The Press-Schechter, excursion set approach allows one to make predictions about the shape and evolution of the mass function of bound objects. The approach combines the assumption that objects collapse spherically with the assumption that the initial density fluctuations were Gaussian and small. The predicted mass function is reasonably accurate, although it has fewer high-mass and more low-mass objects than are seen in simulations of hierarchical clustering. We show that the discrepancy between theory and simulation can be reduced substantially if bound structures are assumed to form from an ellipsoidal, rather than a spherical, collapse. In the original, standard, spherical model, a region collapses if the initial density within it exceeds a threshold value, δsc. This value is independent of the initial size of the region, and since the mass of the collapsed object is related to its initial size, this means that δsc is independent of final mass. In the ellipsoidal model, the collapse of a region depends on the surrounding shear field, as well as on its initial overdensity. In Gaussian random fields, the distribution of these quantities depends on the size of the region considered. Since the mass of a region is related to its initial size, there is a relation between the density threshold value required for collapse and the mass of the final object. We provide a fitting function to this δec(m) relation which simplifies the inclusion of ellipsoidal dynamics in the excursion set approach. We discuss the relation between the excursion set predictions and the halo distribution in high-resolution N-body simulations, and use our new formulation of the approach to show that our simple parametrization of the ellipsoidal collapse model represents an improvement on the spherical model on an object-by-object basis. Finally, we show that the associated statistical predictions, the mass function and the large-scale halo-to-mass bias relation, are also more accurate than the standard predictions

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 these links 1 . Subject headings: dark matter -large-scale structure of the universe -galaxies: halos -methods: statistical 1 Shanghai Astronomical Observatory, the Partner Group of MPA,

We use the conditional luminosity function Φ(L | M) dL, which gives the number of galaxies with luminosities in the range L± d L/2 that reside in a halo of mass M, to link the distribution of galaxies to that of dark matter haloes. Starting from the number density of dark matter haloes predicted by current models of structure formation, we seek the form of Φ(L | M) that reproduces the galaxy luminosity function and the luminosity dependence of the galaxy clustering strength. We test the models of Φ(L | M) by comparing the resulting mass‐to‐light ratios with constraints from the Tully–Fisher (TF) relation and from galaxy clusters. A comparison between model predictions and current observations yields a number of stringent constraints on both galaxy formation and cosmology. In particular, this method can break the degeneracy between Ω0 and the power‐spectrum normalization σ8, inherent in current weak‐lensing and cluster‐abundance studies. For flat ΛCDM cosmogonies with σ8 normalized by recent weak gravitational lensing observations, the best results are obtained for Ω0∼ 0.3; Ω0≲ 0.2 leads to too large galaxy correlation lengths, while Ω0≳ 0.4 gives too high mass‐to‐light ratios to match the observed TF relation. The best‐fitting model for the ΛCDM concordance cosmology with Ω0= 0.3 and ΩΛ= 0.7 predicts mass‐to‐light ratios that are slightly too high to match the TF relation. We discuss a number of possible effects that might remedy this problem, such as small modifications of σ8 and the Hubble parameter with respect to the concordance values, the assumption that the Universe is dominated by warm dark matter, systematic errors in current observational data, and the existence of dark galaxies. We use the conditional luminosity function derived from the present data to predict several statistics about the distribution of galaxy light in the local Universe. We show that roughly 50 per cent of all light is produced in haloes less massive than 2 × 1012h−1 M⊙. We also derive the probability distribution P(M | L) dM that a galaxy of luminosity L resides in a halo with virial masses in the range M± dM/2.

A large amount of observations have constrained cosmological parameters and the initial density fluctuation spectrum to a very high accuracy. However, cosmological parameters change with time and the power index of the power spectrum dramatically varies with mass scale in the so-called concordance ΛCDM cosmology. Thus, any successful model for its structural evolution should work well simultaneously for various cosmological models and different power spectra. We use a large set of high-resolution N-body simulations of a variety of structure formation models (scale-free, standard CDM, open CDM, and ΛCDM) to study the mass accretion histories, the mass and redshift dependence of concentrations, and the concentration evolution histories of dark matter halos. We find that there is significant disagreement between the much-used empirical models in the literature and our simulations. Based on our simulation results, we find that the mass accretion rate of a halo is tightly correlated with a simple function of its mass, the redshift, parameters of the cosmology, and of the initial density fluctuation spectrum, which correctly disentangles the effects of all these factors and halo environments. We also find that the concentration of a halo is strongly correlated with the universe age when its progenitor on the mass accretion history first reaches 4% of its current mass. According to these correlations, we develop new empirical models for both the mass accretion histories and the concentration evolution histories of dark matter halos, and the latter can also be used to predict the mass and redshift dependence of halo concentrations. These models are accurate and universal: the same set of model parameters works well for different cosmological models and for halos of different masses at different redshifts, and in the ΛCDM case the model predictions match the simulation results very well even though halo mass is traced to about 0.0005 times the final mass, when cosmological parameters and the power index of the initial density fluctuation spectrum have changed dramatically. Our model predictions also match the PINOCCHIO mass accretion histories very well, which are much independent of our numerical simulations and our definitions of halo merger trees. These models are also simple and easy to implement, making them very useful in modeling the growth and structure of dark matter halos. We provide appendices describing the step-by-step implementation of our models. A calculator which allows one to interactively generate data for any given cosmological model is provided on the Web, together with a userfriendly code to make the relevant calculations and some tables listing the expected concentration as a function of halo mass and redshift in several popular cosmological models. We explain why ΛCDM and open CDM halos on nearly all mass scales show two distinct phases in their mass growth histories. We discuss implications of the universal relations we find in connection to the formation of dark matter halos in the cosm...

We use the halo occupation model to calibrate galaxy group finders in magnitude limited redshift surveys. Because, according to the current scenario of structure formation, galaxy groups are associated with cold dark matter (CDM) haloes, we make use of the properties of the halo population in the design of our group finder. The method starts with an assumed mass-to-light ratio to assign a tentative mass to each group. This mass is 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). This procedure is repeated until no further changes occur in group memberships. We find that the final groups selected this way are insensitive to the mass-to-light ratio assumed. We use mock catalogues, constructed using the conditional luminosity function (CLF), to test the performance of our group finder in terms of completeness of true members and contamination by interlopers. Our group finder is more successful than the conventional friends-of-friends (FOF) group finder in assigning galaxies in common dark matter haloes to a single group. We apply our group finder to the 2-degree Field Galaxy Redshift Survey (2dFGRS) and compare the resulting group properties with model predictions based on the CLF. For the CDM concordance cosmology, we find a clear discrepancy between the model and data in the sense that the model predicts too many rich groups. In order to match the observational results, we have to either increase the mass-to-light ratios of rich clusters to a level significantly higher than current observational estimates, or to assume σ 8 0.7, compared with the concordance value of 0.9.

We investigate various galaxy occupation statistics of dark matter halos using a large galaxy group catalog constructed from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4) with an adaptive haloYbased group finder. The conditional luminosity function (CLF) is measured separately for all, red, and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modeled with a lognormal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses M h k10 14 h À1 M are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with M h $ 10 12 h À1 M . For halos of a given mass, the distribution of the luminosities of central galaxies, L c , has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as L c / M 0:17 h (M Ã;c / M 0:22 h ) for halos with masses M 310 12:5 h À1 M , and both relations are significantly steeper for less massive halos. We also measure the luminosity and stellar mass gaps between the first and second brightest (most massive) member galaxies, log L 1 À log L 2 (log M Ã;1 À log M Ã; 2 ). These gap statistics, especially in halos with M h P10 14:0 h À1 M , indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with log L 1 À log L 2 ! 0:8, ranges from $2.5% for groups with M h $ 10 14 h À1 M to 18%Y60% for groups with M h $ 10 13 h À1 M . Finally, we measure the fraction of satellites, which changes from $5.0% for galaxies with 0:1 M r À 5log h $ À22:0 to $40% for galaxies with 0:1 M r À 5 log h $ À17:0. Subject headingg s: dark matter -galaxies: halos -large-scale structure of universe -methods: statistical

We present a new model to describe the galaxy-dark matter connection across cosmic time, which unlike the popular subhalo abundance matching technique is self-consistent in that it takes account of the facts that (i) subhalos are accreted at different times, and (ii) the properties of satellite galaxies may evolve after accretion. Using observations of galaxy stellar mass functions out to z ∼ 4, the conditional stellar mass function at z ∼ 0.1 obtained from SDSS galaxy group catalogues, and the two-point correlation function (2PCF) of galaxies at z ∼ 0.1 as function of stellar mass, we constrain the relation between galaxies and dark matter halos over the entire cosmic history from z ∼ 4 to the present. This relation is then used to predict the median assembly histories of different stellar mass components within dark matter halos (central galaxies, satellite galaxies, and halo stars). We also make predictions for the 2PCFs of high-z galaxies as function of stellar mass. Our main findings are the following: (i) Our model reasonably fits all data within the observational uncertainties, indicating that the ΛCDM concordance cosmology is consistent with a wide variety of data regarding the galaxy population across cosmic time. (ii) At low-z, the stellar mass of central galaxies increases with halo mass as M 0.3 and M 4.0 at the massive and low-mass ends, respectively. The ratio M * ,c /M reveals a maximum of ∼ 0.03 at a halo mass M ∼ 10 11.8 h −1 M ⊙ , much lower than the universal baryon fraction (∼ 0.17). At higher redshifts the maximum in M * ,c /M remains close to ∼ 0.03, but shifts to higher halo mass. (iii) The inferred time-scale for the disruption of satellite galaxies is about the same as the dynamical friction time scale of their subhalos. (iv) The stellar mass assembly history of central galaxies is completely decoupled from the assembly history of its host halo; the ratio M * ,c /M initially increases rapidly with time until the halo mass reaches ∼ 10 12 h −1 M ⊙ , at which point M * ,c /M ∼ 0.03. Once M > ∼ 10 12 h −1 M ⊙ , there is little growth in M * ,c , causing the ratio M * ,c /M to decline. In Milky-Way sized halos more than half of the central stellar mass is assembled at z 0.5. (v) In low mass halos, the accretion of satellite galaxies contributes little to the formation of their central galaxies, indicating that most of their stars must have formed in situ. In massive halos more than half of the stellar mass of the central galaxy has to be formed in situ, and the accretion of satellites can only become significant at z 2. (vi) The total mass in halo stars is more than twice that of the central galaxy in massive halos, but less than 10 percent of M * ,c in Milky Way sized halos. (vii) The 2PCFs of galaxies on small scales holds important information regarding the evolution of satellite galaxies, and at high-z is predicted to be much steeper than at low-z, especially for more massive galaxies. We discuss various implications of our findings regarding the formation and evolution of galaxies in a Λ...

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