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 8, 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 (LjMh), and from this the mean M/L ratio as a function of halo massMh. We also use (LjMh) 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 cosmo-logical models, theM/L ratio in high-mass halos or high-density regions is approximately independent of halo mass or smoothing scale. However, the ‘‘plateau’ ’ value ofM/L depends on 8 in addition to the obvious proportionality with the matter density parameterm, and it represents the universal value hM /Li mcrit /lum only for models in which the galaxy correlation function is approximately unbiased, i.e., with 8 8g. Our results for cluster mass halos follow the trend (M /L)cl 577(m /0:3)(8 /0:9)1:7 h M /L. Combined with the meanM/L ratio for CNOC galaxy clusters, this relation implies (8 /0:9)(m /0:3)