Galaxies, luminosity, and mass: Gravitational lensing measurements of the correlation between dark and luminous matter

We present a galaxy lensing study from 400 degrees2 of Sloan Digital Sky Survey (SDSS) data. The mean projected mass density contrast S&d1; (<R) - S&d1; (R) around 30,000 foreground galaxies with SDSS redshifts is studied as a function of galaxy luminosity, morphology, and local density over the radial range 25--1000h-1kpc. The amplitude, but not the radial dependence, of the density contrast is strongly correlated with the luminosity of the central galaxy when the luminosity is measured in the redder SDSS bandpasses. A power law fit between luminosity and mean density contrast within 250 kpc is consistent with linear. The amplitude is also strongly dependent on galaxy morphology. Early types have higher amplitude, but the red luminosity is also proportionately higher. The radial dependence of the density contrast varies strongly with local density for radii greater than about 250h-1kpc where the density contrast is sensitive to the large scale structure surrounding the lens galaxies.; For a smaller set of lens galaxies (∼16,000) we measure the density contrast on 2 Mpc scales where it is proportional to the projected galaxy-mass correlation function wgm. The radial dependence of wgm is consistent with the galaxy-galaxy and galaxy-luminosity correlation functions around the same lenses. This indicates scale independent bias bℓ around these ∼ L* galaxies. This also implies a constant mass-to-light ratio (M/L) up to the bias bℓ for the large scale structure surrounding these galaxies: M/L x bℓ = (192 +/- 20)h M⊙/L⊙ in i'. The integrated M/L around L* galaxies approaches this asymptote, reaching half its global value at 210 +/- 10h-1 kpc. From the global M/L we infer Om x bℓ = 0.22 +/- 0.07.