The time-evolution of bias

We study the evolution of the bias factor b and the mass-galaxy correlation coefficient r in a simple analytic model for galaxy formation and the gravitational growth of clustering. The model shows that b and r can be strongly time-dependent, but tend to approach unity even if galaxy formation never ends as the gravitational growth of clustering debiases the older galaxies. The presence of random fluctuations in the sites of galaxy formation relative to the mass distribution can cause large and rapidly falling bias values at high redshift.Comment: 4 pages, with 2 figures included. Typos corrected to match published ApJL version. Color figure and links at http://www.sns.ias.edu/~max/bias.html or from [email protected]

The cosmological light-cone effect on the power spectrum of galaxies and quasars in wide-field redshift surveys

We examine observational consequences of the cosmological light-cone effect on the power spectrum of the distribution of galaxies and quasars from upcoming redshift surveys. First we derive an expression for the power spectrum of cosmological objects in real space on a light cone, $P^{\rm LC}_{\rm R,lin}(k)$, which is exact in linear theory of density perturbations. Next we incorporate corrections for the nonlinear density evolution and redshift-space distortion in the formula in a phenomenological manner which is consistent with recent numerical simulations. On the basis of this formula, we predict the power spectrum of galaxies and quasars on the light cone for future redshift surveys taking account of the selection function properly. We demonstrate that this formula provides a reliable and useful method to compute the power spectrum on the light cone given an evolution model of bias.Comment: 18 pages, 3 figures, to be published in the Astrophysical Journa

Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions

We present an analytic model for the fully nonlinear power spectrum P and bispectrum Q of the cosmological mass density field. The model is based on physical properties of dark matter halos, with the three main model inputs being analytic halo density profiles, halo mass functions, and halo-halo spatial correlations, each of which has been well studied in the literature. We demonstrate that this new model can reproduce the power spectrum and bispectrum computed from cosmological simulations of both an n=-2 scale-free model and a low-density cold dark matter model. To enhance the dynamic range of these large simulations, we use the synthetic halo replacement technique of Ma & Fry (2000a), where the original halos with numerically softened cores are replaced by synthetic halos of realistic density profiles. At high wavenumbers, our model predicts a slope for the nonlinear power spectrum different from the often-used fitting formulas in the literature based on the stable clustering assumption. Our model also predicts a three-point amplitude Q that is scale dependent, in contrast to the popular hierarchical clustering assumption. This model provides a rapid way to compute the mass power spectrum and bispectrum over all length scales where the input halo properties are valid. It also provides a physical interpretation of the clustering properties of matter in the universe.Comment: Final version to appear in the Astrophysical Journal 544 (2000). Minor revisions; 1 additional figure. 25 pages with 6 inserted figure

Nonlinear Gravitational Clustering: dreams of a paradigm

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap

A Simple Method for Computing the Non-Linear Mass Correlation Function with Implications for Stable Clustering

We propose a simple and accurate method for computing analytically the mass correlation function for cold dark matter and scale-free models that fits N-body simulations over a range that extends from the linear to the strongly non-linear regime. The method, based on the dynamical evolution of the pair conservation equation, relies on a universal relation between the pair-wise velocity and the smoothed correlation function valid for high and low density models, as derived empirically from N-body simulations. An intriguing alternative relation, based on the stable-clustering hypothesis, predicts a power-law behavior of the mass correlation function that disagrees with N-body simulations but conforms well to the observed galaxy correlation function if negligible bias is assumed. The method is a useful tool for rapidly exploring a wide span of models and, at the same time, raises new questions about large scale structure formation.Comment: 10 pages, 3 figure

An excursion set model of the cosmic web: The abundance of sheets, filaments and halos

We discuss an analytic approach for modeling structure formation in sheets, filaments and knots. This is accomplished by combining models of triaxial collapse with the excursion set approach: sheets are defined as objects which have collapsed along only one axis, filaments have collapsed along two axes, and halos are objects in which triaxial collapse is complete. In the simplest version of this approach, which we develop here, large scale structure shows a clear hierarchy of morphologies: the mass in large-scale sheets is partitioned up among lower mass filaments, which themselves are made-up of still lower mass halos. Our approach provides analytic estimates of the mass fraction in sheets, filaments and halos, and its evolution, for any background cosmological model and any initial fluctuation spectrum. In the currently popular $\Lambda$CDM model, our analysis suggests that more than 99% of the cosmic mass is in sheets, and 72% in filaments, with mass larger than $10^{10} M_{\odot}$ at the present time. For halos, this number is only 46%. Our approach also provides analytic estimates of how halo abundances at any given time correlate with the morphology of the surrounding large-scale structure, and how halo evolution correlates with the morphology of large scale structure.Comment: 22 pages, 7 figures, Accepted for publication in Ap

The Far-Infrared Background Correlation with CMB Lensing

The intervening large--scale structure distorts cosmic microwave background (CMB) anisotropies via gravitational lensing. The same large--scale structure, traced by dusty star--forming galaxies, also induces anisotropies in the far--infrared background (FIRB). We investigate the resulting inter--dependence of the FIRB and CMB with a halo model for the FIRB. In particular, we calculate the cross--correlation between the lensing potential and the FIRB. The lensing potential can be quadratically estimated from CMB temperature and/or polarization maps. We show that the cross--correlation can be measured with high signal--to--noise with data from the Planck Surveyor. We discuss how such a measurement can be used to understand the nature of FIRB sources and their relation to the distribution of dark matter.Comment: 9 pages, 5 figures, submitted to Ap

Galaxy Groups in the SDSS DR4: II. halo occupation statistics

We investigate various halo occupation statistics using a large galaxy group catalogue constructed from the SDSS DR4 with an adaptive halo-based group finder. The conditional luminosity function (CLF) is measured separately for all, red and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modelled with a log-normal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses M_h\ga 10^{14}\msunh are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with M_h \sim 10^{12}\msunh. For halos of a given mass, the distribution of the luminosities of central galaxies, $L_c$, has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as $L_c\propto M_h^{0.17}$ ($M_{*,c}\propto M_h^{0.22}$) for halos with masses M\gg 10^{12.5}\msunh, and both relations are significantly steeper for less massive halos. We also measure the luminosity (stellar mass) gap between the first and second brightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\log M_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with M_h \la 10^{14.0}\msunh, indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with $\log L_1 - \log L_2\ge 0.8$, ranges from $\sim 2.5$ for groups with M_h\sim 10^{14}\msunh to 18-60% for groups with M_h\sim 10^{13}\msunh. Finally, we measure the fraction of satellites, which changes from $\sim 5.0$ for galaxies with \rmag\sim -22.0 to $\sim40$ for galaxies with \rmag\sim -17.0. (abridged)Comment: 16 pages, 11 figures. Accepted for publication in Ap

The Shapiro Conjecture: Prompt or Delayed Collapse in the head-on collision of neutron stars?

We study the question of prompt vs. delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. We discuss the insight provided by Shapiro's conjecture and its limitation. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations in the Einstein theory with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out in our study.Comment: 4 pages, 7 figure