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Register a new userTheoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies
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Zheng Zheng
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The halo occupation distribution (HOD) describes the relation between galaxies and dark matter at the level of individual dark matter halos. The properties of galaxies residing at the centers of halos differ from those of satellite galaxies because of differences in their formation histories. Using a smoothed particle hydrodynamics (SPH) simulation and a semi-analytic (SA) galaxy formation model, we examine the separate contributions of central and satellite galaxies to the HOD, more specifically to the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class. In agreement with earlier results for dark matter subhalos, we find that the mean occupation function <N> for galaxies above a baryonic mass threshold can be approximated by a step function for central galaxies plus a power law for satellites, and that the distribution of satellite numbers is close to Poisson at fixed halo mass. For galaxy samples defined by different baryonic mass thresholds, there is a nearly linear relation between the minimum halo mass Mmin required to host a central galaxy and the mass M1 at which an average halo hosts one satellite, with M1 ~ 14 Mmin (SPH) or M1 ~ 18 Mmin (SA). The mean occupation number of young galaxies exhibits a local minimum at M ~ 10 Mmin where halos are too massive to host a young central galaxy but not massive enough to host satellites. We show that the conditional galaxy mass function at fixed halo mass cannot be described by a Schechter function because central galaxies produce a bump at high masses. We suggest parameterizations for the HOD and the conditional luminosity function that can be used to model observed galaxy clustering. Many of our predictions are in good agreement with recent results inferred from clustering in the Sloan Digital Sky Survey.
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We investigate the clustering of Lyman-break galaxies (LBGs) at $zsim4$. Using the hierarchical galaxy formation model GALFORM, we predict, for the first time using a semi-analytical model with feedback from active galactic nuclei (AGN), the angular correlation function (ACF) of LBGs and find agreement within $3,sigma$ with new measurements of the ACF from surveys including the Hubble eXtreme Deep Field (XDF) and CANDELS field. Our simulations confirm the conclusion reached using independent models that although the predicted ACFs reproduce the trend of increased clustering with luminosity, the dependence is less strong than observed. We find that for the detection limits of the XDF field central LBGs at $zsim 4$ predominantly reside in haloes of mass $sim 10^{11}-10^{12}h^{-1}M_{rm odot}$ and that satellites reside in larger haloes of mass $sim 10^{12}-10^{13}h^{-1}M_{rm odot}$. The model predicts fewer bright satellite LBGs at $zsim4$ than is inferred from measurements of the ACF at small scales. By analysing the halo occupation distribution (HOD) predicted by the model, we find evidence that AGN feedback affects the HOD of central LBGs in massive haloes. This is a new high-redshift test of this important feedback mechanism. We investigate the effect of photometric errors in the observations on the ACF predictions. We find that the observational uncertainty in the galaxy luminosity reduces the clustering amplitude and that this effect increases towards faint galaxies, particularly on small scales. To compare properties of model with observed LBGs this uncertainty must be considered.
We perform Halo Occupation Distribution (HOD) modeling to interpret small-scale and intermediate-scale clustering of 35,000 luminous early-type galaxies and their cross-correlation with a reference imaging sample of normal L* galaxies in the Sloan Digital Sky Survey. The modeling results show that most of these luminous red galaxies (LRGs) are central galaxies residing in massive halos of typical mass M ~ a few times 10^13 to 10^14 Msun/h, while a few percent of them have to be satellites within halos in order to produce the strong auto-correlations exhibited on smaller scales. The mean luminosity Lc of central LRGs increases with the host halo mass, with a rough scaling relation of Lc propto M^0.5. The halo mass required to host on average one satellite LRG above a luminosity threshold is found to be about 10 times higher than that required to host a central LRG above the same threshold. We find that in massive halos the distribution of L* galaxies roughly follows that of the dark matter and their mean occupation number scales with halo mass as M^1.5. The HOD modeling results also allows for an intuitive understanding of the scale-dependent luminosity dependence of the cross-correlation between LRGs and L_* galaxies. Constraints on the LRG HOD provide tests to models of formation and evolution of massive galaxies, and they are also useful for cosmological parameter investigations. In one of the appendices, we provide LRG HOD parameters with dependence on cosmology inferred from modeling the two-point auto-correlation functions of LRGs.
We have traced the past 7 Gyr of red galaxy stellar mass growth within dark matter halos. We have determined the halo occupation distribution, which describes how galaxies reside within dark matter halos, using the observed luminosity function and clustering of 40,696 0.2<z<1.0 red galaxies in Bootes. Half of 10^{11.9} Msun/h halos host a red central galaxy, and this fraction increases with increasing halo mass. We do not observe any evolution of the relationship between red galaxy stellar mass and host halo mass, although we expect both galaxy stellar masses and halo masses to evolve over cosmic time. We find that the stellar mass contained within the red population has doubled since z=1, with the stellar mass within red satellite galaxies tripling over this redshift range. In cluster mass halos most of the stellar mass resides within satellite galaxies and the intra-cluster light, with a minority of the stellar mass residing within central galaxies. The stellar masses of the most luminous red central galaxies are proportional to halo mass to the power of a third. We thus conclude that halo mergers do not always lead to rapid growth of central galaxies. While very massive halos often double in mass over the past 7 Gyr, the stellar masses of their central galaxies typically grow by only 30%.
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