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]

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

Low Redshift QSO Lyman alpha Absorption Line Systems Associated with Galaxies

In this paper we present Monte-Carlo simulations of Lyman alpha absorption systems which originate in galactic haloes, galaxy discs and dark matter (DM) satellites around big central haloes. It is found that for strong Lyman alpha absorption lines galactic haloes and satellites can explain ~20% and 40% of the line number density of QSO absorption line key project respectively. If big galaxies indeed possess such large numbers of DM satellites and they possess gas, these satellites may play an important role for strong Lyman alpha lines. However the predicted number density of Lyman-limit systems by satellites is \~0.1 (per unit redshift), which is four times smaller than that by halo clouds. Including galactic haloes, satellites and HI discs of spirals, the predicted number density of strong lines can be as much as 60% of the HST result. The models can also predict all of the observed Lyman-limit systems. The average covering factor within 250 kpc/h is estimated to be ~0.36. And the effective absorption radius of a galaxy is estimated to be ~150 kpc/h. The models predict W_r propto rho^{-0.5} L_B^{0.15} (1+z)^{-0.5}. We study the selection effects of selection criteria similar to the imaging and spectroscopic surveys. We simulate mock observations through known QSO lines-of-sight and find that selection effects can statistically tighten the dependence of line width on projected distance. (abridged)Comment: 23 pages, 9 postscript figures; references updated, minor change in section

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

Formation time distribution of dark matter haloes: theories versus N-body simulations

This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB) model. Three sets of simulations (6 realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy like haloes ($M=10^{-3} M_*$, where $M_*$ is the characteristic non-linear mass scale) to massive haloes of $M=8.7 M_*$. None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytic models of galaxy formation, based on EPS merger trees, under-predict the number of high redshift galaxies compared with recent observations.Comment: 7 pages, 5 figures, accepted for publication in MNRA

An Analytical Approach to Inhomogeneous Structure Formation

We develop an analytical formalism that is suitable for studying inhomogeneous structure formation, by studying the joint statistics of dark matter halos forming at two points. Extending the Bond et al. (1991) derivation of the mass function of virialized halos, based on excursion sets, we derive an approximate analytical expression for the ``bivariate'' mass function of halos forming at two redshifts and separated by a fixed comoving Lagrangian distance. Our approach also leads to a self-consistent expression for the nonlinear biasing and correlation function of halos, generalizing a number of previous results including those by Kaiser (1984) and Mo & White (1996). We compare our approximate solutions to exact numerical results within the excursion-set framework and find them to be consistent to within 2% over a wide range of parameters. Our formalism can be used to study various feedback effects during galaxy formation analytically, as well as to simply construct observable quantities dependent on the spatial distribution of objects. A code that implements our method is publicly available at http://www.arcetri.astro.it/~evan/GeminiComment: 41 Pages, 11 figures, published in ApJ, 571, 585. Reference added, Figure 2 axis relabele

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

The Evolution of Bias - Generalized

Fry (1996) showed that galaxy bias has the tendency to evolve towards unity, i.e. in the long run, the galaxy distribution tends to trace that of matter. Generalizing slightly Fry's reasoning, we show that his conclusion remains valid in theories of modified gravity (or equivalently, complex clustered dark energy). This is not surprising: as long as both galaxies and matter are subject to the same force, dynamics would drive them towards tracing each other. This holds, for instance, in theories where both galaxies and matter move on geodesics. This relaxation of bias towards unity is tempered by cosmic acceleration, however: the bias tends towards unity but does not quite make it, unless the formation bias were close to unity. Our argument is extended in a straightforward manner to the case of a stochastic or nonlinear bias. An important corollary is that dynamical evolution could imprint a scale dependence on the large scale galaxy bias. This is especially pronounced if non-standard gravity introduces new scales to the problem: the bias at different scales relaxes at different rates, the larger scales generally more slowly and retaining a longer memory of the initial bias. A consistency test of the current (general relativity + uniform dark energy) paradigm is therefore to look for departure from a scale independent bias on large scales. A simple way is to measure the relative bias of different populations of galaxies which are at different stages of bias relaxation. Lastly, we comment on the possibility of directly testing the Poisson equation on cosmological scales, as opposed to indirectly through the growth factor.Comment: 8 pages, 2 figures. References added. Accepted for publication in Physical Review

Environmental Dependence of Cold Dark Matter Halo Formation

We use a high-resolution $N$-body simulation to study how the formation of cold dark matter (CDM) halos is affected by their environments, and how such environmental effects produce the age-dependence of halo clustering observed in recent $N$-body simulations. We estimate, for each halo selected at redshift $z=0$, an `initial' mass $M_{\rm i}$ defined to be the mass enclosed by the largest sphere which contains the initial barycenter of the halo particles and within which the mean linear density is equal to the critical value for spherical collapse at $z=0$. For halos of a given final mass, $M_{\rm h}$, the ratio $M_{\rm i}/M_{\rm h}$ has large scatter, and the scatter is larger for halos of lower final masses. Halos that form earlier on average have larger $M_{\rm i}/M_{\rm h}$, and so correspond to higher peaks in the initial density field than their final masses imply. Old halos are more strongly clustered than younger ones of the same mass because their initial masses are larger. The age-dependence of clustering for low-mass halos is entirely due to the difference in the initial/final mass ratio. Low-mass old halos are almost always located in the vicinity of big structures, and their old ages are largely due to the fact that their mass accretions are suppressed by the hot environments produced by the tidal fields of the larger structure. The age-dependence of clustering is weaker for more massive halos because the heating by large-scale tidal fields is less important.Comment: 18 pages,19 figures, accepted by MNRA