Cross-Correlation Weak Lensing of SDSS Galaxy Clusters. Iii. Mass-to-Light Ratios

We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with masses ranging from ~5x10^12 to ~10^15 Mₒₔ₍/h. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean (r) = (r) - for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density l (r) = l (r) - l measured in the z=0. 25 i-band. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25 kpc/ to 22 Mpc/h. From these profiles we calculate the cumulative excess mass M (r) and excess light L (r) as a function of separation from the BCG. On small scales, where (r) >>, the integrated mass-to-light profile may be interpreted as the cluster mass-to-light ratio. We find the M/L₂₀₀, the mass-to-light ratio within r₂₀₀, scales with cluster mass as a power law with index 0. 33+/-0. 02. On large scales, where (r) ~, the M/L approaches an asymptotic value independent of cluster richness. For small groups, the mean M/L₂₀₀ is much smaller than the asymptotic value, while for large clusters it is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe. We find /b²₌₋ = 362+/-54 h (statistical). There is additional uncertainty in the overall calibration at the ~10% level. The parameter b₌₋ 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 ₘ/b²₌₋ = 0. 02+/-0. 03, independent of the Hubble parameter.