The Galaxy Distribution Function from the 2MASS Survey

We determine the spatial distribution function of galaxies from a wide range of samples in the 2MASS survey. The results agree very well with the form of the distribution predicted by the theory of cosmological gravitational many-body galaxy clustering. On large scales we find a value of the clustering parameter b = 0.867 +/- 0.026, in agreement with b = 0.83 +/- 0.05 found previously for the Pisces-Perseus supercluster. We measure b(theta) as a function of scale, since this is a powerful test of the applicability of computer simulations. The results suggest that when galaxies clustered they were usually surrounded by individual, rather than by communal haloes.Comment: Astrophysical Journal, accepted: 14 pages with 23 embedded reduced resolution Postscript figures & 2 table

The galaxy counts-in-cells distribution from the SDSS

We determine the galaxy counts-in-cells distribution from the Sloan Digital Sky Survey (SDSS) for 3D spherical cells in redshift space as well as for 2D projected cells. We find that cosmic variance in the SDSS causes the counts-in-cells distributions in different quadrants to differ from each other by up to 20%. We also find that within this cosmic variance, the overall galaxy counts-in-cells distribution agrees with both the gravitational quasi-equilibrium distribution and the negative binomial distribution. We also find that brighter galaxies are more strongly clustered than if they were randomly selected from a larger complete sample that includes galaxies of all luminosities. The results suggest that bright galaxies could be in dark matter haloes separated by less than ~10 Mpc/h.Comment: Accepted for publication in the Astrophysical Journal. Revised version with referee suggestions and corrected typo

Spin-dependent correlation in two-dimensional electron liquids at arbitrary degeneracy and spin-polarization: CHNC approach

We apply the classical mapping technique developed recently by Dharma-wardana and Perrot for a study of the uniform two-dimensional electron system at arbitrary degeneracy and spin-polarization. Pair distribution functions, structure factors, the Helmhotz free energy, and the compressibility are calculated for a wide range of parameters. It is shown that at low temperatures T/ T_F <0.1, T_F being the Fermi temperature, our results almost reduce to those of zero-temperature analyses. In the region T/ T_F >= 1, the finite temperature effects become considerable at high densities for all spin-polarizations. We find that, in our approximation without bridge functions, the finite temperature electron system in two dimensions remains to be paramagnetic fluid until the Wigner crystallization density. Our results are compared with those of three-dimensional system and indicated are the similarities in temperature, spin-polarization, and density dependencies of many physical properties.Comment: 8 pages, 9 figure

Phases in Strongly Coupled Electronic Bilayer Liquids

The strongly correlated liquid state of a bilayer of charged particles has been studied via the HNC calculation of the two-body functions. We report the first time emergence of a series of structural phases, identified through the behavior of the two-body functions.Comment: 5 pages, RevTEX 3.0, 4 ps figures; Submitted to Phys. Rev. Let

The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions

A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle $\theta$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^{\i}tre universe with arbitrary cosmological parameters $\Omega_0$ and $\lambda_0$. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is $\theta \le 10^\circ$.Comment: 45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000

First Measurement of the Clustering Evolution of Photometrically-Classified Quasars

We present new measurements of the quasar autocorrelation from a sample of \~80,000 photometrically-classified quasars taken from SDSS DR1. We find a best-fit model of $\omega(\theta) = (0.066\pm^{0.026}_{0.024})\theta^{-(0.98\pm0.15)}$ for the angular autocorrelation, consistent with estimates from spectroscopic quasar surveys. We show that only models with little or no evolution in the clustering of quasars in comoving coordinates since z~1.4 can recover a scale-length consistent with local galaxies and Active Galactic Nuclei (AGNs). A model with little evolution of quasar clustering in comoving coordinates is best explained in the current cosmological paradigm by rapid evolution in quasar bias. We show that quasar biasing must have changed from b_Q~3 at a (photometric) redshift of z=2.2 to b_Q~1.2-1.3 by z=0.75. Such a rapid increase with redshift in biasing implies that quasars at z~2 cannot be the progenitors of modern L* objects, rather they must now reside in dense environments, such as clusters. Similarly, the duration of the UVX quasar phase must be short enough to explain why local UVX quasars reside in essentially unbiased structures. Our estimates of b_Q are in good agreement with recent spectroscopic results, which demonstrate the implied evolution in b_Q is consistent with quasars inhabiting halos of similar mass at every redshift. Treating quasar clustering as a function of both redshift and luminosity, we find no evidence for luminosity dependence in quasar clustering, and that redshift evolution thus affects quasar clustering more than changes in quasars' luminosity. We provide a new method for quantifying stellar contamination in photometrically-classified quasar catalogs via the correlation function.Comment: 34 pages, 10 figures, 1 table, Accepted to ApJ after: (i) Minor textual changes; (ii) extra points added to Fig.

Pressure formulas for liquid metals and plasmas based on the density-functional theory

At first, pressure formulas for the electrons under the external potential produced by fixed nuclei are derived both in the surface integral and volume integral forms concerning an arbitrary volume chosen in the system; the surface integral form is described by a pressure tensor consisting of a sum of the kinetic and exchange-correlation parts in the density-functional theory, and the volume integral form represents the virial theorem with subtraction of the nuclear virial. Secondly on the basis of these formulas, the thermodynamical pressure of liquid metals and plasmas is represented in the forms of the surface integral and the volume integral including the nuclear contribution. From these results, we obtain a virial pressure formula for liquid metals, which is more accurate and simpler than the standard representation. From the view point of our formulation, some comments are made on pressure formulas derived previously and on a definition of pressure widely used.Comment: 18 pages, no figur

Yukawa potentials in systems with partial periodic boundary conditions I : Ewald sums for quasi-two dimensional systems

Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.Comment: 40 pages, 5 figures and 4 table

Melting of the classical bilayer Wigner crystal: influence of the lattice symmetry

The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures, which is a consequence of the specific topology of the temperature induced defects. A new melting criterion is formulated which we show to be universal for bilayers as well as for single layer crystals.Comment: 4 pages, 5 figures (postscript files). Accepted in Physical Review Letter

Clustering Analyses of 300,000 Photometrically Classified Quasars--I. Luminosity and Redshift Evolution in Quasar Bias

Using ~300,000 photometrically classified quasars, by far the largest quasar sample ever used for such analyses, we study the redshift and luminosity evolution of quasar clustering on scales of ~50 kpc/h to ~20 Mpc/h from redshifts of z~0.75 to z~2.28. We parameterize our clustering amplitudes using realistic dark matter models, and find that a LCDM power spectrum provides a superb fit to our data with a redshift-averaged quasar bias of b_Q = 2.41+/-0.08 ($P_{<\chi^2}=0.847$) for $\sigma_8=0.9$. This represents a better fit than the best-fit power-law model ($\omega = 0.0493\pm0.0064\theta^ {-0.928\pm0.055}$; $P_{<\chi^2}=0.482$). We find b_Q increases with redshift. This evolution is significant at >99.6% using our data set alone, increasing to >99.9999% if stellar contamination is not explicitly parameterized. We measure the quasar classification efficiency across our full sample as a = 95.6 +/- ^{4.4}_{1.9}%, a star-quasar separation comparable with the star-galaxy separation in many photometric studies of galaxy clustering. We derive the mean mass of the dark matter halos hosting quasars as MDMH=(5.2+/-0.6)x10^{12} M_solar/h. At z~1.9 we find a $1.5\sigma$ deviation from luminosity-independent quasar clustering; this suggests that increasing our sample size by a factor of 1.8 could begin to constrain any luminosity dependence in quasar bias at z~2. Our results agree with recent studies of quasar environments at z < 0.4, which detected little luminosity dependence to quasar clustering on proper scales >50 kpc/h. At z < 1.6, our analysis suggests that b_Q is constant with luminosity to within ~0.6, and that, for g < 21, angular quasar autocorrelation measurements are unlikely to have sufficient statistical power at z < 1.6 to detect any luminosity dependence in quasars' clustering.Comment: 13 pages, 9 figures, 2 tables; uses amulateapj; accepted to Ap