The Halo Occupation Distribution: Toward an Empirical Determination of the Relation between Galaxies and Mass

By A. Berlind, D. Weinberg. 2001

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We investigate galaxy bias in the framework of the "halo occupation distribution" (HOD), which defines the bias of a population of galaxies by the conditional probability P(N|M) that a dark matter halo of virial mass M contains N galaxies, together with prescriptions that specify the relative spatial and velocity distributions of galaxies and dark matter within halos. By populating the halos of a cosmological N-body simulation using a variety of HOD models, we examine the sensitivity of different galaxy clustering statistics to properties of the HOD. The galaxy correlation function responds to different aspects of P(N|M) on different scales. Obtaining the observed power-law form of ξg(r) requires rather specific combinations of HOD parameters, implying a strong constraint on the physics of galaxy formation; the success of numerical and semianalytic models in reproducing this form is entirely nontrivial. Other clustering statistics such as the galaxy-mass correlation function, the bispectrum, the void probability function, the pairwise velocity dispersion, and the group multiplicity function are sensitive to different combinations of HOD parameters and thus provide complementary information about galaxy bias. We outline a strategy for determining the HOD empirically from redshift survey data. This method starts from an assumed cosmological model, but we argue that cosmological and HOD parameters will have nondegenerate effects on galaxy clustering, so that a substantially incorrect cosmological model will not reproduce the observations for any choice of HOD. Empirical determinations of the HOD as a function of galaxy type from the Two-Degree Field (2dF) and Sloan Digital Sky Survey (SDSS) redshift surveys will provide a detailed target for theories of galaxy formation, insight into the origin of galaxy properties, and sharper tests of cosmological models.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/75b345e0051d79cc8766fa37bf8714fc253fcf00

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Citations in the corpus

The Intermediate-Scale Clustering of Luminous Red Galaxies (2004, background): “…between halos (Kauffmann et al. 1997, 1999; Jing et al. 1998; Benson et al. 2000; Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Berlind et al. 2003; Magliocchetti & Porciani 2003; Kravtsov et al. 2004; Zehavi et al. 2004a; Zheng 2004).”
GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY (2010, methodology): “In the context of HOD models, Watson, Berlind, & Zentner (2011) discuss the physical processes that lead both to an approximate power law correlation function and to deviations from a power law (see also Benson et al. 2000, Berlind & Weinberg 2002, and Appendix A of Zheng et al. 2009).”
Lightcone mock catalogues from semi-analytic models of galaxy formation – I. Construction and application to the BzK colour selection (2012, methodology): “…phenomenological models to assign galaxies to dark matter particles in the simulation (e.g. Cole et al. 1998) or using empirically derived statistics, such as the halo occupation distribution (HOD, Berlind & Weinberg 2002; Song et al. 2012) or sub-halo abundance matching (Vale & Ostriker 2004).”
The dark side of galaxy colour (2013, background): “…al. 2003; van den Bosch et al. 2007)), which adopts parametric forms for the biased relation between galaxies and halo mass (e.g., Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Cooray & Sheth 2002; Zheng et al. 2007; Leauthaud et al. 2011; Watson et al. 2012).”
The dependence of clustering on galaxy properties (2005, background): “These ideas have been further developed into the so-called “halo occupation distribution” (HOD) approach by many different authors (for example Jing, Mo & Börner 1998, Seljak 2000; Peacock & Smith 2000; Berlind & Weinberg 2002; Cooray & Sheth 2002; Yang, Mo & van den Bosch 2003).”
A halo-based galaxy group finder: calibration and application to the 2dFGRS (2004, background): “…Börner 1998; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; White 2001; Jing, Börner & Suto 2002; Bullock, Wechsler & Somerville 2002; Berlind & Weinberg 2002; Scranton 2002; Kang et al. 2002; Marinoni & Hudson 2002; Zheng et al. 2002; Magliocchetti & Porciani 2003; Kochanek et al.…”
A COMPREHENSIVE ANALYSIS OF UNCERTAINTIES AFFECTING THE STELLAR MASS–HALO MASS RELATION FOR 0 < z < 4 (2010, background): “Halo occupation (e.g., Berlind & Weinberg 2002; Bullock et al. 2002; Cooray & Sheth 2002; Tinker et al. 2005; Zheng et al. 2007) and conditional luminosity function modeling (e.g., Yang et al. 2003; Cooray 2006) fall into this category.”
The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations (2011, methodology): “The LasDamas collaboration generated realistic LRG mock catalogues‡ by placing galaxies inside dark matter halos using a Halo Occupation Distribution (HOD; Berlind & Weinberg 2002).”
THE AVERAGE STAR FORMATION HISTORIES OF GALAXIES IN DARK MATTER HALOS FROM z = 0–8 (2012, methodology): “…associated galaxies with dark matter halos at a given epoch, using a variety of techniques, including Halo Occupation Distribution modeling (e.g., Berlind & Weinberg 2002; Bullock et al. 2002) the Conditional Luminosity Function modeling (e.g., Yang et al. 2003), and variants of the abundance…”
GAMA: towards a physical understanding of galaxy formation (2009, background): “Empirically, astronomers thus have to consider the halo occupation distribution: the number of galaxies hosted by a halo as a function of its mass and other properties (e.g. Peacock and Smith 2000, Berlind and Weinberg 2002).”
The Non-Parametric Model for Linking Galaxy Luminosity with Halo/Subhalo Mass: Are First Brightest Galaxies Special? (2005, background): “…of the distribution of the galaxy population through different haloes while bypassing the complications of the physics of galaxy formation (e.g., Berlind & Weinberg 2002; Vale & Ostriker 2004; Tasitsiomi et al. 2004; Yang et al. 2005; Zehavi et al. 2005; Zheng et al. 2005; Cooray 2006; Conroy,…”
Cosmological Constraints from a Combination of Galaxy Clustering and Lensing -- III. Application to SDSS Data (2012, methodology): “…realistic model for galaxy bias is provided by halo occupation models, which describe, in a statistical sense, how galaxies are distributed over dark matter haloes (e.g., Jing, Mo & Börner 1998; Peacock & Smith 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Yang, Mo & van den Bosch 2003).”
What Aspects of Galaxy Environment Matter? (2006, methodology): “…we want to test is how adequately we can model the relationship between environment and colors using the HOD description, and one of the main uses of that description is to model correlation functions (e.g., Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Zheng et al. 2005).”
THE CLUSTERING OF MASSIVE GALAXIES AT z ∼ 0.5 FROM THE FIRST SEMESTER OF BOSS DATA (2010, methodology): “…of galaxies with the clustering of the underlying mass, and to make realistic mock catalogs, we interpret our measurements within the context of the halo occupation distribution (Peacock & Smith 2000; Seljak 2000; Benson et al. 2000; White et al. 2001; Berlind & Weinberg 2002; Cooray & Sheth 2002).”