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

Abstract

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 p ( r p ) and the galaxy luminosity function. For a sequence of cosmological models with a fixed, observationally motivated power spectrum shape and increasing normalization σ 8 , we find parameters of the galaxy halo occupation distribution (HOD) that reproduce w p ( r p ) 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 | M h ), and from this the mean M / L ratio as a function of halo mass M h . We also use Φ( L | M h ) 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 σ 8 in addition to the obvious proportionality with the matter density parameter Ω m , and it represents the universal value ⟨ M / L ⟩ = Ω m ρ crit /ρ lum only for models in which the galaxy correlation function is approximately unbiased, i.e., with σ 8 ≈ σ 8 g . Our results for cluster mass halos follow the trend ( M / L ) cl = 577(Ω m /0.3)(σ 8 /0.9) 1.7 h M ☉ / L ☉ . Combined with the mean M / L ratio for CNOC galaxy clusters, this relation implies (σ 8 /0.9)(Ω m /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 σ 8 Ω , while the CAIRNS estimates for cluster infall regions imply a lower value. These results are inconsistent with parameter values Ω m ≈ 0.3, σ 8 ≈ 0.9 favored by recent joint analyses of cosmic microwave background measurements and other large-scale structure data, although they agree with values inferred from the van den Bosch et al. analysis of the 2dF Galaxy Redshift Survey. We discuss possible resolutions of this discrepancy, none of which seems entirely satisfactory. In appendices we present an improved formula for halo bias factors calibrated on our 360 3 N -body simulations and an improved analytic technique for calculating the galaxy correlation function from a given cosmological model and HOD.