Cross-correlation Weak Lensing of SDSS Galaxy Clusters III: Mass-to-light Ratios

We present measurements of the excess mass-to-light ratio measured around MaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with M{sub 200} {approx} 5 x 10{sup 12}h{sup -1}M{sub {circle_dot}} to clusters with M{sub 200} {approx} 5 x 10{sup 15}h{sup -1}M{sub {circle_dot}}. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean {Delta}{yields}(r) = {rho}(r) -- {bar {rho}} for clusters in bins of richness and optical luminosity. We also measure the excess {sup 0.25}i-band luminosity density {Delta}{ell}(r) = {ell}(r) -- {bar {ell}}. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25h{sup -1} kpc to 22h{sup -1} Mpc. From these profiles we calculate the cumulative excess mass {Delta}M(r) and excess light {Delta}L(r) as a function of separation from the BCG. On small scales, where {rho}(r) >> {bar {rho}}, the integrated mass-to-light profile ({Delta}M/{Delta}L)(r) may be interpreted as the cluster mass-to-light ratio. We find the ({Delta}M/{Delta}L){sub 200}, the mass-to-light ratio within r{sub 200}, scales with cluster mass as a power law with index 0.33{+-}0.02. On large scales, where {rho}(r) {approx} {bar {rho}}, the {Delta}M/{Delta}L approaches an asymptotic value independent of scale or cluster richness. For small groups, the mean ({Delta}M/{Delta}L){sub 200} is much smaller than the asymptotic value, while for large clusters ({Delta}M/{Delta}L)200 is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe {l_angle}M/L{r_angle}. We find {l_angle}M/L{r_angle} b{sup -2}{sub M/L} = 362 {+-} 54h measured in the {sup 0.25}i-bandpass. The parameter b{sup 2}{sub M/L} is primarily a function of the bias of the L {approx}< L* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find {Omega}{sub m}b{sup -2}{sub M/L}= 0.20 {+-} 0.03, independent of the Hubble parameter