Stochastic Biasing and Galaxy-Mass Density Relation in the Weakly Non-linear Regime

It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey might allow us to explore the time evolution of the galaxy distribution. In this paper, the analytic study of the galaxy-mass density relation and its time evolution is presented within the framework of the stochastic biasing. In the weakly non-linear regime, we derive a general formula for the galaxy-mass density relation as a conditional mean using the Edgeworth expansion. The resulting expression contains the joint moments of the total mass and galaxy distributions. Using the perturbation theory, we investigate the time evolution of the joint moments and examine the influence of the initial stochasticity on the galaxy-mass density relation. The analysis shows that the galaxy-mass density relation could be well-approximated by the linear relation. Compared with the skewness of the galaxy distribution, we find that the estimation of the higher order moments using the conditional mean could be affected by the stochasticity. Therefore, the galaxy-mass density relation as a conditional mean should be used with a caution as a tool for estimating the skewness and the kurtosis.Comment: 22 pages, 7 Encapusulated Postscript Figures, aastex, The title and the structure of the paper has been changed, Results and conclusions unchanged, Accepted for publication in Ap

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]

Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations

We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters f_NL and g_NL. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the halo overdensity depends not only on the underlying matter density fluctuation delta, but also on the Gaussian part of the primordial gravitational potential phi. This corresponds to a non-local bias scheme in terms of delta only. We derive the coefficients of the bias expansion as a function of the halo mass by applying the peak-background split to common parametrizations for the halo mass function in the non-Gaussian scenario. We then compute the halo power spectrum and halo-matter cross spectrum in the framework of Eulerian perturbation theory up to third order. Comparing our results against N-body simulations, we find that our model accurately describes the numerical data for wavenumbers k < 0.1-0.3 h/Mpc depending on redshift and halo mass. In our multivariate approach, perturbations in the halo counts trace phi on large scales and this explains why the halo and matter power spectra show different asymptotic trends for k -> 0. This strongly scale-dependent bias originates from terms at leading order in our expansion. This is different from what happens using the standard univariate local bias where the scale-dependent terms come from badly behaved higher-order corrections. On the other hand, our biasing scheme reduces to the usual local bias on smaller scales where |phi| is typically much smaller than the density perturbations. We finally discuss the halo bispectrum in the context of multivariate biasing and show that, due to its strong scale and shape dependence, it is a powerful tool for the detection of primordial non-Gaussianity from future galaxy surveys.Comment: 26 pages, 16 figures. Minor modifications, version accepted by Phys. Rev.

What Can the Distribution of Intergalactic Metals Tell us About the History of Cosmological Enrichment?

I study the relationship between the spatial distribution of intergalactic metals and the masses and ejection energies of the sources that produced them. Over a wide range of models, metal enrichment is dominated by the smallest efficient sources, as the enriched volume scales roughly as E^{3/5} ~ M^{3/5} while the number density of sources goes as 1/M. In all cases, the earliest sources have the biggest impact, because fixed comoving distances correspond to smaller physical distances at higher redshifts. This means that most of the enriched volume is found around rare peaks, and intergalactic metals are naturally highly clustered. Furthermore, this clustering is so strong as to lead to a large overlap between individual bubbles. Thus the typical radius of enriched z ~ 3 regions should be interpreted as a constraint on groupings of sources rather than the ejection radius of a typical source. Similarly, the clustering of enriched regions should be taken as a measurement of source bias rather than mass.Comment: 10 pages, 2 figures, ApJL in pres

The Accretion and Cooling of Preheated Gas in Dark Matter Halos

(abridged) We use a one-dimensional hydrodynamical code to investigate the effects of preheating on gas accretion and cooling in cold dark matter halos. In the absence of radiative cooling, preheating reduces the amount of gas that can be accreted into a halo, and the accreted gas fraction is determined by the ratio of the initial specific entropy of the gas to the virial entropy of the halo. In the presence of radiative cooling, preheating affects the gas fraction that can cool in two different ways. For small halos with masses <10^12Msun, preheating suppresses gas accretion, but most of the accreted gas can cool. For more massive halos, preheating not only reduces the amount of accreted gas, but also reduces the cooling efficiency. For both small and massive halos, gas cooling is delayed by preheating and in an inside-out fashion if the halo gas is assumed to be a single-phase medium. However, cooling can occur over a wider range of redshifts and radii, if we assume a multi-phase medium. As examples, two specific preheating cases are investigated. In the first case, the preheating entropy is assumed to be proportional to the virial entropy of the halo, as expected from AGN feedback. Such preheating effectively suppresses radiative cooling in halos with M>10^13Msun. We suggest that this may be the reason why the stellar mass function of galaxies breaks sharply at the massive end. Such preheating also helps create the hot diffused halos within which the "radio mode" feedback of AGNs can act effectively. In the second case, we assume the intergalactic medium is warm. Here the total amount of gas that can cool in a halo scales with halo mass as ~M^2, as would be required to match the observed stellar- and HI-mass functions in the current CDM model at the small mass end.Comment: 14 pages, 13 figures, submitted to MNRA

Accurate determination of the Lagrangian bias for the dark matter halos

We use a new method, the cross power spectrum between the linear density field and the halo number density field, to measure the Lagrangian bias for dark matter halos. The method has several important advantages over the conventional correlation function analysis. By applying this method to a set of high-resolution simulations of 256^3 particles, we have accurately determined the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our result for massive halos with $M \ge M_*$ ($M_*$ is a characteristic non-linear mass) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias, but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos $M < M_*. Our simulation result however can be satisfactorily described, with an accuracy better than 15%, by the fitting formula of Jing for Eulerian bias under the assumption that the Lagrangian clustering and the Eulerian clustering are related with a linear mapping. It implies that it is the failure of the Press-Schechter theories for describing the formation of small halos that leads to the inaccuracy of the Mo & White formula for the Eulerian bias. The non-linear mapping between the Lagrangian clustering and the Eulerian clustering, which was speculated as another possible cause for the inaccuracy of the Mo & White formula, must at most have a second-order effect. Our result indicates that the halo formation model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages with 2 figures include

Observational evidence for stochastic biasing

We show that the galaxy density in the Las Campanas Redshift Survey (LCRS) cannot be perfectly correlated with the underlying mass distribution since various galaxy subpopulations are not perfectly correlated with each other, even taking shot noise into account. This rules out the hypothesis of simple linear biasing, and suggests that the recently proposed stochastic biasing framework is necessary for modeling actual data.Comment: 4 pages, with 2 figures included. Minor revisions to match accepted ApJL version. Links and color fig at http://www.sns.ias.edu/~max/r_frames.html or from [email protected]

Do galactic potential wells depend on their environment?

Using galaxies in complete samples as tracers of the galaxy density field and about 1000 galaxies with measured circular velocities as targets, we examine the cross-correlation functions between the targets and tracers as a function of galaxy circular velocities. The correlation strength does not vary with the circular velocities except for elliptical galaxies with the highest velocity dispersions, where the effect may well be due to morphological segregations in clusters of galaxies. This is contrasted with the strong dependence of the correlation functions of dark halos on their circular velocities in some models of galaxy formation