 + 105 by violent magnetic reconnection , astron . astrophys . , 441 , 845853 , 2005 . gaensler , b. m. , haverkorn , m. , burkhart , b. , newton - mcgee , k. j. , ekers , r. d. , lazarian , a. , mcclure - griffiths , n. m. , robishaw , t. , dickey , j. m. , and green , a. j. : low - mach - number turbulence in interstellar gas revealed by radio polarization gradients , nature , 478 , 214217 , 2011 . goldstein , m. l. , matthaeus , w. h. , and ambrosiano , j. j. : acceleration of charged particles in magnetic reconnection solar flares , the magnetosphere , and solar wind , geophys . lett . , 13 , 205208 , 1986 . kulpa - dybe , k. , otmianowska - mazur , k. , kulesza - ydzik , b. , hanasz , m. , kowal , g. , wltaski , d. , and kowalik , k. : global simulations of the magnetic field evolution in barred galaxies under the influence of the cosmic - ray - driven dynamo , astrophys . j. lett . , 733 , l18 , 2011 . santos - lima , r. , lazarian , a. , de gouveia dal pino , e. m. , and cho , j. : diffusion of magnetic field and removal of magnetic flux from clouds via turbulent reconnection , astrophys . j. , 714 , 442461 , 2010 . servidio , s. , matthaeus , w. h. , shay , m. a. , dmitruk , p. , cassak , p. a. , and wan , m. : statistics of magnetic reconnection in two - dimensional magnetohydrodynamic turbulence , phys . plas . , 17 , 032315 , 2010 . sweet , p. a. : the neutral point theory of solar flares , electromagnetic phenomena in cosmical physics , 6 , 123134 , 1958 . iau symposium 6 , _ electromagnetic phenomena in cosmical physics _ b. lehnert , ( cambridge , uk : cambridge university press ) sych , r. , nakariakov , v. m. , karlicky , m. , and anfinogentov , s. : relationship between wave processes in sunspots and quasi - periodic pulsations in active region flares , astron . astrophys . , 505 , 791799 , 2009 . valle , j. p. : observations of the magnetic fields inside and outside the milky way , starting with globules ( ~ 1 parsec ) , filaments , clouds , superbubbles , spiral arms , galaxies , superclusters , and ending with the cosmological universe s background surface ( at ~ 8 teraparsecs ) , fund . phys . , 19 , 189 , 1997 . valle , j. p. : observations of the magnetic fields inside and outside the solar system : from meteorites ( ~ 10 attoparsecs ) , asteroids , planets , stars , pulsars , masers , to protostellar cloudlets ( < 1 parsec ) , fund . , 19 , 319422 , 1998 .

we study a model of fast magnetic reconnection in the presence of weak turbulence proposed by using three - dimensional direct numerical simulations . we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving . the new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space . we provide exact relations between the eddy parameters and turbulent power and injection scale . magnetic fields are observed in many astrophysical objects and usually play an important or even crucial role in their dynamics ( see * ? ? ? however , observations indicate that the mean and turbulent components of magnetic fields in many astrophysical objects are of similar strengths ( see * ? ? ? * for example ) . the first analytic model for magnetic reconnection was proposed independently by and . two regions with uniform magnetic fields are separated by thin current sheet . the realization that sweet - parker reconnection is inadequate to explain magnetic reconnection in an astrophysical context was immediately apparent , and gave rise to decades of research on models of fast reconnection ( see * ? ? ? the first proposal was to replace the current sheet with an x - point configuration , so that the `` sheet '' thickness and length are comparable . this is the basis for petschek s model of fast reconnection . numerical simulations have been encouraging . first , it is not clear that this kind of fast reconnection persists on scales greater than the ion inertial scale ( see * ? ? ? several numerical studies have found large scale reconnection speeds which depend on resistivity , i.e. are not fast . second , in many circumstances the magnetic field geometry does not allow the formation of x - point reconnection . for example , a saddle - shaped current sheet can not be spontaneously replaced by an x - point . the energy required to do so is comparable to the magnetic energy liberated by reconnection , and must be available beforehand . finally , the requirement that reconnection occur in a collision less plasma restricts this model to a small fraction of astrophysical applications . this condition is not satisfied in many environments which one might naively consider to be collisionless , among them the interstellar medium . the conclusion that stellar interiors and atmospheres , accretion disks , and the interstellar medium in general does not allow fast reconnection is drastic and unpalatable . in addition , it is now generally accepted that the `` big power law in the sky '' indicates the presence of turbulence on scales from tens of parsecs to thousands of kilometers . among other sources , the first test of the lv99 model using three - dimensional ( 3d ) mhd simulations was performed in .

we study a model of fast magnetic reconnection in the presence of weak turbulence proposed by using three - dimensional direct numerical simulations . the model has been already successfully tested in confirming the dependencies of the reconnection speed on the turbulence injection power and the injection scale expressed by a constraint and no observed dependency on ohmic resistivity . in , in order to drive turbulence , we injected velocity fluctuations in fourier space with frequencies concentrated around , as described in alvelius ( 1999 ) . in this paper we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving . the new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space . we provide exact relations between the eddy parameters and turbulent power and injection scale . we performed simulations with new forcing in order to study turbulent power and injection scale dependencies . the results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases . this is in agreement with the lazarian & vishniac ( 1999 ) predictions . in addition , we performed a series of models with varying viscosity . although lazarian & vishniac ( 1999 ) do not provide any prediction for this dependence , we report a weak relation between the reconnection speed with viscosity , . magnetic fields are observed in many astrophysical objects and usually play an important or even crucial role in their dynamics ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * e.g. ) . they are a key ingredient of astrophysical processes such as magneto - rotational instability , magnetic dynamo , transport and acceleration of cosmic rays , accretion disks , turbulence , solar phenomena , gamma ray bursts , etc . . magnetic fields are solenoidal and evolve only through changes in the curl of the electric field . in the limit of zero resistivity the topology of the field lines is a constant of motion and the magnetic flux threading any fluid element is constant . generating large scale magnetic fields requires some kind of battery effect , like the biermann battery and generating strong large scale magnetic fields requires a dynamo ( see * ? ? ? * for example ) . in the limit of very small resistivity , which is typical for astrophysical objects , the magnetic flux is `` frozen in '' and magnetic field lines will resist passing through one another or changing their topology . due to the presence of plasma motions , in particular turbulence , this would result in a very complex tangle of field lines in real objects , with negligible large scale magnetic flux . however , observations indicate that the mean and turbulent components of magnetic fields in many astrophysical objects are of similar strengths ( see * ? ? ? * for example ) . this implies the existence of a process which can violate the frozen - in condition on dynamical time scales , i.e. fast magnetic field reconnection . the first analytic model for magnetic reconnection was proposed independently by and . sweet - parker reconnection has the virtue that it relies on a robust and straightforward geometry . two regions with uniform magnetic fields are separated by thin current sheet . the speed of reconnection is given roughly by the resistivity divided by the sheet thickness . however , the plasma in the current sheet is constrained to move along the local field lines , and is ejected from the edge of the current sheet at the alfvn speed , . since the width of the current sheet limits the flux of expelled plasma , the overall reconnection speed is reduced from the alfvn speed by the square root of the lundquist number , , where is the resistivity and is the length of the current sheet . in most astrophysical contexts is very large and the sweet - parker reconnection speed , , is negligible . fast reconnection requires that the dependence on be erased . given the simplicity of the sweet - parker setup , this requires that the simple geometry of the current sheet must be broken . the realization that sweet - parker reconnection is inadequate to explain magnetic reconnection in an astrophysical context was immediately apparent , and gave rise to decades of research on models of fast reconnection ( see * ? ? ? * ; * ? ? ? * for reviews ) . the first proposal was to replace the current sheet with an x - point configuration , so that the `` sheet '' thickness and length are comparable . this is the basis for petschek s model of fast reconnection . however , a dynamically self - consistent x - point requires that the outflow prevent a general collapse into a narrow current sheet . otherwise we would expect that the same bulk forces that brought the magnetic field lines together would lead to sweet - parker reconnection . proposed that slow - mode shocks on either side of the x - point would serve this purpose . moreover , those shocks are responsible for converting most of the magnetic energy into the heat and kinetic energy . the x - point in this model has an overall size which depends on resistivity , but since the magnetic field decrease logarithmically when approaching the current sheet ( due to the assumption of the current - free magnetic field in the inflow region ) , the resulting reconnection speed is some fraction of . numerical simulations with uniform resistivity have showed that in the mhd limit the shocks fade away and the contact region expands into a sheet . the only way to make the petschek configuration stable is by introducing the local nonuniform resistivity . this leaves the possibility that x - point reconnection is stable when the plasma is collisionless . numerical simulations have been encouraging . however , there are several important issues that remain unresolved . first , it is not clear that this kind of fast reconnection persists on scales greater than the ion inertial scale ( see * ? ? ? * ) . several numerical studies have found large scale reconnection speeds which depend on resistivity , i.e. are not fast . second , in many circumstances the magnetic field geometry does not allow the formation of x - point reconnection . for example , a saddle - shaped current sheet can not be spontaneously replaced by an x - point . the energy required to do so is comparable to the magnetic energy liberated by reconnection , and must be available beforehand . finally , the requirement that reconnection occur in a collision less plasma restricts this model to a small fraction of astrophysical applications . for example , while reconnection in stellar coronae might be described in this way , stellar chromospheres are not . more generally estimated that the scale of the reconnection sheet should not exceed about 40 times the electron mean free path . this condition is not satisfied in many environments which one might naively consider to be collisionless , among them the interstellar medium . the conclusion that stellar interiors and atmospheres , accretion disks , and the interstellar medium in general does not allow fast reconnection is drastic and unpalatable . an alternative to the x - point geometry is to consider magnetic fields that are chaotic , even if only weakly so . requiring the plasma to flow along the local magnetic field implies a powerful constraint on reconnection only if the field lines themselves are laminar . ( * ? ? ? * hereinafter lv99 ) proposed a model for fast reconnection which depends on the presence of turbulence , and its production of weakly stochastic field lines ( also briefly described in section [ sec : lv99model ] ) . turbulence is a natural consequence of convection in stars and of the magnetorotational instability in accretion disks ( for a review see * ? ? ? * ) . in addition , it is now generally accepted that the `` big power law in the sky '' indicates the presence of turbulence on scales from tens of parsecs to thousands of kilometers . among other sources , evidence for this comes from studies of atomic hydrogen spectra in molecular clouds and galaxies ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * see also review by , and references therein ) , as well as recent studies of emission lines and faraday rotation ( see * ? ? ? * ; * ? ? ? * ) . lv99 s model uses the properties of turbulence to predict broad outflows from extended current sheets . the diffusivity of magnetic field line trajectories in a turbulent plasma implies that flows can follow local magnetic field lines without being confined to the current sheet . when the turbulent diffusivity is less than the ohmic resistivity , this model reduces to the sweet - parker reconnection model . the first test of the lv99 model using three - dimensional ( 3d ) mhd simulations was performed in . the main predictions of the model were confirmed . in this paper we provide additional numerical evidence of magnetic reconnection in turbulent environments by testing different mechanisms for injecting turbulence . in [ sec : lv99model ] we briefly review the lv99 model of reconnection and its theoretical predictions . in [ sec : setup ] we describe in details the numerical model studied in this paper and new method of turbulence driving . although the initial setup and boundary conditions are similar to our previous studies , and described in details in , we briefly describe them here for completeness , as well . in [ sec : results ] we present an extensive description of new results obtained from studying our numeric model , which we discuss later in [ sec : discussion ] . in [ sec : summary ] we present our main conclusions .

1107.0813

i

inflationary cosmology has become the prevalent paradigm to understand the early stage of our universe , with its advantages of resolving the flatness , homogeneity and monopole problems @xcite , and predicting a approximately scale - invariant primordial power spectrum consistent with current cosmological observations @xcite very well . however , a single field inflation model often suffers from fine tuning problems on the parameters of its potential , such as the mass and the coupling constant . in recent years , people has noticed that , when a number of scalar fields are involved in the inflationary stage , they can relax many limits on the single scalar inflation model @xcite . usually , these fields are able to work cooperatively to give an inflationary stage long enough , even none of them can sustain inflation separately . models of this type have been considered later in refs . the main results showed that both the e - folding number @xmath1 and the curvature perturbation @xmath2 are approximately proportional to the number of the scalars @xmath3 . later , the model of n - flation was proposed by dimopoulos _ @xcite , which showed that a number of axions predicted by string theory can give rise to a radiatively stable inflation . this model has explored the possibility for an attractive embedding of multi - field inflation in string theory . over the past several years , based on the recent developments in string theory , there have been many studies on its applications to the early universe in inflationary cosmology . an interesting inflation model , which has a non - canonical kinetic term inspired by string theory , was studied intensively in the literature . due to a non - canonical kinetic term , the propagation of field fluctuations in this model is characterized by a sound speed parameter and the perturbations get freezed not on hubble radius , but on the sound horizon instead . one specific realization of this type of models can be described by a dirac - born - infeld - like ( dbi ) action @xcite . based on brane inflation @xcite , the model with a single dbi field was investigated in detail@xcite , which has explored a window of inflation models without flat potentials . in this model , a warping factor was applied to provide a speed limit which keeps the inflaton near the top of a potential even if the potential is steep . motivated by the effective description of multiple d - brane dynamics in string theory @xcite , an interesting inflation model involving multiple sound speeds with each sound speed characterizing one field fluctuation was proposed @xcite . the authors of refs.@xcite suggest this scenario can be realized by a number of general scalar fields with arbitrary kinetic forms , and these scalars have their own sound speeds respectively . therefore , this model is dubbed as _ multi - speed inflation _ " ( msi ) . in this model , the propagations of field fluctuations are individual , and the usual conceptions in multi - field inflation models might be not suitable in this scenario . for example , in a usual generalized n - flation model , the length scale for perturbations being freezed takes the unique sound horizon ; however , in our model it corresponds to the maximum sound horizon . it is worth emphasizing that the model of msi is different from the usual dbi n - flation in which only multiple moduli fields are involved in one dbi action @xcite , but msi is constructed by multiple kessence type actions . for example , an explicit model of msi is made of two dbi fields in ref @xcite , and its primordial perturbations including curvature and entropy modes and their non - gaussianities were considered . in the current paper we extend the model into a much more generic case by relaxing the form of the lagrangian . we find that even there are no coupling terms among the inflaton fields , their perturbation modes are coupled due to the nonlinear gravitational interaction . we also find that if these couplings are weak , the independent components of the fields can be treated as a combination of normal modes , by which the curvature perturbation at the horizon - crossing can be calculated in detail up to leading order of slow variation parameters via @xmath0 formalism . as a specific example , we consider a model of multi - speed inflation involving two dbi fields . we show that in the relativistic limit , the coupling between two fields is mainly reflected by the damping terms in the perturbation equations . the difference between the sound speeds of these two fields is able to generate a considerable amplification on the amplitude of the primordial curvature perturbation . this is greatly different from the usual analysis on the inflationary model constructed by two canonical fields@xcite . the paper is organized as follows . in section ii , we study the cosmological perturbation theory of the msi model in a generic case , then show that the inflaton fluctuations could be decoupled through a redefinition of fields at leading order under the assumption of weak couplings . in section iii , we focus on a model of msi involving two fields , and study the detailed field transformation matrix to illustrate that the decoupling process of the field fluctuations is reliable under the weak coupling approximation . specifically , we analyze a specific model constructed by two dbi fields and give its curvature perturbation . section iv presents a summary and discussion . in the paper we take the normalization @xmath4 and the sign of metric is adopted as @xmath5 in the following .

, these fields can be treated as a combination of decoupled fields , which are similar to normal modes in coupled oscillation . by virtue of such fields , the curvature perturbation at the horizon - crossing can be calculated up to the leading order of slow variation parameters via formalism . explicitly , we consider a model of multi - speed dbi inflation , and calculate the power spectrum in detail .

we study a multi - field inflationary theory with separable lagrangian , which has different speed of sound for each field . we find that the fields always coupled at perturbative level through gravitational interaction . we show that if the coupling terms among the perturbation fields are weak enough , these fields can be treated as a combination of decoupled fields , which are similar to normal modes in coupled oscillation . by virtue of such fields , the curvature perturbation at the horizon - crossing can be calculated up to the leading order of slow variation parameters via formalism . explicitly , we consider a model of multi - speed dbi inflation , and calculate the power spectrum in detail . the result depends on the ratio of different speeds of sound , and shows an apparent amplification when the ratio deviates from unity .

1608.03339

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in the era of big data , the rapid expansion of computing capacities in automatic data generation and acquisition brings data of unprecedented size and complexity , and raises a series of scientific challenges such as storage bottleneck and algorithmic scalability @xcite . to overcome the difficulty , some approaches for generating scalable approximate algorithms have been introduced in the literature such as low - rank approximations of kernel matrices for kernel principal component analysis @xcite , incomplete cholesky decomposition @xcite , early - stopping of iterative optimization algorithms for gradient descent methods @xcite , and greedy - type algorithms . another method proposed recently is distributed learning based on a divide - and - conquer approach and a particular learning algorithm implemented in individual machines @xcite . this method produces distributed learning algorithms consisting of three steps : partitioning the data into disjoint subsets , applying a particular learning algorithm implemented in an individual machine to each data subset to produce an individual output ( function ) , and synthesizing a global output by utilizing some average of the individual outputs . this method can successfully reduce the time and memory costs , and its learning performance has been observed in many practical applications to be as good as that of a big machine which could process the whole data . theoretical attempts have been recently made in @xcite to derive learning rates for distributed learning with least squares regularization under certain assumptions . this paper aims at error analysis of the distributed learning with regularized least squares and its approximation to the algorithm processing the whole data in one single machine . recall @xcite that in a reproduced kernel hilbert space ( rkhs ) @xmath1 induced by a mercer kernel @xmath2 on an input metric space @xmath3 , with a sample @xmath4 where @xmath5 is the output space , the least squares regularization scheme can be stated as @xmath6 here @xmath7 is a regularization parameter and @xmath8 is the cardinality of @xmath9 . this learning algorithm is also called kernel ridge regression in statistics and has been well studied in learning theory . see e.g. @xcite . the regularization scheme ( [ all estimate ] ) can be explicitly solved by using a standard matrix inversion technique , which requires costs of @xmath10 in time and @xmath11 in memory . however , this matrix inversion technique may not conquer challenges on storages or computations arising from big data . the distributed learning algorithm studied in this paper starts with partitioning the data set @xmath9 into @xmath12 disjoint subsets @xmath13 . then it assigns each data subset @xmath14 to one machine or processor to produce a local estimator @xmath15 by the least squares regularization scheme ( [ all estimate ] ) . finally , these local estimators are communicated to a central processor , and a global estimator @xmath16 is synthesized by taking a weighted average @xmath17 of the local estimators @xmath18 . this algorithm has been studied with a matrix analysis approach in @xcite where some error analysis has been conducted under some eigenfunction assumptions for the integral operator associated with the kernel , presenting error bounds in expectation . in this paper we shall use a novel integral operator approach to prove that @xmath16 is a good approximation of @xmath19 . we present a representation of the difference @xmath20 in terms of empirical integral operators , and analyze the error @xmath20 in expectation without any eigenfunction assumptions . as a by - product , we present the best learning rates for the least squares regularization scheme ( [ all estimate ] ) in a general setting , which surprisingly has not been done for a general kernel in the literature ( see detailed comparisons below ) .

we study distributed learning with the least squares regularization scheme in a reproducing kernel hilbert space ( rkhs ) . by a divide - and - conquer approach , the algorithm partitions a data set into disjoint data subsets , applies the least squares regularization scheme to each data subset to produce an output function , and then takes an average of the individual output functions as a final global estimator or predictor . we show with error bounds in expectation in both the-metric and rkhs - metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine . our error bounds are sharp and stated in a general setting without any eigenfunction assumption . the analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach . even for the classical least squares regularization scheme in the rkhs associated with a general kernel , we give the best learning rate in the literature . distributed learning , divide - and - conquer , error analysis , integral operator , second order decomposition .

we study distributed learning with the least squares regularization scheme in a reproducing kernel hilbert space ( rkhs ) . by a divide - and - conquer approach , the algorithm partitions a data set into disjoint data subsets , applies the least squares regularization scheme to each data subset to produce an output function , and then takes an average of the individual output functions as a final global estimator or predictor . we show with error bounds in expectation in both the-metric and rkhs - metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine . our error bounds are sharp and stated in a general setting without any eigenfunction assumption . the analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach . even for the classical least squares regularization scheme in the rkhs associated with a general kernel , we give the best learning rate in the literature . distributed learning , divide - and - conquer , error analysis , integral operator , second order decomposition .

0809.5141

i

one of the most exciting recent events in physics has been the increasing overlap between two previously disjoint fields , quantum optics and condensed matter physics . this has become possible due to the enormous progress in cooling dilute bosonic and also fermionic gases down to temperatures where respectively bose - einstein condensation and fermi degeneracy ( temperatures well below the fermi energy ) are reached . a very attractive feature of this new class of experiments is that they provide the arguably cleanest realization of the ( bosonic ) hubbard model @xcite , which with nearest - neighbor hopping and onsite interaction is the minimal model of strong correlation physics @xcite . here , we describe and analyze numerically a particular setup with ultracold bosons of two species in an optical superlattice , described by a bose - hubbard model . in the limit of strong onsite interactions , the system can be described by the spin-1/2 heisenberg antiferro- or ferromagnet , depending on the parameters of the superlattice . the motivation is fourfold : \(i ) in the vein of feynman s idea to simulate quantum systems by other quantum systems @xcite , it would be a great achievement to implement models of magnets like the heisenberg model with ultracold atoms in optical lattices . in condensed matter systems , collective magnetism arises from the coulomb interaction and the particle statistics which cause ( super)exchange processes @xcite . in particular , exchange interactions resulting from second order hopping processes in the fermi - hubbard model dominate its behavior in the limit of strong onsite interaction and are captured by an effective spin model , namely the heisenberg antiferromagnet @xcite . while collective magnetism has been widely studied in solids over the decades , several experimental restrictions apply quite generally : it is generally far from clear to what extent the typical simplified models are quantitatively realistic , and how to obtain the interaction parameters . external control of these parameters is very difficult . moreover , quantum magnetism becomes particularly interesting in low dimensions . in real effectively low - dimensional solids it is however hard to control or assert the effect of the weaker interactions in the second and/or third dimension . last but not least , solids give us only access to the linear response regime as sampled e.g. by neutron scattering . questions of out - of - equilibrium many - body dynamics are essentially inaccessible . experiments with ultracold atoms in optical lattices constitute clean and well - tunable manifestations of the bose- or fermi - hubbard model @xcite . to implement magnetic systems , the most straight forward approach would hence be to use a gas of ultracold fermions . however , cooling of fermionic gases to the quantum regime is a considerably harder task due to the lack of s - wave scattering among identical fermions @xcite . hence it is desirable to develop an alternative route via gases of ultracold bosons . our investigations follow this idea @xcite . although we focus here on one dimension , analogous setups in higher dimensions @xcite could be used to investigate a plethora of frustrated spin systems that are hard to access analytically and numerically . \(ii ) the superlattice structure chosen in our setup ( in analogy to the recent experiments @xcite ) allows in contrast to @xcite for the tuning of the effective spin - spin interaction by changing an alternating scalar potential @xmath0 ; fig [ fig : systemparameters ] . with the hopping strength @xmath1 and the onsite interaction @xmath2 of the hubbard model , the coupling in the corresponding effective spin model is then @xmath3 . this allows on the one hand to switch for the effective model between the heisenberg ferro- and antiferromagnet . on the other hand one might hope to increase for a fixed onsite interaction @xmath2 the effective coupling , by choosing @xmath4 . in this case , the relevant physics would become visible at correspondingly higher temperatures . however , the validity of the effective model breaks down in the vicinity of @xmath4 . so one has to balance the validity of the heisenberg description and the temperatures needed to observe the quantum effects . to this purpose , the parameter @xmath0 can be easily varied and used to tune to the heisenberg regime in controlled fashion . \(iii ) in recent experiments @xcite by the bloch group , the same optical superlattice as the one discussed here was used . but its parameters were chosen such that the superlattice decomposed actually into isolated double wells . the experiments analyzed dynamics in these double wells and contrasted in particular first order ( hopping ) processes ( hubbard regime ) versus slower second order processes ( heisenberg regime ) . the next step would be to observe coherent many - particle dynamics after coupling the double wells . we analyze such a situation by the time - dependent density matrix renormalization group method ( dmrg ) @xcite . we focus on the coherent evolution of an initial nel state and the differences between the heisenberg and the hubbard regimes and present the experimentally available observables . \(iv ) besides testing the coherence in the experiments , the setup allows to address questions of non - equilibrium many - particle systems , which is in general difficult for all present analytical and numerical methods . contrary to the setup of isolated double wells , one observes for the many - particle dynamics in our setup a relaxation of local quantities . this is an indicator for convergence of subsystems with finite real - space extent to a steady state . recently , the mechanism of how such a relaxation may occur was clarified for ( free ) integrable systems in @xcite . corresponding examples can also be found in @xcite . for a few nonintegrable systems the question was analyzed numerically in @xcite and analytically e.g. in @xcite . in general one expects that in nonintegrable models , thermalization occurs ( due to scattering processes ) , and that in integrable models , relaxation ( to a nonthermal steady state ) occurs via phase averaging effects @xcite . this is demonstrated here analytically for the heisenberg model . our setup could be used to study experimentally such relaxation processes in particular , the qualitative differences between nonintegrable systems , here the bose - hubbard model , and bethe ansatz integrable models @xcite , here the heisenberg model . we also fill a certain gap of current literature on such topics ( see e.g. @xcite ) by emphasizing that the heisenberg spins of the effective model , obtained by the schrieffer - wolff transformation ( in appendix [ sec : derivation ] ) @xcite , should not be identified directly with the two boson species . a spin up of the effective model corresponds rather to a particle of species 1 dressed by hole - double - occupancy fluctuations . the analogy holds only for small @xmath5 . the consequences for experimentally available observables are surprisingly strong . recently in @xcite a setup of coupled double wells ( @xmath6 , but alternating hopping @xmath7 in fig . [ fig : systemparameters ] ) was analyzed numerically in particular , the possibilities to generate entangled pairs of particles were studied . again , a perfect mapping to a spin model was assumed from the outset . the validity of this mapping is one central topic of our article . the paper is organized as follows . section [ sec : setupandmodel ] describes the experimental setup and how it can be described by a bose - hubbard model . restricting to half filling , section [ sec : effectivemodel ] and appendix [ sec : derivation ] derive by a schrieffer - wolff transformation for the limit of large onsite interactions an effective model which is the heisenberg antiferro- or ferromagnet . in section [ sec : evolution ] , we investigate by time - dependent density - matrix renormalization - group ( dmrg ) the evolution of typical observables like magnetization , momentum - space and real - space correlators , where the first two are also available experimentally . the focus is on contrasting the differences between the full hubbard dynamics and the corresponding effective spin model , and also the differences to the case of isolated double wells @xcite . we observe indications for ( local ) relaxation to steady states . this is discussed in section [ sec : relaxation ] where we also explain how the relaxation for the heisenberg model is connected to a phase averaging effect . section [ sec : validity ] addresses in more detail the question why and under what circumstances the effective model is a valid description for the full hubbard hamiltonian , especially for the dynamics . in section [ sec : groundstates ] we argue that the groundstate of the heisenberg antiferromagnet could be prepared by tuning an alternating hopping parameter of the superlattice adiabatically . section [ sec : conclusion ] gives a short conclusion .

, we provide the evolution of typical experimentally available observables . _ , nature * 448 * , 1029 ( 2007 ) ; s. trotzky _ et al . _ , we provide theoretical background for the next step , the observation of coherent many - particle dynamics after coupling the double wells . contrary to the case of isolated double wells , relaxation of local observables can be observed . we show that the relaxation in the heisenberg model is connected to a phase averaging effect , which is in contrast to the typical scattering driven thermalization in nonintegrable models . we discuss the preparation of magnetic groundstates by adiabatic tuning of the superlattice parameters .

we study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice . the system is captured by a two - species bose - hubbard model , but realizes in a certain parameter regime actually the physics of a spin-1/2 heisenberg magnet , describing the second order hopping processes . tuning of the superlattice allows for controlling the effect of fast first order processes versus the slower second order ones . using the density - matrix renormalization - group method , we provide the evolution of typical experimentally available observables . the validity of the description via the heisenberg model , depending on the parameters of the hubbard model , is studied numerically and analytically . the analysis is also motivated by recent experiments [ s. flling _ et al . _ , nature * 448 * , 1029 ( 2007 ) ; s. trotzky _ et al . _ , sience * 319 * , 295 ( 2008 ) ] where coherent two - particle dynamics with ultracold bosonic atoms in isolated double wells were realized . we provide theoretical background for the next step , the observation of coherent many - particle dynamics after coupling the double wells . contrary to the case of isolated double wells , relaxation of local observables can be observed . the tunability between the bose - hubbard model and the heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and bethe ansatz integrable models . we show that the relaxation in the heisenberg model is connected to a phase averaging effect , which is in contrast to the typical scattering driven thermalization in nonintegrable models . we discuss the preparation of magnetic groundstates by adiabatic tuning of the superlattice parameters .

1101.2982

i

in this paper we study a system of polynomials , orthogonal with respect to two different weight functions of meixner - pollaczek type . our work is motivated by the analysis of the six - vertex model in statistical mechanics introduced in @xcite and studied in many papers since then , see e.g. @xcite . colomo and pronko @xcite studied the role of orthogonal polynomials in the six - vertex model , and in particular the meixner - pollaczek polynomials . an object of major physical interest is the _ partition function _ of this model . a rather complete analysis of the large @xmath0 asymptotics in the homogeneous case is based on the analysis of a riemann - hilbert problem for orthogonal polynomials @xcite . in the inhomogeneous case , the corresponding reasoning leads to questions of asymptotics of _ multiple orthogonal _ polynomials , as we will discuss in section [ section : sixvertex ] . here we will focus on a particular regime of the six - vertex model , known as the `` free fermion line '' . in the homogeneous case , this case is trivial , the partition function being identically @xmath1 . also in the inhomogeneous case , a closed expression for the partition function can be calculated explicitly , so the present results do not give any new insights into the original model , but should rather be considered as providing exact and asymptotic information in its own right on the associated polynomials , the _ multiple meixner - pollaczek polynomials_. an important tool in the study of ( usual ) orthogonal polynomials @xmath2 on the real line , appropriately scaled in order to have @xmath0-dependent weights , is that their limiting zero distribution satisfies an equilibrium problem . this equilibrium problem is an important ingredient for the steepest descent analysis of the riemann - hilbert problem for orthogonal polynomials , thereby allowing to obtain strong and uniform asymptotics of the polynomials , see e.g.@xcite . for the case of multiple orthogonal polynomials , however , no general result is known about the existence of an equilibrium problem . the aim of this paper is to obtain such an equilibrium problem for multiple meixner - pollaczek polynomials . the equilibrium problem will be posed in terms of a couple of measures @xmath3 and it involves both an external source acting on @xmath4 and a constraint acting on @xmath5 . this structure is very similar to the equilibrium problem for the gue with external source model , @xcite . our method for obtaining the equilibrium problem is similar to that applied to other systems of multiple orthogonal polynomials @xcite , but a distinguishing feature is the characterization in terms of the eigenvalue distributions of block toeplitz matrices , rather than usual ( scalar ) toeplitz matrices . we will provide some general results on this topic that are of independent interest . along the way we also obtain rodrigues formulae and closed expressions for the recurrence coefficients for multiple meixner - pollaczek polynomials . inspired by the scalar case @xcite , one might hope that the equilibrium problem presented in this paper can be used in the steepest descent analysis of the riemann - hilbert problem for multiple meixner - pollaczek polynomials , thereby obtaining strong and uniform asymptotics for these polynomials . this approach , although interesting , will not be carried out in this paper . we also hope that our equilibrium problem might serve as an inspiration to obtain similar results for the general inhomogeneous six - vertex model , not necessarily on the free fermion line , which in turn could serve as the first step in finding the large @xmath0 asymptotic analysis for this model .

we also provide a rodrigues formula and closed expressions for the recurrence coefficients . the proof of the main result follows from a connection with the eigenvalues of block toeplitz matrices , for which we provide some general results of independent interest . the motivation for this paper is the study of a model in statistical mechanics , the so - called six - vertex model with domain wall boundary conditions , in a particular regime known as the free fermion line .

we study multiple orthogonal polynomials of meixner - pollaczek type with respect to a symmetric system of two orthogonality measures . our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem . we also provide a rodrigues formula and closed expressions for the recurrence coefficients . the proof of the main result follows from a connection with the eigenvalues of block toeplitz matrices , for which we provide some general results of independent interest . the motivation for this paper is the study of a model in statistical mechanics , the so - called six - vertex model with domain wall boundary conditions , in a particular regime known as the free fermion line . we show how the multiple meixner - pollaczek polynomials arise in an inhomogeneous version of this model . * keywords * : multiple orthogonal polynomial , meixner - pollaczek polynomial , recurrence relation , block toeplitz matrix , potential theory , six - vertex model .

1101.2982

r

let @xmath6 and @xmath7 denote two distinct weight functions of meixner - pollaczek type ; @xmath8 with @xmath9 where @xmath10 , @xmath11 and @xmath12 are fixed parameters and @xmath13 denotes euler s gamma function @xcite . note that in the gamma function is evaluated in a complex argument and that @xmath14 furthermore , for @xmath15 fixed , @xmath16 as @xmath17 , so the restrictions on @xmath18 guarantee that @xmath19 is exponentially decaying for @xmath20 . [ lemma : interlacing ] ( existence , uniqueness , real and interlacing zeros ) for any nonnegative integers @xmath21 and @xmath22 , there is a unique monic polynomial @xmath23 of degree @xmath24 satisfying the orthogonality conditions @xmath25 the zeros of these polynomials are real and interlacing , in the sense that each @xmath26 has @xmath27 distinct real zeros @xmath28 such that @xmath29 and @xmath30 whenever @xmath31 . lemma [ lemma : interlacing ] will be proved in section [ subsection : proofinterlacing ] . in analogy with the case of meixner - pollaczek orthogonal polynomials @xcite we refer to the @xmath26 as _ multiple meixner - pollaczek polynomials _ ; see also ( * ? ? ? these polynomials are related to the six - vertex model ; see section [ section : sixvertex ] . for information on other systems of multiple orthogonal polynomials in the literature , see e.g. @xcite . in this paper we will derive a rodrigues type formula for the polynomials @xmath26 , enabling us to compute explicitly the following four term recurrence relations , to be proved in section [ section : recurrence ] . [ theorem : recurrencemmpp ] ( recurrence relations ) let @xmath32 with @xmath33 . then , for nonnegative integers @xmath21 and @xmath22 , the multiple meixner - polleczek polynomials satisfy the recurrence relations @xmath34 and @xmath35 where @xmath36 @xmath37 @xmath38 @xmath24 , and where we set @xmath39 , @xmath40 for any @xmath41 . the above theorem is the basis for the main purpose of the paper , namely to study the asymptotic zero distribution of the appropriately rescaled multiple meixner - pollaczek polynomials . fix @xmath42 and @xmath43 . for simplicity we choose a particular sequence of indices @xmath44 along which we analyze the large @xmath27 asymptotics of @xmath45 , and form the single sequence @xmath46 of polynomials . we will show that the zero - distribution of the rescaled polynomials @xmath47 has a weak limit as @xmath27 goes to infinity , and in order to study this we let @xmath48 and introduce the doubly indexed sequence of monic polynomials @xmath49 defined by @xmath50 from ( [ recurrencemp ] ) and we obtain an explicit recurrence relation for @xmath51 , @xmath52 with initial conditions @xmath53 , where @xmath54 for @xmath27 even and @xmath55 for @xmath27 odd . using the recurrence relation , standard considerations show that the zeros of @xmath56 are the eigenvalues of the @xmath57-diagonal matrix @xmath58 so the problem of the asymptotic zero - distribution of @xmath56 reduces to finding the eigenvalue asymptotics of ( [ jacobi ] ) . if @xmath27 and @xmath0 both tend to infinity in such a way that @xmath59 for some constant @xmath60 , then the coefficients @xmath61 have two subsequential limits @xmath62 and @xmath63 for even and odd @xmath27 respectively . similarly , @xmath64 and @xmath65 have subsequential limits @xmath66 and @xmath67 along subsequences consisting of even and odd @xmath27 respectively . using the identity @xmath68 , these limits become @xmath69 @xmath70 if we consider ( [ jacobi ] ) in @xmath71 blocks , it is tri - diagonal with blocks @xmath72 @xmath73 and @xmath74 in view of the limits and , the blocks are slowly varying along the diagonals if @xmath0 is large . in other words , for large @xmath0 , the matrix ( [ jacobi ] ) has a _ locally block toeplitz _ structure with square blocks of size @xmath75 . this allows its limiting eigenvalue distribution to be obtained from a general machinery to which we turn now . in this subsection we will work in the following general setting . let @xmath0 be a fixed parameter and let @xmath76 be a sequence of monic polynomials , where @xmath51 has degree @xmath27 and depends parametrically on @xmath0 . assume that the @xmath51 are generated by the recurrence relation @xmath77 where @xmath78 is a semi - infinite matrix with unit lower hessenberg structure , i.e. , the strictly upper triangular part of @xmath78 is equal to zero , except for the first superdiagonal , on which all entries are @xmath1 . we also assume that the lower triangular part of @xmath78 has a finite bandwidth , which is independent of @xmath0 . the entries of @xmath78 are assumed to have asymptotically periodic behavior with period @xmath79 ( @xmath80 ) . more precisely , suppose @xmath78 is partitioned into blocks of size @xmath81 , with one superdiagonal and a fixed finite number @xmath82 of subdiagonal non - zero blocks , @xmath83 where @xmath84 where the @xmath85 s denote arbitrary constants . we will assume that the block entries @xmath86 in are slowly varying with @xmath0 , in the sense that the limits @xmath87 exist for any @xmath88 and @xmath89 . here the notation @xmath90 means that we let both @xmath27 and @xmath0 tend to infinity , in such a way that the ratio @xmath91 tends to a limit @xmath89 . the relation is on the level of @xmath81 matrices , with the limit taken entry - wise . if holds then the matrix in is said to have _ locally block toeplitz _ structure , in the spirit of @xcite . for fixed @xmath60 , we collect the limiting matrices in into the following matrix - valued laurent polynomial @xmath92 : @xmath93 we will sometimes refer to @xmath92 as the _ symbol_. from it follows that @xmath94 where @xmath95 denotes all the terms in that tend to zero as @xmath96 . define for each @xmath97 , the algebraic equation @xmath98 where @xmath99 denotes the identity matrix of size @xmath79 . note that @xmath100 depends on two complex variables @xmath101 and @xmath102 . by expanding the determinant and using , we can write @xmath100 as a ( scalar ) laurent polynomial in @xmath101 : @xmath103 where @xmath104 , @xmath105 , are polynomials in @xmath102 , with @xmath106 . we define @xmath107 in as the largest positive integer for which @xmath108 . let us solve for @xmath101 ; this yields @xmath109 roots @xmath110 we assume that for each @xmath111 these roots are ordered such that @xmath112 in the cases we are interested in , we will have that @xmath113 supposing this to hold , we define a measure @xmath114 on @xmath115 with density @xmath116 here the prime denotes the derivative with respect to @xmath102 , and @xmath117 are the boundary values of @xmath118 obtained from the @xmath119-side ( upper side ) and @xmath120-side ( lower side ) respectively of @xmath115 . these boundary values exist for all but a finite number of points . as discussed in @xcite , the measure @xmath114 can be interpreted as the weak limit as @xmath121 of the normalized eigenvalue counting measures for the block toeplitz matrices @xmath122 associated to the symbol . [ lemma : mu0prob ] with the above notation , we have * @xmath123 as @xmath124 . * @xmath114 in is a borel probability measure on @xmath125 . see @xcite . with this notation in place , let us return to the sequence of polynomials @xmath126 in . this sequence is said to have _ real and interlacing _ zeros if each @xmath51 has @xmath27 distinct real zeros @xmath127 such that @xmath128 whenever @xmath31 . the next result states that , under certain conditions , the normalized zero - counting measures of the polynomials @xmath56 have a ( weak ) limit for @xmath121 , which is precisely the average of the measures . here the average is with respect to the parameter @xmath60 . [ theorem : locallytoepeig ] ( limiting zero distribution of @xmath56 ) let the sequence of polynomials @xmath126 be such that hold . assume that @xmath126 has real and interlacing zeros for each @xmath0 , as described above . also assume that holds for every @xmath89 . then as @xmath129 , the normalized zero - counting measure @xmath130 of the polynomial @xmath56 , @xmath131 where @xmath132 denotes the dirac point mass at @xmath101 , has the limit @xmath133 in the sense of weak convergence of measures , where @xmath114 is defined in . theorem [ theorem : locallytoepeig ] will be proven in section [ section : zeroasymptotics ] . this theorem generalizes a result for the scalar case @xmath134 by kuijlaars - romn ( * ? ? ? * theorem 1.2 ) ; see also @xcite . we apply theorem [ theorem : locallytoepeig ] to the polynomials @xmath51 in section [ subsection : mmpp ] . in what follows , we will assume the condition of symmetric weights , @xmath135 for this case we can characterize the limiting zero distribution in terms of a constrained vector equilibrium problem , theorem [ theorem : equilibriumproblem ] , which is the main result of the paper . the symmetry condition in proposition [ theorem : zeroseigenvalues ] is needed to prove that @xmath136 ; in the general case this may fail . the recurrence coefficients in and then become @xmath137 we partition the matrix @xmath78 from into blocks as in with @xmath75 and @xmath138 . then the limiting values in exist and are given by @xmath139 @xmath140 and @xmath141 with @xmath62 , @xmath142 and @xmath143 as in . the symbol @xmath92 in now becomes @xmath144 so reduces to @xmath145 this equation has three roots , @xmath146 , @xmath147 which we label in order of increasing modulus : @xmath148 [ theorem : zeroseigenvalues ] ( limiting zero distribution ) suppose @xmath149 . as @xmath129 , the normalized zero - counting measure @xmath130 of the multiple meixner - pollaczek polynomial @xmath56 in section [ subsection : mmpp ] , see , converges weakly to the average @xmath150 of the measures @xmath114 in . this is a consequence of theorem [ theorem : locallytoepeig ] . the assumptions in the latter theorem are indeed satisfied : the interlacing condition follows from lemma [ lemma : interlacing ] , and the fact that @xmath115 follows from proposition [ monotonoussupports ] . in addition to the set @xmath125 in , we define @xmath151 we will now characterize the limiting zero distribution @xmath4 in terms of a vector equilibrium problem from logarithmic potential theory @xcite . recall that for a pair of borel measures @xmath152 supported in the complex plane , the _ mixed logarithmic energy _ of @xmath153 and @xmath154 is defined as @xcite @xmath155 [ theorem : equilibriumproblem ] ( equilibrium problem ) suppose @xmath149 . then the asymptotic zero distribution , @xmath4 , of @xmath56 is the first component of the unique minimizer @xmath3 of the energy functional @xmath156 among all vectors @xmath152 of positive measures such that @xmath157 , @xmath158 , @xmath159 , @xmath160 and @xmath154 is absolutely continuous with density satisfying @xmath161 the measures have the properties @xmath162\ ] ] and @xmath163 where @xmath164 is the positive , absolutely continuous measure on @xmath165 with constant density @xmath166 , and where @xmath167 and @xmath168 are positive constants given by @xmath169 and @xmath170 with @xmath171 furthermore , @xmath4 is absolutely continuous with respect to lebesgue measure and has density @xmath172,\ ] ] where @xmath173 and @xmath174 is the complex solution to the algebraic equation @xmath175 such that @xmath176 . for ( a ) @xmath177 and ( b ) @xmath178.,title="fig : " ] for ( a ) @xmath177 and ( b ) @xmath178.,title="fig : " ] in general , there is no closed expression for the density of @xmath4 , but in the limiting case @xmath179 , corresponding to the ordinary meixner - pollaczek orthogonal polynomials , ( [ densityrel3 ] ) can be explicitly solved , @xmath180 , giving @xmath181 . thus ( [ densityrel2 ] ) becomes @xmath182 and the density ( [ densityrel3 ] ) takes the form @xmath183 for non - zero values of @xmath184 , the density of @xmath4 turns out to have the same qualitative features as ; see figure [ fig : mp ] for some illustrations . theorem [ theorem : equilibriumproblem ] will be proven in section [ section : equilibrium ] . the proof uses a general result for block toeplitz matrices @xcite , see also @xcite , together with some explicit calculations using . multiple meixner - pollaczek polynomials appear in the study of the six - vertex model in statistical mechanics , as we explain now . consider an @xmath185 square lattice in the plane . a configuration of the six - vertex model is an assignment of an orientation to the edges of the lattice in such a way that each vertex is surrounded by precisely two incoming and two outgoing edges . see fig . [ fig : grid5x5 ] for a configuration with @xmath186 . the name _ six - vertex model _ refers to the fact that the local behavior near each vertex is given by six possible edge configurations ( see fig . [ fig:6vertices ] ) . we consider the six - vertex model with domain wall boundary conditions ( dwbc ) . this means that the edges at the top and bottom of the lattice must be directed outwards and those at the left and right of the lattice must be directed inwards . ( 80,50)(-20,20 ) ( 10,10 ) ( 10,20 ) ( 10,30 ) ( 10,40 ) ( 10,50 ) ( 20,10 ) ( 20,20 ) ( 20,30 ) ( 20,40 ) ( 20,50 ) ( 30,10 ) ( 30,20 ) ( 30,30 ) ( 30,40 ) ( 30,50 ) ( 40,10 ) ( 40,20 ) ( 40,30 ) ( 40,40 ) ( 40,50 ) ( 50,10 ) ( 50,20 ) ( 50,30 ) ( 50,40 ) ( 50,50 ) ( 1,10)(1,0)58 ( 1,20)(1,0)58 ( 1,30)(1,0)58 ( 1,40)(1,0)58 ( , 50)(1,0)58 ( 10,1)(0,1)58 ( 20,1)(0,1)58 ( 30,1)(0,1)58 ( 40,1)(0,1)58 ( 50,1)(0,1)58 ( 5,10 ) ( 5,20 ) ( 5,30 ) ( 5,40 ) ( 5,50 ) ( 55,10 ) ( 55,20 ) ( 55,30 ) ( 55,40 ) ( 55,50 ) ( 10,5 ) ( 20,5 ) ( 30,5 ) ( 40,5 ) ( 50,5 ) ( 10,55 ) ( 20,55 ) ( 30,55 ) ( 40,55 ) ( 50,55 ) ( 15,10)(1,0)1 ( 15,20)(1,0)1 ( 15,30)(1,0)1 ( 15,40)(-1,0)1 ( 15,50)(1,0)1 ( 25,10)(1,0)1 ( 25,20)(1,0)1 ( 25,30)(-1,0)1 ( 25,40)(1,0)1 ( 25,50)(-1,0)1 ( 35,10)(-1,0)1 ( 35,20)(1,0)1 ( 35,30)(-1,0)1 ( 35,40)(1,0)1 ( 35,50)(-1,0)1 ( 45,10)(-1,0)1 ( 45,20)(-1,0)1 ( 45,30)(1,0)1 ( 45,40)(-1,0)1 ( 45,50)(-1,0)1 ( 10,15)(0,-1)1 ( 20,15)(0,-1)1 ( 30,15)(0,1)1 ( 40,15)(0,-1)1 ( 50,15)(0,-1)1 ( 10,25)(0,-1)1 ( 20,25)(0,-1)1 ( 30,25)(0,1)1 ( 40,25)(0,1)1 ( 50,25)(0,-1)1 ( 10,35)(0,-1)1 ( 20,35)(0,1)1 ( 30,35)(0,1)1 ( 40,35)(0,-1)1 ( 50,35)(0,1)1 ( 10,45)(0,1)1 ( 20,45)(0,-1)1 ( 30,45)(0,1)1 ( 40,45)(0,1)1 ( 50,45)(0,1)1 ( 60,49)@xmath187 ( 60,39)@xmath188 ( 60,29)@xmath189 ( 60,19)@xmath190 ( 60,9)@xmath191 ( 48,-1)@xmath192 ( 38,-1)@xmath193 ( 28,-1)@xmath194 ( 18,-1)@xmath195 ( 8,-1)@xmath196 ( 20,20)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(1,0)1 ( 15,10)(-1,0)1 ( 10,5)(0,-1)1 ( 10,15)(0,1)1 ( 9,-5)1 ( 20,20)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(-1,0)1 ( 15,10)(1,0)1 ( 10,5)(0,1)1 ( 10,15)(0,-1)1 ( 9,-5)2 ( 20,20)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(1,0)1 ( 15,10)(1,0)1 ( 10,5)(0,1)1 ( 10,15)(0,1)1 ( 9,-5)3 ( 20,20)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(-1,0)1 ( 15,10)(-1,0)1 ( 10,5)(0,-1)1 ( 10,15)(0,-1)1 ( 9,-5)4 ( 20,20)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(-1,0)1 ( 15,10)(-1,0)1 ( 10,5)(0,1)1 ( 10,15)(0,1)1 ( 9,-5)5 ( 10,10)(0,0 ) ( 10,10 ) ( 10,10)(1,0)8 ( 10,10)(-1,0)8 ( 10,10)(0,1)8 ( 10,10)(0,-1)8 ( 5,10)(1,0)1 ( 15,10)(1,0)1 ( 10,5)(0,-1)1 ( 10,15)(0,-1)1 ( 9,-5)6 to each of the @xmath197 rows of the lattice we associate a parameter @xmath198 and similarly to each column a parameter @xmath199 , @xmath200 . we also fix a positive parameter @xmath201 and we assume that @xmath202 for all @xmath203 and @xmath204 . we define the weight of the vertex in row @xmath203 and column @xmath204 according to its type as @xmath205 ( type 1 or 2 ) , @xmath206 ( type 3 or 4 ) , or @xmath207 ( type 5 or 6 ) . note that the weights are parameterized according to the so - called disordered phase convention . the weight of a configuration is defined as the product of the weights of all the @xmath185 vertices in the configuration . the partition function @xmath208 is defined as the sum of the weights of all the consistent configurations of the @xmath185 six - vertex model with dwbc . an explicit expression for the partition function in terms of an @xmath185 determinant was found by izergin and korepin @xcite , see also @xcite . in the case where @xmath209 for all @xmath200 , for some fixed parameter @xmath210 , the izergin - korepin formula reduces to @xmath211^{n^2}}{\left ( \displaystyle \prod_{n=0}^{n-1 } n ! \right)^2}\det m,\ ] ] where the matrix @xmath212 has entries @xmath213 with @xmath214 see e.g. @xcite . the matrix @xmath215 is then precisely the _ moment matrix _ corresponding to the weight function @xmath216 on the real line . ( e.g. @xcite ) show that @xmath217 can be expressed in terms of the monic orthogonal polynomials @xmath218 defined by @xmath219 for all @xmath0 and @xmath220 for all @xmath221 with @xmath222 . in fact , @xmath217 is expressed in terms of the numbers @xmath223 in through the formula @xmath224 special choices of parameters lead to known families of orthogonal polynomials . indeed , colomo and pronko @xcite showed that the continuous hahn , meixner - pollaczek and continuous dual hahn polynomials appear in this way . in more general cases , the expressions were used to compute the asymptotics of the partition function @xmath225 for large @xmath197 in great detail by means of the riemann - hilbert method @xcite , see also @xcite . the situation in this paper corresponds to the case where @xmath226 for some @xmath227 and all @xmath228 . following the reasoning in @xcite , see also the appendix in @xcite , one sees that the izergin - korepin formula reduces to @xmath229^{n_1n}[\sin(\gamma+t_2)\sin(\gamma - t_2)]^{n_2n}}{\left(\displaystyle \prod_{n=0}^{n_1 - 1 } n ! \right ) \left ( \displaystyle \prod_{n=0}^{n_2 - 1 } n!\right ) \left(\displaystyle \prod_{n=0}^{n-1 } n!\right ) } \det m\ ] ] where the matrix @xmath230 now has entries @xmath231 with @xmath232 still given by ( [ def : mx ] ) . thus @xmath215 is a moment matrix with respect to the system of weight functions @xmath233 and @xmath234 on the real line . the inhomogeneous model was studied in @xcite in connection with the calculation of the arctic curve . leading order asymptotics of the partition function for the case @xmath235 in was computed in @xcite for the disordered regime , and in @xcite for the anti - ferroelectric regime . the analysis is valid in fact for any @xmath236 as long as @xmath237 as @xmath238 . it turns out that @xmath217 can be expressed in terms of monic _ multiple _ orthogonal polynomials @xmath239 with respect to the system of weight functions @xmath233 and @xmath234 . the polynomial @xmath239 is defined for any nonnegative integers @xmath41 by @xmath240 and @xmath241 we now have the following generalization of the formula . ( partition function ) let @xmath242 , @xmath243 , @xmath227 and recall the notation @xmath244 in and @xmath245 in . then the moment matrix @xmath215 in has determinant @xmath246 where @xmath247 is any sequence of @xmath1 s and @xmath248 s such that @xmath1 appears @xmath236 times and @xmath248 appears @xmath249 times . and where the associated sequences @xmath250 , @xmath251 , are defined recursively by @xmath252 and @xmath253 for any @xmath254 and @xmath251 . we will give the proof for the particular sequence @xmath255 ; it will be straightforward to extend the proof to the more general sequences @xmath247 in the statement of the proposition . from the definition it follows that @xmath256 where we define the inner product @xmath257 and where we use the functions @xmath258 and @xmath259 define functions @xmath260 and @xmath261 , @xmath262 , by bi - orthogonalizing the functions @xmath263 and @xmath264 in the following way : @xmath265 @xmath266 for appropriate coefficients @xmath267 and @xmath268 , subject to the orthogonality relations @xmath269 it is not hard to see that we can identify @xmath270 and @xmath271 . then we have that @xmath272 where the last step follows in a trivial way from . in view of the identifications mentioned in the previous paragraph , we then obtain . it is straightforward to generalize the above reasoning to the case of multiple values of the differences in . in general , one could even allow _ both _ @xmath273 and @xmath274 to take multiple values and then one should deal with _ multiple orthogonal polynomials of mixed type_. we leave the details to the interested reader . the value @xmath275 corresponds to the so - called free fermion line . as first observed in @xcite , in this case the above weight functions are related to the meixner - pollaczek weight . indeed , we then have @xmath276 we may compare this with the classical meixner - pollaczek weight function @xcite , @xmath277 by invoking the identity @xmath278 we see that for @xmath279 and @xmath280 reduces to @xmath281 thus the weight functions and are the same up to a scaling of the variable @xmath102 by a factor @xmath57 . it is an easy job to evaluate the izergin - korepin formula for the partition function explicitly on the free fermion line , so our results will not lead to new insights in that perspective . they should rather be considered as giving exact and asymptotic information on the multiple meixner - pollaczek polynomials in its own right . the rest of this paper is organized as follows : in section [ section : recurrence ] we consider multiple meixner - pollaczek polynomials with respect to two general weights and prove theorem [ theorem : recurrencemmpp ] . in section [ section : zeroasymptotics ] we establish theorem [ theorem : locallytoepeig ] and lemma [ lemma : interlacing ] , which together lead to proposition [ theorem : zeroseigenvalues ] . in section [ section : equilibrium ] we prove theorem [ theorem : equilibriumproblem ] using the theory of eigenvalue asymptotics for banded block toeplitz matrices .

our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem . we show how the multiple meixner - pollaczek polynomials arise in an inhomogeneous version of this model . * keywords * : multiple orthogonal polynomial , meixner - pollaczek polynomial , recurrence relation , block toeplitz matrix , potential theory , six - vertex model .

we study multiple orthogonal polynomials of meixner - pollaczek type with respect to a symmetric system of two orthogonality measures . our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem . we also provide a rodrigues formula and closed expressions for the recurrence coefficients . the proof of the main result follows from a connection with the eigenvalues of block toeplitz matrices , for which we provide some general results of independent interest . the motivation for this paper is the study of a model in statistical mechanics , the so - called six - vertex model with domain wall boundary conditions , in a particular regime known as the free fermion line . we show how the multiple meixner - pollaczek polynomials arise in an inhomogeneous version of this model . * keywords * : multiple orthogonal polynomial , meixner - pollaczek polynomial , recurrence relation , block toeplitz matrix , potential theory , six - vertex model .

astro-ph0311377

i

rotation is observed ubiquitously in star - forming cores . on the scale of @xmath00.1 pc , the detected rotation rate is small , with a typical value corresponding to a ratio of rotational to gravitational energy of @xmath1 ( goodman et al . 1993 ) . the rotation rate is much lower than expected if the core is condensed out of a low density background medium with angular momentum conserved . the slow core rotation is thought to be due to magnetic braking ( mestel 1985 ; mouschovias & ciolek 1999 ) , which is particularly efficient during the long , magnetically subcritical phase of cloud evolution driven by ambipolar diffusion ( basu & mouschovias 1994 ) . this assumes that the clouds are strongly magnetized to begin with , as envisioned in the standard picture of isolated low - mass star formation ( shu , adams & lizano 1987 ) . once a magnetically supercritical core develops , it begins to collapse dynamically . it is often assumed that magnetic braking then becomes inefficient , with most of the angular momentum of the core material carried by the collapsing flow into the central star - plus - disk or binary system . however , the typical value of specific angular momentum inferred for dense cores is an order of magnitude higher than the typical binary value , at least in the taurus cloud complex ( see fig . 8 of simon et al . 1995 and discussion in 8.5 of myers 1995 ) . this suggests that a large fraction of the core angular momentum may still be removed _ during collapse_. the problem of angular momentum redistribution in a collapsing magnetized core thus warrants a closer examination . the efficiency of magnetic braking depends sensitively on the magnetic field geometry ( mestel 1985 ) . the exact field geometry of a magnetized core on the verge of collapse is difficult to determine without following the cloud evolution in three dimensions . simplified numerical calculations of cloud evolution driven by ambipolar diffusion have shown , however , that by the time a central density cusp is formed the mass - to - flux ratio is approximately spatially constant in the supercritical core , and the ( volume ) density decreases with radius roughly as a power - law of @xmath2 ( lizano & shu 1989 ; basu & mouschovias 1994 ) . this self - similar behavior motivated li & shu ( 1996 ) to idealize the end state of the ambipolar diffusion - driven core formation as a scale - free configuration supported in part by a large scale magnetic field and in part by the thermal pressure gradient , with a fixed mass - to - flux ratio and an exact @xmath2 density profile . such a configuration turns out to be a singular isothermal toroid , for which the magnetic field geometry can be computed exactly ( see also baureis , ebert , & schmitz 1989 ) . the field geometry is distorted by fluid motions during the subsequent inside - out collapse . in a companion paper to this journal ( allen , shu & li 2003 ; hereafter paper i ) , we have studied the collapse of magnetized , singular isothermal toroids without rotation . the main features of the collapse solution are governed by the anisotropy in the magnetic forces , which induces in the toroid an evacuated region near the axis , where the plasma @xmath3 parameter ( the ratio of thermal to magnetic energy density ) drops below unity ( see fig . 4a of paper i ) . as the core collapses from inside out , matter in the magnetically dominated region slides along the field lines towards the equatorial region , creating a dense , flattened structure a pseudodisk ( galli & shu 1993a , b ) . the material in the pseudodisk collapses radially towards the central point mass in a magnetically diluted free - fall , dragging the footpoints of field lines along with it ( see fig . 4b of paper i ) . a highly pinched field configuration ( split monopole " ) is produced , with important implications for the magnetic transport of angular momentum from inside to outside . in the presence of rotation , the collapse would lead to a spinup of the pseudodisk , which is linked magnetically to a more slowly rotating envelope of infalling and nearly static material . we will show in this paper that the twisting of magnetic field lines actually drives a slow outflow during the core collapse , which can remove much of the angular momentum remaining in the infalling pseudodisk . this removal poses a substantial brake against the eventual formation of a centrifugally supported disk unless the trapped magnetic field is lost in the realistic situation by nonideal mhd effects . as the first step toward the dynamical calculations , we will generalize the magnetized , singular isothermal toroid solutions of li & shu ( 1996 ) to include rotation in [ initial ] . these magnetized rotating toroids are then induced to collapse from inside out in [ collapse ] , and the collapse is followed numerically in a manner similar to that described in paper i. the numerical solutions are discussed in [ discussion ] , with an emphasis on the efficiency of magnetic braking during core collapse and the implications for the difficulty of forming rotationally supported disks unless significant flux loss appears in the realistic problem at small scales , as is expected theoretically for high - density situations ( e.g. , nishi , nakano & umebayashi 1991 ; desch & mouschovias 2001 ) . we end with a brief summary and conclusion in [ conclusion ] .

we study numerically the collapse of rotating , magnetized molecular cloud cores , focusing on rotation and magnetic braking during the main accretion phase of isolated star formation . motivated by previous numerical work and analytic considerations , we idealize the pre - collapse core as a magnetized singular isothermal toroid , with a constant rotational speed everywhere . the collapse starts from the center , and propagates outwards in an inside - out fashion , satisfying exact self - similarity in space and time . for rotation rates and field strengths typical of dense low - mass cores , the specific angular momentum can be greatly reduced on the way , by an order of magnitude or more , even when the pre - collapse field strength is substantially below the critical value for dominant cloud support . both effects enhance the magnetic transport of angular momentum from inside to outside .

we study numerically the collapse of rotating , magnetized molecular cloud cores , focusing on rotation and magnetic braking during the main accretion phase of isolated star formation . motivated by previous numerical work and analytic considerations , we idealize the pre - collapse core as a magnetized singular isothermal toroid , with a constant rotational speed everywhere . the collapse starts from the center , and propagates outwards in an inside - out fashion , satisfying exact self - similarity in space and time . for rotation rates and field strengths typical of dense low - mass cores , the main feature remains the flattening of the mass distribution along field lines the formation of a pseudodisk , as in the nonrotating cases . the density distribution of the pseudodisk is little affected by rotation . on the other hand , the rotation rate is strongly modified by pseudodisk formation . most of the centrally accreted material reaches the vicinity of the protostar through the pseudodisk . the specific angular momentum can be greatly reduced on the way , by an order of magnitude or more , even when the pre - collapse field strength is substantially below the critical value for dominant cloud support . the efficient magnetic braking is due to the pinched geometry of the magnetic field in the pseudodisk , which strengthens the magnetic field and lengthens the level arm for braking . both effects enhance the magnetic transport of angular momentum from inside to outside . the excess angular momentum is carried away in a low - speed outflow that has , despite claims made by other workers , little in common with observed bipolar molecular outflows . we discuss the implications of our calculations for the formation of true disks that are supported against gravity by rotation .

1211.5133

c

we have analyzed the normal state of a degenerate fermi gas in the presence of artificial spin - orbit coupling and crossed zeeman fields . the specific form of the spin - orbit field chosen corresponds to a mixture of equal rashba and dresselhaus ( erd ) terms @xmath417 , which has been experimentally realized . the artificial zeeman field @xmath22 along a defined spin quantization @xmath10 corresponds to the raman intensity of the laser beams , and the crossed zeeman field @xmath16 pointing along the same direction the erd spin - orbit field corresponds to the frequency detuning from the atomic transition coupling two spin states . in such configuration , the eigenvalues of the non - interacting problem are obtained in a generalized helicity basis , where the helicity spin projection points either along or opposite to the quantization axis defined by the effective magnetic field @xmath418 in this case , we have shown that the presence of spin - orbit and crossed zeeman fields lead to parity violation in the excitation spectrum of the non - interacting fermi gas , which has immediate consequences for the fermi surface , spectral density and momentum distribution , which also do not have well defined parity . such parity violation emerges in momentum - resolved spectroscopic quantities because they are all functions of the magnitude @xmath419 of the effective field @xmath420 , which does not have well defined parity , since @xmath421 . in addition , we have shown that information on parity violation can be extracted from momentum - averaged thermodynamic properties such as pressure , entropy , chemical potential , compressibility , and spin - polarization as a function of crossed zeeman field components @xmath251 and @xmath252 for fixed spin - orbit coupling @xmath148 at fixed temperature @xmath422 . a signature of parity violation is the different behavior of any chosen thermodynamic quantity as a function of @xmath16 for @xmath141 and as a function of @xmath22 for @xmath116 . this anisotropy of thermodynamic properties in the @xmath423 plane for finite spin - orbit coupling @xmath148 is a direct reflection of the lack of parity ( inversion symmetry ) . lastly , we analyzed the effects of interactions for a degenerate fermi gas when parity is broken , and investigated how parity violation influences the order parameter of a uniform superfluid and the fermion pairing temperature . we noticed that the order parameter tensor for a uniform superfluid in the generalized helicity basis no longer possesses inversion symmetry , however singlet and triplet pairing in can still be defined this basis and preserves parity . furthermore , we found that the effects of parity violation are strong in the pairing temperature of fermions , because it becomes increasingly more difficult to pair states with zero center of mass momentum between helicity bands with progressively larger loss of inversion symmetry . j. p. gaebler , j. t. stewart , j. l. bohn , and d. s. jin phys . 98 * , 200403 ( 2007 ) . yasuhisa inada , munekazu horikoshi , shuta nakajima , makoto kuwat - gonokami , masahito ueda , and takashi mukaiyama , phys . * 101 * , 100401 ( 2008 ) . j. fuchs , c. ticknor , p. dyke , g. veeravalli , e. kuhnle , w. rowlands , p. hannaford , and c. j. vale , phys . a * 77 * , 053616 ( 2008 ) . r. a. w. maier , c. marzok , c. zimmermann , and ph . w. courteille , phys . a * 81 * , 064701 ( 2010 ) . n. navon , s. nascimbne , f. chevy , and c. salomon , science * 328 * , 729 , ( 2010 ) , mark j. h. ku , ariel t. sommer , lawrence w. cheuk , martin w. zwierlein science * 335 * , 563 ( 2012 ) . cheng and s .- k . yip , phys . rev . b * 75 * , 014526 ( 2007 ) . li han , c. a. r. s de melo , phys . a * 85 * , 011606(r ) ( 2012 ) . kangjun seo , li han , c. a. r. s de melo , phys . a * 85 * , 033601 ( 2012 ) . kangjun seo , li han and c. a. r. s de melo , arxiv:1110.6364v1 ( 2011 ) . kangjun seo , li han , c. a. r. s de melo , phys . lett . * 109 * , 105303 ( 2012 ) . pengjun wang , zeng - qiang yu , zhengkun fu , jiao miao , lianghui huang , shijie chai , hui zhai , and jing zhang , phys . 109 * , 095301 ( 2012 ) . lawrence w. cheuk , ariel t. sommer , zoran hadzibabic , tarik yefsah , waseem s. bakr , and martin w. zwierlein , phys . lett . * 109 * , 095302 ( 2012 ) . lifshitz , zh . . fiz . * 38 * , 1569 ( 1960 ) [ sov . jetp * 11 * , 1130 ( 1960 ) ] .

we study quantum degenerate ultra - cold fermi gases in the presence of artificial spin - orbit coupling and crossed zeeman fields . we emphasize the case where parity is violated in the excitation spectrum and compare it with the simpler situation where parity is preserved . similarly , we show that thermodynamic properties such as pressure , chemical potential , entropy , specific heat , isothermal compressibility and induced spin polarization become anisotropic as a function of zeeman field components , when parity is violated .

we study quantum degenerate ultra - cold fermi gases in the presence of artificial spin - orbit coupling and crossed zeeman fields . we emphasize the case where parity is violated in the excitation spectrum and compare it with the simpler situation where parity is preserved . we investigate in detail spectroscopic properties such as the excitation spectrum , the spectral function , momentum distribution and density of states for the cases where parity is preserved or violated . similarly , we show that thermodynamic properties such as pressure , chemical potential , entropy , specific heat , isothermal compressibility and induced spin polarization become anisotropic as a function of zeeman field components , when parity is violated . lastly , we discuss the effects of interactions and present results for the pairing temperature as the precursor for the transition to a superfluid state . in particular , we find that the pairing temperature is dramatically reduced in the weak interaction regime as parity violation gets stronger , and that the momentum dependence of the order parameter for superfluidity violates parity when crossed zeeman fields are present for finite spin - orbit coupling .

0710.4600

i

in four dimensions , stationary black hole spactimes have been studied by many authors and these studies are known as _ uniqueness theorems of black holes _ @xcite . israel showed that the only static , asymptotically flat vacuum solution with a regular event horizon is the schwarzschild solution specified only by its mass @xcite . shortly afterward , he generalized the theorem to the situation with an electromagnetic field @xcite , i.e , he presented the proof that the only static , asymptotically flat electrovac solution with a regular non - degenerate event horizon is the reissner - nordstrm solution with two parameters , the mass @xmath1 and the electric charge @xmath2 which are subject to the inequality @xmath3 . bunting and masood - ul - alam succeeded in proving these two theorems without the assumption of a single connected component of a black hole @xcite by using the positive energy theorem @xcite . on the other hand , for non - static and stationary space - times , the einstein - maxwell system can be reduced to two - dimensional boundary value problem . the field equation is derived by the ernst potential associated with the axial killing vector field . the essential part in showing the uniqueness theorem for stationary black holes is that two solutions with the same asymptotic condition are isometric to each other . carter @xcite showed that the infinitesimally neighboring vacuum solutions with the same asymptotic conditions are equal , and robinson generalized its theorem to the stationary electrovac system @xcite . thereafter , using so - called _ robinson identity _ , robinson also succeeded in proving the uniqueness of the vacuum kerr family @xcite with @xmath4 among all asymptotically flat , stationary and axisymmetric black hole solutions with a non - degenerate event horizon , i.e. , showing that two arbitrary , not necessarily infinitesimally neighboring , solutions with the same boundary conditions are equal to each other . in electromagnetic system , mazur derived the divergence identity ( _ mazur identity _ ) @xcite , which is based on that the ernst equation describe a non - linear sigma model on the symmetric space @xmath5 , and showed that the only possible and axisymmetric black hole solutions to the einstein - maxwell equations is the kerr - newman solution specified by the mass @xmath1 , the angular momentum @xmath6 and the electric charge @xmath2 with the constraint @xmath7 . in recent years , studies of black holes in higher dimensions have attracted much attention in the context of string theory and the brane world scenario . in fact , it has been predicted that higher - dimensional black holes would be produced in a future linear collider @xcite . such physical phenomena are expected not only to give us a piece of evidence for the existence of extra dimensions but also to help us to draw some information toward quantum gravity . studies on stationary black hole solutions are important since we may detect the hawking radiation after the formation of stationary black holes in a collider . a striking feature of asymptotically flat stationary black hole solutions in five dimensions is that they admit event horizons with non - spherical topologies in contrast to four dimensions . for instance , the topology of the event horizon in higher dimensions can not be uniquely determined @xcite in contrast to four - dimensional ones , which is restricted only to the two sphere @xcite . in five dimensions , however , the possible geometric types of the horizon topology are @xmath8 and @xmath9 @xcite , and in dimensions higher than five , more complicated @xcite . the black ring solutions with the horizon topology @xmath0 , which rotate along the @xmath10 direction , were found by emparan and reall as solutions to the five - dimensional vacuum einstein equations @xcite . this is the first example of black hole solution with non - spherical topology . in addition to the black ring solution , the rotating black hole solution with @xmath8 horizon topology had been already found by myers and perry @xcite . remarkably , within some range of the parameters , there are one black hole and two black rings with the same values of the mass and the angular momentum , which means the violation of the uniqueness known in four dimensions . subsequently , other black ring solutions were found . the black ring solutions with a rotating two sphere were found by mishima and iguchi @xcite , and moreover , one with two angular momenta was constructed by pomeransky and senkov @xcite by using the inverse scattering method @xcite . for the asymptotically flat , static solutions of higher - dimensional vacuum einstein equations , the schwarzschild - tangherlini solution @xcite is the unique solution @xcite , and moreover , which is stable against linear perturbations @xcite . it has been shown that the five - dimensional myers - perry solution is unique if the topology is restricted to @xmath8 and the spacetime admits three commuting killing vectors @xcite . hence it is natural to ask whether the pomeransky - senkov black ring solution is also unique under the assumptions of the existence of three commuting killing vector field and the horizon topology of @xmath11 . as mentioned above , however , there are two different black ring solutions for the same mass and the same angular momenta . therefore , we must add some additional information to consider the bondary value problem for black ring solutions . one of the examples is the _ rod structure _ introduced by harmark @xcite . by introducing the rod structure , hollands and yazadjiev @xcite applied the discussion of morisawa and ida to the case of non - spherical horizon topology and showed that two asymptotically flat and five - dimensional black hole solutions with the same topology , the same mass , the same angular momenta and the same rod structure are isometric to each other . in this article , we study the boundary value problem for stationary black ring solutions to the five - dimensional vacuum einstein equations . assuming the existence of two additional commuting axial killing vector fields and the horizon topology of @xmath0 , we show that the only asymptotically flat black ring solution with a regular horizon is the pomeransky - senkov black ring solution . our proof consists of two steps : first , we present a more general black ring solution than the pomeransky - senkov black ring solution in the sense that the solution , in general , has a conical singularity and is characterized by independent four parameters , i.e. , the mass , two angular momenta and an additional parameter . by the requirement of the absence of a conical singularity on the solution , it coincides with the pomeransky - senkov black ring solution . second , following the discussion in ref . @xcite , two arbitrary asymptotically flat black ring solutions with the same mass , the same two angular momenta and the same ratio of the radius of @xmath12 to the radius of @xmath13 as the solution are isometric . hence we can conclude that the only asymptotically flat black ring solution without a conical singularity to the five - dimensional vacuum einstein equations is the pomeransky - senkov black ring solution . the remainder of this article is organized as follows : in sec.[sec : solution ] we present general black ring solutions with four parameters . in sec.[sec : boundary ] , we study the rod structure of the solutions . in sec.[sec : mazur ] , we give a short explanation of the mazur identity . in sec.[sec : coincidence ] , using the mazur identity , we show that an arbitrary asymptotically black ring solution with the same mass , the same two angular momenta and the same rod structure as our solution are isometric to it . in sec.[sec : conclusion ] , we state the final results and the theorem .

we study the boundary value problem for asymptotically flat stationary black ring solutions to the five - dimensional vacuum einstein equations . assuming the existence of two additional commuting axial killing vector fields and the horizon topology of , we show that the only asymptotically flat black ring solution with a regular horizon is the pomeransky - senkov black ring solution .

we study the boundary value problem for asymptotically flat stationary black ring solutions to the five - dimensional vacuum einstein equations . assuming the existence of two additional commuting axial killing vector fields and the horizon topology of , we show that the only asymptotically flat black ring solution with a regular horizon is the pomeransky - senkov black ring solution .

1205.2068

i

equilibration can be defined as the evolution of a system out of equilibrium towards a stationary state in the long - time limit . for quantum systems , the question arises how equilibration is possible in spite of the linear and unitary time evolution , how the stationary state depends on the initial conditions , and to which extent it can be described as a thermal state . general arguments relate equilibration to dephasing of quantum states @xcite . starting from the expansion of an initial state @xmath0 in the eigenstates @xmath1 of the hamiltonian @xmath2 , the time evolution of an operator expectation value is given by @xmath3 in the thermodynamic limit we can expect that only diagonal terms @xmath4 survive for @xmath5 , such that the long - time limit of the expectation value is @xmath6 \quad ( n \to \infty ) \;,\ ] ] with the density matrix @xmath7 . this argument can be justified with the riemann - lebesgue lemma @xcite that states @xmath8 for any integrable function @xmath9 ( here : the density of states @xmath10 ) . although this argument explains the origin of equilibration , not much is learned about the properties of the stationary state @xmath11 . especially the question of thermalization is left open . in this paper we study equilibration and thermalization of dissipative quantum harmonic oscillators , using the standard model of a central oscillator coupled to a harmonic oscillator bath . for this example we can determine the stationary state @xmath11 explicitly and analyze its dependence on the initial conditions completely . crucially , we allow for arbitrary non - thermal bath preparations in our study . thermalization is subject to additional conditions in this more general situation , and we show how the temperature of the asymptotic stationary state is obtained from the initial energy distribution of the oscillator bath rather than from the initial bath temperature . we also include the case study of an interaction quench in an infinite harmonic chain , where undamped oscillations can prevent equilibration at strong damping . the dissipative quantum harmonic oscillator is studied extensively in the literature @xcite , covering such diverse topics as brownian motion @xcite , quantum fluctuations @xcite , driven dissipative systems @xcite , entanglement @xcite , the existence of local temperatures @xcite , or the second law of thermodynamics @xcite . reviews are given , e.g. , in @xcite . with an exact solution this model is also an important example for the derivation of master equations @xcite , the discussion of fundamental statistical relations such as fluctuation - dissipation theorems @xcite and their connection to detailed balance and the kubo - martin - schwinger condition @xcite , or for the assessment of numerical methods that provide a perspective for non - linear models @xcite . it appears , however , that the questions addressed here have not been previously analyzed in detail , especially not for non - thermal bath preparations . to obtain our results we proceed as follows . after introduction of the model in sec . [ sec : model ] , we construct the exact solution for non - thermal initial states in sec . [ sec : eom ] , including the propagating function in sec . [ sec : prop ] . further details , including the extension to driven oscillators , are given in app . [ app : deriv ] and app . [ app : prop ] . the central results for equilibration and thermalization are formulated in sec . [ sec : equil ] . we discuss these results for the example of an infinite chain of harmonic oscillators in sec . [ sec : chain ] , before we conclude in sec . [ sec : summary ] .

we study the dissipative quantum harmonic oscillator with general non - thermal preparations of the harmonic oscillator bath . we find a hierarchy of conditions for thermalization , together with the relation of the asymptotic temperature to the energy distribution in the initial bath state . we discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators , and illustrate the general findings about thermalization for the non - thermal environment that results from a quench .

we study the dissipative quantum harmonic oscillator with general non - thermal preparations of the harmonic oscillator bath . the focus is on equilibration of the oscillator in the long - time limit and the additional requirements for thermalization . our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion , which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function . we find a hierarchy of conditions for thermalization , together with the relation of the asymptotic temperature to the energy distribution in the initial bath state . we discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators , and illustrate the general findings about thermalization for the non - thermal environment that results from a quench .

1009.4364

i

the notion of subgroup distortion was first formulated by gromov in @xcite . for a group @xmath7 with finite generating set @xmath8 and a subgroup @xmath9 of @xmath7 finitely generated by @xmath10 , the distortion function of @xmath9 in @xmath7 is @xmath11 where @xmath12 represents the word length with respect to the given generating set @xmath10 , and similarly for @xmath13 . this function measures the difference in the word metrics on @xmath7 and on @xmath9 . as usual , we only study distortion up to a natural equivalence relation . for non - decreasing functions @xmath14 and @xmath15 on @xmath16 , we say that @xmath17 if there exists an integer @xmath18 such that @xmath19 for all @xmath20 . we say two functions are equivalent , written @xmath21 , if @xmath17 and @xmath22 . when considered up to this equivalence , the distortion function becomes independent of the choice of finite generating sets . if the subgroup @xmath9 is infinite then the growth of the distortion function is at least linear , and therefore one does not extend the equivalence classes using the equivalence defined by the inequality @xmath23 a subgroup @xmath9 of @xmath7 is said to be undistorted if @xmath24 . if a subgroup @xmath9 is not undistorted , then it is said to be distorted , and its distortion refers to the equivalence class of @xmath25 . [ poa ] suppose there exists a subsequence of @xmath16 given by @xmath26 where @xmath27 for @xmath28 . if there exists @xmath29 such that @xmath30 , for all @xmath28 , and @xmath31 , then @xmath32 . here we study the effects of distortion in various subgroups of the wreath products @xmath33 , for @xmath34 , and more generally , in @xmath0 where @xmath1 is finitely generated abelian . note that wreath products @xmath35 where @xmath1 is abelian play a very important role in group theory for many reasons . given any semidirect product @xmath36 with abelian normal subgroup @xmath37 then any two homomorphisms from @xmath38 and @xmath39 ( uniquely ) extend to a homomorphism from @xmath35 to @xmath40 also , if @xmath41 is presented as a factor - group @xmath42 of a @xmath43-generated free group @xmath44 then the maximal extension @xmath45 $ ] of @xmath41 with abelian kernel is canonically embedded in @xmath46 ( see @xcite . ) wreath products of abelian groups give an inexhaustible source of examples and counter - examples in group theory . for instance , the group @xmath47 is the simplest example of a finitely generated ( though not finitely presented ) group containing a free abelian group of infinite rank . in @xcite the group @xmath47 is studied in connection with diagram groups and in particular with thompson s group . in the same paper , it is shown that for @xmath48 , where the group @xmath49 appears @xmath50 times , there is a subgroup @xmath51 having distortion function @xmath52 . in contrast to the study of these iterated wreath products , here we obtain polynomial distortion of arbitrary degree in the group @xmath47 itself . in @xcite the distortion of @xmath47 in baumslag s metabelian group is shown to be at least exponential , and an undistorted embedding of @xmath47 in thompson s group is constructed . in this note , rather than embedding the group @xmath47 into larger groups , or studying multiple wreath products , we will study distorted and undistorted subgroups in the wreath products @xmath0 with @xmath1 finitely generated abelian . the main results are as follows . [ x ] let @xmath1 be a finitely generated abelian group . 1 . for any finitely generated infinite subgroup @xmath53 there exists @xmath54 such that the distortion of @xmath9 in @xmath0 is @xmath55 2 . if @xmath1 is finite , then @xmath56 ; that is , all subgroups are undistorted . if @xmath1 is infinite , then for every @xmath54 , there is a @xmath3-generated subnormal subgroup @xmath9 of @xmath0 having distortion function @xmath55 the following will be explained in subsection [ fs ] . [ ot ] for every @xmath54 , there is a @xmath3-generated subgroup @xmath9 of the free @xmath57-generated metabelian group @xmath58 having distortion function @xmath59 [ xx ] if we let the standard generating set for @xmath47 be @xmath60 , then the subgroup @xmath61,b ] , \cdots , b ] \rangle$ ] , where the commutator is @xmath62-fold , is @xmath63 subnormal , isomorphic to the whole group @xmath47 , with distortion @xmath64 . in particular the normal subgroup @xmath65 \rangle$ ] has quadratic distortion . corollary [ xx ] is proved at the end of this paper . because the subgroup @xmath66 , b \rangle$ ] of @xmath47 is normal , it follows by induction that the distorted subgroup @xmath67 is subnormal . [ mmm ] there are distorted embeddings from the group @xmath47 into itself as a normal subgroup . for example , the map defined on generators by @xmath68 $ ] extends to an embedding , and the image is a quadratically distorted subgroup by corollary [ xx ] . by lemma [ t2 ] , @xmath47 is the smallest example of a metabelian group embeddable to itself as a normal subgroup with distortion . [ sc ] there is a distorted embedding of @xmath47 into thompson s group @xmath69 . under the embedding of remark [ mmm ] , @xmath47 embeds into itself as a distorted subgroup . it is proved in @xcite that @xmath47 embeds to @xmath69 . therefore , corollary [ sc ] is true . it is interesting to contrast theorem [ x ] part @xmath70 with the following , which will be discussed in section [ ppq ] . throughout this paper , we use the convention that @xmath71 represents the finite group @xmath72 . [ pqp ] the group @xmath73 for @xmath74 , has a finitely generated subgroup @xmath9 with distortion at least @xmath75 . some of the techniques to be introduced in this paper include some computations with polynomials . we will use the theory of modules over principal ideal domains in section [ mt ] to reduce the problem of subgroup distortion in @xmath33 to the consideration of certain @xmath3-generated subgroups in @xmath47 . every such subgroup is associated with a polynomial , and therefore we need to define and compute the distortion of arbitrary polynomial , as in theorem [ tgs ] . all of these techniques are used in conjunction with theorem [ t6 ] , which provides a formula for computing the word length in arbitrary wreath product and makes computing subgroup distortion more tangible in the examples we consider .

we study the effects of subgroup distortion in the wreath products , where is finitely generated abelian . moreover , for infinite , and for any polynomial , there is a-generated subgroup of having distortion function equivalent to the given polynomial . also a formula for the length of elements in arbitrary wreath product easily shows that the group has distorted subgroups , while the lamplighter group has no distorted ( finitely generated ) subgroups .

we study the effects of subgroup distortion in the wreath products , where is finitely generated abelian . we show that every finitely generated subgroup of has distortion function equivalent to some polynomial . moreover , for infinite , and for any polynomial , there is a-generated subgroup of having distortion function equivalent to the given polynomial . also a formula for the length of elements in arbitrary wreath product easily shows that the group has distorted subgroups , while the lamplighter group has no distorted ( finitely generated ) subgroups .

math0301270

i

a periodic two - dimensional lorentz gas ( sinai billiard ) is a billiard system on the two - dimensional torus with one or more circular regions ( scatterers ) removed . this model in classical mechanics was introduced by lorentz @xcite in 1905 to describe the dynamics of electrons in metals . the associated dynamical system is simple enough to allow a comprehensive study , yet complex enough to exhibit chaos . according to gutzwiller @xcite : `` the original billiard of sinai was designed to imitate , in the most simple - minded manner , a gas of hard spherical balls which bounce around inside a finite enclosure . the formidable technical difficulties of this fundamental problem were boiled down to the shape of a square for the enclosure , and the collisions between the balls were reduced to a single point particle hitting a circular hard wall at the center of the enclosure . '' the model was intensively studied from the point of view of dynamical systems @xcite . our primary goal here is to estimate the _ free - path length _ ( _ first return time _ ) in this periodic two - dimensional model in the small - scatterer limit . we solve the following three open problems : * the existence and computation of the distribution of the free path length , previously considered in @xcite . * the existence and computation of the distribution of the geometric free path length , previously shown , but not fully proved , in @xcite . * the existence and computation of the second ( constant ) term in the asymptotic formula of the ks entropy @xmath2 of the billiard map in this model , previously studied in @xcite . for each @xmath3 let @xmath4 denote by @xmath5 the boundary @xmath6 of @xmath7 , and define the _ free path length _ ( also called _ first exit time _ ) as the borel map given by @xmath8 if @xmath9 is irrational , then @xmath10 for every @xmath11 . we consider the probability space @xmath12 , with @xmath13 and @xmath14 the normalized lebesgue measure on @xmath15 . let @xmath16 denote the characteristic function of @xmath17 . for every @xmath18 the probability that @xmath19 is given by @xmath20 lower and upper bounds for @xmath21 of correct order of magnitude were established by bourgain , golse and wennberg @xcite , using the rational channels introduced by bleher @xcite . more recently , caglioti and golse @xcite have proved the existence of the cesaro @xmath22 and @xmath23 means , proving for large @xmath24 that @xmath25 in sections 2 - 7 below we prove the existence of the limit @xmath26 of @xmath27 as @xmath28 and explicitly compute it . [ t1.1 ] for every @xmath18 and @xmath29 @xmath30 with @xmath31 after a direct computation the above formula for @xmath26 yields @xmath32 and thus for large @xmath24 we find @xmath33 which agrees with . the related homogeneous " problem when the trajectory starts at the origin @xmath34 and the phase space is a subinterval of the velocity range @xmath35 was studied by gologan and the authors . the limit distribution @xmath36 where @xmath37 denotes the lebesgue measure , was shown to exist and explicitly computed in @xcite . unlike @xmath38 , the function @xmath39 is compactly supported on the interval @xmath40 $ ] . interestingly , in the particular situation where the scatterers are vertical segments , this case is related to some old problems in diophantine approximation investigated by erd " os , sz " usz and tur ' an @xcite , friedman and niven @xcite , and by kesten @xcite . the main tools used to prove theorem [ t1.1 ] are a certain three - strip partition of @xmath41 and the weil - sali ' e estimate for kloosterman sums @xcite . the latter is used in infinitesimal form with respect to the parameter @xmath42 to count the number of solutions of equations of form @xmath43 in various regions in @xmath44 . this approach , somehow reminiscent of the circle method , produces good estimates , allowing us to keep under control the error terms . it was developed and used recently in many situations to study problems related to the spacing statistics of farey fractions and lattice points in @xmath44 @xcite . a possible source for getting better estimates for the error terms might come from further cancellations in certain sums of kloosterman sums , of the form @xcite @xmath45 the three - strip partition of @xmath46 is related to the continued fraction decomposition of the slope of the trajectory . following work of blank and krikorian @xcite on the longest orbit of the billiard , caglioti and golse explicitly introduced this partition and used it in conjunction with ergodic properties of the gauss map @xcite to prove . we will use it in section 3 in a suitable setting for our computations . one can also consider the phase space @xmath47 with @xmath48 the inward unit normal at @xmath49 and the probability measure @xmath50 on @xmath51 obtained by normalizing the liouville measure @xmath52 to mass one . consider also the distribution @xmath53 of the _ geometric free path length _ @xmath54 . the first moment ( _ geometric mean free path length _ ) of @xmath55 with respect to @xmath50 can be expressed as @xmath56 equality is a consequence of a more general formula of santal ' o @xcite who extended earlier work of p ' olya on the mean visible distance in a forrest @xcite . the formulation from appears in @xcite . knowledge of the mean free path does not give however any information on other moments or on the limiting distribution of the free path in the small - scatterer limit . our number theoretical analysis leads to the following solution of this limiting distribution problem , proved in sections 8 - 11 below . [ t1.2 ] for every @xmath18 and @xmath29 @xmath57 with @xmath58 , @xmath59 , and respectively @xmath60,title="fig : " ] , @xmath59 , and respectively @xmath60,title="fig : " ] , @xmath59 , and respectively @xmath60,title="fig : " ] we note the equalities @xmath61 and @xmath62 the latter also yields @xmath63 remarkably , formulas and were found by dahlqvist @xcite . that approach however does not provide a rigorous proof for the existence of the limit distribution , because it fails to control in a quantitative way the uniform distribution of his variable @xmath64 ( see the comments after formulas ( 75 ) and ( 86 ) in @xcite ) . in the final section we use some standard analysis arguments and properties of the dilogarithm and trilogarithm to estimate @xmath65 it was conjectured by friedman , kubo and oono @xcite that @xmath66 is convergent as @xmath28 . its hypothetical limit @xmath67 was estimated to be @xmath68 in @xcite and @xmath69 in @xcite . this conjecture was known to imply @xcite the asymptotic formula @xmath70 for the ks entropy of the associated billiard map . in @xcite chernov proved that @xmath66 remains bounded when @xmath28 , without giving however any estimate for the bounds . the constant @xmath67 was identified by dahlqvist ( * ? ? ? * formula ( 73 ) ) as being @xmath71 . the conjecture of friedman , kubo and oono , in the more precise form provided by dahlqvist , follows now from theorem [ t1.2 ] . [ t1.3 ] in the small scatterer limit @xmath28 the following holds : * @xmath72 * @xmath73 these methods work for any convex scatterer due to the good error control they give when integrating over the velocity in very short intervals . to keep the presentation of the paper neat we have chosen to only consider circular scatterers . in dimension @xmath74 the problem of the existence of the limiting distribution of the free - path length in the small - scatterer limit remains open and is manifestly difficult . partial results in this direction have appeared in @xcite .

we study the free path length and the geometric free path length in the model of the periodic two - dimensional lorentz gas ( sinai billiard ) . we give a complete and rigorous proof for the existence of their distributions in the small - scatterer limit and gets a complete proof for the existence of the constant term in the asymptotic formula of the ks entropy of the billiard map in this model , as conjectured by p. dahlqvist .

we study the free path length and the geometric free path length in the model of the periodic two - dimensional lorentz gas ( sinai billiard ) . we give a complete and rigorous proof for the existence of their distributions in the small - scatterer limit and explicitly compute them . as a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the ks entropy of the billiard map in this model , as conjectured by p. dahlqvist .

1206.5861

i

the general analysis of the evolution of material systems interacting with their own gravitational field is undoubtedly a very important and very difficult problem in general relativity . as usual in any physical theory , one can gain insight into the more difficult issues by considering idealized simplified models that , nevertheless , still preserve some of the relevant features of the general problem . one of these simplified examples was described some time ago by apostolatos and thorne @xcite . the material contents in this example is given by a cylindrical shell of counter rotating particles , and one is interested in the dynamics that results as a consequence of its interaction with its own gravitational field . as shown in @xcite , once some appropriate choice of coordinates is made , it is a straightforward matter to obtain a set of coupled equations for the evolution of the matter and field variables , which is described in some detail in the next section . in their original paper apostolatos and thorne were interested in general features of the evolution , in particular the possibility of naked singularities forming as the result of the collapse of these structures , but the detailed evolution of the shell in a situation close to one of its static configuration was only qualitatively mentioned , with no detailed results . this problem is interesting in particular because in the newtonian approximation the shell is either in a static configuration or performs periodic oscillations about this static configuration , but , once the radiative modes of the gravitational field are introduced , one expects these oscillations to be eventually damped as the results of the transfer of energy to the radiative modes . thus , in the fully relativistic description one expects to find the characteristic `` quasi normal ringing '' ( qnr ) , related to the `` quasi normal modes '' ( qnm)@xcite of the system . a recent analysis of the dynamics of the apostolatos and thorne model was given by hamity , et.al . we notice , however , that the approximations introduced in the explicit examples considered in @xcite are such that the radiative modes are effectively neglected , and , therefore , the results obtained are possibly relevant only close to the newtonian limit . a detailed analysis of the full relativistic equations in the linearized approximation was carried out by the present authors in @xcite , where we obtained the general solution for the harmonic modes with real frequencies , and considered the solutions obtained by general linear combinations of these modes . although in all the examples considered in @xcite we found a stable evolution under perturbations of ( essentially ) compact support , at least two questions remained unanswered . the first was the possible completeness of the mode expansion , and its relation to the initial value problem for the system . the second was the apparent lack of qnr in the example solutions . the main purpose of the present work is to give answers to those questions . we first review in sections 2 and 3 , mostly for completeness , the main features of the model . then , in section 4 , we review the derivation of the periodic solutions in the linearized regime , introducing a modified form , as compared with that given in @xcite , that allows us to establish , in section 5 , the completeness of expansion in the context of the characteristic value problem for the system , and , therefore , the completeness of the mode expansion . this completeness , in turn , as discussed in section 6 , implies the linear stability of static configurations under this type of perturbations , a result that differs from some conclusions reached in @xcite , and recent results obtained by kurita and nakao @xcite . next , in section 7 , we discuss the existence of qnms for the system . as shown there , these are related to the zeros of a complex expression that appears in the relation between the incoming and outgoing wave amplitudes as functions of the frequency . this expression has a complicated form involving bessel functions that makes it very difficult its analysis . for this reason we have not been able to obtain explicit expressions for the frequencies of the qnm , or even to ascertain whether there is finite number or infinite number of these frequencies . nevertheless , by resorting to numerical methods we found at least a couple of qnm corresponding to a range of parameters characterizing static configurations . the values obtained are also displayed in section 7 . in section 8 we consider the numerical evaluation of the integrals obtained in section 7 that provide the evolution of the system for arbitrary characteristic data . the examples chosen display clearly the quasi normal ringing associated to one of the qnm . the reason why this qnr was not seen in @xcite is discussed in section 12 , using the price - husain toy model as an illustration . in section 9 we consider again the full relativistic equations and assuming a general linear departure from a static configuration obtain the general linearized equations for the system . then , in section 10 we prove the existence of an associated positive definite constant of the motion that puts absolute bounds on the dynamic variables of the system , establishing the stability of the motion of the shell under arbitrary , finite perturbations . in section 11 we show that the corresponding set of coupled ordinary and partial differential equations for the relevant dynamical variables can be solved numerically as an initial plus boundary values problem , without resorting to expansions in terms of bessel or other functions . we provide a couple of examples , using the same shell parameters as in the mode expansion , but a different form for the incoming wave form . the results , that clearly display quasi normal ringing are in complete agreement with those of the mode expansion , and with the computed qnm frequencies , although the techniques used in both approaches are totally different , confirming their separate correctness . we end the paper with some comments and conclusions , as well as comments on related work by other authors , in particular to that of reference @xcite .

we obtain a proof of the stability of static solutions under this type of perturbations . the explicit expression for the mode expansion are then used to obtain numerical values for some of the quasi normal mode complex frequencies . some examples involving the numerical evaluation of the integral mode expansions are described and analyzed , and the quasi normal ringing displayed by the solutions is found to be in agreement with quasi normal modes found previously . going back to the full relativistic equations of motion we find their general linear form by expanding to first order about a static solution . we then show that the resulting set of coupled ordinary and partial differential equations for the dynamical variables of the system can be used to set an initial plus boundary values problem , and prove that there is an associated positive definite constant of the motion that puts absolute bounds on the dynamic variables of the system , establishing the stability of the motion of the shell under arbitrary , finite perturbations .

we study the perturbative evolution of the static configurations , quasinormal modes and quasi normal ringing in the apostolatos - thorne cylindrical shell model . we consider first an expansion in harmonic modes and show that it provides a complete solution for the characteristic value problem for the finite perturbations of a static configuration . as a consequence of this completeness we obtain a proof of the stability of static solutions under this type of perturbations . the explicit expression for the mode expansion are then used to obtain numerical values for some of the quasi normal mode complex frequencies . some examples involving the numerical evaluation of the integral mode expansions are described and analyzed , and the quasi normal ringing displayed by the solutions is found to be in agreement with quasi normal modes found previously . going back to the full relativistic equations of motion we find their general linear form by expanding to first order about a static solution . we then show that the resulting set of coupled ordinary and partial differential equations for the dynamical variables of the system can be used to set an initial plus boundary values problem , and prove that there is an associated positive definite constant of the motion that puts absolute bounds on the dynamic variables of the system , establishing the stability of the motion of the shell under arbitrary , finite perturbations . we also show that the problem can be solved numerically , and provide some explicit examples that display the complete agreement between the purely numerical evolution and that obtained using the mode expansion , in particular regarding the quasi normal ringing that results in the evolution of the system . we also discuss the relation of the present work to some recent results on the same model that have appeared in the literature .

hep-ph9806541

i

the nonperturbative calculation of the anomalous moment of the electron @xmath0 , besides being of intrinsic interest itself , exposes many important issues for nonperturbative calculations within gauge theories which occur in the context of a truncated fock space . these include nonperturbative mass and coupling renormalization , control of spurious infrared singularities , determination of zero - mode contributions , and the construction of finite counterterms which restore symmetries . each of these has been addressed in the preceding sections , and the first two have been incorporated into a dlcq calculation where as many as two photons are included in the basis . we have presented results for @xmath0 computed in a light - cone - gauge fock space truncated to include one bare electron and at most two photons ; _ i.e. _ , up to two photons in flight . the calculational scheme uses an invariant mass cutoff , discretized light - cone quantization ( dlcq ) , a tamm dancoff truncation of the fock space , and a photon mass regulator . we have utilized new weighting methods which greatly improve convergence to the continuum within dlcq . a large renormalized coupling strength @xmath1 is then used to make the nonperturbative effects in the electron anomalous moment from the one - electron , two - photon fock state sector numerically detectable . results are given in fig . [ fig : results ] . the disagreement between these results and what one would expect from perturbation theory at order @xmath3 indicates that the effect of z graphs needs to be included in a systematic way . this can be done as an effective interaction , to avoid expansion of the fock basis to include pair states . the corresponding piece of the instantaneous fermion interaction , as depicted in fig . [ fig : infraredcancel](c ) , must then also be included to maintain an infrared cancellation . new counterterms : one piece of the infinite renormalization is missing in the calculation . as discussed in section [ sec : fourptgraphs ] , it requires a new nonperturbative counterterm for the logarithmic divergences present in diagrams of the type shown in fig . [ fig : fourpointgraphs](a ) and ( b ) . the divergence arises because the tamm dancoff truncation prevents certain cancellations . construction of the counterterm will likely require analysis of scattering processes . zero modes in dlcq : before full consideration of photon zero modes is undertaken , we recommend renewed study of zero modes in a scalar theory where the constraint equation can be solved exactly@xcite . this may show that , when the invariant mass cutoff ( [ eq : cutoff ] ) is used , zero modes do not make a significant numerical contribution . if instead there is an important contribution , it should be computed only to leading order in the numerical resolution , to be consistent with the level of approximation used in the basic dlcq approach . use of symmetries in dlcq renormalization : the restoration of symmetries should then complete construction of the light - cone hamiltonian . one can normalize to specific physical processes@xcite or take an abstract approach based on the algebra of the poincar generators@xcite . higher fock states : once the two - photon calculation is fully under control , the addition of @xmath220 states can be considered . this will require analysis of photon mass and wave function renormalization . many of the complications of the light - cone fock state analysis presented here can be traced to the complexity of sector - dependent renormalization . given such complications the newly developed alternative of pauli villars regularization@xcite may be the preferred approach . within such a scheme , it is also likely that the limitation to a small number of photons can be relaxed . the analysis presented here is the first step in a systematic program to compute physical quantities in gauge theory systematically utilizing a light - cone fock expansion . it will also be interesting to use these methods and the present knowledge of the dressed - electron state in qed in order to systematically construct the neutral positronium state as a composite of a dressed electron and positron . such an analysis can serve as the prototype for systemic nonperturbative construction of colorless bound state hadrons in qcd . this work was supported in part by the minnesota supercomputer institute through grants of computing time and by the department of energy . we thank g. mccartor , r. perry , st . gazek , d. robertson , and a. kalloniatis for helpful discussions .

we present results for computed in a light - cone gauge fock space truncated to include one bare electron and at most two photons ; i.e. , up to two photons in flight . the calculational scheme uses an invariant mass cutoff , discretized light - cone quantization ( dlcq ) , a tamm dancoff truncation of the fock space , and a photon mass regulator . we introduce new weighting methods which greatly improve convergence to the continuum within dlcq . is then used to make the nonperturbative effects in the electron anomalous moment from the one - electron , two - photon fock state sector numerically detectable .

we study the physical electron in quantum electrodynamics expanded on the light - cone fock space in order to address two problems : ( 1 ) the physics of the electron s anomalous magnetic moment in nonperturbative qed , and ( 2 ) the practical problems of ultraviolet regularization and renormalization in truncated nonperturbative light - cone hamiltonian theory . we present results for computed in a light - cone gauge fock space truncated to include one bare electron and at most two photons ; i.e. , up to two photons in flight . the calculational scheme uses an invariant mass cutoff , discretized light - cone quantization ( dlcq ) , a tamm dancoff truncation of the fock space , and a photon mass regulator . we introduce new weighting methods which greatly improve convergence to the continuum within dlcq . nonperturbative renormalization of the coupling and electron mass are carried out , and a limit on the magnitude of the effective physical coupling strength is computed . a large renormalized coupling strength is then used to make the nonperturbative effects in the electron anomalous moment from the one - electron , two - photon fock state sector numerically detectable .

1103.4868

i

designs for multi - user communications networks and systems have been extensively used during the past decade to implement low - cost , scalable , and limited - message - passing networks . in doing so , transmitter and receiver pairs with local information determine their transmission strategies in an autonomous manner . to deploy such designs , it is essential to know whether they converge to a ( preferably unique ) equilibrium , and evaluate their performances at the emerging equilibrium / equilibria . strategic non - cooperative game theory provides an appropriate framework for analyzing and designing such environments where users ( i.e. , transmitter - receiver pairs ) are rational and self - interested players that aim to maximize their own utilities by choosing their transmission strategies . the notion of nash equilibrium ( ne ) , at which no user can attain a higher utility by unilaterally changing its strategy , is frequently used to analyze the equilibrium point of non - cooperative games . to derive the conditions for ne s existence and uniqueness , different approaches such as fixed point theory , contraction mapping and _ variational inequalities ( vi ) _ @xcite have been widely applied in both wired and wireless communication networks , including applications to flow and congestion control , network routing , and power control in interference channels @xcite . however , there are numerous sources of uncertainty in measured parameter values of communication systems and networks such as joining or leaving new users , delays in the feedback channel , estimation errors and channel variations . therefore , obtaining accurate values of users interactions may not be practical , and considering uncertainty and proposing a robust approach are essential in designing reliable communications systems and networks . to make a ne robust against uncertainties , two distinct approaches have been proposed in the literature : the bayesian approach where the statistics of uncertain parameters are considered and the utility of each user is probabilistically guaranteed , and the worst - case approach where a deterministic closed region , called the uncertainty region , is considered for the distance between the exact and the estimated values of uncertain parameters , and the utility of each user is guaranteed for any realization of uncertainty within the uncertainty region @xcite . both of these approaches have been applied to the power allocation problem in spectrum sharing environments and cognitive radio networks @xcite to study the conditions for ne s existence and uniqueness , where the uncertain parameters are interference levels and channel gains . however , to incorporate robustness in communications systems and networks , there exist multiple challenges such as : 1 ) how to implement robustness in a wider class of problems in communication systems ? 2 ) how to derive the conditions for existence and uniqueness of the robust ne ( rne ) ? 3 ) what is the impact of considering uncertainties on the system s performance at its equilibrium compared to that of the case with no uncertainty ? 4 ) how to design a distributed algorithm for reaching the robust equilibrium ? in this paper , we aim to answer the above questions using the worst - case robust optimization . in doing so , we consider a general class of games where the impact of users on each other is an additive function of their actions , which causes couplings between users . we refer to this class of game as the additively coupled games ( acgs ) . in the acg , we consider that the users observations of such impacts are uncertain due to variations in system parameters and changes in other users strategies . via the worst - case approach , we assume that uncertain observations by each user are bounded in the uncertainty region , and each user aims to maximize its utility for the worst - case condition of error . we refer to an acg that considers uncertainty as a robust acg ( racg ) , and an acg that does not consider uncertainty as the nominal acg ( nacg ) . to study the conditions for existence and uniqueness of the rne , we apply _ vi _ @xcite , and show that with bounded and convex uncertainty , the rne always exists . we also show that the rne is a perturbed solution of _ vi _ , and derive the condition for rne s uniqueness based on the condition for ne s uniqueness . furthermore , we compare the performance of the system at the rne with that at the ne in terms of two measures : 1 ) the difference between the users strategies at the rne and the ne , 2 ) the difference between the social utility at the rne and at the ne . when the rne is unique , we derive the upper bound for the difference between social utilities at the rne and at the ne , and show that the social utility at the rne is always less than that at the ne . however , obtaining these two measures is not straightforward when the ne is not unique . in this case , we demonstrate a condition in which the social utility at a rne is higher than that at the corresponding ne . finally , we apply the proximal response map to propose a distributed algorithm for reaching the rne , and derive the conditions for its convergence . the rest of this paper is organized as follows . in section ii , we summarize the system model of the nacg . in section iii , we introduce the racg and its rne . section iv covers the existence and uniqueness conditions if the rne . in section v , we show that when the utility function is logarithmic , the rne can be obtained via affine _ vi _ ( _ avi _ ) , and its uniqueness condition is simplified . in section vi , we propose distributed algorithm for reaching rne . in section vii , we discuss the effects of robustness for the case of multiple nash equilibria , followed by section viii , where we provide simulation results to illustrate our analytical developments for the power allocation problem and for the jackson networks . finally , conclusions are drawn in section ix .

the existence and uniqueness conditions of rne are derived using finite - dimensions variational inequalities . to describe the effect of uncertainty on the performance of the system , we use two criteria measured at the rne and at the equilibrium of the game without uncertainty . the first is the difference between the respective social utility of users and , the second is the differences between the strategies of users at their respective equilibria . these differences are obtained for the case of a unique ne and multiple nes . to reach the rne , we propose a distributed algorithm based on the proximal response map and derive the conditions for its convergence . resource allocation , robust game theory , variational inequality , worst - case robust optimization .

we study the robust nash equilibrium ( rne ) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies . each user measures this impact , which may be corrupted by uncertainty in feedback delays , estimation errors , movements of users , etc . to study the outcome of the game in which such uncertainties are encountered , we utilize the worst - case robust optimization theory . the existence and uniqueness conditions of rne are derived using finite - dimensions variational inequalities . to describe the effect of uncertainty on the performance of the system , we use two criteria measured at the rne and at the equilibrium of the game without uncertainty . the first is the difference between the respective social utility of users and , the second is the differences between the strategies of users at their respective equilibria . these differences are obtained for the case of a unique ne and multiple nes . to reach the rne , we propose a distributed algorithm based on the proximal response map and derive the conditions for its convergence . simulations of the power control game in interference channels , and jackson networks validate our analysis . resource allocation , robust game theory , variational inequality , worst - case robust optimization .

1103.4868

c

we studied the rne for a wide range of problems in communication systems and networks when users impact on each other can be modeled as an additive function of system parameters and users strategies . in this game , since the user s observations of these impacts are uncertain , each user optimizes its utility using worst - case robust optimization . we showed that the theory of finite - dimension _ vi _ and its sensitivity analysis can be used to obtain the conditions for the existence and uniqueness of the rne when there is no closed - form solution to the optimization problem of each entity . we also proposed a distributed algorithm for reaching the rne . in the case of multiple nes , simulations showed that at a rne , the social utility may be higher than that at the ne , and we derived the conditions for observing such a case . to benefit from this , we proposed a distributed algorithm to improve the social utility at the rne . simulations confirmed our analysis for two examples , namely , the power control in interference channels , and delay minimization in jackson networks .

we study the robust nash equilibrium ( rne ) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies . simulations of the power control game in interference channels , and jackson networks validate our analysis .

we study the robust nash equilibrium ( rne ) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies . each user measures this impact , which may be corrupted by uncertainty in feedback delays , estimation errors , movements of users , etc . to study the outcome of the game in which such uncertainties are encountered , we utilize the worst - case robust optimization theory . the existence and uniqueness conditions of rne are derived using finite - dimensions variational inequalities . to describe the effect of uncertainty on the performance of the system , we use two criteria measured at the rne and at the equilibrium of the game without uncertainty . the first is the difference between the respective social utility of users and , the second is the differences between the strategies of users at their respective equilibria . these differences are obtained for the case of a unique ne and multiple nes . to reach the rne , we propose a distributed algorithm based on the proximal response map and derive the conditions for its convergence . simulations of the power control game in interference channels , and jackson networks validate our analysis . resource allocation , robust game theory , variational inequality , worst - case robust optimization .

cond-mat0606740

r

the main goal of our experiment is the verification of the numerical simulation results of shifting and broadening of spectral lines caused by inhomogeneities and the possibility of resonator spectrum `` rarefaction '' . the another goal is as follows . in the paper [ 3 ] we detected strong spectrum stochastization caused by inhomogeneities such as anisotropic sapphire particles with the dimensions of order of operating wavelength placed into the cavity resonator . the spectrum has mixed state due to both regular and chaotic spectrum part exist . in contrast to [ 3 ] , in the present paper we study the influence on the resonator spectrum relatively small isotropic inhomogeneities . such inhomogeneities can be made by styrofoam particles with the average value of the permittivity closed to one and with small dielectric loss angle . thus , there is a question : is it possible the spectrum chaotization here ? the study of the influence of inhomogeneities on the cavity resonator spectrum we carried out at frequency range of 32 - 37 ghz . we took a quasi - optical cylinder millimeter wave resonator random filled with styrofoam particles ( fig.4 ) . the styrofoam particles have the real part of permittivity is about one , close to the open - air permittivity and small dielectric loss , @xmath135 . the quasi - optical cylinder cavity millimeter wave resonator filled with inhomogeneities , 1,6 are input / output waveguides , 2,5 are holes coupling with waveguides , 3 is the resonator body , 4 is styrofoam particles , @xmath136 is the resonator diameter , @xmath2 is its hight ; @xmath137 mm , @xmath138 mm . , width=307 ] to study the influence of small dielectric particles on the resonator spectrum it is necessary to provide high quality factor for the resonator oscillations without inhomogeneities . for that we excited @xmath4 mode . the magnetic field vector of this mode is directed along the resonator z - axis , and microwave currents do not cross the interface between the flat resonator face and cylinder surface . owing to that the empty resonator has high quality factor up to @xmath139 . to excite the selected mode we used a waveguide diffraction antenna . it is the circular hole with the diameter of 2 mm in a thin diaphragm with the thickness of 0.1 mm closing the input waveguide . the diaphragm surface is flush - mounted with the side - cut cylinder surface of the resonator . the same antenna is used to receive the oscillations on the opposite side of the cylinder surface . the resonator spectrum was detected using `` on pass '' regime in 32 - 37 ghz wave range by the wide frequency standing wave ratio meter . measurement process was automated . signal from the measurement device using analog - digital conversion goes into computer . the further signal processing ( the determination of the spectral line intensity , its quality factor , and frequency ) was done by special software gui application . it gives resource in a short space of time to handle measurement data for a huge number of realizations of the random inhomogeneities distribution in the resonator . owing to that the frequency and quality factor measurement accuracy for spectral lines do not exceed 0.1% and 1% , respectively . the styrofoam particles that are used as inhomogeneities have the size about of 2 - 3 mm . the space distribution of them was arbitrary for each realization . the spectral characteristics were measured depending on the number of these inhomogeneities . the spectrum of the empty resonator is dense enough and consists of 84 narrow spectral lines in the range of 32 - 37 ghz ( fig.5 ) . each line was identified according to mode indexes of corresponding to its eigen resonator oscillation . we found out the oscillations with high quality factor ( @xmath125 ) of order of @xmath140 and higher have small azimuth indexes ( @xmath141 ) and high radial indexes ( @xmath142 ) . for the base oscillation mode ( @xmath143 ) that has the field distribution concentrated inside of the resonator side - cut ( whispering - gallery oscillations [ 5 ] ) , @xmath125 is about @xmath144 . the spectrum of the resonator with inhomogeneities is essentially different from the spectrum of the empty one . by the increase of the number of inhomogeneities spectral lines are getting wider , and @xmath125 is getting smaller . the intensity of broadening lines is decreased as well . the spectrum keeps only few lines with enough high intercity and @xmath125 value . for such lines the @xmath125 value is close to the @xmath125-factor of the spectral lines in the empty resonator . so , the number of spectral lines with enough high intensity and with @xmath145 is 52 in the empty resonator ( fig.5a ) , at filling the resonator by styrofoam particles the number of such lines is 10 ( fig.5b ) , and at filling the resonator by pressed styrofoam particles the number of lines is 3 ( fig.5c ) . the spectrum of the empty resonator ( 84 spectral lines ) ( a ) ; the resonator filled with styrofoam particles ( 77 spectral lines ) ( b ) ; the resonator filled with pressed styrofoam particles ( 57 spectral lines ) ( c ) ; the normalization of amplitude was made on the maximal amplitude value for the empty resonator.,width=307 ] the presence in the resonator with inhomogeneities together with broadening lines few high @xmath125 spectral lines is equivalent to the spectrum `` rarefaction '' ( fig.5 ) . it is necessary to note that the presence of lines with high @xmath125 indicates that the broadening is specified , mainly , by the inhomogeneous of the resonator filling permittivity and is not specified by additional dissipation loss caused by small dielectric loss in the styrofoam . except broadening of spectral lines they have frequency shifting . this frequency shifting has both regular component and random one as well ( fig.6 ) . the dependence of the frequency shifting @xmath146 on frequency @xmath129 for the resonator filled by inhomogeneities . the dotted line is the value of shifting regular component.,width=307 ] the regular shifting happens towards the low frequency direction because of the increase of average dielectric permittivity of inhomogeneous medium in the resonator . for example , it is 150 mgz for the resonator fully filled with styrofoam particles . it is significant that if the distance between resonances is enough small they can both come close and depart from each other because of influence of inhomogeneities . their @xmath125 is essentially changed ( fig.7,8 ) : it can increase for one of them and decrease for another . the relative @xmath125-factor deviation @xmath147 depends upon frequency @xmath129 for the resonator filled by inhomogeneities . for major part of resonances the relative @xmath125-factor deviation is more than zero , i.e. , their @xmath125 is less than for the empty resonator . the relative @xmath125-factor deviation is less than zero for several nearest adjacent resonances that have overlapped spectral lines ( in the case of the empty resonator ) and split into separate resonances at the presence of inhomogeneities , i.e. , the spectral line repulsion takes place here ( see fig.8 ) . , width=307 ] the adjacent resonances with indexes @xmath148 in the empty resonator ( a ) and in the resonator filled by inhomogeneities ( b ) . the normalization of the spectral lines amplitude was made on the maximal spectral line amplitude for the empty resonator . , width=307 ] both the spectral lines broadening and their shifting have quality agreement with described above theory and can be interpreted in the terms of intermode scattering . the maximal broadening is for the adjacent lines that is agreed with theory . we can give the following physical explanation of spectral lines broadening caused by random inhomogeneities based on quantum mechanics interpretation of resonator oscillations . in empty resonator the lifetime of a resonant mode in a given state ( describing by an eigen resonant frequency ) and its spectral line width define by dissipation loss in the resonator body . the uncertainty of mode energy within the spectral line width is caused by this loss . the intermode interaction appears at inserting inhomogeneities into the resonator . owing to that the uncertainty of mode energy and , correspondingly , the spectral line width increase due to the mode transition between nearest states . the mode energy loss due to dissipation loss in the resonator body and transition to the neighboring state are additive to the spectral line width . if the number of inhomogeneities increases the spectrum of the quasi - optical resonator possesses stochastic character that is visualized in distribution of if intervals . in order to define the relation between regular and random spectral components the comparison of if intervals distribution obtained experimentally with different theoretical distributions based on a priori data about statistical process is usually used . in particular , we use the brody function determined the distribution of if intervals probability @xmath149 that is given by @xmath150 where @xmath151 , @xmath152 is the spectral line frequency , @xmath153 is the spectral density - the superposition of regular and random motion density , @xmath154 is the measure of stochastic motion , constants @xmath155 and @xmath156 are defined from the condition of standardization : @xmath157 , @xmath158 , @xmath159 is the gamma function . at @xmath160 if intervals in the spectrum are not correlated and can be described by the poisson distribution , and at @xmath161 we have wigner distribution , when the repulsion effect of spectral lines exists , that is the probability of closest to zero inter - frequency interval is equal zero as well . if stochastization measure in the spectrum is relatively small and the distribution of if intervals is close to the poisson one we can use berry - robnik distribution @xmath162 [ 26 ] that is given by @xmath163\left ( { 1 - \rho } \right)e^ { - \rho s - \frac{\pi } { 4}\left ( { 1 - \rho } \right)^2 s^2 } \\ \end{array}\ ] ] where @xmath164 . @xmath165 is relative phase volume occupied with regular trajectory in mixed systems . the limit @xmath166 corresponds to regular system ; @xmath167 is completely chaotic system . @xmath168 is relative phase volume occupied with chaotic motion . the experimental data show that in the empty resonator the if intervals distribution is close enough to the berry - robnik distribution with @xmath165 ( poisson distribution , @xmath169)(fig.9a ) . by increase of the number of inhomogeneities ( styrofoam particles ) the function @xmath170 is reduced and it has maximum at small @xmath171 . the presence of the maximum @xmath170 indicates the appearance of the repulsion effect of spectral lines , and the random component is increased . we found out that at full filling the resonator by styrofoam particles @xmath172 ( fig.9b ) . the distribution of if intervals , @xmath170 . figure 9a is for the empty resonator spectrum . solid line is for the berry - robnik distribution at @xmath173 or the brody distribution at @xmath160 . figure 9b is for the spectrum of the resonator fully filled with styrofoam particles . the curve 1 is for brody distribution at @xmath174 ; the curve 2 is for berry - robnik distribution at @xmath172 ; the curve 3 is for podolskiy - narimanov distribution at @xmath172 and @xmath175 [ 27].,title="fig:",width=307 ] the distribution of if intervals , @xmath170 . figure 9a is for the empty resonator spectrum . solid line is for the berry - robnik distribution at @xmath173 or the brody distribution at @xmath160 . figure 9b is for the spectrum of the resonator fully filled with styrofoam particles . the curve 1 is for brody distribution at @xmath174 ; the curve 2 is for berry - robnik distribution at @xmath172 ; the curve 3 is for podolskiy - narimanov distribution at @xmath172 and @xmath175 [ 27].,title="fig:",width=307 ] as we can see in fig.9 the function @xmath176 has maximum at small @xmath171 that is not described by the berry - robnik dependence [ 26 ] . the presence of such a maximum can be explained by chaos - assisted tunneling ( cat ) [ 27 ] in the resonator with random inhomogeneities . the proposed in [ 27 ] if distribution function gives the possibility to describe the observed distribution at the parameter @xmath172 corresponding to the classical dynamics in the system and the parameter @xmath175 describing the tunneling between different states of modes . we calculated the spectral rigidity for the resonator with inhomogeneities . the spectral rigidity @xmath177 is an integral characteristic of degree of spectral lines ordering for frequency distances that is much more than inter - frequency interval . it is given by [ 15 ] @xmath178 ^ 2 d\varepsilon } \ ] ] where @xmath179 is the interval length on which the function @xmath180 is determined . the function @xmath181 is built as follows [ 15 ] . for the sequence of the frequencies @xmath182 normalized on unit density ( @xmath183 ) , we introduce a staircase function @xmath184 equals the number of frequencies with @xmath185 . the function @xmath184 has a staircase view with average unit tilt . the function @xmath186 is determined as the minimum of quadratic deviation @xmath184 in the interval @xmath187 from the straight line . the meaning of the averaged in @xmath188 spectral rigidity ( eq.(34 ) ) @xmath189 depends only on @xmath179 and is denoted as @xmath190 . the obtained curve @xmath191 for the resonator with random inhomogeneities is shown in fig.10 . this curve ( 2 ) is placed between the spectral rigidity for the poisson distribution ( curve 1 , @xmath192 ) ) and curve 3 that is corresponded to the spectral rigidity for gauss orthogonal ensemble ( goa ) @xmath193 [ 15 ] . the latter is observed at the modeling of quantum chaos in microwave cavity unstable resonators similar to sinai and bunimovich billiards [ 14 ] . the spectral rigidity for the resonator filled with styrofoam particles ( curve 2 ) . the straight line is for the spectral rigidity of poisson distribution ( curve 1 ) , curve 3 is for goa.,width=307 ]

the solitary spectral lines which have the distance to the nearest lines quite large is slightly changed due to small inhomogeneities . owing to such selective influence of inhomogeneities on the spectral lines the effective spectrum rarefaction appears . both the shift and broadening of spectral lines as well as spectrum rarefaction in quasi - optical cavity millimeter wave resonator were detected experimentally .

we suggest the statistical spectral theory of oscillations in quasi - optical cavity resonator filled with random inhomogeneities . it is shown that inhomogeneities in the resonator result in intermode scattering leading to the shift and broadening of spectral lines . the shift and broadening of each line essentially depends on frequency distance to adjacent spectral lines . with increasing the distance the influence of inhomogeneities sharply reduces . the solitary spectral lines which have the distance to the nearest lines quite large is slightly changed due to small inhomogeneities . owing to such selective influence of inhomogeneities on the spectral lines the effective spectrum rarefaction appears . both the shift and broadening of spectral lines as well as spectrum rarefaction in quasi - optical cavity millimeter wave resonator were detected experimentally . we found out that inhomogeneities result in stochastization of the resonator spectrum in that mixed state appears , i.e. the spectrum acquires both regular and random parts . the active self - oscillator system based on the inhomogeneous quasi - optical cavity millimeter wave resonator with gunn diode was studied as well . the inhomogeneous quasi - optical cavity millimeter wave resonator ( passive and active ) can serve as a model of semiconductor quantum billiard . based on our results we suggest using such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser .

cond-mat0606740

c

the statistical spectral theory of quasi - optical cavity resonator filled with random dielectric inhomogeneities was developed in the present paper . we showed that the presence of inhomogeneities leads to the broadening and shifting of spectral lines . it is found out that the nature of broadening and shifting of spectral lines is relevant to the intermode scattering . the scattering effect for the given spectral line essentially depends on frequency distance between of it and adjacent ones and is sharply decreased for bigger distances . under the influence of ransom inhomogeneities original spectrum modification occurs that can be interpreted as spectrum rarefaction . the spectrum is rarefied because of solitary spectral lines are not practically subjected to the influence of inhomogeneities . the quality factor of such lines and , correspondingly , their intensity stay high at the resonator excitation . the intensity of adjacent lines broadened under the influence of inhomogeneities is essentially reduced . owing to that at the great number of inhomogeneities the resonator spectrum is `` rarefied '' - few solitary high quality factor spectral lines prevail in the spectrum . theoretical prediction of broadening and shifting of resonator spectral lines and spectrum `` rarefaction '' are subject to experimental check . for that purpose we studied experimentally in 8-millimeter wave range the spectrum of the quasi - optical cavity resonator filled with random small - scattered bulk inhomogeneities . these inhomogeneities were styrofoam particles with smaller size than operating wavelength . it is found out that such inhomogeneities lead to broadening and shifting the spectral lines . as experiment showed the maximum of their influence was on frequency adjacent spectral lines . the solitary lines , according to our theory , were subjected to this influence in much smaller degree . we detected the effect of stochastic spectrum `` rarefaction '' . they prove that the main mechanism of broadening and shifting of spectral lines is relevant to inhomogeneities intermode scattering . we studied also chaotic properties of oscillations in our resonator . it is found out that the empty resonator has if intervals distribution similar to poisson distribution that is typical to the spectrum with non - correlated if intervals . even at small number of inhomogeneities the resonator spectrum has random part that increases in proportion to the number of inhomogeneities in the resonator . at that if intervals distribution in random inhomogeneous resonator is described by brody and berry - robnik distributions of if intervals . we obtained the results concerning the influence of bulk inhomogeneities on the process of generation in a self - oscillatory system . the self - oscillatory system was a quasi - optical millimeter wave cavity resonator containing inhomogeneities with an active element as gunn diode . we detected that inhomogeneities leads to the essential `` rarefaction '' of the spectrum and creates conditions for monochromatic stable generation in self - oscillatory system . the inhomogeneous quasi - optical cavity millimeter wave resonator ( passive and active ) can serve as a model of semiconductor quantum billiard . based on our results we suggest using such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser . 99 s.m . rytov , ya.a . kravtsov , and v.i . tatarskii , _ principles of statistical radiophysics _ ( springer verlag , v.4 . berlin , 1987 ) . f.g.bass , i.m.fuks , _ wave scattering from statistically rough surfaces _ ( pergamon press , n.y . , 1979 ) . ganapolski , z.e . eremenko , phys . e , * 65 * , 056218 ( 2002 ) . braginskii , v.p . mitrofanov , and v.i . panov , _ systems with low dissipations _ ( nauka , moscow , 1981 ) . a.n.oraevskii , m.scally , and v.l . velichanskii , quantum electronics , * 25 * , 211 ( 1998 ) . b.e.little , j - p . laine , s.chu , optics letters , * 22 * , 4 ( 1997 ) . l. goldstein , f. glass , j.y . marzin , m.n . charasse , and g.le . roux , appl . * 47 * , 1099 ( 1985 ) . p.m.petroff , s.p . den baars , superlat . , * 15 * , 15 ( 1994 ) . m. moison , f. houzay , f. barthe , l. leprince , e.andre , o. vatel , appl . lett . , * 64 * , 196 ( 1994 ) . zh.i . alferov et al , fizika i tekhnika poluprovodnikov [ soviet physics semiconductors ] , * 30 * , 351 ( 1996 ) . i. alferov et al , fizika i tekhnika poluprovodnikov [ soviet physics semiconductors ] , * 30 * , 357 ( 1996 ) . m. schernjakov et al , pisma v zhurnal tekhnicheskoi fiziki [ soviet technical physics letters ] , * 23 * , 51 ( 1997 ) . beljavskii , s.v.shevtsov , fizika i tekhnika poluprovodnikov [ soviet physics semiconductors ] , * 36 * , 874 ( 2002 ) . stockmann , _ quantum chaos an introduction _ ( cambridge university press , 1999 ) . elutin , uspekhi fizicheskikh nauk [ soviet physics uspekhi ] , * 155 * , 397 ( 1988 ) . h. alt , h. d.graf , r. hofferbert et al . e , * 54 * , 2303 ( 1996 ) . e.m.ganapolskii , z.e.eremenko , dopovidi akademii nauk ukrayiny [ ukraniain physics doklady ] , no.12 , 93 ( 2000 ) . tarasov , waves in random media , * 10 * , 395 ( 2000 ) . tarasov , low temp . phys . , * 29 * , 45 ( 2003 ) . vainstein , _ electromagnetic waves _ ( radio i svjaz , moscow , 1988 ) . yu.v . tarasov , phys . b , * 71 * , 125112 ( 2005 ) . yu.v . tarasov , phys . b , * 73 * , 014202 ( 2006 ) . r. newton . _ scattering theory of waves and particles _ ( mcgraw - hill , new - york , 1968 ) . lifshitz , s.a . gredeskul , l.a . pastur , _ intriduction in theory of disordered systems _ ( nauka , moscow , 1982 ) . gradshtein , i.m . ryzhik , _ tables of integrals , sums , series and products _ ( nauka , moscow , 1971 ) . m.v . berry , m. robnik , j. phys . , * a17 * , 2413 ( 1984 ) . podolskiy , e.e . narimanov , phys . lett . , * 91 * , 263601 ( 2003 ) ; v.podolskiy , e.narimanov , arxiv : nlin.cd/0310034 . tzarapkin , _ microwave gann oscillators _ ( radio i svjaz , moscow , 1982 ) .

we suggest the statistical spectral theory of oscillations in quasi - optical cavity resonator filled with random inhomogeneities . the inhomogeneous quasi - optical cavity millimeter wave resonator ( passive and active ) can serve as a model of semiconductor quantum billiard . based on our results we suggest using such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser .

we suggest the statistical spectral theory of oscillations in quasi - optical cavity resonator filled with random inhomogeneities . it is shown that inhomogeneities in the resonator result in intermode scattering leading to the shift and broadening of spectral lines . the shift and broadening of each line essentially depends on frequency distance to adjacent spectral lines . with increasing the distance the influence of inhomogeneities sharply reduces . the solitary spectral lines which have the distance to the nearest lines quite large is slightly changed due to small inhomogeneities . owing to such selective influence of inhomogeneities on the spectral lines the effective spectrum rarefaction appears . both the shift and broadening of spectral lines as well as spectrum rarefaction in quasi - optical cavity millimeter wave resonator were detected experimentally . we found out that inhomogeneities result in stochastization of the resonator spectrum in that mixed state appears , i.e. the spectrum acquires both regular and random parts . the active self - oscillator system based on the inhomogeneous quasi - optical cavity millimeter wave resonator with gunn diode was studied as well . the inhomogeneous quasi - optical cavity millimeter wave resonator ( passive and active ) can serve as a model of semiconductor quantum billiard . based on our results we suggest using such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser .

1006.0590

i

the decision problem of whether a graph has a hamilton cycle is np - complete and so a satisfactory characterization of hamiltonian graphs seems unlikely . thus it makes sense to ask for degree conditions which ensure that a graph has a hamilton cycle . one such result is dirac s theorem @xcite , which states that every graph on @xmath0 vertices with minimum degree at least @xmath1 contains a hamilton cycle . this is strengthened by ore s theorem @xcite : if @xmath2 is a graph with @xmath0 vertices such that every pair @xmath3 of non - adjacent vertices satisfies @xmath4 , then @xmath2 has a hamilton cycle . dirac s theorem can also be strengthened considerably by allowing many of the vertices to have small degree : psa s theorem @xcite states that a graph on @xmath5 vertices has a hamilton cycle if its degree sequence @xmath6 satisfies @xmath7 for all @xmath8 and if additionally @xmath9 when @xmath10 is odd . again , this is best possible none of the degree conditions can be relaxed . chvtal s theorem @xcite is a further generalization . it characterizes all those degree sequences which ensure the existence of a hamilton cycle in a graph : suppose that the degrees of the graph @xmath2 are @xmath11 . if @xmath12 and @xmath7 or @xmath13 for all @xmath14 then @xmath2 is hamiltonian . this condition on the degree sequence is best possible in the sense that for any degree sequence @xmath11 violating this condition there is a corresponding graph with no hamilton cycle whose degree sequence dominates @xmath15 . these four results are among the most general and well - known hamiltonicity conditions . there are many more often involving additional structural conditions like planarity . the survey @xcite gives an extensive overview ( which concentrates on undirected graphs ) . in this survey , we concentrate on recent progress for directed graphs . though the problems are equally natural for directed graphs , it is usually much more difficult to obtain satisfactory results . additional results beyond those discussed here can be found in the corresponding chapter of the monograph @xcite . in section [ digraph ] , we discuss digraph analogues and generalizations of the above four results . the next section is devoted to oriented graphs these are obtained from undirected graphs by orienting the edges ( and thus are digraphs without @xmath16-cycles ) . section [ tournament ] is concerned with tournaments . section [ general ] is devoted to several generalizations of the notion of a hamilton cycle , e.g. pancyclicity and @xmath17-ordered hamilton cycles . the final section is devoted to the concept of ` robust expansion ' . this has been useful in proving many of the recent results discussed in this survey . we will give a brief sketch of how it can be used . in this paper , we also use this notion ( and several results from this survey ) to obtain a new result ( theorem [ cover ] ) which gives further support to kelly s conjecture on hamilton decompositions of regular tournaments . in a similar vein , we use a result of @xcite to deduce that the edges of every sufficiently dense regular ( undirected ) graph can be covered by hamilton cycles which are almost edge - disjoint ( theorem [ regularii ] ) .

we also combine some of these to prove the following approximate result towards kelly s conjecture on hamilton decompositions of regular tournaments : the edges of every regular tournament can be covered by a set of hamilton cycles which are ` almost ' edge - disjoint . new and old open problems are discussed . # 1 # 1

we survey some recent results on long - standing conjectures regarding hamilton cycles in directed graphs , oriented graphs and tournaments . we also combine some of these to prove the following approximate result towards kelly s conjecture on hamilton decompositions of regular tournaments : the edges of every regular tournament can be covered by a set of hamilton cycles which are ` almost ' edge - disjoint . we also highlight the role that the notion of ` robust expansion ' plays in several of the proofs . new and old open problems are discussed . # 1 # 1

1007.3510

i

we have used rc stars to trace the long tidal tail of the sgr dsph galaxy in the portion of the northern sky sampled by the sdss - dr6 . structures along the line - of - sight are identified as peaks in the ( otherwise smoothly increasing ) @xmath36- and @xmath37-band scps of color - selected samples of candidate rc stars , from @xmath146 fields covering the whole extension of the two main branches ( a and b ) of the sgr stream identified by @xcite in the same dataset . any other part of the stream in addition to these branches is expected to lie ( approximately ) in the same plane , i.e. it should be visible in the considered fields . the analysis was focused on obtaining the most accurate and reliable distances to all the wraps of the stream that we were able to detect . many significant peaks were consistently found in both the scps of several fields . the observed scps were modeled as a series of gauss curves ( one for each peak ) superposed to a polynomial accounting for the smooth fore / background population . for each significant peak we derived a purely differential estimate of its distance ( with uncertainties @xmath147 10% ) , an estimate of the fwhm along the _ los _ , and an estimate of the associated density of rc stars attributable to the considered structure . all the derived quantities are provided in tab . [ tab_dmag ] as powerful constraints for the new generations of models of the disruption of the progenitor of sgr dsph within the milky way halo . to illustrate the potential of our measures in that context we compared them with the three models made publicly available by l05 . these provide a realistic realization of the present epoch configuration of particles that were originally bound to a progenitor similar to sgr that was evolved for @xmath148 orbital periods within a static galactic potential with different degrees of flattening ( a spherical , oblate and prolate halo , respectively ) . the models ( and in particular the prolate halo one , that matches well most of our observations ) are also used as guidelines for the interpretation of our results . the great complexity of a structure like the sgr stream , multiply - wrapped around the galaxy , requires a process of convergence between models and observations : the latter must constrain models but the former are indispensable to re - conduce such a complexity to a single structure ( see sect . [ tri ] ) . our technique resulted in higher - accuracy distance estimates with respect to previous studies , and demonstrated high sensitivity to feeble structures . however , the sensitivity is easily destroyed by contamination from galactic sources : for these reasons we had to limit our survey to @xmath149 , while other ( more abundant ) tracers are able to follow the stream down to @xmath150 . the overall agreement with previous analyses is good ( see sect . [ comp ] ) . finally , and most importantly , our method proved especially efficient in the detection of ( relatively ) nearby structures . in the following we summarize and briefly discuss the main conclusions of the present study , taking fig . [ ldist ] and fig . [ xy_pro ] , as references . * for @xmath151 ( @xmath152 kpc ) the leading arm of the stream is cleanly and coherently detected in both branches , going from @xmath153 kpc at @xmath5 to @xmath154 kpc at @xmath155 . this is in full agreement with the results obtained with other tracers @xcite . this portion of the leading arm is the most unambiguous and robustly constrained . * in the same range of @xmath13 ( and @xmath86 ) a remarkably coherent structure is also very clearly detected at nearly constant distance from us , @xmath8 kpc . according to the s and p models by l05 this can be interpreted as a wrap of the trailing arm , while it has no obvious counterpart in the recently presented t model @xcite . the p model matches the observed structure very well . previous detections of this wrap were reported only around @xmath156 ( see * ? ? ? * for discussion and references ) . * the comparison with the l05 models strongly suggest that the run of the relative distance as a function of @xmath13 of the two wraps described above has a strong power in discriminating between different models of the stream . in particular the s and o models by l05 clearly fail to reproduce the observed trends . on the other hand the p model reproduces the trend nearly perfectly . * weak detections of a further , more distant wrap ( running parallel to the leading arm , in the same range of @xmath13 as above ) were also obtained . these support similar results by @xcite . an enhancement of the density of this wrap at @xmath157 , predicted by the s , p and t models , seems to be excluded by the present analysis ( in agreement with bel06 ) . * turning to the @xmath9 ( @xmath158 kpc ) portion of the survey , this is characterized by a very complex structure , partly due to the crossing of multiple wraps predicted to occur in this region by all the models . hence the interpretation of these structures is less straightforward , and must be considered as tentative . however , the p model appears to provide a reasonable match to all the detections in this region : for these reasons we adopt it as a guideline for our best - effort interpretation of the data ( see sect . [ tri ] for an alternative view ) . * the leading arm seems to be traced beyond @xmath155 , continuing its trend of linear decrease of its distance down to @xmath159 kpc at @xmath10 . extrapolating from the observed trend one would expect the arm to cross the galactic disk at @xmath122 kpc from the sun , in agreement with the conclusions by @xcite . the degree of coherence of the detections in this portion of the leading arm is lower , suggesting the possible presence of further ( unresolved ) substructure or due to higher uncertainties associated to weaker and overlapped structures . * in the same region , the continuation of the trailing arm is coherently traced where predicted by the p model up to @xmath160 ( @xmath161 kpc ) . for @xmath162 , in particular , we lack any detection corresponding to the well defined structure predicted by the model ( the same is true for the t model ) . on the other hand , coherent detections are obtained _ behind _ the main wrap of the trailing arm as predicted by the p model for @xmath163 . these detections may indicate a different shape for that portion of the trailing arm . however , as discussed above , they match two more feeble structures running parallel to the main arm . it is obvious that the p model is not adequate to fit all our observations , in spite of the good overall match . * the most nearby detections are the more difficult to interpret robustly . however the single primary detection at @xmath62 kpc and @xmath164 ( just beyond the @xmath165 kpc `` zone of avoidance '' of our technique ) matches the prediction of all the three l05 models , as well as for the model by @xcite . for this reason we are quite confident to have detected for the first time the nearest wrap of the leading arm . we are currently following up this finding , to check if the predicted @xmath166 kpc wrap can be detected also in other _ * the three detections at @xmath167 kpc and @xmath168 are matched by a spur of the p model . the two detections at @xmath169 kpc and @xmath170 have been tentatively ascribed to the s297 + 63 - 20.5/vss overdensity . the t model matches very well _ all _ of these detections with a single narrow wrap of the sgr trailing arm . however @xcite confirm that the kinematics predicted by their model toward vss is markedly different from what observed by @xcite and @xcite . * the overall trends of fwhm along the _ los _ as a function of @xmath13 of the p model provide a reasonable match to our primary detections of the leading arm . it is especially interesting to note that the model reproduces the different trends encountered in the two branches , even if it does not produce the observed bifurcation . this seems to provide further support to the view ( adopted by * ? ? ? * ; * ? ? ? * ) that branch a and branch b are substructures within the same wrap of the stream , and not different wraps as proposed by @xcite . however , a limited set of tests performed on intra - branches fields suggests that the bifurcation in the dec direction shown by @xcite is real . probably a deeper , thorough and independent analysis of the dec structure of this wrap of the stream is warranted ( see @xcite for possible alternative explanations ) . * the observed trends of density as a function of ra along the leading arm ( branches a and b ) are in fair agreement with those by @xcite . our estimates of the total luminosity per kpc at any given ra are lower than theirs by a factor of @xmath171 . * kinematic follow up of the newly identified structures is clearly urgent . @xcite recently demonstrated that this can be carried on using exactly the same tracer stars , i.e. rc stars . this research make use of sdss data . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http : www.sdss.org . the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . , e. f. , zucker , d. b. , belokurov , v. , sharma , s. , johnston , k. v. , bullock , j. s. , hogg , d. w. , jahnke , k. , de jong , j. t. a. , beers , t. c. , evans , n. w. , grebel , e. k. , ivezi , . , koposov , s. e. , rix , h. , schneider , d. p. , steinmetz , m. , & zolotov , a. 2008 , , 680 , 295 , v. , evans , n. w. , irwin , m. j. , lynden - bell , d. , yanny , b. , vidrih , s. , gilmore , g. , seabroke , g. , zucker , d. b. , wilkinson , m. i. , hewett , p. c. , bramich , d. m. , fellhauer , m. , newberg , h. j. , wyse , r. f. g. , beers , t. c. , bell , e. f. , barentine , j. c. , brinkmann , j. , cole , n. , pan , k. , & york , d. g. 2007 , , 658 , 337 correnti , m. , bellazzini , m. , & ferraro , f.r . , 2007 , in stellar populations as building blocks of galaxies , a. vazdekis and r. f. peletier eds . , cambridge : cambridge university press , iau symp . , 241 , 329 , . , goldston , j. , finlator , k. , knapp , g. r. , yanny , b. , mckay , t. a. , amrose , s. , krisciunas , k. , willman , b. , anderson , s. , schaber , c. , erb , d. , logan , c. , stubbs , c. , chen , b. , neilsen , e. , uomoto , a. , pier , j. r. , fan , x. , gunn , j. e. , lupton , r. h. , rockosi , c. m. , schlegel , d. , strauss , m. a. , annis , j. , brinkmann , j. , csabai , i. , doi , m. , fukugita , m. , hennessy , g. s. , hindsley , r. b. , margon , b. , munn , j. a. , newberg , h. j. , schneider , d. p. , smith , j. a. , szokoly , g. p. , thakar , a. r. , vogeley , m. s. , waddell , p. , yasuda , n. , & york , d. g. 2000 , , 120 , 963 , g. m. , gilmore , g. , siebert , a. , bienaym , o. , binney , j. , bland - hawthorn , j. , campbell , r. , freeman , k. c. , gibson , b. , grebel , e. k. , helmi , a. , munari , u. , navarro , j. f. , parker , q. a. , siviero , a. , steinmetz , m. , watson , f. g. , wyse , r. f. g. , zwitter , t. , pearrubia , j. , smith , m. c. , & williams , m. 2008 , , 384 , 11 , m. h. , dotter , a. , majewski , s. r. , sarajedini , a. , chaboyer , b. , nidever , d. l. , anderson , j. , marn - franch , a. , rosenberg , a. , bedin , l. r. , aparicio , a. , king , i. , piotto , g. , & reid , i. n. 2007 , , 667 , l57 , b. , newberg , h. j. , johnson , j. a. , lee , y. s. , beers , t. c. , bizyaev , d. , brewington , h. , fiorentin , p. r. , harding , p. , malanushenko , e. , malanushenko , v. , oravetz , d. , pan , k. , simmons , a. , & snedden , s. 2009 , , 700 , 1282

we trace the tidal stream of the sagittarius dwarf spheroidal galaxy ( sgr dsph ) using red clump stars from the catalog of the sloan digital sky survey - data release 6 , in the range , corresponding to the range of orbital azimuth . substructures along the line of sight are identified as significant peaks in the differential star count profiles ( scp ) of candidate red clump stars . a proper modeling of the scps allows us to obtain : ( a )% accurate , purely differential distances with respect to the main body of sgr , ( b ) estimates of the fwhm along the line of sight , and ( c ) estimates of the local density , for each detected substructure . in the range we cleanly and continuously trace various coherent structures that can be ascribed to the stream , in particular : the well known northern portion of the leading arm , running from kpc at to kpc at , and a more nearby coherent series of detections lying at constant distance kpc , that can be identified with a wrap of the trailing arm . the latter structure , predicted by several models of the disruption of sgr dsph , , more distant wrap in the same portion of the sky is detected only along a couple of lines of sight . for

we trace the tidal stream of the sagittarius dwarf spheroidal galaxy ( sgr dsph ) using red clump stars from the catalog of the sloan digital sky survey - data release 6 , in the range , corresponding to the range of orbital azimuth . substructures along the line of sight are identified as significant peaks in the differential star count profiles ( scp ) of candidate red clump stars . a proper modeling of the scps allows us to obtain : ( a )% accurate , purely differential distances with respect to the main body of sgr , ( b ) estimates of the fwhm along the line of sight , and ( c ) estimates of the local density , for each detected substructure . in the range we cleanly and continuously trace various coherent structures that can be ascribed to the stream , in particular : the well known northern portion of the leading arm , running from kpc at to kpc at , and a more nearby coherent series of detections lying at constant distance kpc , that can be identified with a wrap of the trailing arm . the latter structure , predicted by several models of the disruption of sgr dsph , was never traced before ; comparison with existing models indicates that the difference in distance between these portions of the leading and trailing arms may provide a powerful tool to discriminate between theoretical models assuming different shapes of the galactic potential . a further , more distant wrap in the same portion of the sky is detected only along a couple of lines of sight . for the detected structures are more complex and less easily interpreted . we are confident to be able to trace the continuation of the leading arm down to and kpc ; the trailing arm is seen up to where it is replaced by more distant structures . possible detections of more nearby wraps and of the virgo stellar stream are also discussed . these measured properties provide a coherent set of observational constraints for the next generation of theoretical models of the disruption of sgr .

0807.4934

i

according to the current paradigm of structure formation , galaxies form and reside inside extended cold dark haloes . while the formation and evolution of dark matter haloes in the cosmic density field is mainly determined by gravitational processes , the formation and evolution of galaxies involves much more complicated , and poorly understood processes , such as radiative cooling , star formation , and all kinds of feedback . one important step in understanding how galaxies form and evolve in the cosmic density field is therefore to understand how the galaxies of different physical properties occupy dark matter haloes of different masses . theoretically , the connection between galaxies and dark matter haloes can be studied using numerical simulations ( e.g. , katz , weinberg & hernquist 1996 ; pearce et al . 2000 ; springel 2005 ; springel et al . 2005 ) or semi - analytical models ( e.g. white & frenk 1991 ; kauffmann et al . 1993 , 2004 ; somerville & primack 1999 ; cole et al . 2000 ; van den bosch 2002 ; kang et al . 2005 ; croton et al . these approaches try to model the process of galaxy formation from first principles . however , since our understanding of the relevant processes is still poor , the predicted connection between the properties of galaxies and dark matter haloes needs to be tested against observations . more recently , the halo occupation model has opened another avenue to probe the galaxy - dark matter halo connection ( e.g. jing , mo & brner 1998 ; peacock & smith 2000 ; berlind & weinberg 2002 ; cooray & sheth 2002 ; scranton 2003 ; yang , mo & van den bosch 2003 ; van den bosch , yang & mo 2003 ; yan , madgwick & white 2003 ; tinker et al . 2005 ; zheng et al . 2005 ; cooray 2006 ; vale & ostriker 2006 ; van den bosch et al . this technique uses the observed galaxy luminosity function and clustering properties to constrain the average number of galaxies of given properties that occupy a dark matter halo of given mass . although the method has the advantage that it can yield much better fits to the data than the semi - analytical models or numerical simulations , one typically needs to assume a somewhat ad - hoc functional form to describe the halo occupation model . a more direct way of studying the galaxy - halo connection is to use galaxy groups , provided that they are defined as sets of galaxies that reside in the same dark matter halo . recently , yang et al . ( 2005 ; 2007 ) have developed a halo - based group finder that is optimized for grouping galaxies that reside in the same dark matter halo . using mock galaxy redshift surveys constructed from the conditional luminosity function model ( e.g. yang et al . 2003 ) and a semi - analytical model ( kang et al . 2005 ) , it is found that this group finder is very successful in associating galaxies with their common dark matter haloes ( see yang et al . 2007 ; hereafter y07 ) . the group finder also performs reliably for poor systems , including isolated galaxies in small mass haloes , making it ideally suited for the study of the relationship between galaxies and dark matter haloes over a wide range of halo masses . however , in order to interpret the properties of the galaxy systems in terms of dark matter haloes , one needs to know the halo mass associated with each of the groups . one approach commonly adopted is to use some halo mass indicator ( such as the total stellar mass or luminosity contained in member galaxies ) to rank the groups . with the assumption that the corresponding halo masses have the same ranking and that the mass function of the haloes associated with groups is the same as that given by a model of structure formation , one can assign a halo mass to each of the observed groups . this approach was adopted by y07 for the group catalogue used in this paper . there are three potential problems with this approach . first , the approach is model - dependent , in the sense that the assumption of a different model of structure formation will lead to a different halo mass function , and hence assign different masses to the groups . second , even if the assumed model of structure formation is correct , it is still not guaranteed that the mass assignment based on the ranking of group stellar mass ( or luminosity ) is valid . finally , even if all groups are assigned with accurate halo masses , the question how dark matter is distributed within the galaxy groups remains open . clearly , it is important to have independent mass measurements of the haloes associated with galaxy groups to test the validity of the mass estimates based on the stellar mass ( luminosity ) ranking . gravitational lensing observations , which measure the image distortions of background galaxies caused by the gravitational field of the matter distribution in the foreground , provide a promising tool to probe the dark matter distribution directly . in particular , galaxy - galaxy weak lensing , which focuses on the image distortions around lensing galaxies , can be used to probe the distribution of dark matter around galaxies , hence their dark matter haloes . the galaxy - galaxy lensing signal produced by individual galaxies is usually very weak , and so one has to stack the signal from many lens galaxies to have a statistical measurement . the first attempt to detect such galaxy - galaxy lensing signal was reported by tyson et al . more recently , with the advent of wide and deep surveys , galaxy - galaxy lensing can be studied for lens galaxies of different luminosities , stellar masses , colors and morphological types ( e.g. brainerd et al . 1996 ; hudson et al . 1998 ; mckay et al . 2001 ; hoekstra et al . 2003 ; hoekstra 2004 ; sheldon et al . 2004 ; mandelbaum et al . 2005 , 2006 ; sheldon et al . 2007a ; johnston et al . 2007 ; sheldon et al . 2007b ; mandelbaum et al . 2008 ) . given that galaxies reside in dark matter haloes , these results provide important constraints on the mass distribution associated with galaxies in a statistical way . in this paper , we use the galaxy groups of y07 selected from the sloan digital sky survey ( sdss ) , together with mass models for individual groups , to predict the galaxy - galaxy lensing signal expected from sdss galaxies . we compare our model predictions with the observational results obtained by mandelbaum et al . ( 2006 ) for the same galaxies . our goal is threefold . first , we want to test whether the method of halo - mass assignment to groups adopted by y07 is reliable . since the method provides a potentially powerful way to obtain the halo masses associated with the galaxy groups , the test results have general implications for the study of the relationship between galaxies and dark matter haloes . second , we want to examine in detail the contributions to the galaxy - galaxy lensing signal from different systems , such as central versus satellite galaxies , early - type versus late - type galaxies , and groups of different masses . such analysis can help us interpreting the observational results . finally , we would like to study how the predicted galaxy - galaxy lensing signal depends on model assumptions , such as the cosmological model and the density profiles of dark matter haloes . in a companion paper ( cacciato et al . 2008 , hereafter c08 ) , we use the relationship between galaxies and dark matter haloes obtained from the conditional luminosity function ( clf ) modeling ( yang et al . 2003 ; van den bosch et al . 2007 ) to predict the galaxy - galaxy cross correlation and to calculate the lensing signal , while here we directly use the observed galaxy groups and their galaxy memberships . this paper is organized as follows . in section [ sec_analysis ] we define the statistical measure that characterizes the galaxy - galaxy lensing effect expected from the mass distribution associated with the galaxy groups . we provide a brief description of the galaxy group catalogue and the models of the mass distribution associated with galaxy groups in section [ sec_sdss ] . we present our results in section [ sec_results ] and conclude in section [ sec_conclusions ] . unless specified otherwise , we adopt a @xmath0cdm cosmology with parameters given by the wmap 3-year data ( spergel et al . 2007 , hereafter wmap3 cosmology ) in our analysis : @xmath2 , @xmath3 , and @xmath4 , @xmath5 .

we use galaxy groups selected from the sloan digital sky survey ( sdss ) together with mass models for individual groups to study the galaxy - galaxy lensing signals expected from galaxies of different luminosities and morphological types . we compare our model predictions with the observational results obtained from the sdss by mandelbaum et al . ( 2006 ) for the same samples of galaxies . we model , separately , the contributions to the galaxy - galaxy lensing signals from different galaxies : central versus satellite , early - type versus late - type , and galaxies in haloes of different masses . we also examine how the predicted galaxy - galaxy lensing signal depends on the shape , density profile , and the location of the central galaxy with respect to its host halo . [ firstpage ] dark matter - large - scale structure of the universe - galaxies : haloes - methods : statistical

we use galaxy groups selected from the sloan digital sky survey ( sdss ) together with mass models for individual groups to study the galaxy - galaxy lensing signals expected from galaxies of different luminosities and morphological types . we compare our model predictions with the observational results obtained from the sdss by mandelbaum et al . ( 2006 ) for the same samples of galaxies . the observational results are well reproduced in acdm model based on the wmap 3-year data , but acdm model with higher , such as the one based on the wmap 1-year data , significantly over - predicts the galaxy - galaxy lensing signal . we model , separately , the contributions to the galaxy - galaxy lensing signals from different galaxies : central versus satellite , early - type versus late - type , and galaxies in haloes of different masses . we also examine how the predicted galaxy - galaxy lensing signal depends on the shape , density profile , and the location of the central galaxy with respect to its host halo . [ firstpage ] dark matter - large - scale structure of the universe - galaxies : haloes - methods : statistical

1701.03213

i

branching objects are found very widely @xcite , ranging from natural patterns like river networks , plants , and dendritic crystals , to conceptual expressions like binary search trees in computer science @xcite and phylogenetic trees in taxonomy @xcite . the topological structure of a branching pattern is modeled by a binary tree if a segment bifurcates ( does not trifurcate or more ) at every branching point . let @xmath0 denote the set of the different binary trees having @xmath1 leaves . the number of leaves is called the _ magnitude _ in research of branching patterns . as known well @xcite , the number of the different binary trees of magnitude @xmath1 is given by @xmath2 which iscalled the @xmath3st catalan number . in fig . [ fig2 ] , @xmath0 for @xmath4 , and 4 are schematically shown . introducing the uniform probability measure @xmath5 on @xmath0 ( so that each binary tree is assigned equal probability @xmath6 ) , we obtain the probability space @xmath7 referred to as the _ random model _ @xcite . the formation of real - world branching patterns more or less involves stochastic effects , and the random model is a kind of mathematical simplification of such random factors . in hydrology , methods for measuring the hierarchical structure of a river network have been proposed by horton @xcite , strahler @xcite , shreve @xcite , tokunaga @xcite , and other researchers . their methods define how to assign an integer number ( called the _ order _ ) to each stream . among all , strahler s method is currently the most popular because of its simple computation rule . strahler s method is a refinement of horton s method , so it is sometimes called the _ horton - strahler ordering method_. the horton - strahler method recursively defines the order of each node by the following rules . ( i ) the leaf nodes are defined to have order one . ( ii ) a node whose children have different order @xmath8 and @xmath9 ( @xmath10 ) has order @xmath11 . ( iii ) a node whose two children have the same order @xmath12 has order @xmath13 . we define a _ branch _ of order @xmath12 as a maximal connected path made by nodes of equal order @xmath12 . ( a branch here is called a _ stream _ in the analysis of river networks . ) an example of strahler s ordering is shown in fig . [ fig1 ] . for a binary tree @xmath14 , we let @xmath15 denote the number of branches of order @xmath12 in @xmath16 . by the definition of the order , @xmath17 and @xmath18 ( @xmath19 ) . note that @xmath20 if @xmath21 , because a node of order 2 is produced by the merge of two leaves . for the binary tree @xmath22 in fig . [ fig1 ] , @xmath23 , @xmath24 , @xmath25 , and @xmath26 for @xmath27 . @xmath28 is a random variable on @xmath7 , and its stochastic property is of main interest in this study . for any function @xmath29 , @xmath30 is a real - valued random variable on @xmath0 . according to ref . @xcite , the recursive relation between the averages of the @xmath12th and @xmath31st variables @xmath32 } = \frac{n!(n-1)!(n-2)!}{(2n-2)!}\sum_{m=1}^{{\lfloorn/2\rfloor } } \frac{2^{n-2m}}{(n-2m)!m!(m-1)!}{e\left[f(s_{r-1,m})\right ] } \label{eq:1 - 1}\ ] ] holds , where @xmath33}$ ] denotes the average on the random model . the coefficient @xmath34 represents the probability @xmath35 . in particular , putting @xmath36 in eq . , we have @xmath37}=\frac{n!(n-1)!(n-2)!}{(2n-2)!}\sum_{m=1}^{{\lfloorn/2\rfloor}}\frac{2^{n-2m}}{(n-2m)!m!(m-1)!}f(m ) . \label{eq2}\ ] ] mathematical properties of @xmath38 have been investigated thoroughly . for instance , the average and variance are respectively given by @xcite @xmath39 } = \frac{n(n-1)}{2(2n-3)},\quad { \operatorname{var}\left[s_{2,n}\right ] } = \frac{n(n-1)(n-2)(n-3)}{2(2n-3)^2(2n-5)}. \label{eq : werner}\ ] ] moreover , from eq . , the moment generating function @xmath40 of @xmath38 is given by @xmath41 } = \frac{n!(n-1)!(n-2)!}{(2n-2)!}\sum_{m=1}^{{\lfloorn/2\rfloor}}\frac{2^{n-2m}}{(n-2m)!m!(m-1)!}e^{mt},\ ] ] and this summation can be expressed using the gauss hypergeometric function @xmath42 @xcite : @xmath43 the ratio @xmath44 is called the _ bifurcation ratio _ of order @xmath12 or simply the @xmath12th bifurcation ratio . hydrologists have empirically confirmed that the bifurcation ratios of an actual river network become almost constant for different orders , and this relation is referred to as _ horton s law of stream numbers_. by definition , the bifurcation ratio is always smaller than or equal to @xmath45 . when @xmath46 , we reasonably define @xmath47 . the random variable @xmath48 is also called the @xmath12the bifurcation ratio . the lowest bifurcation ratio @xmath49 is relatively easy to deal with , because it is similar to @xmath38 . the central limit theorem for @xmath50 has been shown by wang and waymire @xcite : [ thm1 ] on the random model , @xmath51 where `` @xmath52 '' denotes convergence in distribution , and @xmath53 is the normal distribution with mean @xmath54 and variance @xmath55 . it is a simple and natural idea that we extend theorem [ thm1 ] to general order @xmath12 . compared with @xmath38 , however , higher - order branches @xmath28 for @xmath56 and the bifurcation ratio of order @xmath19 is difficult to handle and less studied . in this paper , we generalize theorem [ thm1 ] in two ways ( theorems [ thm2 ] and [ thm3 ] in [ sec2 ] ) , and further generalize them ( theorem [ thm4 ] in [ sec6 ] ) . in [ sec3][sec5 ] , we give proofs of lemmas , which are necessary for the main theorems . in these proofs , eq . and its variant @xmath57 } = \frac{n!(n-1)!(n-2)!}{(2n-2)!}\sum_{m=1}^{{\lfloorn/2\rfloor } } \frac{2^{n-2m}}{(n-2m)!m!(m-1)!}{e\left[f\left(\frac{s_{r , m}}{s_{r-1,m}}\right)\right]}. \label{eq:1 - 3}\ ] ] are very useful .

* abstract * + the horton - strahler ordering method , originating in hydrology , formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio . the main result of this paper is the central limit theorem for bifurcation ratio of general branch order . some useful relations are also derived in the proofs of the main theorems .

* abstract * + the horton - strahler ordering method , originating in hydrology , formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio . the main result of this paper is the central limit theorem for bifurcation ratio of general branch order . this is a generalized form of the central limit theorem for the lowest bifurcation ratio , which was previously proved . some useful relations are also derived in the proofs of the main theorems .

astro-ph0602490

i

the _ swift _ gamma - ray burst explorer @xcite has been returning unprecedented data about gamma ray bursts ( grbs ) for the past 18 months . of particular interest in the bursts followed by _ swift _ have been the early time lightcurves of the afterglows which have shown much greater structure and different temporal decay properties than expected , leading to much discussion in the literature regarding the nature of the transition between the prompt emission , thought to be due to synchrotron radiation from internal collisions @xcite , and the afterglow , also thought to be due to synchrotron radiation , though it remains somewhat unclear whether the emission arises in internal or external shocks . _ swift _ observations have shown that grb lightcurves can be described by a canonical 3-segment shape . this shape consists of 1 - an early steep decay phase ( f@xmath2 where 3@xmath3 @xmath4 @xmath3 5 ; t @xmath5 500 s ) 2 - a very shallow decay phase ( 0.5 @xmath3 @xmath6 @xmath3 1.0 ; 500 s @xmath5 t @xmath5 @xmath7 s ) and 3 - a normal decay phase ( 1 @xmath3 @xmath8 @xmath3 1.5 ; @xmath7 s @xmath5 t ) @xcite . superimposed on this smooth decay profile , _ swift _ has shown that bright x - ray flares , 2 to 100 times as bright as the underlying afterglow , are common during the early ( t @xmath3 10 ks ) stages of grbs @xcite . the observation of grb050117 @xcite marked the first time that _ swift _ slewed to and settled on a grb while the prompt gamma ray emission was still in progress , arriving 192 seconds after the burst alert telescope ( bat ) triggered on the burst which had a t@xmath9 of 168 seconds . due to irregularities in the observing mode of the xrt and the proximity of the south atlantic anomaly to _ swift _ during the observation of grb050117 , however , only very sparse data was collected by the xrt , totaling 11.4 seconds in the first orbit and 946 seconds overall . this left large gaps in the lightcurve coverage and severely limited the quality of the spectral analysis that could be performed . we report here on the observation of grb 050713a @xcite , a burst of t@xmath9 = 70 seconds to which _ swift _ slewed and began collecting data with the narrow field instruments ( nfis ) in just 72.6 seconds , while the prompt gamma ray emission was still detectable by the bat . this burst marks just the second time that the bat and xrt have collected simultaneous data on a burst and it marks the first time that both instruments have produced a well sampled , simultaneous dataset covering multiple flares in the prompt emission . in addition to the _ swift _ coverage of grb 050713a , we report also on prompt and followup observations carried out by konus - wind , magic , _ xmm - newton _ and ground based optical observatories . in section 2 we describe the observations and data analysis from all instruments including ground follow - up . in section 3 we discuss the implications of the observations in light of the new theoretical understanding emerging from _ swift _ observations of grbs . in section 4 we summarize and present our conclusions . quoted uncertainties are at the 90% confidence level for one interesting parameter ( i.e. , @xmath10=2.71 ) unless otherwise noted .

_ swift _ discovered grb 050713a and slewed promptly to begin observing with its narrow field instruments 72.6 seconds after the burst onset , while the prompt gamma - ray emission was still detectable in the bat . this burst marks just the second time that the bat and xrt have simultaneously detected emission from a burst and the first time that both instruments have produced a well sampled , simultaneous dataset covering multiple x - ray flares . the temporal rise and decay parameters of the flares are consistent with the internal shock mechanism . in addition to the _ swift _ coverage of grb 050713a , we report on the konus - wind ( k - w ) detection of the prompt emission , an upper limiting gev measurement of the prompt emission made by the magic imaging atmospheric cherenkov telescope and _ xmm - newton _ observations of the afterglow . simultaneous observations between _ swift _ xrt and _ xmm - newton _ produce consistent results , showing a break in the lightcurve at t+ ks .

_ swift _ discovered grb 050713a and slewed promptly to begin observing with its narrow field instruments 72.6 seconds after the burst onset , while the prompt gamma - ray emission was still detectable in the bat . simultaneous emission from two flares is detected in the bat and xrt . this burst marks just the second time that the bat and xrt have simultaneously detected emission from a burst and the first time that both instruments have produced a well sampled , simultaneous dataset covering multiple x - ray flares . the temporal rise and decay parameters of the flares are consistent with the internal shock mechanism . in addition to the _ swift _ coverage of grb 050713a , we report on the konus - wind ( k - w ) detection of the prompt emission , an upper limiting gev measurement of the prompt emission made by the magic imaging atmospheric cherenkov telescope and _ xmm - newton _ observations of the afterglow . simultaneous observations between _ swift _ xrt and _ xmm - newton _ produce consistent results , showing a break in the lightcurve at t+ ks . together , these four observatories provide unusually broad spectral coverage of the prompt emission and detailed x - ray follow - up of the afterglow for two weeks after the burst trigger . simultaneous spectral fits of k - w with bat and bat with xrt data indicate that an absorbed broken powerlaw is often a better fit to grb flares than a simple absorbed powerlaw . these spectral results together with the rapid temporal rise and decay of the flares suggest that flares are produced in internal shocks due to late time central engine activity .

astro-ph0602490

c

the k - w light curve in the 181160 kev energy range is similar to the _ swift_-bat light curve ( fig 1 ) . the small precursor peak detected by bat at t@xmath070 to t@xmath050 s is seen by k - w at statistically significant levels in all three broad , pre - trigger bands : g1 ( 1870 kev ) , g2 ( 70300 ) , and g3 ( 3001160 kev ) . the other smaller peaks detected by the bat after the burst trigger are not seen at statistically significant levels in the k - w data , despite the fact that the peaks at t@xmath0 + 50 s and at t@xmath0 + 65 s are more intense in the bat energy range than the precursor is . the detection by k - w of the precursor but not the later flares is indicative of the harder spectral index seen in the precursor as compared to the later flares ( see section 3.3 for discussion of separate spectral fits to individual flares ) . the xrt lightcurve with bat data overplotted is shown in figure 4 . both the x - ray and gamma - ray data in the first orbit are dominated by flaring activity , making it difficult to draw a conclusion regarding the underlying powerlaw decay index from this orbit alone . the xrt data beginning at t@xmath0 + 4 ks ( orbit 2 ) and extending until t@xmath0 + 40 ks show a significantly flatter powerlaw decay slope of @xmath105 , implying that a break in the powerlaw decay has occurred near the end of the first orbit of xrt coverage at t@xmath0+@xmath1300 s and that a period of energy injection occurs from t@xmath0+@xmath1300 s to t@xmath0+@xmath115 ks . another break in the lightcurve then occurs near t@xmath0 + 25 ks to a steeper , `` normal '' , pre - jetbreak decay slope , as shown by the _ xmm - newton _ data ( @xmath106 ) . support for this notion of the presence of an energy injection phase may be drawn from the harder x - ray spectral slope of the second orbit of xrt data ( photon index = 1.9 @xmath102 0.13 ) compared to the first orbit ( photon index = 2.28 @xmath102 0.04 ) , the third orbit ( photon index = 2.25 @xmath102 0.23 ) , and the later data ( photon index = 2.8 @xmath102 0.6 ) ( table 5 ) . _ xmm - newton _ data coverage nicely fills much of the data gap in the xrt coverage between t@xmath0 + 15 ks and t@xmath0 + 40 ks and provides high signal to noise data in this regime , producing a confident determination of the lightcurve break . the global picture of the lightcurve of this burst is one in which the early data ( prior to t@xmath0 + 12 s ) shows a bright plateau in the 15 kev to 1 mev energy range , consisting of multiple overlapping peaks . at t@xmath0 + 12 s the emission drops rapidly , consistent with a curvature radiation falloff @xcite until subsequent flaring activity begins to be seen in the 0.3150 kev region with some indication of flux at higher energies from k - w . due to the rapid rise and decay of the flares , internal shocks from continued central engine activity appears to be the most likely explanation for these flares @xcite . the earliest ground based optical detections are reported at this time also , suggesting that the flares may also be optically bright . the lack of higher resolution timing information in the optical data , though , admits the possibility that the optical emission may be unassociated with the emission mechanism responsible for the x - ray flares . it is possible that the optical emission is due to synchrotron emission from the reverse shock ( rs ) , though the much higher flux level of the x - ray flare peaks compared to the optical measurements suggests that the x - ray flares themselves are not due to inverse compton scattering of the optical synchrotron emission of the rs @xcite . following this prompt emission phase , an energy injection phase begins which dominates the lightcurve until at least t@xmath0 + 16 ks . during the energy injection phase , continued activity of the central engine adds energy to the afterglow of the burst , either through additional ejection events or through the realization of energy contained in previously ejected outward moving relativistic shells which only collide at later times , producing late time internal shock emission which is then added to the overall decay @xcite . it may be expected , if the energy injection phase is due to continued central engine activity , that flaring behavior would continue to be observed during this period and , indeed , some evidence for small scale flaring activity during both the second and third orbit of xrt data can be seen , though at a much reduced significance in comparison to the flaring activity of the first orbit . near t@xmath0 + 25 ks , the energy injection phase ends , giving way to a steeper decay slope similar to what is often seen in grbs after the prompt emission phase and prior to the possible onset of a traditional jet - break @xcite . many flares superimposed on top of the overall decay of grb 050713a show the typical properties seen in other bursts : that @xmath107t / t @xmath1 0.1 and that the peak flux level is negatively correlated with the time of the flare @xcite . these two properties of flares seen in _ swift _ grb afterglows have been cited as evidence for flares being produced through accretion processes onto the central compact object @xcite , but we offer here that the constancy of the @xmath107t / t value of flares may partly be a by - product of the overall decay of the afterglow in so much as the sensitivity of the xrt to flares is naturally degraded as the overall flux level of the afterglow decays , thus _ requiring _ flares at later times ( and hence , lower flux levels ) to be longer in duration for enough counts to be collected to produce a significant flare seen above the background . such a case can be seen in comparing the early time flares in the first orbit of grb 050713a to the flare seen in the the third orbit . during the first orbit , the underlying flux level beneath the flares is poorly determined , but can be assumed to be 10 - 100 counts s@xmath13 . we are dominated in this portion of the lightcurve by the poissonian error in the flux , which in a 10 second integration will be 10 - 32 counts , or 3 - 10@xmath108 . thus , for a flare to appear at the 6 sigma level above the background during this portion of the lightcurve , at most a 60@xmath108 increase in fluence above the normal powerlaw decay is needed , which can be acquired in a few seconds by the introduction of a flare with twice the flux of the underlying afterglow . during the third orbit , however , the underlying afterglow flux level has dropped to @xmath1 0.1 counts s@xmath13 . during a 10 second integration at 0.1 counts s@xmath13 the poisson error alone is 1 count , so for a flare to be detectable at 6 sigma above background at these count levels , the total fluence must be 6 counts , implying an increase in the rate from 0.1 counts s@xmath13 to 0.6 counts s@xmath13 during the 10 s interval , a 6 fold increase , which has been seen only in the brighter flares . in order to be sensitive to the same 60@xmath108 increase in flux level as during the first orbit , the flare which occurs at a flux level of 0.1 counts s@xmath13 needs to have a poission error which is 1/6 of the total counts in the observation , i.e. , 36 counts must be collected , which implies an exposure time of at least 180 s if produced by the introduction of a flare with twice the flux of the underlying afterglow . in other words , because the afterglow flux level decays as t@xmath27 , the exposure time needed to acquire the same fluence level increases as t@xmath109 . thus , we see that in moving from the first orbit at t@xmath0 + 100 s to the third orbit at t@xmath0 + 10000 s , assuming a typical underlying powerlaw decay of the afterglow of @xmath110 1 , we have greatly decreased the temporal resolution of xrt to detect flares ( from a few seconds to a few hundred seconds ) . this is not to imply that there is not another more physical cause for the constancy of the @xmath107t / t ratio seen in flares , but rather to note that the typical grb seen by the _ swift _ xrt does not provide sufficient flux at times typically greater than a few ks to detect the shorter timescale flares that are so often seen during the first orbit . in grb 050713a , a hint of emission above the afterglow powerlaw decay appears in the xrt data at t@xmath0 + 45 ks , though the statistics are , predictably , poor . this time is overlapped by _ xmm - newton _ data , though , so we can look for evidence of a short flare in the _ xmm - newton _ data at this time . in figure 9 we show the _ xmm - newton _ lightcurve , plotted linearly and zoomed near t@xmath0 + 45 ks . though a 1 - 2 sigma deviation above the background decay is seen at t@xmath0 + 45 ks , the _ xmm - newton _ data appear consistent with a statistical fluctuation rather than a true flare similar to those seen earlier during the burst . the presence of multiple flares in grb050713a argues against `` one - shot '' emission mechanisms such as synchrotron self - compton emission in a reverse shock or deceleration of the blastwave @xcite and it argues in favor of a mechanism which can produce repeated flares , such as late time central engine activity . while it may remain possible that one of the several flares in grb050713a is due to the rs or the onset of the afterglow due to external shocks , the steep temporal decays of all the temporally fitted flares coupled with the photon indices of the flares ( 1.25 @xmath1 2.5 ; table 6 ) do not satisfy the closure relations of sari et al . , ( 1998 ) , chevalier & li ( 1999 ) and sari et al . , ( 1999 ) for propagation of the blast wave into either a wind or constant density ism . together these points seem to argue in favor of an internal shock origin for the flares seen in this burst . due to the relatively narrow spectral response function of the bat ( 15150 kev for mask - tagged events ) and the xrt ( 0.310 kev ) , a spectral fit to data from only one of the two high energy instruments on _ swift _ is usually not able to discriminate between higher order spectral models . analysts and authors are usually limited to choosing between a power - law or band function . in grb 050713a we have a rare case of data coverage overlap between bat and xrt ( 0.3150 kev ) and also between bat and k - w ( 15 kev14 mev ) . taking advantage of this where appropriate , considering the relative flux levels in the three instruments , we have jointly fitted spectral datasets between the two pairs of instruments . during the precursor and from t@xmath0 + 0 to t@xmath0 + 16.5 s , we perform joint fitting between bat and k - w data . from t@xmath0 + 16.5 to t@xmath0 + 78 s we have only bat data . from t@xmath0 + 78 to t@xmath0 + 116 s and during the onset of the flare at t@xmath0 + 160 we perform joint fitting between xrt and bat . we have grouped the data into segments ( as shown in table 6 ) in order to temporally separate data which we expect may show significantly different spectral parameters . segments 1 - 4 contain bat and k - w data and are segmented to separate the precursor from the prompt emission and the prompt emission from the rapid decay phase . segment 5 contains bat data only and segments 6 - 10 contain xrt and bat data . these are segmented to distinguish the 3 flares which have overlapping data and also to separate the rise of each flare from the decay of each flare . we attempt fits to each of these segments using 4 different spectral models : 1 ) an absorbed powerlaw 2 ) an absorbed cutoff or broken powerlaw ( cutoff for data extending beyond 150 kev , broken otherwise ) 3 ) an absorbed band function and 4 ) an absorbed blackbody plus powerlaw . the precursor is the most poorly sampled of all the regions . despite the low number of counts in the region , a cutoff powerlaw is favored over a single powerlaw at @xmath111 confidence according to the f - test . of all the segments fit , the precursor has the hardest photon index , regardless of the model which is used to perform the fits . the plateau of the prompt emission is best fit by an exponentially cutoff powerlaw model with photon index @xmath112 and e@xmath113 kev . next to the precursor , the prompt plateau has the second hardest photon index of all segments fit , regardless of the model used . as with the other data segments which contain k - w data , the rapid decay segment is poorly fit by a simple powerlaw and is best fit by a cutoff powerlaw or band function . the photon index of the cutoff powerlaw in segment 3 is quite similar to that in the prompt plateau , but the cutoff energy is somewhat lower ( 312 kev compared to 421 kev in the plateau ) , suggesting that the highest energy flux is `` shutting off '' during the rapid decay phase . this segment is an extension of the prompt segment to slightly later times , encompassing slightly more data . the cutoff powerlaw or band function is the best fit , with photon indices similar to segment 2 and e@xmath114 between that in segments 2 and 3 . this segment contains only bat data and is included for completeness , though the narrowness of the bat spectral response limits the ability to distinguish between models . a simple powerlaw is a good fit with photon index of 1.83 . is unconstrained . the powerlaw plus blackbody model produces a good fit to this segment but only with a very minimal blackbody component , effectively reproducing the fit of the simple absorbed powerlaw . therefore we consider the powerlaw plus blackbody model inapplicable to this segment . only in this segment , the data time ranges are mismatched between xrt and bat ( due to xrt observations beginning towards the end of the flare decay ) . rather than ignore this flare or consider only the later part of the flare decay where xrt and bat data coverage overlap , we have chosen to fit the entire bat time range from t@xmath0 + 68 to t@xmath0 + 95 s together with the t@xmath0 + 79 to t@xmath0 + 95 s xrt data ( note that the image mode data taken at t@xmath0 + 73 s are highly piled up and can not be used spectrally ) for consistency with our treatment of the other flares . a simple powerlaw is a good fit to this segment , yielding @xmath115@xmath12 and a photon index of 2.47 , significantly softer than the rise of the flare , as expected . in the rise of the brightest flare seen in xrt , both an absorbed powerlaw plus blackbody model and an absorbed broken powerlaw model are significantly better fits ( f - test probability @xmath116 ) than a simple absorbed powerlaw . the powerlaw plus blackbody indicates @xmath117@xmath12 and a relatively soft photon index of 2.0 with a blackbody temperature of kt@xmath118 kev . we note that this value of kt is below the xrt energy band and may therefore indicate a non - physical spectral solution . the absorbed broken powerlaw indicates @xmath119@xmath12 and photon indices of @xmath120 and @xmath121 , broken at 3.4 kev . these two models are somewhat degenerate in this dataset , with both models producing a roll over in flux at low ( below 0.5 kev ) and high ( above 50 kev ) energies . the decay portion of this flare is well fit by a simple absorbed powerlaw with @xmath122@xmath12 and photon index of 2.68 . we note , however , that both an absorbed broken powerlaw and absorbed powerlaw plus blackbody are equally good fits to the data . the rise of the last flare with overlapping data is well fit by a simple absorbed powerlaw with @xmath123@xmath12 and photon index @xmath124 , however the absorbed powerlaw plus blackbody is , strictly , a better fit according to the f - test , though only at about the @xmath125 confidence level ( f - test probability = 0.219 ) , with @xmath126@xmath12 , kt=200 kev and photon index of 2.43 . we note that this value of kt is above the xrt - bat energy band and may therefore indicate a non - physical spectral solution . the decay of this flare is well fit by an absorbed powerlaw with @xmath127@xmath12 and photon index of 2.55 , though as with segment 9 , the absorbed powerlaw plus blackbody is also an acceptable fit with @xmath128@xmath12 , kt=5.2 kev and photon index of 2.83 . it should be noted that the bat flux is very near the noise level in this segment and really provides only an upper limit on the spectral fitting process in the higher energy region . we have produced the broadband sed ( spectral energy distribution ) of the afterglow of grb 050713a over the time range from t@xmath0 + 20 s to t@xmath0 + 1000 s ( fig 10 ) . this timerange includes detections of the burst afterglow in the optical from the raptor - s and liverpool telescopes ( corrected for the galactic extinction in this direction of @xmath129=1.04 @xcite ) and in the x - ray from _ swift _ bat and xrt . it also includes upper limits in the gamma - ray energy range from k - w ( whose detectable emission ends at t@xmath0+@xmath110 s ) and in the gev energy range from magic . a similar sed has been addressed by the magic collaboration in their paper regarding the magic flux upper limit @xcite in which they note that the sed composed of data from _ swift _ and magic ( 0.2 kev to 400gev ) is fit by a band function at low energy and that the magic data are consistent with a single unbroken powerlaw extending from e@xmath114 ( at @xmath1 400 kev ) to the magic limits up to 500 gev . we confirm this result , citing a best fit photon index for a single powerlaw fit from 400 kev to 500 gev of @xmath130 = 2.1 @xmath102 0.1 and a reduced @xmath131 = 1.66 for 63 dof . we further note that in performing our fit to the magic data , we have treated the magic upper limits as data points during our fit , thus our photon index or 2.1 is only a lower limit on the true photon index of a powerlaw which would fit the true flux level at gev energies . our results here are , therefore , consistent with the analysis of the albert et . , in which they show that their data are consistent with a powerlaw photon index of 2.5 from 400 kev to 500 gev . we add that a band function fit is not , however , consistent with the data when we also consider the contemporaneous optical detections . the relative faintness of the optical detections compared to the x - ray detections combined with the upper limits from k - w and magic requires an absorbed broken powerlaw fit . figure 10 shows the best fit to the entire sed using an absorbed powerlaw ( dotted ) , absorbed broken powerlaw ( solid ) and absorbed band function ( dashed ) . the spectral parameters and fit characteristics for each of these fits are shown in table 7 . we have not corrected for the attenuation of flux above 10gev due to photon - photon interactions with the infrared background @xcite , however , our spectral fit results will remain valid independent of this effect due to the constraints placed by the k - w limiting flux measurement from 20 kev to 14 mev .

together , these four observatories provide unusually broad spectral coverage of the prompt emission and detailed x - ray follow - up of the afterglow for two weeks after the burst trigger . these spectral results together with the rapid temporal rise and decay of the flares suggest that flares are produced in internal shocks due to late time central engine activity .

_ swift _ discovered grb 050713a and slewed promptly to begin observing with its narrow field instruments 72.6 seconds after the burst onset , while the prompt gamma - ray emission was still detectable in the bat . simultaneous emission from two flares is detected in the bat and xrt . this burst marks just the second time that the bat and xrt have simultaneously detected emission from a burst and the first time that both instruments have produced a well sampled , simultaneous dataset covering multiple x - ray flares . the temporal rise and decay parameters of the flares are consistent with the internal shock mechanism . in addition to the _ swift _ coverage of grb 050713a , we report on the konus - wind ( k - w ) detection of the prompt emission , an upper limiting gev measurement of the prompt emission made by the magic imaging atmospheric cherenkov telescope and _ xmm - newton _ observations of the afterglow . simultaneous observations between _ swift _ xrt and _ xmm - newton _ produce consistent results , showing a break in the lightcurve at t+ ks . together , these four observatories provide unusually broad spectral coverage of the prompt emission and detailed x - ray follow - up of the afterglow for two weeks after the burst trigger . simultaneous spectral fits of k - w with bat and bat with xrt data indicate that an absorbed broken powerlaw is often a better fit to grb flares than a simple absorbed powerlaw . these spectral results together with the rapid temporal rise and decay of the flares suggest that flares are produced in internal shocks due to late time central engine activity .

1512.02381

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for @xmath9 , a _ @xmath0-box _ is the cartesian product @xmath10 of @xmath0 intervals of @xmath1 . @xmath0-box representation _ of a graph @xmath11 is a collection @xmath12 of @xmath0-boxes in @xmath3 such that any two boxes @xmath13 and @xmath14 intersect if and only if the corresponding vertices @xmath15 and @xmath16 are adjacent in @xmath2 . in other words , @xmath2 is the intersection graph of the boxes @xmath17 . the _ boxicity _ of a graph @xmath2 , denoted by @xmath18 and introduced by roberts in 1969 @xcite , is the smallest integer @xmath0 such that @xmath2 has a @xmath0-box representation . it was proved by thomassen in 1986 that planar graphs have boxicity at most 3 @xcite , which is best possible ( as shown by the planar graph obtained from a complete graph on 6 vertices by removing a perfect matching @xcite ) . it is natural to investigate how this result on planar graphs extends to graphs embeddable on surfaces of higher genus . let @xmath19 be the supremum of the boxicity of all graphs embeddable in a surface of euler genus @xmath5 . the result of thomassen on planar graphs was extended in @xcite by showing that for any @xmath20 , @xmath21 ( prior to this result , it was not known whether @xmath19 was finite ) . in @xcite , we proved the existence of two constants @xmath22 , such that @xmath23 . the proof of the upper bound relies on a connection between boxicity and acyclic coloring established in @xcite . it was noted there that using this connection and a result of kawarabayashi and mohar @xcite , it could be proved that there is a function @xmath4 such that any graph embedded in a surface of euler genus @xmath5 , such that all non - contractible cycles have length at least @xmath6 , has boxicity at most 42 . the main result of this paper is to reduce this bound to 5 for orientable surfaces ( theorem [ thm : locpla ] ) . similar ideas are then used to show that toroidal graphs have boxicity at most 6 , and toroidal graphs without non - contractible triangles have boxicity at most 5 ( theorem [ thm : tor ] ) . this improves on @xcite , where it was proved that toroidal graphs have boxicity at most 7 , while there are toroidal graphs of boxicity 4 . an immediate consequence of theorem [ thm : locpla ] is that if @xmath2 has genus @xmath5 , then a set of at most @xmath24 vertices can be removed in @xmath2 so that the resulting graph has boxicity at most 5 . however , the bound we obtain for @xmath6 in theorem [ thm : locpla ] is exponential in @xmath5 . we show the following improvement : if @xmath2 is embedded in a surface of euler genus @xmath25 , then a set of at most @xmath26 vertices can be removed in @xmath2 so that the resulting graph has boxicity at most 5 ( theorem [ thm : linex1 ] ) . note that this result is proved for any surface , orientable or not . in @xcite , it was proved that there is a function @xmath27 such that if @xmath2 is embedded in a surface of euler genus @xmath5 , and has no cycle of length less than @xmath28 , then @xmath2 has boxicity at most 4 . here , we show there is a function @xmath27 such that if @xmath2 has no @xmath29-minor and no cycle of length less than @xmath30 , then @xmath2 has boxicity at most 3 ( corollary [ cor : minor ] ) . this is best possible already for @xmath31 . this result follows from a more general theorem on path - degenerate graphs ( theorem [ thm:6path ] ) . this general result also implies , together with earlier results from @xcite , that there is a constant @xmath27 such that any graph embeddable in a surface of euler genus @xmath5 , with no cycle of length less than @xmath32 , has boxicity at most 3 ( corollary [ cor : girth ] ) . this is best possible up to the choice of the constant @xmath27 . some of the results we will use originate from the proof of thomassen @xcite that planar graphs have boxicity at most 3 , without being explicitly stated there . in section [ sec : pla ] , we explain how these results can be derived from @xcite , which might be of independent interest . we will then prove the main results of this paper in sections [ sec : locpla ] , [ sec : linext ] , and [ sec : girth ] . in the remainder of this section , we review the necessary background on boxicity and graphs on surfaces . we then give a simple proof that embedded graphs of large edge - width have boxicity at most 7 ( this will be improved to 5 in section [ sec : locpla ] ) . let @xmath11 be a graph , and let @xmath33 be a @xmath0-box representation of @xmath2 . for a @xmath0-box @xmath34 , and an integer @xmath35 , we refer to @xmath36 as _ the @xmath37-th interval of @xmath16_. for @xmath35 , let @xmath38 be the interval representation consisting of all @xmath37-th intervals of the vertices of @xmath2 in @xmath39 . each interval representation @xmath38 , @xmath35 , corresponds to an interval graph @xmath40 with vertex - set @xmath41 . observe that each graph @xmath40 is a supergraph of @xmath2 , and any two @xmath0-boxes @xmath13 and @xmath14 intersect if and only if for all @xmath42 the intervals corresponding to @xmath15 and @xmath16 intersect in @xmath38 , or equivalently , if the vertices @xmath15 and @xmath16 are adjacent in the interval graph @xmath40 . for two graphs @xmath43 and @xmath44 on the same vertex - set @xmath41 , the _ intersection @xmath45 _ of @xmath46 and @xmath47 is defined as the graph @xmath48 . the discussion above implies that the boxicity of a graph @xmath2 can be equivalently defined as the least @xmath49 such that @xmath2 can be expressed as the intersection of @xmath49 interval graphs on the same vertex - set . in this paper , the two definitions will be used and we will often switch from one to the other , depending of the situation , i.e whenever we consider some @xmath0-box representation @xmath33 we will implicitly consider it as a representation @xmath50 as defined in the previous paragraph , and vice - versa . if @xmath39 is a representation of @xmath2 , we will often say that @xmath39 _ represents _ @xmath2 , or _ induces _ @xmath2 . we refer the reader to the book by mohar and thomassen @xcite for more details or any notion not defined here . all the graphs in this paper are simple ( i.e. , without loops and multiple edges ) . a _ surface _ is a non - null compact connected 2-manifold without boundary . a surface can be orientable or non - orientable . the _ orientable surface @xmath51 of genus @xmath52 _ is obtained by adding @xmath53 _ handles _ to the sphere ; while the _ non - orientable surface @xmath54 of genus @xmath49 _ is formed by adding @xmath55 _ cross - caps _ to the sphere . the _ euler genus _ of a surface @xmath56 is defined as twice its genus if @xmath56 is orientable , and as its non - orientable genus otherwise . we say that an embedding is _ cellular _ if every face is homeomorphic to an open disk of @xmath57 . using the fact that the boxicity of a graph @xmath2 is at most @xmath49 if and only if all the connected components of @xmath2 have boxicity at most @xmath49 , we will always be able to assume in this paper ( using ( * ? ? ? * propositions 3.4.1 and 3.4.2 ) ) that the considered embeddings are cellular ( and we will do so implicitly ) . let @xmath2 be a graph embedded in a surface of euler genus @xmath25 . the _ edge - width _ of @xmath2 is defined as the length of a smallest non - contractible cycle of @xmath2 , and the _ face - width _ of @xmath2 is defined as the minimum number of points of @xmath2 intersected by a non - contractible curve on the surface . given a 2-sided cycle @xmath58 in @xmath2 , and an orientation of @xmath58 , the set of neighbors of @xmath58 incident to an edge leaving the left side of @xmath58 is denoted by @xmath59 , and the set of neighbors of @xmath58 incident to an edge leaving the right side of @xmath58 is denoted by @xmath60 ( see figure [ fig : lrc ] , left , for an example in a triangulation ) . note that @xmath59 and @xmath60 might not be disjoint . given two non - contractible cycles @xmath61 and @xmath62 , @xmath63 denotes the minimum distance between a vertex of @xmath61 and a vertex of @xmath62 in @xmath2 . if @xmath58 is a non - contractible 2-sided cycle , we also define @xmath64 as the minimum length ( number of edges ) of a path starting with an edge incident to @xmath58 and @xmath59 , and ending with an edge incident to @xmath58 and @xmath60 ( note that @xmath64 does not depend of the chosen orientation of @xmath58 ) . and @xmath60 in a triangulation ( left ) and the embedded graph resulting from the removal of @xmath58 ( right).[fig : lrc ] ] let @xmath2 be a triangulation of @xmath65 . a collection of pairwise disjoint non - contractible cycles @xmath66 of @xmath2 is _ planarizing _ if the graph obtained from @xmath2 by removing the vertices of @xmath66 is planar . if for any @xmath67 , @xmath68 , then the planarizing collection @xmath66 is said to have _ minimum distance _ at least @xmath0 . the following was proved by thomassen @xcite : @xcite[thm : placc ] let @xmath69 be integers , and let @xmath2 be a triangulation of @xmath65 of edge - width at least @xmath70 . then @xmath2 contains a planarizing collection of induced cycles with mininum distance at least @xmath0 . to give a taste of the proofs of the main results is this paper , we now prove that _ if @xmath11 is a triangulation of @xmath65 , @xmath71 , with edge - width at least @xmath72 , then @xmath2 has boxicity at most 7 . _ let @xmath66 be a planarizing collection of induced cycles with mininum distance at least 4 ( whose existence follows from theorem [ thm : placc ] ) in @xmath2 . we denote by @xmath58 the set of vertices lying in one of the @xmath73 s . we also denote by @xmath74 the set of vertices not in @xmath58 with at least one neighbor in @xmath58 , and set @xmath75 . since the collection @xmath66 is planarizing , the set @xmath76 induces a planar graph and therefore has a 3-box representation @xmath77 by the result of thomassen @xcite . we extend this representation to @xmath58 by mapping all the vertices of @xmath58 to a big 3-box containing all the other 3-boxes of the representation . since the distance in @xmath2 between any two cycles @xmath78 is at least 4 , there is no edge between a neighbor of @xmath73 and a neighbor of @xmath79 . as a consequence , the set @xmath80 induces a disjoint union of @xmath5 planar graphs ( and is therefore planar ) . let @xmath81 be a 3-box representation of this graph . we extend this representation to @xmath82 by mapping all the vertices of @xmath82 to a big 3-box containing all the other 3-boxes of the representation @xmath81 . finally , let @xmath83 be the interval graph mapping all the vertices of @xmath58 to @xmath84 , all the vertices of @xmath74 to @xmath85 $ ] , and all the vertices of @xmath82 to @xmath86 . we now prove that @xmath87 induces @xmath2 . each interval graph @xmath38 is clearly a supergraph of @xmath2 , so we only need to show that every pair of non - adjacent vertices @xmath88 in @xmath2 is non - adjacent in at least one of the @xmath38 s . this follows from the definition of @xmath77 if @xmath89 , and from the definition of @xmath81 if @xmath90 . finally if @xmath91 and @xmath92 then they are non - adjacent in @xmath83 , as desired.@xmath93 in section [ sec : locpla ] we will show that this argument can be applied to any embedded graph ( not only triangulations ) and that the bound on the boxicity can be improved to 5 . the idea will be to group @xmath94 , @xmath95 , and @xmath83 in a single interval graph . but for this we first need to see how much flexibility we have in choosing 3-box representations for planar graphs , which is the topic of the next section .

-box representation _ of a graph is a representation of as the intersection graph of a set of-boxes in . it was proved by thomassen in 1986 that every planar graph has a 3-box representation . in this paper we prove that every graph embedded in a fixed orientable surface , without short non - contractible cycles , has a 5-box representation . we show that such a function can be made linear in .

a _-box _ is the cartesian product of intervals of and a _ -box representation _ of a graph is a representation of as the intersection graph of a set of-boxes in . it was proved by thomassen in 1986 that every planar graph has a 3-box representation . in this paper we prove that every graph embedded in a fixed orientable surface , without short non - contractible cycles , has a 5-box representation . this directly implies that there is a function , such that in every graph of genus , a set of at most vertices can be removed so that the resulting graph has a 5-box representation . we show that such a function can be made linear in . finally , we prove that for any proper minor - closed class , there is a constant such that every graph of without cycles of length less than has a 3-box representation , which is best possible .

physics0605225

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it is now twenty years since ceperley and pollock ( cp ) carried out the first path integral monte carlo ( pimc ) simulation of the superfluid transition of liquid 4.@xcite albeit restricted to a system of 64 4 atoms with periodic boundary conditions , that study demonstrated the feasibility of _ ab initio _ numerical studies of quantum many - body systems , the mass of the particles and the interaction potential being the sole input to the calculation . the pimc method , in the form developed by cp ( henceforth referred to as conventional " ) , has since played a major role in the theoretical investigation of quantum many - body systems . not only has it provided quantitative results for a wide range of physical systems , it has also shaped , to some extent , our qualitative understanding of such phenomena as superfluidity ( sf ) and bose condensation , at the microscopic level . at least for bose systems , pimc is the _ only _ presently known method capable of furnishing in principle _ exact _ numerical estimates of physical observables at finite temperature ( @xmath3 ) , including the superfluid ( @xmath4 ) and condensate ( @xmath5 ) fractions . moreover , despite the notorious _ sign _ problem , that has so far made it impossible to obtain equally high quality results for fermi systems , pimc proves a valid option in this case as well , allowing one to obtain approximate estimates of accuracy at least comparable to that afforded by the other leading methods.@xcite it thus seems reasonable to regard pimc as a realistic option to investigate ever more complex quantum many - body systems , and it makes sense to try and overcome its most important present limitations . aside from the above - mentioned _ sign _ problem , which we do _ not _ discuss in this paper , the main bottleneck of the current pimc technology is inarguably the maximum system size ( i.e. , number @xmath6 of particles ) for which accurate estimates can be obtained , in a reasonable amount of computer time . specifically , the computational effort required to study properties that most directly depend on particle indistinguishability , is observed to scale prohibitively with @xmath6 . for example , the superfluid fraction @xmath4 is obtained in a pimc simulation of bulk condensed matter , by means of the so - called winding number estimator,@xcite which can only take on a nonzero value if long permutation cycles of identical particles occur . in conventional pimc , the frequency with which such cycles are sampled , is an _ exponentially _ decreasing function of @xmath6 . for this reason , and in spite of ( at least ) a hundredfold increase in computer speed,@xcite since the pioneering work of ref . it has not proven possible to obtain estimates of the superfluid fraction in bulk liquid 4 for finite systems of more than @xmath6=64 particles . besides the unfavorable scaling of computing resources as a function of @xmath6 , another major issue that this entails is the difficulty of assessing reliably whether the observed absence of long permutation cycles reflects a genuine physical effect , or merely lack of ergodicity of the path sampling scheme.@xcite how important is the above size limitation ? for most observables diagonal in the coordinate representation , one can often approach surprisingly closely the thermodynamic limit by simulating as few as @xmath7 30 particles , especially for systems characterized by short - ranged , lennard - jones - type interactions . on the other hand , an accurate _ quantitative _ characterization of the superfluid transition ( including the calculation of the transition temperature @xmath8 ) can only be obtained via finite - size scaling analysis of results for @xmath9 and/or @xmath10 . the reliability of this procedure crucially hinges on the availability of data for large systems of significantly different sizes . attempts to estimate @xmath8 for superfluid 4 , based on pimc data for @xmath9 for systems of size @xmath6=64 and smaller , failed to yield quantitative results.@xcite but there are other reasons , arguably more important than the mere pursuit of numerical accuracy , pointing to the importance and timeliness of extending by one or two orders of magnitude the size of the systems accessible to pimc . quite generally , in order for a scientific question to be meaningfully addressed by numerical simulations , the size of the simulated system should be greater than all characteristic length scales affecting the physics of interest . this is particularly important in the study of inhomogeneous phases of matter , or fluids in confinement , or restricted geometries . an example is provided by the study of helium fluid in porous glass , such as vycor ; the diameter of a characteristic pore is of the order of a few tens of . thus , a realistic calculation , at the typical liquid helium density , requires that one be able to simulate a system comprising several thousands of atoms . other examples are the numerical investigations of multicomponent systems , as well as of grain boundaries , dislocations and other defects in quantum solids , or of incommensurate phases of films of helium or _ para_-hydrogen adsorbed over substrates such as graphite . over the past two decades , there has been relatively little experimentation with approaches to pimc simulations differing in some important aspects from the conventional one of cp , thoroughly described in ref . . as mentioned above , in conventional pimc the simulation of properties that are most directly affected by quantum statistics ( i.e. , by many - particle permutations ) , suffers from a very unfavorable scaling of required computer time with system size . this hurdle seems difficult to conquer within conventional pimc , and more generally within any monte carlo scheme formulated in the canonical ensemble , in which the winding number becomes `` topologically locked '' in the @xmath11 limit.@xcite on the other hand , the same hurdle has been completely overcome in quantum monte carlo ( qmc ) simulations of lattice models . a lattice path integral scheme based on an alternative sampling approach , known as _ worm algorithm _ ( wa ) , @xcite has been demonstrated to allow for efficient calculations of winding numbers and of the one - particle green function @xmath12 , for systems of as many as @xmath7 10@xmath13 particles.@xcite it is particularly useful for the studies of critical phenomena since it does not suffer from the critical slowing down problem @xcite present in other local - update schemes . the wa has been recently extended to the study of systems in continuous space;@xcite it has first been shown to afford the simulation of the superfluid transition in liquid 4 in two dimensions , for systems comprising as many as 2500 particles , i.e. , about 100 times greater than those accessible to conventional pimc . subsequently , it has been applied to the study of bose condensation in crystalline 4,@xcite as well as to the investigation of superfluid properties of _ para_-hydrogen droplets.@xcite in all of these applications , the wa has provided accurate numerical results , simply not obtainable with any other existing method . it need be stressed , however , that the wa is not merely about doing large system sizes ( important as this is ) ; it is also the first _ grand canonical _ qmc method with local updates to incorporate in full quantum statistics . it affords the exact computation of imaginary - time off - diagonal correlations , such as the one - particle matsubara green function , that are not accessible to conventional pimc ( nor to any other qmc technique in continuous space ) . in this paper , we provide a detailed description of this new , powerful computational tool , which promises to open novel avenues to the theoretical exploration of strongly correlated many - body system . the manuscript is organized as follows : in the next section ( [ simplest ] ) , we describe the simplest implementation of the wa , also introducing our nomenclature , configurational space and data structure . in section [ mgf ] , we discuss in detail the computation of the matsubara green function , as well as of its equal - time limit , namely the one - particle density matrix . in section [ dia ] , we describe an important enhancement of the simple implementation , namely the expansion of ( the attractive part of ) the potential energy of interaction among particles in elementary ( diagrammatic ) contributions , that are then sampled by a monte carlo method . this scheme , which falls in the general category of diagrammatic monte carlo techniques,@xcite allows for the full inclusion of the contribution of the potential energy ( for an important class of potentials ) at a computational cost that is _ independent _ of the size of the system . in sec . [ add ] , we provide some quantitative information related to the specific utilization of the wa in simulation studies of superfluid 4 . in sec . [ resu ] , we offer a quantitative demonstration of the power of the wa , by illustrating in detail our results for simulations of the superfluid transition of liquid 4 in two and three dimensions . we outline our conclusions , and discuss outlook for future applications of the wa , in sec . [ conclusions ] .

a detailed description is provided of a new worm algorithm , enabling the accurate computation of thermodynamic properties of quantum many - body systems in continuous space , at finite temperature . the algorithm is formulated within the general path integral monte carlo ( pimc ) scheme , but also allows one to perform quantum simulations in the grand canonical ensemble , as well as to compute off - diagonal imaginary - time correlation functions , such as the matsubara green function , simultaneously with diagonal observables . another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary ( diagrammatic ) contributions , which are then statistically sampled . this affords a complete microscopic account of the long - range part of the potential energy , while keeping the computational complexity of all updates independent of the size of the simulated system .

a detailed description is provided of a new worm algorithm , enabling the accurate computation of thermodynamic properties of quantum many - body systems in continuous space , at finite temperature . the algorithm is formulated within the general path integral monte carlo ( pimc ) scheme , but also allows one to perform quantum simulations in the grand canonical ensemble , as well as to compute off - diagonal imaginary - time correlation functions , such as the matsubara green function , simultaneously with diagonal observables . another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary ( diagrammatic ) contributions , which are then statistically sampled . this affords a complete microscopic account of the long - range part of the potential energy , while keeping the computational complexity of all updates independent of the size of the simulated system . the computational scheme allows for efficient calculations of the superfluid fraction and off - diagonal correlations in space - time , for system sizes which are orders of magnitude larger than those accessible to conventional pimc . we present illustrative results for the superfluid transition in bulk liquid 4 in two and three dimensions , as well as the calculation of the chemical potential of _ hcp _ 4 . 4he 2 3

physics0605225

r

in this section , we present wa simulation results for bulk liquid @xmath0he in two and three dimensions , with the aim of demonstrating that superfluid properties and off - diagonal correlations can be calculated with the wa for very large system sizes , orders of magnitude larger than accessible to the conventional pimc technology . we use the standard interatomic ( aziz ) potential for helium , in an early form for consistency with other calculations.@xcite the reason for our choice of illustrative system , is simply that the simulation of 4 in its condensed phase is a _ de facto _ test bench for new computational many - body techniques . as mentioned above , we have utilized the form for @xmath209 suggested in ref . for all the calculations for which results are presented here . in both two and three dimensions , we have observed convergence of the kinetic energy estimates ( computed with the usual thermodynamic estimator@xcite ) using a time step @xmath251=1/640 k@xmath296 ; for all other quantities , four times a value of @xmath251 can be used , and the estimates are seeing to coincide , within their statistical uncertainties , with those extrapolated to the @xmath38 limit . we start with the two dimensional case and extend the study of the superfluid - normal liquid ( sf - n ) transition first carried out in ref . , at a density @xmath297 @xmath1 ; we consider system sizes up to hundred times larger than in the original study.@xcite in fig . [ fig5 ] we present data for the superfluid fraction @xmath9 , for systems comprising @xmath298 , @xmath299 , and @xmath300 atoms . since the sf - n transition in 2d is in the kosterlitz - thouless universality class,@xcite with strong ( logarithmic ) finite - size corrections , a reliable extrapolation to the thermodynamic limit requires that simulations be performed for significantly different number of particles . in the vicinity of the transition point , one may then employ the asymptotic ( in the limit of large distances ) vortex - pair renormalization group ( rg ) theory to fit the data . in our study , we used the same rg procedure as in ref . @xcite , which is based on the notion of the vortex core diameter , @xmath14 ( as a short - range cut - off for rg equations ) , and vortex energy , @xmath301 , to control vortex density at distance @xmath14 . only data in the narrow vicinity of the transition point 0.65 @xmath302 @xmath303 0.8 @xmath302 were used in the fitting procedure . our estimates for the values of the fitting parameters are @xmath304 for the vortex core diameter , and @xmath305=2.18 @xmath306 0.04 k for the vortex energy , which lead to an estimate for the critical temperature @xmath8=0.653@xmath3060.010 k. the vortex diameter ( roughly twice the interatomic distance ) turns out to be comparable to the linear system size @xmath307 for @xmath298 , clearly showing that the use of the asymptotic rg analysis is questionable for such a small system size . this fact also explains why our result for @xmath8 is significantly different from the previous estimate , 0.72@xmath3060.02 k , deduced from the @xmath298 data.@xcite in fig . [ fig6 ] , we show results for the single - particle density matrix @xmath308 . for 2d helium , this quantity is expected to decay to zero at all finite temperatures . in the normal phase , and far from the critical point , the decay is exponential . at the critical point , the decay is described by a slow power - law @xmath309 . the same law should be observed in the vicinity of the critical point up to exponentially large distances . at low @xmath3 , the exponent in the power law approaches zero . the data in fig . [ fig6 ] are in line with these expectations ; quantitatively , the slope of the @xmath308 curve on the log - log plot shown in the inset is close to one quarter . we wish to conclude this subsection by giving an example of typical ( without any extensive optimization ) algorithm parameters used for the two - dimensional helium . for the @xmath310 , @xmath311 , and @xmath298 system with @xmath312 , @xmath313 , @xmath314 , and @xmath315 the measured acceptance probabilities were @xmath316 , @xmath317 , @xmath318 , @xmath319 , @xmath320 , @xmath321 , @xmath322 , @xmath323 @xmath324 . as mentioned in the introduction , simulations of bulk 3d liquid helium were among the first remarkably successful applications of the pimc method . @xcite however , previous predictions made for the superfluid properties were never at the same level of accuracy as for energetic or structural properties , for reasons mentioned in the introduction . in this subsection , we show how the wa , based on updates described above , eliminates the shortcomings of the existing pimc method , by allowing simulations of several thousand atoms with sufficient precision to determine , for example , the critical temperature of the sf - n transition at the saturated vapor pressure ( svp ) with accuracy of three significant digits . in fig . [ fig7 ] , we show our data for the density matrix @xmath308 in the vicinity of the critical point , at the saturated vapor pressure ( at a temperature @xmath3=2.14 k and at a density @xmath325=0.02198 @xmath2 ) for system sizes @xmath326 and @xmath327 . though the data for small and large system sizes appear nearly identical in the main plot , the crucial difference is clearly seen in the inset . the @xmath326 curve terminates right after the first coordination shell oscillation ; the best estimate that can be obtained of the condensate fraction @xmath5 ( namely , the asymptotic value to which @xmath308 should plateau at long distances ) from this set of data alone , would be about @xmath328 . obviously , the same coordination shell oscillation prohibits _ a fortiori _ any reliable finite - size scaling for smaller system sizes , e.g. using series @xmath329 . in contrast , the @xmath327 system is large enough to see the effect of long - wavelength hydrodynamic phase fluctuations . the bogoliubov expression for the asymptotic behavior of @xmath330 at large distances in the superfluid , is given by @xmath331 \;. \label{ph_fl}\ ] ] since @xmath4 is calculated independently , the shape of the density matrix decay is fixed . the condensate fraction controls only the overall normalization of the theoretical curve , and this allows precise extrapolation of the data to the thermodynamic limit . an example of such extrapolation is shown in fig . [ fig7 ] by the solid line , which predicts @xmath332 for the condensate fraction @xmath5 at @xmath333nearly a factor of two smaller than the @xmath328 estimate obtained on a 64-atom system . the hydrodynamic correction to the tail of @xmath308 is less important at low temperature and for large values of @xmath4 . for comparison , in fig . [ fig8 ] we present data for a system of @xmath334 atoms , at a temperature @xmath310 ( in this case , the density is @xmath325=0.02184 @xmath2 ) . in this temperature range , smaller system sizes can be used to obtain reliable thermodynamic estimates of @xmath5 . our estimate for @xmath5 at @xmath3=1 k is 0.082@xmath3060.002 . this is consistent with the existing pimc estimate ( 0.07@xmath3060.01 at @xmath3=1.2 k , from ref . ) , obtained on a system of 64 4 atoms , but somewhat above the most recent @xmath3=0 estimate ( 0.069@xmath3060.005 , ref . ) . although the difference is only slightly greater than the combined statistical uncertainties , it should be noted that finite temperature calculations are _ unbiased _ , whereas ground state calculations are based on an input trial wave function . while it is in principle possible to remove the variational bias associated to the trial wave function , this may be difficult a goal to achieve in practice . having access to system sizes which allow asymptotic hydrodynamic description is a necessary condition for determining critical parameters using finite - size scaling techniques ( see , e.g. , ref ) . the idea is to consider quantities which are determined by system properties at the largest scales , becoming scale - invariant at the critical point . for small deviations from criticality , @xmath335 , the dependence on system size for such quantities is given by @xmath336 where @xmath337 and @xmath338 are the corresponding universal scaling functions ( @xmath338 is analytic at @xmath339 ) and @xmath340 is the correlation length which diverges at the critical point as @xmath341 . for the u(1 ) universality class in 3d , the best numerical estimate currently available for the correlation length exponent is @xmath342.@xcite the intersection of @xmath343 curves for different system sizes provides very accurate and unbiased estimates of critical parameters . previous attempts to determine @xmath344 from the scale - invariance of @xmath345 ( josephson relation ) have failed.@xcite though the authors of ref . correctly argue that the statistical uncertainty in the data is too large to accurately determine @xmath344 from the crossing of these [ scaling ] two curves " , it seems that coordination shell oscillations also contribute to several intersections in the 1.6 k @xmath346 2.4 k interval . in fig . [ fig9 ] , we show the temperature dependence of the superfluid fraction for various system sizes . after extrapolation to the thermodynamic limit , there is nearly perfect agreement between the numerical and experimental results . in order to determine the transition temperature @xmath8 , we perform finite - size scaling analysis of @xmath347 where * w*=@xmath348 is the winding number.@xcite the raw data are shown in fig [ fig10 ] . as an independent check , we also draw a horizontal line at the known u(1)-universality class value for winding number fluctuations at the critical point . @xcite from the intersection of scaling curves ( which is seen to take place at the universal value , within the statistical uncertainties ) , we find @xmath349 . the difference between this prediction and the experimental value , 2.177 k , is very small , i.e. , simulations of the superfluid density dependence on system size in the vicinity of the critical point , do allow us to calculate @xmath8 with a relative accuracy of better than 0.5% . there is no reason to expect the aziz pair potential to reproduce @xmath8 with much better accuracy , as it was not optimized for this purpose . it is only a very good approximation to the true interatomic potential for @xmath0he which , in reality , includes irreducible forces acting between three and more particles.@xcite condensate density has been consistently one the most difficult properties to compute and measure for helium . shown in fig . [ fig11 ] are available experimental data @xcite along with the previous pimc results @xcite and new estimates obtained in the present study , extrapolated to the thermodynamic limit as explained above . with new technology we substantially reduce theoretical uncertainties on predictions of @xmath350 at the svp . we conclude by mentioning that we have also obtained estimates for all other standard thermodynamic quantities , such as the kinetic energy , pair correlation function etc . our data are generally consistent with those of existing calculations ; specifically , our @xmath3=1 k results are indistinguishable , within statistical uncertainties , from those yielded by numerically exact ground state methods ( see , e.g. , ref . ) .

the computational scheme allows for efficient calculations of the superfluid fraction and off - diagonal correlations in space - time , for system sizes which are orders of magnitude larger than those accessible to conventional pimc . we present illustrative results for the superfluid transition in bulk liquid 4 in two and three dimensions , as well as the calculation of the chemical potential of _ hcp _ 4 .

a detailed description is provided of a new worm algorithm , enabling the accurate computation of thermodynamic properties of quantum many - body systems in continuous space , at finite temperature . the algorithm is formulated within the general path integral monte carlo ( pimc ) scheme , but also allows one to perform quantum simulations in the grand canonical ensemble , as well as to compute off - diagonal imaginary - time correlation functions , such as the matsubara green function , simultaneously with diagonal observables . another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary ( diagrammatic ) contributions , which are then statistically sampled . this affords a complete microscopic account of the long - range part of the potential energy , while keeping the computational complexity of all updates independent of the size of the simulated system . the computational scheme allows for efficient calculations of the superfluid fraction and off - diagonal correlations in space - time , for system sizes which are orders of magnitude larger than those accessible to conventional pimc . we present illustrative results for the superfluid transition in bulk liquid 4 in two and three dimensions , as well as the calculation of the chemical potential of _ hcp _ 4 . 4he 2 3

1606.00390

i

photonic crystals , which consist of a periodically arranged lattice of dielectric scatterers , have attracted substantial research interest over the past decade @xcite . most commonly these structures are used to trap , guide , and otherwise manipulate pulses of light , and have led to a variety of important applications in modern nanophotonics , including extremely high - q electromagnetic cavities @xcite and slow - light propagation of electromagnetic pulses @xcite . however , a new and increasingly important application of photonic crystal structures is in the field of photovoltaics . it has long been known that structured materials can be used to achieve photovoltaic conversion efficiency beyond the yablonovitch limit @xcite , and indeed researchers have recently proposed photonic crystals @xcite and arrays of dielectric nanowires @xcite as inexpensive ways to create highly efficient absorbers . recent research in this area has been driven by advances in nanostructure fabrication @xcite concurrent with increased investment in renewable energy technology ( for the latest developments see @xcite ) . one aspect in which the use of photonic crystals in photovoltaics differs markedly from their employment in optical nanophotonics is the important role played by material absorption . for most nanophotonic applications absorption is an undesirable effect which must in general be minimized and can in many cases be neglected . this is in stark contrast to photovoltaics , in which the main aim is to exploit the properties of the structure to increase the overall absorption efficiency . modeling of absorbing photonic crystals has thus far been performed using direct numerical methods such as the finite - difference time - domain ( fdtd ) method @xcite , the finite element method ( fem ) @xcite or using the transfer matrix method @xcite . although these methods have produced valuable information about the absorption properties of such structures they do not allow us to gain direct physical insight into the mechanism of the absorption within them . furthermore , these calculations require substantial computational time and resources . here we present a rigorous modal formulation of the scattering and absorption of a plane wave by an array of absorbing nanowires , or , correspondingly , an absorbing photonic crystal slab ( fig . [ slab ] ) . the approach is a generalization of diffraction by capacitive grids formulated initially in refs @xcite for perfectly conducting cylinders . in contrast to conventional photonic crystal calculations the material absorption is taken into account rigorously , using measured values for the real and the imaginary parts of the refractive indices of the materials comprising the array . our formulation can be applied to array elements of arbitrary composition and cross - section . the semi - analytical nature of this modal approach results in a method which is quick , accurate , and gives extensive physical insight into the importance of the various absorption and scattering mechanisms involved in these structures . the method is based on an expansion in terms of the fundamental eigenmodes of the structure in each different region . within the photonic crystal slab the fields are expanded in terms of bloch modes , while the fields in free space above and below the slab are expanded in a basis of plane waves . these expansions are then matched using the continuity of the tangential components of the fields at the top and the bottom interfaces of the slab to compute fresnel interface reflection and transmission matrices . an important aspect of this approach is that the set of bloch modes must form a complete basis . this is not a trivial matter , as even for structures consisting of lossless materials the eigenvalue problem for the bloch modes is not formally hermitian . however , it is well known from the classical treatment of non - hermitian eigenvalue problems that a complete basis may be obtained by including the bloch modes of the adjoint problem . here , we use the fem to compute both the bloch modes and the adjoint bloch modes . because the mode computation may be carried out in two dimensions ( 2d ) like waveguide mode calculations , this routine is highly efficient . we note that a previous study @xcite , undertaken using a different method , failed to locate some of the modes , as is demonstrated in sec . [ section : dispersion ] ; we emphasis that the algorithm presented here is capable of generating a complete set of modes . in addition the fem allows us to compute bloch modes for arbitrary materials and cross sections . we note that this approach differs from earlier formulations @xcite in which the photonic crystal had to consist of an array of cylinders with a circular cross - section . with the modes identified , the transmission through , and reflection from , the slab can be computed using a generalization of fresnel reflection and transmission matrices , and the absorption is found using an energy conservation relation . the organization of the paper is as follows . the theoretical foundation of the method is given in sec . [ formulation ] while the numerical verification , validation and characterization of the absorption properties of a particular silicon nanowire array occurs in sec . [ applica ] . the details of the mode orthogonality , normalization , completeness as well as energy and reciprocity relations are given in the appendices .

a finite element - based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications . the semi - analytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell . this approach gives direct physical insight into the absorption mechanism in such structures , which can be used to enhance the absorption .

a finite element - based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications . the semi - analytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell . this approach gives direct physical insight into the absorption mechanism in such structures , which can be used to enhance the absorption . the verification and validation of this approach is applied to a silicon nanowire array and the efficiency and accuracy of the method is demonstrated . the method is ideally suited to studying the manner in which spectral properties ( e.g. , absorption ) vary with the thickness of the array , and we demonstrate this with efficient calculations which can identify an optimal geometry .

0708.3059

i

characterization of statistical properties of coherent waves propagating through an elastically scattering disordered medium is relevant for a variety of physical situations , ranging from propagation of electromagnetic waves through interstellar space or the atmosphere , seismology , and medical imaging by ultrasound or light , to electron transport in disordered conductors . when coherent waves propagate through such media their intensity exhibits random , sample - specific , fluctuations known as speckles . these fluctuations result from the interference of rays traveling along different paths . in this article we study the statistics of speckles . the problem can be characterized by several length scales : the propagation distance of the ray through the medium , @xmath0 , the elastic mean free path , @xmath1 , which is the typical distance the ray travels between two scattering events , and the transport mean free path , @xmath2 which characterizes the typical distance for backscattering . in the limit of very thin sample , @xmath3 , rays move almost ballistically through the sample , since scattering porbability is small . this regime has been extensively studied @xcite . in the opposite limit of a very wide sample , @xmath4 , the rays propagate diffusively in the system . this regime has been considered in refs . . at spatial scales exceeding the transport mean free path the statistical properties of speckles in the diffusive regime ( excluding features associated with rare events ) are characterized by the diffusion coefficient and are independent of the details of the disorder . the crossover between the ballistic and the diffusive regimes depends , in general , on the features of the disorder . however , when the typical deflection angle for a single scattering is small , and therefore the transport mean free path @xmath2 is much larger than the mean free path @xmath1 , a third regime emerges . this regime , known as the directed waves regime , is realized when the sample width is much smaller than the transport mean free path while it is much larger than the elastic mean free path , @xmath5 . in this case , the rays experience many small angle scattering events which result in a diffusive dynamics of the ray direction . the total change in propagation direction , however , remains small . the focus of our study is on directed waves which are important for many applications ranging from laser communications in atmosphere to propagation of acoustic or electromagnetic waves through biological tissues . similarly to the ballistic and the diffusive regimes , the directed waves regime has also been studied in many papers ( see for example refs . and references therein ) . however , our results , in many respects , differ substantially from those obtained in previous studies . one of the main differences is the slow power law decay of the intensity correlation function in space , and the change of its sign , see fig . [ fig : main ] . this difference affects interpretation of any wave intensity measurement which uses a finite aperture apparatus . , in the directed waves regime . @xmath6 is the distance between the observation points , @xmath7 is the light wavelength , @xmath1 is the elastic mean free path , @xmath0 is the slab width , and @xmath8 and @xmath9 are the typical scattering angle of a ray traveling a distance @xmath1 and @xmath0 respectively.,width=302 ] in this article we develop a general method for calculating speckle correlations over distances larger than the light wavelength , @xmath7 . this method , which is similar ( but not identical ) to the langevin scheme for the description of classical fluctuations @xcite , enables one to treat both the diffusive and the directed wave regimes on equal footing . we apply the method to the case of directed waves to evaluate speckle correlations and their sensitivity to various perturbations , such as a change in the frequency of the wave , a variation of the incidence angle , or a change of the refraction index . a short version of these results was published in ref . . the paper is organized as follows . in section [ sec : general ] we present the general method describing speckle statistics . in sections [ sec : angular ] and [ sec : diffusion ] we consider its limiting cases for angular and spatial diffusion . the treatment of sensitivity of speckle patterns to changes in external parameters is presented in section [ sec : sensitivities ] . in section [ sec : directed ] we apply our formalism to study speckle correlations in the directed wave regime , and spatial diffusion . finally , in section [ sec : conclusions ] we present our conclusions . the derivation of the formalism is deferred to the appendices .

a general method for calculating statistical properties of speckle patterns of coherent waves propagating in disordered media is developed . it allows one to calculate speckle pattern correlations in space , as well as their sensitivity to external parameters . this method , which is similar to the boltzmann - langevin approach for the calculation of classical fluctuations , applies for a wide range of systems : from cases where the ray propagation is diffusive to the regime where the rays experience only small angle scattering . we demonstrate the applicability of the method by calculating the correlation function of the wave intensity and its sensitivity to the wave frequency and the angle of incidence of the incoming wave .

a general method for calculating statistical properties of speckle patterns of coherent waves propagating in disordered media is developed . it allows one to calculate speckle pattern correlations in space , as well as their sensitivity to external parameters . this method , which is similar to the boltzmann - langevin approach for the calculation of classical fluctuations , applies for a wide range of systems : from cases where the ray propagation is diffusive to the regime where the rays experience only small angle scattering . the latter case comprises the regime of directed waves where rays propagate ballistically in space while their directions diffuse . we demonstrate the applicability of the method by calculating the correlation function of the wave intensity and its sensitivity to the wave frequency and the angle of incidence of the incoming wave . # 1

1402.2968

i

disentangling the effects of electron - electron interactions in the ground and excited states of low - dimensional systems has become an exciting challenge in contemporary condensed matter physics . @xcite in particular , the discovery of high - tc superconductivity in the cuprates @xcite has acted as a driving force to develop theoretical models able to account for the most relevant correlations in many - electron systems in the simplest possible way . within this context , the repulsive hubbard model @xcite has been widely studied for several reasons including that it represents a prototype for the mott transition between a metal and an antiferromagnetic insulator @xcite and the suggestion @xcite that it contains the basic physics associated with high - tc superconductivity . the phenomenon of colossal magnetic resistance @xcite has also attracted considerable attention . on the other hand , the study of the high - tc iron - based superconductors @xcite has become a very active research area . @xcite here , calculations in terms of multi - orbital hubbard - like models have already provided valuable insight into the interplay between doping and the strength of the electronic correlations in these exotic superconductors . @xcite hubbard models represent valuable tools to study cold fermionic atoms in optical lattices @xcite as well as the properties of graphene . @xcite it has also become clear that their strong coupling limits , i.e. , the heisenberg models , @xcite can be quite useful to study low - dimensional magnets whose properties might be relevant for real materials found in nature and/or synthesized by means of crystal growing . @xcite the previous examples already show the central role of hubbard - like lattice models and their strong coupling versions to obtain insight into the properties associated with the emergent complexity in many - electron problems . precisely , it is this complexity that requires the use of different approximations to describe low - dimensional systems . among the available theoretical tools we have , for example , exact diagonalizations for small lattices @xcite while for the larger ones , we can resort to quantum monte carlo , @xcite variational monte carlo , @xcite coupled cluster , @xcite variational reduced - density - matrix @xcite and density matrix renormalization group @xcite methods , as well as approximations based on matrix product and tensor network states . @xcite both frequency - dependent and frequency - independent embedding approaches @xcite are also actively pursued . [ table1 ] cccccccccccccccccccc + @xmath2 & & & & & @xmath3=30 & @xmath4 & & @xmath3=26 & @xmath4 & & & @xmath3=22 & @xmath4 & & @xmath3=18 & @xmath4 & & @xmath3=14 & @xmath4 + + + 2@xmath5 & & & rhf & & -23.2671 & & & -26.1642 & & & & -26.8921 & & & -25.5587 & & & -22.3390 & + & & & hf & & -23.4792 & 10.02 & & -26.1642 & 0 & & & -26.8921 & 0 & & -25.5587 & 0 & & -22.3390 & 0 + & & & fed & & -25.3800 & 99.83 & & -28.0201 & 99.72 & & & -28.4391 & 99.68 & & -26.7816 & 99.69 & & -23.2365 & 99.74 + & & & fed@xmath6 & & -25.3730 & 99.50 & & - & - & & & - & - & & - & - & & - & + & & & reshf & & -25.3436 & 98.11 & & -27.9979 & 98.52 & & & -28.4268 & 98.88 & & - & - & & - & - + & & & exact & & -25.3835 & & & -28.0253 & & & & -28.4441 & & & -26.7854 & & & -23.2388 & + + + 4@xmath5 & & & rhf & & -8.2671 & & & -14.8975 & & & & -18.8254 & & & -20.1587 & & & -19.0723 & + & & & hf & & -14.0732 & 64.75 & & -17.3756 & 34.96 & & & -20.1328 & 23.42 & & -21.1011 & 22.45 & & -19.8855 & 27.84 + & & & fed & & -17.2081 & 99.71 & & -21.9193 & 99.04 & & & -24.3497 & 99.03 & & -24.3222 & 99.19 & & -21.9824 & 99.63 + & & & fed@xmath6 & & -17.1789 & 99.39 & & - & - & & & - & - & & - & - & & - & + & & & reshf & & -17.0542 & 98.00 & & -21.5720 & 94.15 & & & -24.1582 & 95.56 & & - & - & & - & - + & & & exact & & -17.2335 & & & -21.9868 & & & & -24.4057 & & & -24.3561 & & & -21.9932 & + + + 8@xmath5 & & & rhf & & 21.7329 & & & 7.6358 & & & & -2.6921 & & & -9.3587 & & & -12.5390 & + & & & hf & & -7.8329 & 93.65 & & -11.2049 & 79.45 & & & -14.9299 & 69.32 & & -18.1922 & 70.12 & & -19.0005 & 77.96 + & & & fed & & -9.8260 & 99.95 & & -15.8927 & 99.22 & & & -20.1711 & 99.01 & & -21.8777 & 99.38 & & -20.8062 & 99.75 + & & & fed@xmath6 & & -9.7612 & 99.75 & & - & - & & & - & - & & - & - & & - & + & & & reshf & & -9.5378 & 98.46 & & -15.4059 & 97.17 & & & -19.5552 & 95.52 & & - & - & & - & - + & & & exact & & -9.8387 & & & -16.0761 & & & & -20.3462 & & & -21.9555 & & & -20.8271 & + + the exact bethe ansatz solution of the one - dimensional ( 1d ) hubbard hamiltonian is well known , @xcite which is not the case for the two - dimensional ( 2d ) model . on the other hand , in spite of the considerable progress already made , the exact 1d wave functions still remain difficult to handle in practice when computing several physical properties . @xcite it has also remained difficult to obtain an intuitive physical picture of the basic units of quantum fluctuations @xcite using the lieb - wu solutions @xcite and/or within the theoretical frameworks already mentioned above . this task is further complicated by the fact that quantum fluctuations can exhibit unconventional features in low - dimensional systems . a typical example , is the spin - charge separation in the strong coupling regime of the 1d hubbard model . @xcite angle - resolved photoemission spectroscopy results also reveal a complex pattern of spin - charge coupling / decoupling both in 1d and 2d systems @xcite in the weak and intermediate - to - strong interaction regimes . therefore , it is highly desirable to explore the performance of alternative wave function based approaches that , on the one hand , could complement existing state - of - the - art theoretical tools and , on the other hand , lead us to compact states whose ( intrinsic ) structures are simple enough to be interpreted in terms of basic units of quantum fluctuations in half - filled and doped lattices . within this context , the 1d hubbard model represents a challenging testing ground since both its exact solution and highly accurate density matrix renormalization group results are available . the last years have seen some progress in this direction within the framework of the single - reference ( sr ) and multi - reference ( mr ) symmetry - projected approximations @xcite which are routinely used in nuclear structure physics . @xcite note that in quantum chemistry the names single - component and multi - component have been adopted @xcite instead of single - reference and multi - reference , respectively . recently , a hierarchy of symmetry - projected variational approaches @xcite has been applied to describe both the ground and excited states of the 1d and 2d hubbard models . @xcite in its simplest ( i.e. , sr ) form , the symmetry - projected variation - after - projection ( vap ) method @xcite resorts to a hartree - fock - type @xcite ( hf ) trial state @xmath7 that deliberately breaks several symmetries of the considered hamiltonian . the method then superposes , with the help of projection operators , @xcite a degenerate manifold of goldstone states @xmath8 , with @xmath9 being a symmetry operation . in this way one recovers a set of quantum numbers associated with the original symmetries of the hamiltonian . already at this sr level genuine defects are induced in the intrinsic determinant @xmath7 resulting from the vap procedure . therefore , its structure differs from the one obtained within the standard hf approximation . @xcite this kind of sr symmetry - projected framework has already enjoyed considerable success in quantum chemistry . @xcite an extension of the sr method @xcite has been previously used @xcite to describe half - filled and doped 2d hubbard lattices . with the help of chains of vap calculations , it provides a ( truncated ) basis consisting of a few ( orthonormalized ) symmetry - projected configurations which can then be used to further diagonalize the considered hamiltonian . in this way , one can account on an equal footing for additional correlations in both ground and excited states keeping well defined symmetry quantum numbers . the method also provides a well - controlled ansatz to compute both spectral functions ( sfs ) and density of states ( dos ) . @xcite in quantum chemistry , the first benchmark calculations on the @xmath10 dimer have shown that , with a modest basis set , this methodology provides a high quality description of the low - lying spectrum for the entire dissociation profile . in addition , the same methodology has been applied to obtain the full low - lying spectrum of formaldehyde as well as to a challenging model @xmath11 insertion pathway for beh@xmath12 . @xcite obtained with the fed approximation is plotted as a function of the inverse of the number of ghf transformations for a lattice with @xmath13=30 sites and @xmath3=22 electrons . results are shown for on - site repulsions of @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 . for details , see the main text . , scaledwidth=50.0% ] however , being already more sophisticated than the sr framework , @xcite the extension @xcite mentioned above still essentially describes a given ground and/or excited state in terms of a single symmetry - projected configuration . this certainly limits the amount of correlations that can be accessed for those states . a more correlated description is encoded in a mr scheme . @xcite here , one resorts to a set of symmetry - broken hf states @xmath14 and superposes their goldstone manifolds @xmath15 . in this way , a given state with a well defined set of quantum numbers is expanded in terms of @xmath16 nonorthogonal symmetry - projected configurations @xcite that are optimized with the help of the ritz variational principle @xcite applied to the projected energy . there are several ways to perform the self - consistent optimization of the intrinsic hf states @xmath14 within a mr approach . one possible vap strategy is represented by the resonating hf @xcite ( reshf ) scheme within which all the determinants @xmath14 are optimized at the same time . another vap strategy is represented by the few determinant @xcite ( fed ) approach where , the hf transformations @xmath17 are optimized one - at - a - time . in both the reshf and fed schemes , the corresponding configuration mixing coefficients are determined through resonon - like equations . @xcite we note that there is no need for the fed expansion to be short , as its name would imply , although this is a desirable feature . in the present study , we keep the acronym to remain consistent with the literature . @xcite hybrid mr approximations are also possible . for example , one could optimize @xmath18 states using the reshf scheme and @xmath19 states using the fed one . the fed methodology has already been used @xcite to compute ground state energies , spin - spin correlation functions ( sscfs ) in real space , magnetic structure factors ( msfs ) as well as spin - charge separation tendencies in the sfs of half - filled 1d hubbard lattices of different sizes in the weak , intermediate - to - strong , and strong interaction regimes . we have shown @xcite that short reshf and fed expansions can provide an accurate description of chemical systems such as the nitrogen and water molecules along the entire dissociation profile , as well as an accurate interconversion profile among the peroxo and bis(@xmath20-oxo ) forms of [ cu@xmath12o@xmath12]@xmath22 comparable to other state - of - the - art quantum chemical methods . recent calculations , @xcite have also considered the complex binding pattern in the mo@xmath12 molecule . in addition to ground state properties , the excited few determinant @xcite ( excited fed ) scheme has also been used @xcite to treat excited states , with well defined quantum numbers , as expansions in terms of nonorthogonal symmetry - projected configurations . as a byproduct of vap calculations , the excited fed provides a ( truncated ) basis consisting of a few gram - schmidt orthonormalized states , each of them expanded in a given number of nonorthogonal symmetry - projected configurations , which may be used to perform a final diagonalization of the hamiltonian to account for a more correlated description of both ground and excited states . let us stress , that each of the mr approaches already mentioned has its own advantages and drawbacks . a reshf wave function is stationary with respect to arbitrary changes in the hf transformations @xcite @xmath23 ( i=1 , @xmath24 , @xmath16 ) while a fed one displays stationarity only with respect to the last added transformation . therefore , the reshf wave functions become easier to work with in the evaluation of those properties depending on derivatives of the wave function . however , in a reshf optimization , @xmath25 hamiltonian and norm kernels have to be recomputed at every iteration while only @xmath26 kernels are required in an efficient implementation of the fed method . @xcite regardless of the fed and/or reshf vap strategy adopted , the mr approximations are not restricted by the dimensionality ( i.e. , they can be equally well applied to 1d and 2d systems ) and/or the topology of the considered lattices . on the other hand , one of the most attractive features of the mr approximations is that they offer compact wave functions , with well defined quantum numbers , whose quality can be systematically improved by increasing the number of symmetry - projected configurations included in the corresponding ansatz . @xcite obviously , one is always limited in practical applications to a finite number @xmath16 of symmetry - projected terms in the fed and/or reshf expansions . however , it should also be kept in mind that both the reshf and fed wave functions are nothing else than a discretized form of the exact coherent state representation of a fermion state @xcite and , therefore , become exact in the limit @xmath27 . all in all , we believe that symmetry - projected approximations , already quite successful in nuclear physics , @xcite lead to a rich conceptual landscape and deserve further attention in quantum chemistry @xcite and condensed matter physics . @xcite they also provide @xcite high quality trial states that can be used within the constrained - path monte carlo @xcite scheme , increasing the energy accuracy and decreasing the statistical variance as more symmetries are broken and restored . in this paper we apply , for the first time , the fed approach to doped systems . therefore , our main goal is to test its performance using benchmark calculations . to this end , we have selected the 1d hubbard model for which both exact and highly accurate density matrix renormalization group ( dmrg ) results can be obtained . for the sake of completeness and comparison we will also discuss half - filling results . in sec . [ theory ] , we briefly describe the key ingredients of our mr approach . for a more detailed account , the reader is referred to our previous works . @xcite in sec . [ results ] , we discuss the results of our calculations . we have first paid attention to lattices with @xmath13=30 sites and @xmath3=14 , 18 , 22 , 26 , 30 electrons as illustrative examples . calculations have been performed for the on - site repulsions @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 representing the weak , intermediate - to - strong ( i.e. , noninteracting band width ) , and strong interaction regimes , respectively . in sec . [ gsandcoenergies ] , we compare our ground state and correlation energies with the exact ones as well as with those obtained using other theoretical methods . the dependence of the correlation energies predicted for doped lattices with the number of transformations included in our mr ansatz is also discussed in the same section . the basic units of quantum fluctuations in the case of doped lattices are discussed in sec . [ unitsqf ] , where we consider the structure of the symmetry - broken determinants resulting from the fed vap procedure . next , in secs . [ modistribution ] and [ correfunctions ] , we benchmark our results for momentum distributions , sscfs , and density - density ( ddcfs ) correlation functions with dmrg ones obtained with the open - source alps software . @xcite a typical outcome of our calculations for sfs and dos @xmath28 is presented in sec . [ spectral ] , where we consider a lattice with @xmath13=30 sites and @xmath3=26 electrons at @xmath2=4@xmath5 . next , in sec . [ larger - sites ] , we illustrate the performance of the fed method in the case of larger lattice sizes . finally , sec . [ conclusions ] is devoted to the concluding remarks and work perspectives .

a multi - reference configuration mixing scheme is used to describe the ground state , characterized by well defined spin and space group symmetry quantum numbers as well as doping fractions , of one dimensional hubbard lattices with nearest - neighbor hopping and periodic boundary conditions . within this scheme , each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry - projected configurations . the results obtained for the ground state and correlation energies of half - filled and doped lattices with 30 , 34 and 50 sites , compare well with the exact lieb - wu solutions as well as with the ones obtained with other state - of - the - art approximations . the spectral functions and density of states , computed with an ansatz whose quality can be well - controlled by the number of symmetry - projected configurations used to approximate the electron systems , display features beyond a simple quasiparticle distribution , as well as spin - charge separation trends .

a multi - reference configuration mixing scheme is used to describe the ground state , characterized by well defined spin and space group symmetry quantum numbers as well as doping fractions , of one dimensional hubbard lattices with nearest - neighbor hopping and periodic boundary conditions . within this scheme , each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry - projected configurations . the results obtained for the ground state and correlation energies of half - filled and doped lattices with 30 , 34 and 50 sites , compare well with the exact lieb - wu solutions as well as with the ones obtained with other state - of - the - art approximations . the structure of the intrinsic symmetry - broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations . it is also shown that in the case of doped 1d lattices , a part of such fluctuations can also be interpreted in terms of polarons . in addition to momentum distributions , both spin - spin and density - density correlation functions are studied as functions of doping . the spectral functions and density of states , computed with an ansatz whose quality can be well - controlled by the number of symmetry - projected configurations used to approximate the electron systems , display features beyond a simple quasiparticle distribution , as well as spin - charge separation trends .

1402.2968

c

in this section , we discuss the results of our fed calculations . first , we pay attention to lattices with @xmath13=30 sites and @xmath3=14 , 18 , 22 , 26 , 30 electrons . results are presented for on - site repulsions @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 , respectively . in sec . [ gsandcoenergies ] , we compare the ground state and correlation energies with the exact ones , as well as with results obtained using other theoretical approaches . we also discuss , for the case of doped lattices , the dependence of the correlation energies on the number @xmath16 of nonorthogonal symmetry - projected ghf configurations . next , in sec . [ unitsqf ] , we consider the structure of the intrinsic ghf determinants resulting from our vap procedure in the case of doped lattices . the momentum distributions are presented in sec . [ modistribution ] while the fourier transforms of the sscfs and ddcfs in real space are shown in sec . [ correfunctions ] . they are compared with those obtained within the dmrg framework retaining 1024 states in the renormalization procedure . on the other hand , in sec . [ spectral ] , we discuss spin - charge separation tendencies in the sfs and dos @xmath28 of a lattice with @xmath13=30 sites and @xmath3=26 electrons . finally , in sec . [ larger - sites ] , we illustrate the performance of the fed method in the case of larger lattices . in table [ table1 ] , we compare the exact @xcite and the predicted fed ground state energies for half - filled and doped lattices with @xmath13=30 sites and @xmath3=14 , 18 , 22 , 26 , 30 electrons . the corresponding @xmath55 = ( 0,0 ) ground states have a@xmath72 symmetry , i.e. , they are symmetric under the reflection @xmath73 . for @xmath2=2@xmath5 and 4@xmath5 , the fed energies shown in the table have been obtained by including @xmath16=60 nonorthogonal symmetry - projected ghf configurations in the ansatz eq.([fed - state - general ] ) . on the other hand , @xmath16=150 ghf transformations have been used for @xmath2=8@xmath5 . besides the rhf energies , we have included in table [ table1 ] the lowest possible hf solution for completeness . at @xmath2=2@xmath5 , the lowest - energy hf solution coincides with the rhf one in the case of doped systems while an uhf solution is obtained at half - filling . at @xmath2=4@xmath5 the hf state corresponds to an uhf wave function while for @xmath2=8@xmath5 we have found a ghf solution with predominant ferromagnetic character . in the same table , we also show our previous results @xcite ( fed@xmath6 ) , based on @xmath16=25 ghf transformations , and the reshf ones @xcite obtained with @xmath16=30 uhf transformations . we have computed the ratio @xmath74 in order to check how well the fed correlation energies reproduce the exact ones . for the other approximations , such a ratio is obtained from a similar expression . = 30 lattices with 14 ( orange diamonds ) , 18 ( magenta diamonds ) , 22 ( cyan diamonds ) , 26 ( green diamonds ) , and 30 ( red triangles ) electrons are shown for @xmath2=2@xmath5 ( a ) , 4@xmath5 ( b ) , and 8@xmath5 ( c ) . dmrg results ( black triangles ) are also included for comparison . starting with 26 electrons , all the curves have been successively shifted by 0.3 to accomodate them in a single plot . , scaledwidth=40.0% ] the first noticeable feature from table [ table1 ] is that , at most , the standard hf solutions account for 93.65 @xmath75 of the exact correlation energy . regardless of the filling and/or the interaction strength , the mr fed expansion clearly recovers a very large portion of correlation energy ( i.e. , @xmath76 @xmath77 99 @xmath75 ) in all cases studied . for the half - filled case as well as for the lattices with 26 and 22 electrons , the ground state and correlation energies improve the reshf and fed@xmath6 ones obtained in previous studies . @xcite on the other hand , the dmrg energies ( not shown in the table ) are exact to all the quoted figures . we have further used the dmrg results in secs . [ modistribution ] and [ correfunctions ] to benchmark our calculations for momentum distributions and correlation functions . from these results and the ones obtained in our previous work , @xcite we conclude that the fed scheme provides a reasonable starting point to obtain correlated ground state wave functions , with well defined symmetry quantum numbers , in both half - filled and doped 1d hubbard lattices . in addition , the method offers a systematic way to improve , through chains of vap calculations , the quality of such wave functions by increasing the number @xmath16 of nonorthogonal symmetry - projected ghf configurations included in the fed ansatz . this is illustrated in fig . [ en - vs - tra ] where we have plotted , as a function of the inverse @xmath78 of the number of transformations , the ratio @xmath76 for a doped lattice with @xmath13=30 sites and @xmath3=22 electrons . one sees that @xmath76 increases smoothly and approaches the exact result as the number of symmetry - projected configurations is increased . for example , a single symmetry - projected configuration provides @xmath76=93.14 @xmath75 , 85.67 @xmath75 , 87.08 @xmath75 while increasing the number of ghf transformations up to @xmath16=10 we obtain @xmath76=98.37 @xmath75 , 96.23 @xmath75 and 94.35 @xmath75 for @xmath2=2@xmath5 , 4@xmath5 and 8@xmath5 , respectively . some comments are in order here . first , since the nature of the quantum correlations varies for different doping fractions @xmath79 and on - site repulsions , one can expect that the number of ghf transformations required to obtain a given @xmath76 ratio depends on both of them . as already mentioned the fed wave functions become exact in the limit @xmath27 . in practice we are always limited to a finite number of nonorthogonal symmetry - projected configurations in the fed expansion and it is difficult to assert beforehand how many of them are required . therefore , their number @xmath16 should be tailored , through chains of vap calculations , so as to reach a reasonable accuracy not only in the ground state energy but also in other physical quantities like , for example , the spin - spin correlators . in the present study we have used a fixed number @xmath16=60 for both the weak and intermediate - to - strong interaction regimes while a larger number @xmath16=150 is required to obtain the energies reported in table [ table1 ] at @xmath2=8@xmath5 . as we will see later on in sec . [ correfunctions ] , a larger number of transformations is also required , especially close to half - filling , to improve the quality of the predicted correlation functions . this can be qualitatively understood from the crossover in the sscfs @xcite that explains how the antiferromagnetic spin correlation at half - filling grows near half - filling . one may then expect strong quantum fluctuations near half - filling , whose basic units ( see , sec . [ unitsqf ] ) can only be captured with larger fed expansions . the performance of the fed method for larger lattices will be discussed in sec . [ larger - sites ] . in our previous study @xcite of the half - filled 1d hubbard model we have considered two orders parameters , i.e. , the spin density ( sd ) @xmath80 and the charge density ( cd ) @xmath81 associated with an arbitrary symmetry - broken determinant @xmath7 , with j=1 , @xmath24 , @xmath13 being the lattice index . the comparison of the sd and cd computed with the standard uhf solution and the ones obtained using the ghf determinants @xmath14 resulting from the fed vap procedure , reveals that @xmath82 displays neutral [ i.e. , @xmath83=0 ] solitons @xcite whose translational and breathing motions can be regarded @xcite as the basic units of quantum fluctuations in the fed wave functions eq.([fed - state - general ] ) . the question naturally arises , as to what are the basic units of the quantum fluctuations captured within the fed vap optimization in the case of doped 1d lattices . among all the ghf transformations @xmath17 used to describe the lattice with @xmath13=30 sites and @xmath3=18 electrons ( see , sec . [ gsandcoenergies ] ) , we have selected some typical examples to plot in figs . [ solitons - n30-ne18-u2 ] , [ solitons - n30-ne18-u4 ] and [ solitons - n30-ne18-u8 ] the corresponding sd @xmath82 [ panels ( a ) to ( d ) ] and cd @xmath83 [ panels ( e ) to ( h ) ] as functions of lattice site . results obtained with the lowest - energy standard hf solutions are also included in the plots ( red ) for comparison . in the case of the rhf solution ( fig.[solitons - n30-ne18-u2 ] ) at @xmath2=2@xmath5 , the corresponding sd vanishes while the cd takes the constant value 0.4 . due to the symmetry - broken nature of the uhf solution ( fig.[solitons - n30-ne18-u4 ] ) , the corresponding sd and cd exhibit oscillating patterns around the expected values ( i.e. , 0 and 0.4 , respectively ) at @xmath2=4@xmath5 . in the case of the intrinsic ghf solution ( fig.[solitons - n30-ne18-u8 ] ) at @xmath2=8@xmath5 the sd displays a very fast oscillating pattern , which is a direct consequence of its predominant ferromagnetic character [ note the presence of the factor @xmath84 in the definition eq.([sdw1 ] ) ] . in fact , the energy of this intrinsic ghf solution ( i.e , -18.1922 t ) is only slightly lower than the one ( i.e. , -18.0974 t ) corresponding to a fully ferromagnetic uhf solution with all the spins aligned along the z - direction . on the other hand , the cd takes the constant value 0.4 . regardless of the considered interaction regime , the ghf determinants @xmath85 associated with the fed solution eq.([fed - state - general ] ) exhibit pairs of solitons ( black squares ) where the sd @xmath82 changes its sign . the space group projection operator provides a translational motion for such soliton pairs . when different determinants show soliton pairs with different widths , this can be interpreted as a breathing mechanism . isolated points ( blue circles ) where @xmath82 becomes zero are also apparent from figs . [ solitons - n30-ne18-u2 ] , [ solitons - n30-ne18-u4 ] and [ solitons - n30-ne18-u8 ] . in the case of doped lattices these new defects represent polarons . @xcite in addition , the cd @xmath83 displays local variations around the constant value 0.4 for all the considered on - site repulsions . other ghf determinants @xmath85 ( not shown in the figures ) display the same qualitative features . similar results also hold for other u values and lattices . therefore , in the case of doped 1d lattices , the ansatz eq.([fed - state - general ] ) superposes manifolds @xmath86 containing both solitons and polarons . one is then left with an intuitive physical picture @xcite in which the basic units of quantum fluctuations in 1d lattices can be mainly associated with the translational and breathing motions of neutral and charged solitons . however , in the case of doped 1d systems , a part of such fluctuations can also be described by polarons . within both the fed @xcite and the reshf @xcite schemes , the interference between the defects belonging to different symmetry - broken determinants @xmath14 is accounted for through eq.([hw-1 ] ) . ) ] plotted as functions of ln @xmath87 , with @xmath87 being the corresponding doping parameter . results are shown for on - site repulsions @xmath2=2@xmath5 ( red diamonds ) , 4@xmath5 ( blue diamonds ) , and 8@xmath5 ( green diamonds ) . dmrg values are plotted with open circles . a straight line has been fitted to guide the eye . for more details , see the main text . , scaledwidth=45.0% ] for a given set of quantum numbers @xmath55 , the momentum distribution @xmath88 can be computed as @xmath89 where @xmath90 is the @xmath91-occupation operator at wave vector q. note that , due to the particular form of the operator @xmath90 , the momentum distribution eq.([nkdist ] ) does not depend explicitly on @xmath92 . the ground state momentum distributions for @xmath13=30 lattices with 14 ( orange triangles ) , 18 ( magenta triangles ) , 22 ( cyan triangles ) , 26 ( green triangles ) , and 30 ( red triangles ) electrons are plotted in panels ( a ) , ( b ) and ( c ) of fig . [ momentum - distribution ] for on - site repulsions @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 , respectively . regardless of the interaction strength , the fed and dmrg ( open black circles ) momentum distributions agree well . in all cases , we have obtained a jump at @xmath93 , with @xmath94 being the fermi momentum , that becomes less pronounced , especially at half - filling , for larger u values . such a jump is also found in calculations based on the exact solution at @xmath2=@xmath95 @xcite as well as in previous studies . @xcite as can seen from panel ( c ) , the momentum distribution presents a slight nonmonotonic behavior close to half - filling ( i.e. , @xmath3=26 ) due to a small feature near @xmath96 . previous works @xcite have shown that , contrary to an ordinary fermi liquid , the momentum distribution of the 1d hubbard model exhibits a power - law behavior around @xmath93 given by @xmath97 at half - filling or u @xmath98 @xmath95 . we have used the momentum distributions obtained with the fed approach to fit the functional dependence eq.([power - law - kdist ] ) . the results are shown in panel ( d ) of fig . [ momentum - distribution ] for @xmath2=8@xmath5 . despite the fact that the functional form eq.([power - law - kdist ] ) has been obtained using the exact @xmath2=@xmath95 solution , we observe that it nicely reproduces the trends in the fed ( and also dmrg ) results . let us now turn our attention to the predicted fed sscfs and ddcfs . we compare them with the corresponding dmrg values in the case of @xmath13=30 lattices with 14 ( orange triangles ) , 18 ( magenta triangles ) , 22 ( cyan triangles ) , 26 ( green triangles ) , and 30 ( red triangles ) electrons . this comparison will allow us to reveal to which extent the fed scheme can capture the main short , medium and long range features in these correlators , especially in the case of doped lattices . we have resorted to the momentum space representation ( i.e. , the fourier transforms ) of the sscfs and ddcfs in real space . for a discussion of the predicted fed sscfs in the case of half - filled lattices , the reader is also referred to our previous work . @xcite but for the fourier transforms of the ground state density - density correlation functions in real space . starting with 26 electrons , all the curves have been successively shifted by 0.2 to accomodate them in a single plot . , scaledwidth=40.0% ] the sscfs in real space are given by @xmath99 where the subindex @xmath100 accounts for the dependence with respect to the particular row of the space group irreducible representation used in the projection . let us stress that the wave functions @xmath101 eq.([fed - state - general ] ) are pure spin states where orbital relaxation is allowed . both conditions have already been shown to be important ingredients to improve the description of the long - range behavior of the sscfs . @xcite the fourier transforms ( ft - sscfs ) @xmath102 of the sscfs eq.([ss - cf ] ) are depicted in panels ( a ) , ( b ) and ( c ) of fig . [ spinspin - momentum - space ] for the ground states of the lattices considered in the present study at @xmath2=2@xmath5 , 4@xmath5 and 8@xmath5 , respectively . the first feature apparent from fig . [ spinspin - momentum - space ] , is the prominent antiferromagnetic peak at the wave vector q=@xmath49 in the case of the half - filled system . the peaks of the ft - sscfs always occur at @xmath96 . such peaks have also been found @xcite with the exact @xmath2=@xmath95 solution of the 1d hubbard model as well as in previous calculations . @xcite they are shifted towards smaller linear momenta as we move away from half - filling . in the same plot , we have also included the results of our dmrg calculations ( black triangles ) for comparison . it is satisfying to observe that the predicted fed values closely follow the trend obtained within the dmrg approach . the largest differences between the fed and dmrg ft - sscfs arise in the values of the corresponding peaks near half - filling for large u. for the lattice with 26 electrons the fed peak , obtained with @xmath16=150 ghf transformations , at @xmath2=8@xmath5 overestimates the dmrg one by 5 @xmath75 . on the other hand , using a smaller number @xmath16=60 of transformations , we obtain a poorer ( 10 @xmath75 overestimation ) description of the sscfs and ft - sscfs in the strong interaction regime . of the fed fourier - transformed density - density correlation functions in real space [ eq.([denden - cf ] ) ] are plotted as functions of ln @xmath87 for @xmath2=2@xmath5 ( red diamonds ) , 4@xmath5 ( blue diamonds ) , and 8@xmath5 ( green diamonds ) . dmrg values are plotted with open circles . for more details , see the main text . , scaledwidth=45.0% ] a previous study @xcite has shown the universal character of the crossover in the sscfs as we approach half - filling . as a result of this crossover , the peaks observed in the ft - sscfs at @xmath96 display a linear logarithmic dependence with the doping parameter @xmath103 . the results of our fed calculations are compared in fig . [ spinspin - maxima ] with the dmrg ones . for each u value , we have fitted a straight line to guide the eye . for @xmath2=2@xmath5 and 4@xmath5 , the fed and dmrg values agree well ( we have therefore included only the fitting of the former in the plot ) and exhibit an almost linear behavior as a function of ln @xmath87 . the same linear trend is observed at @xmath2=8@xmath5 though in this case the discrepancy between the fed and dmrg values , arising from a poorer description of the ft - sscfs in the former ( see , fig . [ spinspin - momentum - space ] ) , is larger . the ddcfs in real space can be computed as @xmath104 where @xmath105 and @xmath106 . their ft - ddcfs @xmath107 are shown in panels ( a ) , ( b ) , and ( c ) of fig . [ denden - momentum - space ] for @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 , respectively . dmrg values ( black triangles ) are also plotted for comparison . similar to the momentum distributions and ft - sscfs already discussed above , the fed ft - ddcfs closely follow the trends observed in the dmrg ones , with the largest differences arising for @xmath108 in the case of the lattice with 26 electrons at @xmath2=8@xmath5 . from panels ( a ) , ( b ) , and ( c ) of fig . [ denden - momentum - space ] , we also observe the appearence of inflection points around @xmath96 which become less pronounced as u increases . they are plotted in fig . [ denden - maxima ] as functions of ln @xmath87 . we observe a shift down of the curves as u increases reflecting that the charge fluctuations decrease for larger u values . in addition , we note that the curves bend down more for larger on - site repulsions . a typical outcome of our calculations is shown in panel ( a ) of fig . [ spectral - dos ] , where we have plotted the hole ( black ) and particle ( blue ) sfs , as functions of the excitation energy @xmath109 , for a lattice with @xmath13=30 sites and @xmath3=26 electrons at @xmath2=4@xmath5 . calculations have been performed along the lines described in our previous work . @xcite the fed ground state of the system with @xmath3=26 electrons has been approximated by @xmath16=60 ghf transformations while for the systems with @xmath1 electrons we have superposed @xmath68=25 hole and particle manifolds ( see , sec . [ theory ] ) . smaller values @xmath68=5 and @xmath68=15 have also been investigated . however , increasing the number of hole and particle manifolds to @xmath68=25 leads to a shift of the main peaks and a redistribution of the strength of some of the peaks found for @xmath68=5 and @xmath68=15 as a result of the small number of configurations used in the calculations . in all cases , a lorentzian folding of width @xmath110=0.05 t has been used . we observe prominent hole peaks belonging to the spinon band . such a band resembles the one found in the half - filled case @xcite though the spectral weight of some of the hole peaks found in the latter is redistributed to the particle sector due to the presence of doping . another prominent feature of the sfs shown in panel ( a ) is the very extended distribution of the spectral weight for linear momenta @xmath111 . the splitting of the strength in the corresponding particle sfs reveals that the present finite size results at the intermediate - to - strong interaction regime already display spin - charge separation tendencies beyond a simple quasiparticle distribution as well as shadow features . this agrees well with results obtained using other theoretical approximations . @xcite in panel ( b ) of fig . [ spectral - dos ] we have plotted the dos @xmath28 corresponding to the lattice with @xmath13=30 sites and @xmath3=26 electrons ( black ) . for the sake of comparison , we have also included in the same panel the dos in the half - filled case ( red ) . the last one , has also been computed using @xmath16=60 and @xmath68=25 . it exhibits the characteristic hubbard gap @xcite and particle - hole symmetry . @xcite as can be seen from the figure , this particle - hole symmetry is lost in the doped case . as a result of states intruding the original gap , a smaller pseudogap is developed at @xmath2=4@xmath5 . however , our calculations indicate that such a pseudogap progressively disappears for increasing doping fractions @xmath112 . similar results also hold for both @xmath2=2@xmath5 and @xmath2=8@xmath5 though the effect is less pronounced in the latter due to the larger value of the gap at half - filling . [ table2 ] ccccccccccccc + @xmath13 & & @xmath3 & & u & & fed & & @xmath16 & & exact & & @xmath113 ( @xmath75 ) + + 34 & & 14 & & 4@xmath5 & & -23.0991 & & 60 & & -23.1137 & & 99.46 + + 34 & & 14 & & 4@xmath5 & & -23.1048 & & 100 & & -23.1137 & & 99.67 + + 34 & & 18 & & 4@xmath5 & & -26.4440 & & 60 & & -26.4842 & & 98.99 + + 34 & & 18 & & 4@xmath5 & & -26.4587 & & 100 & & -26.4842 & & 99.35 + + 34 & & 22 & & 4@xmath5 & & -27.8402 & & 60 & & -27.9207 & & 98.48 + + 34 & & 22 & & 4@xmath5 & & -27.8673 & & 100 & & -27.9207 & & 98.99 + + 34 & & 26 & & 4@xmath5 & & -27.1248 & & 60 & & -27.2553 & & 98.05 + + 34 & & 26 & & 4@xmath5 & & -27.1634 & & 100 & & -27.2553 & & 98.63 + + 34 & & 30 & & 4@xmath5 & & -24.2555 & & 60 & & -24.3967 & & 98.28 + + 34 & & 30 & & 4@xmath5 & & -24.2966 & & 100 & & -24.3967 & & 98.78 + + 34 & & 34 & & 4@xmath5 & & -19.4646 & & 60 & & -19.5258 & & 99.40 + + 34 & & 34 & & 4@xmath5 & & -19.4876 & & 100 & & -19.5258 & & 99.62 + + 34 & & 34 & & 8@xmath5 & & -11.0562 & & 60 & & -11.1473 & & 99.74 + + 34 & & 34 & & 8@xmath5 & & -11.0883 & & 100 & & -11.1473 & & 99.83 + + 50 & & 50 & & 2@xmath5 & & -42.1748 & & 60 & & -42.2443 & & 98.46 + + 50 & & 50 & & 2@xmath5 & & -42.1957 & & 100 & & -42.2443 & & 98.62 + + 50 & & 50 & & 4@xmath5 & & -28.1924 & & 60 & & -28.6993 & & 96.62 + + 50 & & 50 & & 4@xmath5 & & -28.2999 & & 100 & & -28.6993 & & 97.33 + + 50 & & 50 & & 8@xmath5 & & -15.7739 & & 60 & & -16.3842 & & 98.84 + + 50 & & 50 & & 8@xmath5 & & -15.9770 & & 100 & & -16.3842 & & 99.22 + now , we turn our attention to larger lattices . let us stress that our aim in this section is not to be exhaustive but to illustrate the fed results in such lattices . to this end the predicted ground state energies are compared with the exact ones in table ii . results are presented for @xmath13=34 lattices with @xmath3=14 , 18 , 22 , 26 , 30 , 34 electrons as well as for the half - filled lattice with @xmath13=50 sites . for the considered on - site repulsions we have performed two different sets of fed calculations based on @xmath16=60 and @xmath16=100 ghf transformations . the ratio of correlation energies @xmath113 , has been computed according to eq.([formulace ] ) . as can be seen from the table , the fed approach , based on @xmath16=60 symmetry - projected configurations , already provides @xmath114 @xmath30 98 @xmath75 . these values significantly improve the ones obtained with the standard hf approximation . for example , for the half - filled lattice with @xmath13=50 , the uhf approximation accounts for @xmath115=12.02 @xmath75 , 65.02 @xmath75 , 92.26 @xmath75 while @xmath114= 98.46 @xmath75 , 96.62 @xmath75 , 98.84 @xmath75 at @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 , respectively . note that , for the same on - site repulsions , the variational monte carlo method provides @xmath113 values of around 87 @xmath75 , 92 @xmath75 , and 96 @xmath75 , respectively . @xcite for the same half - filled lattice , the ground state energies obtained with @xmath16=60 also improve the values reported in our previous work @xcite using a smaller number ( i.e. , @xmath16=25 ) of nonorthogonal symmetry - projected ghf configurations in the fed expansion eq.([fed - state - general ] ) as well as the ones provided by the reshf approximation @xcite based on @xmath16=30 uhf transformations . moreover , further increasing up to @xmath16=100 leads to @xmath114 @xmath77 99.35 @xmath75 in the case of lattices with @xmath13=34 sites . in the case @xmath116=50 , we have obtained @xmath114= 98.62 @xmath75 , 97.33 @xmath75 , 99.22 @xmath75 for @xmath2=2@xmath5 , 4@xmath5 , and 8@xmath5 , respectively . the previous results show that the fed scheme also provides a resonable starting point to obtain correlated wave functions in lattices larger than the ones considered in sec . [ gsandcoenergies ] . in particular , one sees that for increasing lattice sizes the quality of the fed wave functions can also be systematically improved , for different doping fractions , by increasing the number of symmetry - projected configurations included in the mr ansatz eq.([fed - state - general ] ) . we are unable at the moment to anticipate the number of symmetry - projected configurations necessary to achieve a given quality in the fed wave functions for arbitrary lattice sizes and doping fractions . nevertheless , we stress once more that the exact answer can always be approached in a systematic constructive way . finally , as a typical example of the results obtained for the lattices considered in this section , we have plotted in fig . [ momentum - distribution - n34 ] the momentum distributions corresponding to @xmath13=34 sites with 18 ( magenta triangles ) , 26 ( green triangles ) , and 34 ( red triangles ) electrons at @xmath2=4@xmath5 . we have resorted to @xmath16=100 nonorthogonal symmetry - projected states in the calculations . as can be seen from the figure , the momentum distributions still display the main feature already discussed in sec . [ modistribution ] for the case of half - filled and doped lattices with @xmath13=30 sites , i.e. , a jump at @xmath93 that becomes less pronounced at half - filling . ) for @xmath13=34 lattices with 18 ( magenta triangles ) , 26 ( green triangles ) , and 34 ( red triangles ) electrons are shown for @xmath2=4@xmath5 . , scaledwidth=42.0% ]

the structure of the intrinsic symmetry - broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations . it is also shown that in the case of doped 1d lattices , a part of such fluctuations can also be interpreted in terms of polarons . in addition to momentum distributions , both spin - spin and density - density correlation functions are studied as functions of doping .

a multi - reference configuration mixing scheme is used to describe the ground state , characterized by well defined spin and space group symmetry quantum numbers as well as doping fractions , of one dimensional hubbard lattices with nearest - neighbor hopping and periodic boundary conditions . within this scheme , each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry - projected configurations . the results obtained for the ground state and correlation energies of half - filled and doped lattices with 30 , 34 and 50 sites , compare well with the exact lieb - wu solutions as well as with the ones obtained with other state - of - the - art approximations . the structure of the intrinsic symmetry - broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations . it is also shown that in the case of doped 1d lattices , a part of such fluctuations can also be interpreted in terms of polarons . in addition to momentum distributions , both spin - spin and density - density correlation functions are studied as functions of doping . the spectral functions and density of states , computed with an ansatz whose quality can be well - controlled by the number of symmetry - projected configurations used to approximate the electron systems , display features beyond a simple quasiparticle distribution , as well as spin - charge separation trends .

1211.5884

i

relays are often used to aid communications , not only to improve the quality of service ( qos ) of the user pairs , which have weak direct links due to poor channel conditions , but also to increase the multiplexing gain of the network @xcite . among various relay transmit schemes , the most effective ones are amplify - and - forward ( af ) , compute - and - forward ( cf ) and decode - and - forward ( df ) . especially af protocol is standardized as layer 1 relaying @xcite , and thus in popular research , because of its simplicity and low complexity . in this paper we consider the multiple link multiple relay network with non - regenerative relaying . there has been many works discussing the optimization of the relay beamforming weights . for single antenna case , @xcite and @xcite study models to solve the optimal relay af weights , where total relay transmit power is minimized under guaranteed signal - to - interference - plus - noise - ratio ( sinr ) requirements . there is also extension to multiple antenna case . in @xcite the authors explore the network with one multiple - antenna relay , and according to various relay af matrix schemes , proposes irc flexcobf " algorithm for transmit beamforming matrices . for the networks with one user pair and parallel relays , @xcite discusses the joint optimization of source and relay beamforming with different receiver filters . with the similar mimo relay network as @xcite , @xcite investigates the optimal joint source and relay power allocation to maximize the end - to - end achievable rate . extended to one transmitter , multiple receiver and multiple relay network , @xcite proposes a weighted mean square error minimization ( wmmse ) model to solve the source and relay beamforming matrices with mmse receiving filter . recent work of @xcite is based on general mimo af relay networks with multiple links and multiple relays . the authors provide algorithms to jointly optimize users precoders , decoders and the relay af matrices . total leakage interference plus noise ( tlin ) minimization and wmmse models are proposed , both with per user and total relay transmit power constraints . the idea to construct the wmmse models in @xcite and @xcite are similar . the wmmse model in @xcite is also extended to that with individual user and individual relay power constraints . the precoders , decoders and the relay af matrices are solved alternatively , where each subproblem can achieve its optimal solution . however the algorithm has quite high computational complexity . here we propose different approaches to approximate the system sum rate and derive lower complexity algorithm to solve the corresponding optimization problem . the degrees of freedom ( dofs ) of one network is closely related to its channel capacity . in high signal - to - noise - ratio ( snr ) scenarios , the capacity increases linearly with the number of dofs . the authors in @xcite propose a new technique of interference alignment ( ia ) , to maximize the achievable dofs for mimo networks . such technique optimizes the precoders and decoders , in order to eliminate the network interference and approach the capacity of mimo network . in mimo networks , the ia technique has been deeply investigated @xcite . it is shown in @xcite that , with relays the achievable dofs of the mimo interference network are increased , and the capacity as well as the reliability are improved . in two - hop networks , @xcite studies the feasibility conditions and the algorithms for relay aided ia , restricted on single antenna case . aiming to achieve the maximum dofs of the @xmath0 mimo relay network , @xcite and @xcite study similar technique of aligned interference neutralization to explore the optimal transmission scheme for single antenna and multiple antennas cases , respectively @xcite investigates the ergodic capacity of a class of fading 2-user 2-hop networks with interference neutralization technique . in @xcite the maximum achievable dofs for different kinds of mimo interference channels and mimo multiple hop networks are listed and concluded . for the general @xmath1 mimo relay network , the maximum dofs are only analyzed with restriction to the number of relays . interestingly , we observe by simulations that the algorithms proposed in @xcite all lead to precoders with linearly dependent columns , which result in single transmit data stream corresponding to one dof for each user , regardless of the number of antennas at relay and user nodes . this is an impetus for us to propose multiple data stream models . in our paper , we propose several models for the general mimo relay network , according to different purposes and situations . the general transmit process and system model are introduced in section . in section we set up a total signal to total interference plus noise ratio ( tstinr ) maximization model to approximate the system sum rate , with per user and total relay transmit power constraints . then this tstinr model as well as the tlin and wmmse model in @xcite are extended to those with individual user and individual relay power constraints . also , the computational complexity of our algorithm is analyzed and compared with the wmmse algorithm in @xcite . our proposed algorithm is shown to have lower complexity . furthermore , to achieve more than one data streams for each user , we propose a multiple stream tstinr model in section . compared to the tstinr model in section , additional orthogonal constraints for precoders are added . in all the models , the precoding matrices , decoding matrices and relay beamforming matrices are iterated alternatively . each subproblem is efficiently solved , with sufficient reduction of the objective function in each iteration guaranteed . we provide simulation results in section . since the network model in @xcite is more general than @xcite , we compare our proposed algorithms with those in @xcite . the results indicate that tstinr outperforms tlin generally , and achieves higher sum rate than wmmse in medium to high snr scenarios , for the single stream cases . the system sum rate benefits much from the multiple stream model in medium and high snr scenarios . parts of our work are reported in @xcite and @xcite . compared to them , we add more details of the proposed algorithms and provide detailed proof for all the mentioned theorems . furthermore , we analyze and compare the detailed computational complexity of our proposed algorithm and the wmmse algorithm from @xcite . _ notation _ : lowercase and uppercase boldface represent vectors and matrices , respectively . @xmath2 represents the complex domain . @xmath3 means the real part of scalar @xmath4 . @xmath5 and @xmath6 are the trace and the frobenius norm of matrix @xmath7 , respectively . @xmath8 represents the @xmath9 identity matrix . @xmath10 and @xmath11 represent the set of the user indices @xmath12 and that of relay indices @xmath13 , respectively . and we use @xmath14 to denote the statistical expectation . @xmath15 means the same order amount of @xmath16 . @xmath17 is composed of the eigenvectors of @xmath7 corresponding to its @xmath18 smallest eigenvalues .

a multiple - antenna amplify - and - forward two - hop interference network with multiple links and multiple relays is considered . we optimize transmit precoders , receive decoders and relay af matrices to maximize the achievable sum rate . under per user and total relay sum power constraints , we propose an efficient algorithm to maximize the total signal to total interference plus noise ratio ( tstinr ) . we analyze and confirm by simulations that the tstinr , wmmse and the total leakage interference plus noise ( tlin ) minimization models with per user and total relay sum power constraints can only transmit a single data stream for each user . mimo af relay network , sum rate maximization , total signal to total interference plus noise ratio , alternating iteration

a multiple - antenna amplify - and - forward two - hop interference network with multiple links and multiple relays is considered . we optimize transmit precoders , receive decoders and relay af matrices to maximize the achievable sum rate . under per user and total relay sum power constraints , we propose an efficient algorithm to maximize the total signal to total interference plus noise ratio ( tstinr ) . computational complexity analysis shows that our proposed algorithm for tstinr has lower complexity than the existing weighted minimum mean square error ( wmmse ) algorithm . we analyze and confirm by simulations that the tstinr , wmmse and the total leakage interference plus noise ( tlin ) minimization models with per user and total relay sum power constraints can only transmit a single data stream for each user . thus we propose a novel multiple stream tstinr model with requirement of orthogonal columns for precoders , in order to support multiple data streams and thus utilize higher degrees of freedom . multiple data streams and larger multiplexing gains are guaranteed . simulation results show that for single stream models , our tstinr algorithm outperforms the tlin algorithm generally and outperforms wmmse in medium to high signal - to - noise - ratio scenarios ; the system sum rate significantly benefits from multiple data streams in medium to high snr scenarios . mimo af relay network , sum rate maximization , total signal to total interference plus noise ratio , alternating iteration

1211.5884

c

this paper considered the general @xmath1 mimo relay network . with per user and total relay power constraints , an algorithm for the tstinr model was proposed . for the individual user and individual relay fixed power constraints , the tstinr algorithm was extended , and the algorithms for the tlin and wmmse model in @xcite were also modified to solve the problem with such constraints . computational complexity analysis showed that our proposed algorithm for tstinr has much lower complexity than the wmmse algorithm from @xcite . focusing on per user and total relay power constraints , we proposed a multiple stream tstinr model , to overcome the disadvantages of the previous models that only single data stream can be transmitted for each user . simulations showed that for single stream case tstinr algorithm performs better than wmmse in medium and high snr scenarios for both constraint cases , and outperforms tlin generally , in terms of achievable sum rate ; the system sum rate significantly benefits from the multiple data stream transmission in medium to high snr scenarios .

computational complexity analysis shows that our proposed algorithm for tstinr has lower complexity than the existing weighted minimum mean square error ( wmmse ) algorithm . simulation results show that for single stream models , our tstinr algorithm outperforms the tlin algorithm generally and outperforms wmmse in medium to high signal - to - noise - ratio scenarios ; the system sum rate significantly benefits from multiple data streams in medium to high snr scenarios .

a multiple - antenna amplify - and - forward two - hop interference network with multiple links and multiple relays is considered . we optimize transmit precoders , receive decoders and relay af matrices to maximize the achievable sum rate . under per user and total relay sum power constraints , we propose an efficient algorithm to maximize the total signal to total interference plus noise ratio ( tstinr ) . computational complexity analysis shows that our proposed algorithm for tstinr has lower complexity than the existing weighted minimum mean square error ( wmmse ) algorithm . we analyze and confirm by simulations that the tstinr , wmmse and the total leakage interference plus noise ( tlin ) minimization models with per user and total relay sum power constraints can only transmit a single data stream for each user . thus we propose a novel multiple stream tstinr model with requirement of orthogonal columns for precoders , in order to support multiple data streams and thus utilize higher degrees of freedom . multiple data streams and larger multiplexing gains are guaranteed . simulation results show that for single stream models , our tstinr algorithm outperforms the tlin algorithm generally and outperforms wmmse in medium to high signal - to - noise - ratio scenarios ; the system sum rate significantly benefits from multiple data streams in medium to high snr scenarios . mimo af relay network , sum rate maximization , total signal to total interference plus noise ratio , alternating iteration