16,903 research outputs found
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 ( Mpc),
, 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 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
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 CDM
model, our analysis suggests that more than 99% of the cosmic mass is in
sheets, and 72% in filaments, with mass larger than 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
in three typical Cold Dark Matter (CDM) cosmological models, where
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
where
is the real space power spectrum, and equals . The
damping function which should generally depend on , , and
, is found to be a function of only one variable
. This scaling behavior extends into the nonlinear regime,
while can be accurately expressed as a Lorentz function - well known from
linear theory - for values . The difference between
and the pairwise velocity dispersion defined by the 3-D peculiar velocity of
the simulations (taking ) is about 15%. Therefore is a
good indicator of the pairwise velocity dispersion. The exact functional form
of depends on the cosmological model and on the bias scheme. We have given
an accurate fitting formula for the functional form of for the models
studied.Comment: accepted for publication in ApJ;24 pages with 7 figures include
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