The galaxy-mass correlation function measured from weak lensing in the sloan digital sky survey

We present galaxy-galaxy lensing measurements over scales 0.025 to 10 h ^-1 Mpc in the Sloan Digital Sky Survey (SDSS). Using a flux-limited sample of 127,001 lens galaxies with spectroscopic redshifts and mean luminosity 〈L〉 ∼ L* and 9,020,388 source galaxies with photometric redshifts, we invert the lensing signal to obtain the galaxy-mass correlation function ξ _gm. We find ξ _gm is consistent with a power law, ξ _gm = (r/ro) ^-γ, with best-fit parameters γ = 1.79 ± 0.06 and r ₀ = (5.4 ± 0.7)(0.27/Ω _m) ^1/γ h ^-1 Mpc. At fixed separation, the ratio ξ _gg/ξ _gm = b/r, where b is the bias and r is the correlation coefficient. Comparing with the galaxy autocorrelation function for a similarly selected sample of SDSS galaxies, we find that b/r is approximately scale-independent over scales 0.2-6.7 h ^-1 Mpc, with mean (b/r) = (1.3 ± 0.2)(Ω _m/0. 27). We also find no scale dependence in b/r for a volume-limited sample of luminous galaxies (-23.0 < M _r < -21.5). The mean b/r for this sample is 〈b/r〉 _vlim = (2-0 ± 0.7) (Ω _m/0.27). We split the lens galaxy sample into subsets based on luminosity, color, spectral type, and velocity dispersion and see clear trends of the lensing signal with each of these parameters. The amplitude and logarithmic slope of ξ _gm increase with galaxy luminosity. For high luminosities (L ∼ 5 L*), ξ _gm deviates significantly from a power law. These trends with luminosity also appear in the subsample of red galaxies, which are more strongly clustered than blue galaxies.