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 wp(rp) and the galaxy luminosity function. For a sequence of cosmological models with a fixed, observationally motivated power spectrum shape and increasing normalization σ8, we find parameters of the galaxy halo occupation distribution (HOD) that reproduce wp(rp) measurements as a function of luminosity from the Sloan Digital Sky Survey (SDSS). From these HOD models we calculate the r-band conditional luminosity function Φ(L|Mh), and from this the mean M/L ratio as a function of halo mass Mh. We also use Φ(L|Mh) to populate halos of N-body simulations with galaxies and thereby compute M/L in a range of large-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 σ8 in addition to the obvious proportionality with the matter density parameter Ωm, and it represents the universal value 〈M/L〉= Ωmρcrit/ρlum only for models in which the galaxy correlation function is approximately unbiased, i.e., with σ8 ≈ σ8g. Our results for cluster mass halos follow the trend (M/L)cl = 577 (Ωm/0.3) (σ8/0.9) 1.7 hM⊙/L⊙. Combined with Carlberg et al.’s (1996) mean M/L ratio for CNOC galaxy clusters, this relation implies (σ8/0.9) (Ωm/0.3) 0.6 = 0.75 ± 0.06. M/L estimates for SDSS clusters and the virial regions of clusters in the CAIRNS survey imply a similar value of σ8Ω 0.6 m , while the CAIRNS estimates for cluster infall regions imply a lower value. These results are inconsistent with parameter values Ωm ≈ 0.3, σ8 ≈ 0.9 favored by recent joint analyses of cosmic microwave background measurements and other large scale structure data, though they agree with values inferred from van den Bosch et al.’s (2003) analysis of the Department of Astronomy, The Ohio State University, 140 W. 18th Avenue, Columbus, Ohio 43210 Institute for Advanced Study, School of Natural Sciences, Einstein Drive, Princeton, NJ 08540 Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721 Hubble Fellow