Internal Alignments of Red Versus Blue Discs in Dark Matter Halos

Large surveys have shown that red galaxies are preferentially aligned with their halos while blue galaxies have a more isotropic distribution. Since halos generally align with their filaments this introduces a bias in the measurement of the cosmic shear from weak lensing. It is therefore vitally important to understand why this difference arises. We explore the stability of different disc orientations within triaxial halos. We show that, in the absence of gas, the disc orientation is most stable when its spin is along the minor axis of the halo. Instead when gas cools onto a disc it is able to form in almost arbitrary orientation, including off the main planes of the halo (but avoiding an orientation perpendicular to the halos intermediate axis). Substructure helps gasless galaxies reach alignment with the halo faster, but have less effect on galaxies when gas is cooling onto the disc. Our results provide a novel and natural interpretation for why red, gas poor galaxies are preferentially aligned with their halo, while blue, star-forming, galaxies have nearly random orientations, without requiring a connection between galaxies current star formation rate and their merger history.

Statistics of Dark Matter Substructure: II. Comparison of Model with Simulation Results

We compare subhalo mass and velocity functions obtained from different simulations with different subhalo finders among each other, and with predictions from the new semi-analytical model of Jiang & van den Bosch (2014). We find that subhalo mass functions (SHMFs) obtained using different subhalo finders agree with each other at the level of ~ 20 percent, but only at the low mass end. At the massive end, subhalo finders that identify subhaloes based purely on density in configuration space dramatically underpredict the subhalo abundances by more than an order of magnitude. These problems are much less severe for subhalo velocity functions (SHVFs), indicating that they arise from issues related to assigning masses to the subhaloes, rather than from detecting them. Overall the predictions from the semi-analytical model are in excellent agreement with simulation results obtained using the more advanced subhalo finders that use information in six dimensional phase-space. In particular, the model accurately reproduces the slope and host-mass-dependent normalization of both the subhalo mass and velocity functions. We find that the SHMFs and SHVFs have power-law slopes of 0.82 and 2.6, respectively, significantly shallower than what has been claimed in several studies in the literature.

Statistics of Dark Matter Substructure: I. Model and Universal Fitting Functions

We present a new, semi-analytical model describing the evolution of dark matter subhaloes. The model uses merger trees constructed using the method of Parkinson et al. (2008) to describe the masses and redshifts of subhaloes at accretion, which are subsequently evolved using a simple model for the orbit-averaged mass loss rates. The model is extremely fast, treats subhaloes of all orders, accounts for scatter in orbital properties and halo concentrations, and uses a simple recipe to convert subhalo mass to maximum circular velocity. The model accurately reproduces the average subhalo mass and velocity functions in numerical simulations. The inferred subhalo mass loss rates imply that an average dark matter subhalo loses in excess of 80 percent of its infall mass during its first radial orbit within the host halo. We demonstrate that the total mass fraction in subhaloes is tightly correlated with the `dynamical age of the host halo, defined as the number of halo dynamical times that have elapsed since its formation. Using this relation, we present universal fitting functions for the evolved and unevolved subhalo mass and velocity functions that are valid for any host halo mass, at any redshift, and for any {Lambda}CDM cosmology.

Generating Merger Trees for Dark Matter Haloes: A Comparison of Methods

Halo merger trees describe the hierarchical mass assembly of dark matter haloes, and are the backbone for modeling galaxy formation and evolution. Merger trees constructed using Monte Carlo algorithms based on the extended Press-Schechter (EPS) formalism are complementary to those extracted from N-body simulations, and have the advantage that they are not trammeled by limited numerical resolution and uncertainties in identifying (sub)haloes and linking them between snapshots. This paper compares multiple EPS-based merger tree algorithms to simulation results using four diagnostics: progenitor mass function (PMF), mass assembly history (MAH), merger rate per descendant halo, and the unevolved subhalo mass function (USMF). In general, algorithms based on spherical collapse yield major-merger rates that are too high by a factor of two, resulting in MAHs that are systematically offset. Assuming ellipsoidal collapse solves most of these issues, but the particular algorithm investigated here that incorporates ellipsoidal collapse dramatically overpredicts the minor-merger rate for massive haloes. The only algorithm in our comparison that yields MAHs, merger rates, and USMFs in good agreement with simulations, is that by Parkinson et al. (2008). However, this is not a true EPS-based algorithm as it draws its progenitor masses from a PMF calibrated against simulations, rather than `predicted by EPS. Finally we emphasize that the benchmarks used to test the EPS algorithms are obtained from simulations and are hampered by significant uncertainties themselves. In particular, MAHs and halo merger rates obtained from simulations by different authors reveal discrepancies that easily exceed 50 percent, even when based on the same simulation. Given this status quo, merger trees constructed using the Parkinson et al. algorithm are as accurate as those extracted from N-body simulations.

Constraining the Star Formation Histories in Dark Matter Halos: I. Central Galaxies

Using the self-consistent modeling of the conditional stellar mass functions across cosmic time by Yang et al. (2012), we make model predictions for the star formation histories (SFHs) of {it central} galaxies in halos of different masses. The model requires the following two key ingredients: (i) mass assembly histories of central and satellite galaxies, and (ii) local observational constraints of the star formation rates of central galaxies as function of halo mass. We obtain a universal fitting formula that describes the (median) SFH of central galaxies as function of halo mass, galaxy stellar mass and redshift. We use this model to make predictions for various aspects of the star formation rates of central galaxies across cosmic time. Our main findings are the following. (1) The specific star formation rate (SSFR) at high $z$ increases rapidly with increasing redshift [$propto (1+z)^{2.5}$] for halos of a given mass and only slowly with halo mass ($propto M_h^{0.12}$) at a given $z$, in almost perfect agreement with the specific mass accretion rate of dark matter halos. (2) The ratio between the star formation rate (SFR) in the main-branch progenitor and the final stellar mass of a galaxy peaks roughly at a constant value, $sim 10^{-9.3} h^2 {rm yr}^{-1}$, independent of halo mass or the final stellar mass of the galaxy. However, the redshift at which the SFR peaks increases rapidly with halo mass. (3) More than half of the stars in the present-day Universe were formed in halos with $10^{11.1}msunh < M_h < 10^{12.3}msunh$ in the redshift range $0.4 < z < 1.9$. (4) ... [abridged]

On Combining Galaxy Clustering and Weak Lensing to Unveil Galaxy Biasing via the Halo Model

We formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, b_g(r_p), and the galaxy-dark matter cross-correlation function, R_{gm}(r_p), where r_p is the projected distance. We use the analytical halo model to predict how the scale dependence of b_g and R_{gm}, over the range 0.1 Mpc/h < r_p < 30 Mpc/h, depends on the non-linearity and stochasticity in halo occupation models. In particular we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo, and the Poisson character of the probability to have a certain number of satellite galaxies in a halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real-space, we find that galaxy bias becomes scale independent, with R_{gm} = 1, for radii r > 1 - 5 Mpc/h, depending on luminosity. However, galaxy bias is scale-dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo occupation statistics and to unveil the origin of galaxy biasing we propose the use of the bias function Gamma_{gm}(r_p)=b_g(r_p)/R_{gm}(r_p). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.

On the Evolution of the Velocity-Mass-Size Relations of Disk-Dominated Galaxies over the Past 10 Billion Years

We study the evolution of the scaling relations between maximum circular velocity, stellar mass and optical half-light radius of star-forming disk-dominated galaxies in the context of LCDM-based galaxy formation models. Using data from the literature combined with new data from the DEEP2 and AEGIS surveys we show that there is a consistent observational and theoretical picture for the evolution of these scaling relations from zsim 2 to z=0. The evolution of the observed stellar scaling relations is weaker than that of the virial scaling relations of dark matter haloes, which can be reproduced, both qualitatively and quantitatively, with a simple, cosmologically-motivated model for disk evolution inside growing NFW dark matter haloes. In this model optical half-light radii are smaller, both at fixed stellar mass and maximum circular velocity, at higher redshifts. This model also predicts that the scaling relations between baryonic quantities evolve even more weakly than the corresponding stellar relations. We emphasize, though, that this weak evolution does not imply that individual galaxies evolve weakly. On the contrary, individual galaxies grow strongly in mass, size and velocity, but in such a way that they move largely along the scaling relations. Finally, recent observations have claimed surprisingly large sizes for a number of star-forming disk galaxies at z sim 2, which has caused some authors to suggest that high redshift disk galaxies have abnormally high spin parameters. However, we argue that the disk scale lengths in question have been systematically overestimated by a factor sim 2, and that there is an offset of a factor sim 1.4 between Halpha sizes and optical sizes. Taking these effects into account, there is no indication that star forming galaxies at high redshifts (zsim 2) have abnormally high spin parameters.

Galaxy Groups in the SDSS DR4: III. the luminosity and stellar mass functions

Using a large galaxy group catalogue constructed from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4) with an adaptive halo-based group finder, we investigate the luminosity and stellar mass functions for different populations of galaxies (central versus satellite; red versus blue; and galaxies in groups of different masses) and for groups themselves. The conditional stellar mass function (CSMF), which describes the stellar distribution of galaxies in halos of a given mass for central and satellite galaxies can be well modeled with a log-normal distribution and a modified Schechter form, respectively. On average, there are about 3 times as many central galaxies as satellites. Among the satellite population, there are in general more red galaxies than blue ones. For the central population, the luminosity function is dominated by red galaxies at the massive end, and by blue galaxies at the low mass end. At the very low-mass end ($M_ast la 10^9 h^{-2}Msun$), however, there is a marked increase in the number of red centrals. We speculate that these galaxies are located close to large halos so that their star formation is truncated by the large-scale environments. The stellar-mass function of galaxy groups is well described by a double power law, with a characteristic stellar mass at $sim 4times 10^{10}h^{-2}Msun$. Finally, we use the observed stellar mass function of central galaxies to constrain the stellar mass - halo mass relation for low mass halos, and obtain $M_{ast, c}propto M_h^{4.9}$ for $M_h ll 10^{11} msunh$.

Galaxy Groups in the SDSS DR4: I. The Catalogue and Basic Properties

We use a modified version of the halo-based group finder developed by Yang et al. to select galaxy groups from the Sloan Digital Sky Survey (SDSS DR4). In the first step, a combination of two methods is used to identify the centers of potential groups and to estimate their characteristic luminosity. Using an iterative approach, the adaptive group finder then uses the average mass-to-light ratios of groups, obtained from the previous iteration, to assign a tentative mass to each group. This mass is then used to estimate the size and velocity dispersion of the underlying halo that hosts the group, which in turn is used to determine group membership in redshift space. Finally, each individual group is assigned two different halo masses: one based on its characteristic luminosity, and the other based on its characteristic stellar mass. Applying the group finder to the SDSS DR4, we obtain 301237 groups in a broad dynamic range, including systems of isolated galaxies. We use detailed mock galaxy catalogues constructed for the SDSS DR4 to test the performance of our group finder in terms of completeness of true members, contamination by interlopers, and accuracy of the assigned masses. This paper is the first in a series and focuses on the selection procedure, tests of the reliability of the group finder, and the basic properties of the group catalogue (e.g. the mass-to-light ratios, the halo mass to stellar mass ratios, etc.). The group catalogues including the membership of the groups are available at http://gax.shao.ac.cn/data/Group.html and http://www.astro.umass.edu/~xhyang/Group.html