On the Mass‐to‐Light Ratio of Large‐Scale Structure
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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_mρ_crit/ρ_lum only for models in which the galaxy correlation function is approximately unbiased, i.e., with σ_8 approx σ_8g. Our results for cluster mass halos follow the trend (M/L)_cl = 577(Ω_m/0.3)(σ_8/0.9)^1.7 h Msun/Lsun. Combined with the mean M/L ratio for CNOC galaxy clusters, this relation implies (σ_8/0.9)(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 σ_8Ω ^.6 _m, while the CAIRNS estimates for cluster infall regions imply a lower value. These results are inconsistent with parameter values Ω_m approx 0.3, σ_8 approx 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.