Cross-correlation weak lensing of sdss galaxy clusters. III. mass-to-light ratios

We present measurements of the excess mass-to-light ratio (M/L) measured around MaxBCG galaxy clusters observed in the Sloan Digital Sky Survey. This red-sequence cluster sample includes objects from small groups with M ₂₀₀ 5 × 10¹² h ^-1 M_⊙ to clusters with M₂₀₀ 10¹⁵ h^-1 M_⊙. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean Δρ(r) = ρ(r)-ρ̄ for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density Δℓ(r) = ℓ(r)-ℓ̄ measured in the z = 0.25 i band. For both mass and light, we de-project the profiles to produce three-dimensional mass and light profiles over scales from 25 h ^-1 kpc to 22 h ^-1 Mpc. From these profiles we calculate the cumulative excess mass ΔM(r) and excess light ΔL(r) as a function of separation from the BCG. On small scales, where , the integrated mass-to-light profile (ΔM/ΔL)(r) may be interpreted as the cluster M/L. We find the (ΔM/ΔL)₂₀₀, the M/L within r₂₀₀, scales with cluster mass as a power law with index 0.33±0.02. On large scales, where ρ(r)∼ ρ̄, the ΔM/ΔL approaches an asymptotic value independent of cluster richness. For small groups, the mean (ΔM/ΔL) ₂₀₀ is much smaller than the asymptotic value, while for large clusters (ΔM/ΔL)₂₀₀ is consistent with the asymptotic value. This asymptotic value should be proportional to the mean M/L of the universe 〈M/L〉. We find 〈M/L〉b^-2 _M/L = 362 54h (statistical). There is additional uncertainty in the overall calibration at the 10% level. The parameter b ² _M/L is primarily a function of the bias of the L ≲ L _* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find Ω_mb ^-2 _M/L = 0.20±0.03, independent of the Hubble parameter.