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Register a new userThe Halo Occupation Distribution and the Physics of Galaxy Formation
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Andreas A. Berlind
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The halo occupation distribution (HOD) describes the bias between galaxies and dark matter by specifying (a) the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class and (b) the relative distributions of galaxies and dark matter within halos. We calculate predicted HODs for a Lambda-CDM cosmological model using an SPH hydrodynamic simulation and a semi-analytic (SA) galaxy formation model. Although the two methods predict different galaxy mass functions, their HOD predictions agree remarkably well. For mass-selected samples, the mean occupation <N(M)> exhibits a sharp cutoff at low halo masses, a slowly rising plateau for <N>~1-2, and a more steeply rising high occupancy regime. At low <N>, the mean pair and triple counts are well below Poisson expectations, with important consequences for small scale behavior of 2- and 3-point correlation functions. The HOD depends strongly on galaxy age, with high mass halos populated mainly by old galaxies and low mass halos by young galaxies. The SPH simulation supports several simplifying assumptions about HOD bias: the most massive galaxy in a halo usually lies close to the center and moves near the halos mean velocity; satellite galaxies have the same radial profile and velocity dispersion as the dark matter; and the mean occupation at fixed halo mass is independent of the halos larger scale environment. By applying the SPH and SA HODs to a large volume N-body simulation, we show that both methods predict slight, observable departures from a power-law galaxy correlation function. The predicted HODs are closely tied to the underlying galaxy formation physics, they offer useful guidance to theoretical models of galaxy clustering, and they will be tested empirically by ongoing analyses of galaxy redshift surveys. (Shortened)
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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%.
We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a number of subhalos N, and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat LCDM 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 first moment of the HOD, <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 a Poisson statistics at high halo masses but becomes sub-Poisson for <N><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 step-like function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment <Ns>(M). We find that <Ns>~M^b with b~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 fit by a power law down to ~100/h kpc with an amplitude and slope similar to those of observed galaxies. At redshifts z>~1, we find significant departures from the power-law shape of the CF at small scales. 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 likely to bias the estimates of the correlation length and slope of the correlation function.
We model the luminosity-dependent projected two-point correlation function of DEEP2 (z~1) and SDSS (z~0) galaxies within the Halo Occupation Distribution (HOD) framework. At both epochs, there is a tight correlation between central galaxy luminosity and halo mass, with the slope and scatter decreasing for larger halo masses, and the fraction of satellite galaxies decreasing at higher luminosity. Central L* galaxies reside in halos a few times more massive at z~1 than at z~0. We find little evolution in the relation between mass scales of host halos for central galaxies and satellite galaxies above the same luminosity threshold. Combining these HOD results with theoretical predictions of the typical growth of halos, we establish an evolutionary connection between the galaxy populations at the two redshifts by linking z~0 central galaxies to z~1 central galaxies that reside in their progenitor halos, which enables us to study the evolution of galaxies as a function of halo mass. We find that the stellar mass growth of galaxies depends on halo mass. On average, the majority of the stellar mass in central galaxies residing in z~0 low mass halos (~5x10^11 Msun/h) and only a small fraction of the stellar mass in central galaxies of high mass halos (~10^13 Msun/h) result from star formation between z~1 and z~0. In addition, the mass scale of halos where the star formation efficiency reaches a maximum is found to shift toward lower mass with time. Future work can combine HOD modeling of the clustering of galaxies at different redshifts with the assembly history and dynamical evolution of dark matter halos. This can lead to an understanding of the stellar mass growth due to both mergers and star formation as a function of host halo mass and provide powerful tests of galaxy formation theories. (Abridged).
We investigate the dependence of dark matter halo clustering on halo formation time, density profile concentration, and subhalo occupation number, using high-resolution numerical simulations of a LCDM cosmology. We confirm results that halo clustering is a function of halo formation time, and that this trend depends on halo mass. For the first time, we show unequivocally that halo clustering is a function of halo concentration and show that the dependence of halo bias on concentration, mass, and redshift can be accurately parameterized in a simple way: b(c,M|z) = b(M|z) b(c|M/M*). The scaling between bias and concentration changes sign with the value of M/M*: high concentration (early forming) objects cluster more strongly for M <~ M* while low concentration (late forming) objects cluster more strongly for rare high-mass halos, M >~ M*. We show the first explicit demonstration that host dark halo clustering depends on the halo occupation number (of dark matter subhalos) and discuss implications for halo model calculations of dark matter power spectra and galaxy clustering statistics. The effect of these halo properties on clustering is strongest for early-forming dwarf-mass halos, which are significantly more clustered than typical halos of their mass. Our results suggest that isolated low-mass galaxies (e.g. low surface-brightness dwarfs) should have more slowly-rising rotation curves than their clustered counterparts, and may have consequences for the dearth of dwarf galaxies in voids. They also imply that self calibrating richness-selected cluster samples with their clustering properties might overestimate cluster masses and bias cosmological parameter estimation.
We model the projected angular two-point correlation function (2PCF) of obscured and unobscured quasars selected using the Wide-field Infrared Survey Explorer (WISE), at a median redshift of $z sim 1$ using a five-parameter Halo Occupation Distribution (HOD) parameterization, derived from a cosmological hydrodynamic simulation by Chatterjee et al. The HOD parameterization was previously used to model the 2PCF of optically selected quasars and X-ray bright active galactic nuclei (AGN) at $z sim 1$. The current work shows that a single HOD parameterization can be used to model the population of different kinds of AGN in dark matter halos suggesting the universality of the relationship between AGN and their host dark matter halos. Our results show that the median halo mass of central quasar hosts increases from optically selected ($4.1^{+0.3}_{-0.4} times 10^{12} ; h^{-1} ; {M_{sun}}$) and infra-red (IR) bright unobscured populations ($6.3^{+6.2}_{-2.3} times 10^{12} ; h^{-1} ; {M_{sun}}$) to obscured quasars ($10.0^{+2.6}_{-3.7} times 10^{12} ; h^{-1} ; {M_{sun}}$), signifying an increase in the degree of clustering. The projected satellite fractions also increase from optically bright to obscured quasars and tend to disfavor a simple `orientation only theory of active galactic nuclei unification. Our results also show that future measurements of the small-scale clustering of obscured quasars can constrain current theories of galaxy evolution where quasars evolve from an IR- bright obscured phase to the optically bright unobscured phase.
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