Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies

By Zheng Zheng, A. Berlind, D. Weinberg, A. Benson, C. Baugh, Shaun Cole, R. Dav'e, Carlos S. Frenk, Neal Katz, C. Lacey. 2004

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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 semianalytic (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⟩M 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. Since the number of central galaxies is always zero or one, the width of P(N|M) is narrower than a Poisson distribution at low N and approaches Poisson at high N. 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 ≈ 14Mmin (SPH) or M1 ≈ 18Mmin (SA). The stellar population age of central galaxies correlates with halo mass, and this correlation explains much of the age dependence of the galaxy HOD. The mean occupation number of young galaxies exhibits a local minimum at M ~ 10Mmin where halos are too massive to host a young central galaxy but not massive enough to host satellites. Using the SA model, 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/97636b7b8bdb4df898b52ebd155ce33d076a64c7

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Citations in the corpus

Cosmological constraints from the clustering of the Sloan Digital Sky Survey DR7 luminous red galaxies (vol 404, pg 60, 2010) (2009, positive): “In Reid et al. (2009), we adopt the following parametrization for the average number of LRGs in a halo of mass M (Zheng et al. 2005): 〈N (M)〉 = 〈Ncen〉(1 + 〈Nsat〉) (B1) 〈Ncen〉 = 1 2 [ 1 + erf ( log10 M − log10 Mmin σlogM )] (B2) 〈Nsat〉 = ( M − Mcut M1 )α .”
The VIMOS Public Extragalactic Redshift Survey (VIPERS) - Galaxy clustering and redshift-space distortions at z ≃ 0.8 in the first data release (2013, neutral): “Central and satellite galaxy occupations are defined as in (Zheng et al. 2005): 〈Ncen|m〉 = 1 2 [ 1 + erf ( log m − log Mmin σlog m )] , (16) 〈Nsat|m〉 = ( m − M0 M1 )α .”
The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at z ∼ 1.4 (2015, background): “Galaxies are populated into the halos according to the halo occupation distribution (HOD) model (Cooray & Sheth 2002; Zheng et al. 2005) constrained by the real-space clustering of the FastSound galaxies (Hikage et al. in preparation).”
Cosmic X-ray surveys of distant active galaxies (2015, background): “Further useful constraints can be placed by measuring how X-ray AGNs are distributed in dark-matter halos using the halo occupation distribution (HoD; e.g., Berlind and Weinberg 2002; Zheng et al 2005) formalism.”
Cosmology with massive neutrinos I: towards a realistic modeling of the relation between matter, haloes and galaxies (2013, methodology): “To populate the dark matter haloes with mock galaxies we follow the scheme of [68, 69], which consists of the following steps: 1) haloes with masses larger than Mmin contain one central galaxy: haloes with masses smaller than Mmin do not host any, central or satellite, galaxy.”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. I. Galaxy Mergers and Quasar Activity (2007, background): “…‘‘default’’ model (Conroy et al. 2006; see also Vale & Ostriker 2006) and an alternate halo occupation model (Yang et al. 2003; see also Yan et al. 2003; Zheng et al. 2005), which bracket the range of a number of calculations (e.g., Cooray 2005, 2006; Zheng et al. 2005; van den Bosch et al. 2007).”
The missing massive satellites of the Milky Way (2012, result): “These results confirm earlier work (see, e.g., Moore et al. 1999; Kravtsov et al. 2004; Zheng et al. 2005; Weinberg et al. 2008; Springel et al. 2008), and imply that we can combine all well-resolved halos into one large sample to derive robust estimates of the statistical distribution of Nsub(> ν).”
EVOLUTION OF THE GALAXY–DARK MATTER CONNECTION AND THE ASSEMBLY OF GALAXIES IN DARK MATTER HALOS (2011, background): “…are distributed in halos of different masses (e.g. Jing et al. 1998; Peacock & Smith 2000; Yang et al. 2003; van den Bosch et al. 2003a, 2007; Zheng et al. 2005; Tinker et al. 2005; Mandelbaum et al. 2006; Brown et al. 2008; More et al. 2009, 2011; Cacciato et al. 2009; Neistein et al.…”
The MassiveBlack-II simulation: The evolution of haloes and galaxies to z ~ 0 (2014, background): “…for this analysis is to compare the probability distribution of subhaloes N at a given average occupation number 〈N〉, P(N|〈N〉), MNRAS 450, 1349–1374 (2015) with that of a well-defined probability distribution, more specifically a Poisson distribution (e.g. Berlind et al. 2003; Zheng et al. 2005).”
Structure and Kinematics of Early-Type Galaxies from Integral Field Spectroscopy (2016, background): “This picture is similar to the one that motivates the separation of “central” (i.e. the most massive) and “satellite” (i.e. the rest) galaxies in dark matter halos, when building theoretical descriptions of galaxy and halo properties (e.g., Zheng et al. 2005; Zehavi et al. 2005; Conroy et al. 2006).”
Lensing is Low: Cosmology, Galaxy Formation, or New Physics? (2016, methodology): “This connection is typically modelled either via halo occupation distribution (HOD; Jing 1998; Peacock & Smith 2000; Berlind & Weinberg 2002; Zheng et al. 2005; Leauthaud et al. 2011; Hearin et al. 2016) or subhalo abundance matching (SHAM; Kravtsov et al. 2004; Conroy, Wechsler & Kravtsov 2006;…”
The Hierarchical Build-Up of Massive Galaxies and the Intracluster Light since z = 1 (2007, methodology): “It has been shown that the subhalo population in dissipationless simulations is indeed quite similar to the galaxy population in hydrodynamical simulations (Zheng et al. 2005; Weinberg et al. 2006) and semianalytic models (Zheng et al. 2005).”
Galaxy assembly bias: a significant source of systematic error in the galaxy–halo relationship (2013, methodology): “The two most widely used models of the galaxy-halo connection are the Halo Occupation Distribution (HOD, e.g., Berlind & Weinberg 2002; Zheng et al. 2005) and the Conditional Luminosity Function (CLF, e.g., Yang et al. 2003; van den Bosch et al. 2013).”
THE CLUSTERING OF MASSIVE GALAXIES AT z ∼ 0.5 FROM THE FIRST SEMESTER OF BOSS DATA (2010, methodology): “…method generates a “chain” of HOD parameters whose frequency of appearance traces the likelihood 3 Note that our definition ofσ can be interpreted as a fractional “scatter” in mass at threshold but is a factor ln(10)/ √ 2 different than that in Zheng et al. (2005). of that model fitting the data.”
A 2.5 per cent measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies (2014, methodology): “The parametrization of the HOD we adopt follows Zheng et al. (2005), and has been used in a number of studies focusing on the SDSS-II luminous red galaxy sample (Reid & Spergel 2009), the SDSS-III CMASS sample (White et al. 2011), and the SDSS-III LOWZ sample (Parejko et al. 2013).”
THE GALAXY CONTENT OF SDSS CLUSTERS AND GROUPS (2007, background): “Furthermore, the flattening and “saturating” of the red fraction for the most massive systems appears to be a natural product of modeling (Berlind et al. 2003; Zheng et al. 2005).”
The Large-Scale and Small-Scale Clustering of Lyman Break Galaxies at 3.5 ⩽ z ⩽ 5.5 from the GOODS Survey (2005, background): “…have also explored an alternative approach, which is to model central galaxies and satellites separately (Guzik & Seljak 2002; Kravtsov et al. 2004; Zheng et al. 2005) In this model, the probability for a halo to have a central galaxy is a step function, 10 This would be the average ‘‘observed’’…”
GALAXY CLUSTERING IN THE NEWFIRM MEDIUM BAND SURVEY: THE RELATIONSHIP BETWEEN STELLAR MASS AND DARK MATTER HALO MASS AT 1 < z < 2 (2010, methodology): “There are reasonably strong theoretical arguments based on the distribution of sub-halos for α ≃ 1 for all stellar mass limited samples (Kravtsov et al. 2004; Zheng et al. 2005), which are supported by precise clustering measurements in the local universe (e.g. Zehavi et al. 2010).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modelling the clustering and halo occupation distribution of BOSS CMASS galaxies in the Final Data Release (2015, methodology): “One of the most used models is the halo occupation distribution (HOD; e.g. Jing, Mo & Börner 1998; Peacock & Smith 2000; Berlind & Weinberg 2002; Zheng et al. 2005; Leauthaud et al. 2012; Guo et al. 2014).”