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

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

The Small Scale Velocity Dispersion of Galaxies: A Comparison of Cosmological Simulations

The velocity dispersion of galaxies on small scales ($r\sim1h^{-1}$ Mpc), $\sigma_{12}(r)$, can be estimated from the anisotropy of the galaxy-galaxy correlation function in redshift space. We apply this technique to ``mock-catalogs'' extracted from N-body simulations of several different variants of Cold Dark Matter dominated cosmological models to obtain results which may be consistently compared to similar results from observations. We find a large variation in the value of $\sigma_{12}(1 h^{-1} Mpc)$ in different regions of the same simulation. We conclude that this statistic should not be considered to conclusively rule out any of the cosmological models we have studied. We attempt to make the statistic more robust by removing clusters from the simulations using an automated cluster-removing routine, but this appears to reduce the discriminatory power of the statistic. However, studying $\sigma_{12}$ as clusters with different internal velocity dispersions are removed leads to interesting information about the amount of power on cluster and subcluster scales. We also compute the pairwise velocity dispersion directly and compare this to the values obtained using the Davis-Peebles method, and find that the agreement is fairly good. We evaluate the models used for the mean streaming velocity and the pairwise peculiar velocity distribution in the original Davis-Peebles method by comparing the models with the results from the simulations.Comment: 20 pages, uuencoded (Latex file + 8 Postscript figures), uses AAS macro

Galaxy Bias and Halo-Occupation Numbers from Large-Scale Clustering

We show that current surveys have at least as much signal to noise in higher-order statistics as in the power spectrum at weakly nonlinear scales. We discuss how one can use this information to determine the mean of the galaxy halo occupation distribution (HOD) using only large-scale information, through galaxy bias parameters determined from the galaxy bispectrum and trispectrum. After introducing an averaged, reasonably fast to evaluate, trispectrum estimator, we show that the expected errors on linear and quadratic bias parameters can be reduced by at least 20-40%. Also, the inclusion of the trispectrum information, which is sensitive to "three-dimensionality" of structures, helps significantly in constraining the mass dependence of the HOD mean. Our approach depends only on adequate modeling of the abundance and large-scale clustering of halos and thus is independent of details of how galaxies are distributed within halos. This provides a consistency check on the traditional approach of using two-point statistics down to small scales, which necessarily makes more assumptions. We present a detailed forecast of how well our approach can be carried out in the case of the SDSS.Comment: 16 pages, 9 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 Pairwise Peculiar Velocity Dispersion of Galaxies: Effects of the Infall

We study the reliability of the reconstruction method which uses a modelling of the redshift distortions of the two-point correlation function to estimate the pairwise peculiar velocity dispersion of galaxies. In particular, the dependence of this quantity on different models for the infall velocity is examined for the Las Campanas Redshift Survey. We make extensive use of numerical simulations and of mock catalogs derived from them to discuss the effect of a self-similar infall model, of zero infall, and of the real infall taken from the simulation. The implications for two recent discrepant determinations of the pairwise velocity dispersion for this survey are discussed.Comment: minor changes in the discussion; accepted for publication in ApJ; 8 pages with 2 figures include

Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars

The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts, or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes may therefore be inferred from their clustering length, which determines the typical mass of the quasar host. Here we point out that the relationship between the mass of the black-hole and the circular velocity of its host dark-matter halo is more fundamental to the determination of the clustering length. In particular, the clustering length observed in the 2dF quasar redshift survey is consistent with the galactic halo - black-hole relation observed in local galaxies, provided that quasars shine at ~10-100% of their Eddington luminosity. The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black-hole mass whose redshift-independent scaling is with halo circular velocity, rather than halo mass. These results are independent from observations of the number counts of bright quasars which may be used to determine the quasar lifetime and its dependence on redshift. We show that if quasar activity results from galaxy mergers, then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time. Our results imply that as the redshift increases, the central black-holes comprise a larger fraction of their host galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap

Scaling properties of the redshift power spectrum: theoretical models

We report the results of an analysis of the redshift power spectrum $P^S(k,\mu)$ in three typical Cold Dark Matter (CDM) cosmological models, where $\mu$ is the cosine of the angle between the wave vector and the line-of-sight. Two distinct biased tracers derived from the primordial density peaks of Bardeen et al. and the cluster-underweight model of Jing, Mo, & B\"orner are considered in addition to the pure dark matter models. Based on a large set of high resolution simulations, we have measured the redshift power spectrum for the three tracers from the linear to the nonlinear regime. We investigate the validity of the relation - guessed from linear theory - in the nonlinear regime $$P^S(k,\mu)=P^R(k)[1+\beta\mu^2]^2D(k,\mu,\sigma_{12}(k)),$$ where $P^R(k)$ is the real space power spectrum, and $\beta$ equals $\Omega_0^{0.6}/b_l$. The damping function $D$ which should generally depend on $k$, $\mu$, and $\sigma_{12}(k)$, is found to be a function of only one variable $k\mu\sigma_{12}(k)$. This scaling behavior extends into the nonlinear regime, while $D$ can be accurately expressed as a Lorentz function - well known from linear theory - for values $D > 0.1$. The difference between $\sigma_{12}(k)$ and the pairwise velocity dispersion defined by the 3-D peculiar velocity of the simulations (taking $r=1/k$) is about 15%. Therefore $\sigma_{12}(k)$ is a good indicator of the pairwise velocity dispersion. The exact functional form of $D$ depends on the cosmological model and on the bias scheme. We have given an accurate fitting formula for the functional form of $D$ for the models studied.Comment: accepted for publication in ApJ;24 pages with 7 figures include