The Dark Side of the Halo Occupation Distribution

By Andrey V. Kravtsov, A. Berlind, Risa Wechsler, Anatoly Klypin, Stefan Gottloeber, B. Allgood, Joel R. Primack. 2003

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We analyze the halo occupation distribution (HOD) and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat ΛCDM model. The halo samples include both the host halos and the "subhalos," distinct gravitationally bound halos within the virialized regions of larger host systems. We find that the HOD, the probability distribution for a halo of mass M to host a number of subhalos N, is similar to that found in semianalytic and N-body+gasdynamics studies. Its first moment, ⟨N⟩M, has a complicated shape consisting of a step, a shoulder, and a power-law high-mass tail. The HOD can be described by Poisson statistics at high halo masses but becomes sub-Poisson for ⟨N⟩M ≲ 4. We show that the HOD can be understood as a combination of the probability for a halo of mass M to host a central galaxy and the probability to host a given number Ns of satellite galaxies. The former can be approximated by a steplike function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment. The first moment of the satellite HOD can be well described by a simple power law ⟨Ns⟩ ∝ Mβ with β ≈ 1 for a wide range of number densities, redshifts, and different power spectrum normalizations. This formulation provides a simple but accurate model for the halo occupation distribution found in simulations. At z = 0, the two-point correlation function (CF) of galactic halos can be well fitted by a power law down to ~100 h-1 kpc with an amplitude and slope similar to those of observed galaxies. The dependence of correlation amplitude on the number density of objects is in general agreement with results from the Sloan Digital Sky Survey. At redshifts z ≳ 1, we find significant departures from the power-law shape of the CF at small scales, where the CF steepens because of a more pronounced one-halo component. The departures from the power law may thus be easier to detect in high-redshift galaxy surveys than at the present-day epoch. They can be used to put useful constraints on the environments and formation of galaxies. If the deviations are as strong as indicated by our results, the assumption of the single power law often used in observational analyses of high-redshift clustering is dangerous and is likely to bias the estimates of the correlation length and slope of the correlation function.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b304cc93a34060a393343d4a7ad57af32c81d267

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Citations in the corpus

Measures of Galaxy Environment I - What is "Environment"? (2011, background): “…descriptions of galaxy clustering – conditional luminosity functions (e.g. Yang, Mo & van den Bosch 2003) and subhalo abundance matching (e.g. Kravtsov et al. 2004) – would produce similar mock catalogues, although an advantage of the SS09 approach is that it includes a strongly…”
The missing massive satellites of the Milky Way (2012, result): “This is possible because, in agreement with earlier work, we find that the abundance of subhalos, when scaled appropriately, is independent of halo mass (see, e.g., Moore et al. 1999; Kravtsov et al. 2004; Springel et al. 2008).”
Cosmology with massive neutrinos I: towards a realistic modeling of the relation between matter, haloes and galaxies (2013, methodology): “The HOD is a framework used to link the distribution of galaxies to that of dark matter haloes [59–65].”
Linking halo mass to galaxy luminosity (2004, background): “Even though this quantity also shows a large scatter between the maximum value and that at present after stripping (Kravtsov et al. 2004b), its relative change should be smaller than what would be expected for a given change in mass.”
Red Galaxy Growth and the Halo Occupation Distribution (2008, methodology): “The functional form of this model is motivated by HODs observed in galaxy formation simulations (Berlind et al. 2003; Kravtsov et al. 2004; Zheng et al. 2005).”
ROBUST OPTICAL RICHNESS ESTIMATION WITH REDUCED SCATTER (2011, background): “Indeed, it has been argued on the basis of numerical simulations that the intrinsic scatter of the richness–mass relation is Poisson (e.g., Kravtsov et al. 2004; Berlind et al. 2003; Zheng et al. 2005).”
The mass function and average mass-loss rate of dark matter subhaloes (2004, result): “These results are inconsistent with Kravtsov et al. (2004), who find that the number of subhaloes in numerical simulations follow Poisson statistics.”
Galaxy formation theory (2010, background): “…(Davis et al. 1985; White et al. 1987a,b; Efstathiou et al. 1988; Eke et al. 1996; Jenkins et al. 1998; Padilla and Baugh 2002; Bahcall et al. 2004; Kravtsov et al. 2004; Reed et al. 2009), together with the density profiles (Navarro et al. 1997; Bullock et al. 2001b; Navarro et al. 2004; Merritt…”
The kinematic connection between galaxies and dark matter haloes (2010, methodology): “Another technique, known as the (sub) halo abundance matching method (Kravtsov et al. 2004; Vale & Ostriker 2004; Conroy et al. 2006; Conroy & Wechsler 2009), determines the relation between stellar mass and halo mass by assuming that there is a one-to-one mapping (sometimes scatter in this mapping…”
THE CONNECTION BETWEEN GALAXIES AND DARK MATTER STRUCTURES IN THE LOCAL UNIVERSE (2012, methodology): “Abundance matching Abundance matching is a simple and effective method for associating dark matter halos with galaxies (see, e.g., Kravtsov et al. 2004; Vale & Ostriker 2004; Conroy et al. 2006; Behroozi et al. 2010; Moster et al. 2010).”
Measurement of Galaxy Cluster Sizes, Radial Profiles, and Luminosity Functions from SDSS Photometric Data (2004, background): “This power has been found to be close to unity (e.g., Kravtsov et al. 2004; Lin, Mohr, & Stanford 2004; Zehavi et al. 2004; Wechsler et al. 2005).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z = 0.57 from anisotropic clustering (2012, background): “Of particular importance for modelling RSDs is the distinction between ‘central’ and ‘satellite’ galaxies (Kauffmann, White & Guiderdoni 1993; Cole et al. 1994; Diaferio & Geller 1996; Kravtsov et al. 2004).”
MERGERS IN ΛCDM: UNCERTAINTIES IN THEORETICAL PREDICTIONS AND INTERPRETATIONS OF THE MERGER RATE (2010, methodology): “…the subhalo mass function (rather than the differential subhalo merger rate) inside a radius< Rvir , as determined from cosmological simulations in Kravtsov et al. (2004), and evolving these subhalos forward from this already small radius according to 18 Implicit in Figure 6 is the assumption…”
GALAXIES IN ΛCDM WITH HALO ABUNDANCE MATCHING: LUMINOSITY–VELOCITY RELATION, BARYONIC MASS–VELOCITY RELATION, VELOCITY FUNCTION, AND CLUSTERING (2010, background): “It is commonly referred to as abundance matching (Kravtsov et al. 2004; Tasitsiomi et al. 2004; Vale & Ostriker 2004; Conroy et al. 2006; Conroy & Wechsler 2009; Guo et al. 2010; Behroozi et al. 2010).”
Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample (2013, background): “Studies with high-resolution simulations on dark matter haloes and subhaloes suggest a division of galaxies into central and satellite galaxies (e.g. see Kravtsov et al. (2004)).”
Galaxy halo masses and satellite fractions from galaxy–galaxy lensing in the Sloan Digital Sky Survey: stellar mass, luminosity, morphology and environment dependencies (2005, background): “…ǫ = 1 above a cut-off is consistent with semi-analytic models of galaxy formation (Kauffmann et al. 1999; Guzik & Seljak 2002), N-body simulations (Kravtsov et al. 2004; Zehavi et al. 2005), and observational measurements (Jing et al. 1998; Lin et al. 2004; Cooray 2005; Zehavi 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, methodology): “For example, Kravtsov et al. (2004) measured the correlation function of halos above a given mass threshold identified from such simulations at various cosmic epochs.”