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

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]

Observational Evidence for an Age Dependence of Halo Bias

We study the dependence of the cross-correlation between galaxies and galaxy groups on group properties. Confirming previous results, we find that the correlation strength is stronger for more massive groups, in good agreement with the expected mass dependence of halo bias. We also find, however, that for groups of the same mass, the correlation strength depends on the star formation rate (SFR) of the central galaxy: at fixed mass, the bias of galaxy groups decreases as the SFR of the central galaxy increases. We discuss these findings in light of the recent findings by Gao et al (2005) that halo bias depends on halo formation time, in that halos that assemble earlier are more strongly biased. We also discuss the implication for galaxy formation, and address a possible link to galaxy conformity, the observed correlation between the properties of satellite galaxies and those of their central galaxy.Comment: 4 pages, 4 figures, Accepted for publication in ApJ Letters. Figures 3 and 4 replaced. The bias dependence on the central galaxy luminosity is omitted due to its sensitivity to the mass mode

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

The cross-correlation between galaxies of different luminosities and Colors

We study the cross-correlation between galaxies of different luminosities and colors, using a sample selected from the SDSS Dr 4. Galaxies are divided into 6 samples according to luminosity, and each of these samples is divided into red and blue subsamples. Projected auto-correlation and cross-correlation is estimated for these subsample. At projected separations r_p > 1\mpch, all correlation functions are roughly parallel, although the correlation amplitude depends systematically on luminosity and color. On r_p < 1\mpch, the auto- and cross-correlation functions of red galaxies are significantly enhanced relative to the corresponding power laws obtained on larger scales. Such enhancement is absent for blue galaxies and in the cross-correlation between red and blue galaxies. We esimate the relative bias factor on scales r > 1\mpch for each subsample using its auto-correlation function and cross-correlation functions. The relative bias factors obtained from different methods are similar. For blue galaxies the luminosity-dependence of the relative bias is strong over the luminosity range probed (-23.0<M_r < -18.0),but for red galaxies the dependence is weaker and becomes insignificant for luminosities below L^*. To examine whether a significant stochastic/nonlinear component exists in the bias relation, we study the ratio R_ij= W_{ii}W_{jj}/W_{ij}^2, where W_{ij} is the projected correlation between subsample i and j. We find that the values of R_ij are all consistent with 1 for all-all, red-red and blue-blue samples, however significantly larger than 1 for red-blue samples. For faint red - faint blue samples the values of R_{ij} are as high as ~ 2 on small scales r_p < 1 \mpch and decrease with increasing r_p.Comment: 25 pages, 18 figures, Accepted for publication in Ap