The Galaxy-Mass Correlation Function Measured from Weak Lensing in the Sloan Digital Sky Survey

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Abstract
We present galaxy-galaxy lensing measurements over scales 0.025 to 10 Mpc/h in the Sloan Digital Sky Survey. Using a flux-limited sample of 127,001 lens galaxies with spectroscopic redshifts and mean luminosity = L_* and 9,020,388 source galaxies with photometric redshifts, we invert the lensing signal to obtain the galaxy-mass correlation function xi_{gm}. We find xi_{gm} is consistent with a power-law, xi_{gm} = (r/r_0)^{-gamma}, with best-fit parameters gamma = 1.79 +/- 0.06 and r_0 = (5.4+/-0.7)(0.27/Omega_m)^{1/gamma} Mpc/h. At fixed separation, the ratio xi_{gg}/xi_{gm} = b/r where b is the bias and r is the correlation coefficient. Comparing to the galaxy auto-correlation function for a similarly selected sample of SDSS galaxies, we find that b/r is approximately scale independent over scales 0.2-6.7 Mpc/h, with mean = (1.3+/-0.2)(Omega_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 _{Vlim} = (2.0+/-0.7)(Omega_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 xi_{gm} increases with galaxy luminosity. For high luminosities (L ~5 L_*), xi_{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.Comment: 20 pages, 21 figures, prepared with emulateapj, Accepted to AJ, corrected some major typo