A theoretical framework for combining techniques that probe the link between galaxies and dark matter

We develop a theoretical framework that combines measurements of galaxy-galaxy lensing, galaxy clustering, and the galaxy stellar mass function in a self-consistent manner. While considerable effort has been invested in exploring each of these probes individually, attempts to combine them are still in their infancy despite the potential of such combinations to elucidate the galaxy-dark matter connection, to constrain cosmological parameters, and to test the nature of gravity. In this paper, we focus on a theoretical model that describes the galaxy-dark matter connection based on standard halo occupation distribution techniques. Several key modifications enable us to extract additional parameters that determine the stellar-to-halo mass relation and to simultaneously fit data from multiple probes while allowing for independent binning schemes for each probe. In a companion paper, we demonstrate that the model presented here provides an excellent fit to galaxy-galaxy lensing, galaxy clustering, and stellar mass functions measured in the COSMOS survey from z=0.2 to z=1.0. We construct mock catalogs from numerical simulations to investigate the effects of sample variance and covariance on each of the three probes. Finally, we analyze and discuss how trends in each of the three observables impact the derived parameters of the model. In particular, we investigate the various features of the observed galaxy stellar mass function (low-mass slope, plateau, knee, and high-mass cut-off) and show how each feature is related to the underlying relationship between stellar and halo mass. We demonstrate that the observed plateau feature in the stellar mass function at Mstellar~2x10^10 Msun is due to the transition that occurs in the stellar-to-halo mass relation at Mhalo ~ 10^12 Msun from a low-mass power-law regime to a sub-exponential function at higher stellar mass.Comment: 21 pages. Accepted to Ap

On the Mass-to-Light Ratio of Large Scale Structure

We examine the dependence of the mass-to-light (M/L) ratio of large-scale structure on cosmological parameters, in models that are constrained to match observations of the projected galaxy correlation function w(rp). For a sequence of cosmological models with a fixed P(k) shape and increasing normalization \sig8, we find parameters of the galaxy halo occupation distribution (HOD) that reproduce SDSS measurements of w(rp) as a function of luminosity. Using these HOD models we calculate mean M/L ratios as a function of halo mass and populate halos of N-body simulations to compute M/L in larger scale environments, including cluster infall regions. For all cosmological models, the M/L ratio in high mass halos or high density regions is approximately independent of halo mass or smoothing scale. However, the "plateau" value of M/L depends on \sig8 as well as \Omega_m, and it represents the universal mass-to-light ratio only for models in which the galaxy correlation function is approximately unbiased, i.e., with \sig8 ~ \sig8_gal. Our results for cluster mass halos follow the trend M/L = 577(\Omega_m/0.3)(\sig8/0.9)^{1.7} h Msun/Lsun. Combined with Carlberg et al.'s (1996) mean M/L ratio of CNOC galaxy clusters, this relation implies (\sig8/0.9)(\Omega_m/0.3)^{0.6} = 0.75 +/- 0.06. M/L ratios of clusters from the SDSS and CAIRNS surveys yield similar results. This constraint is inconsistent with parameter values \Omega_m ~ 0.3, \sig8 ~ 0.9 favored by recent joint analyses of CMB measurements and other large-scale structure data. We discuss possible resolutions, none of which seems entirely satisfactory. Appendices present an improved formula for halo bias factors and an improved analytic technique for calculating the galaxy correlation function from a given cosmological model and HOD. (Abridged)Comment: Accepted to ApJ (v 630, no 2). Replaced with accepted versio

The Abacus Cosmos: A Suite of Cosmological N-body Simulations

We present a public data release of halo catalogs from a suite of 125 cosmological $N$-body simulations from the Abacus project. The simulations span 40 $w$CDM cosmologies centered on the Planck 2015 cosmology at two mass resolutions, $4\times 10^{10}\;h^{-1}M_\odot$ and $1\times 10^{10}\;h^{-1}M_\odot$, in $1.1\;h^{-1}\mathrm{Gpc}$ and $720\;h^{-1}\mathrm{Mpc}$ boxes, respectively. The boxes are phase-matched to suppress sample variance and isolate cosmology dependence. Additional volume is available via 16 boxes of fixed cosmology and varied phase; a few boxes of single-parameter excursions from Planck 2015 are also provided. Catalogs spanning $z=1.5$ to $0.1$ are available for friends-of-friends and Rockstar halo finders and include particle subsamples. All data products are available at https://lgarrison.github.io/AbacusCosmosComment: 13 pages, 9 figures, 3 tables. Additional figures added for mass resolution convergence tests, and additional redshifts added for existing tests. Matches ApJS accepted versio

Cosmological Constraints from Galaxy Clustering and the Mass-to-Number Ratio of Galaxy Clusters

We place constraints on the average density (Omega_m) and clustering amplitude (sigma_8) of matter using a combination of two measurements from the Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p, and the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to cluster M/L ratios. Our w_p measurements are obtained from DR7 while the sample of clusters is the maxBCG sample, with cluster masses derived from weak gravitational lensing. We construct non-linear galaxy bias models using the Halo Occupation Distribution (HOD) to fit both w_p and M/N for different cosmological parameters. HOD models that match the same two-point clustering predict different numbers of galaxies in massive halos when Omega_m or sigma_8 is varied, thereby breaking the degeneracy between cosmology and bias. We demonstrate that this technique yields constraints that are consistent and competitive with current results from cluster abundance studies, even though this technique does not use abundance information. Using w_p and M/N alone, we find Omega_m^0.5*sigma_8=0.465+/-0.026, with individual constraints of Omega_m=0.29+/-0.03 and sigma_8=0.85+/-0.06. Combined with current CMB data, these constraints are Omega_m=0.290+/-0.016 and sigma_8=0.826+/-0.020. All errors are 1-sigma. The systematic uncertainties that the M/N technique are most sensitive to are the amplitude of the bias function of dark matter halos and the possibility of redshift evolution between the SDSS Main sample and the maxBCG sample. Our derived constraints are insensitive to the current level of uncertainties in the halo mass function and in the mass-richness relation of clusters and its scatter, making the M/N technique complementary to cluster abundances as a method for constraining cosmology with future galaxy surveys.Comment: 23 pages, submitted to Ap

From Galaxy-Galaxy Lensing to Cosmological Parameters

Galaxy-galaxy lensing measures the mean excess surface density DS(r) around a sample of lensing galaxies. We develop a method for combining DS(r) with the galaxy correlation function xi_gg(r) to constrain Omega_m and sigma_8, going beyond the linear bias model to reach the level of accuracy demanded by current and future measurements. We adopt the halo occupation distribution (HOD) framework, and we test its applicability to this problem by examining the effects of replacing satellite galaxies in the halos of an SPH simulation with randomly selected dark matter particles from the same halos. The difference between dark matter and satellite galaxy radial profiles has a ~10% effect on DS(r) at r<1 Mpc/h. However, if radial profiles are matched, the remaining impact of individual subhalos around satellite galaxies and environmental dependence of the HOD at fixed halo mass is <5% in DS(r) for 0.1<r<15 Mpc/h. We develop an analytic approximation for DS(r) that incorporates halo exclusion and scale-dependent halo bias, and we demonstrate its accuracy with tests against a suite of populated N-body simulations. We use the analytic model to investigate the dependence of DS(r) and the galaxy-matter correlation function xi_gm(r) on Omega_m and sigma_8, once HOD parameters for a given cosmological model are pinned down by matching xi_gg(r). The linear bias prediction is accurate for r>2 Mpc/h, but it fails at the 30-50% level on smaller scales. The scaling of DS(r) ~ Omega_m^a(r) sigma_8^b(r) approaches the linear bias expectation a=b=1 at r>10 Mpc/h, but a(r) and b(r) vary from 0.8 to 1.6 at smaller r. We calculate a fiducial DS(r) and scaling indices a(r) and b(r) for two SDSS galaxy samples; galaxy-galaxy lensing measurements for these samples can be combined with our predictions to constrain Omega_m and sigma_8.Comment: 18 pages, 10 figures, accepted for publication in The Astrophysical Journa

Cosmic Voids and Galaxy Bias in the Halo Occupation Framework

(Abridged) We investigate the power of void statistics to constrain galaxy bias and the amplitude of dark matter fluctuations. We use the halo occupation distribution (HOD) framework to describe the relation between galaxies and dark matter. After choosing HOD parameters that reproduce the mean space density n_gal and projected correlation function w_p measured for galaxy samples with M_r<-19 and M_r<-21 from the Sloan Digital Sky Survey (SDSS), we predict the void probability function (VPF) and underdensity probability function (UPF) of these samples by populating the halos of a large, high-resolution N-body simulation. If we make the conventional assumption that the HOD is independent of large scale environment at fixed halo mass, then models constrained to match n_gal and w_p predict nearly identical void statistics, independent of the scatter between halo mass and central galaxy luminosity or uncertainties in HOD parameters. Models with sigma_8=0.7 and sigma_8=0.9 also predict very similar void statistics. However, the VPF and UPF are sensitive to environmental variations of the HOD in a regime where these variations have little impact on w_p. For example, doubling the minimum host halo mass in regions with large scale (5 Mpc/h) density contrast delta<-0.65 has a readily detectable impact on void probabilities of M_r<-19 galaxies, and a similar change for delta<-0.2 alters the void probabilities of M_r<-21 galaxies at a detectable level. The VPF and UPF provide complementary information about the onset and magnitude of density- dependence in the HOD. By detecting or ruling out HOD changes in low density regions, void statistics can reduce systematic uncertainties in the cosmological constraints derived from HOD modeling, and, more importantly, reveal connections between halo formation history and galaxy properties.Comment: emulateapj, 16 pages, 13 figure