Weak lensing with sloan digital sky survey commissioning data: The galaxy-mass correlation function to 1 h ^-1 Mpc

We present measurements of galaxy-galaxy weak lensing from 225 deg ² of early commissioning imaging data from the Sloan Digital Sky Survey (SDSS). We measure a mean tangential shear around a stacked sample of foreground galaxies in three bandpasses (g′, r′, and i′) out to angular radii of 600″, detecting the shear signal at very high statistical significance. The shear profile is well described by a power law γ _T = γ _T0 (1′/θ) ^η , with best-fit slope of η = 0.7-1.1 (95% confidence). In the range θ = 10″-600″, the mean tangential shear is approximately 6 ± 1 × 10 ^-4 in all three bands. A variety of rigorous tests demonstrate the reality of the gravitational lensing signal and confirm the uncertainty estimates. In particular, we obtain shear measurements consistent with zero when we rotate the background galaxies by 45°, replace foreground galaxies with random points, or replace foreground galaxies with bright stars. We interpret our results by assuming that all matter correlated with galaxies belongs to the galaxies. We model the mass distributions of the foreground galaxies, which have a mean luminosity 〈L(θ < 5″)〉 = 8.7 ± 0.7 × 10 ⁹ h ^-2 L _g′⊙ , 1.4 ± 0.12 × 10 ¹⁰ h ^-2 L _r′⊙ , 1.8 ± 0.14 × 10 ¹⁰ h ^-2 L _i′⊙ , as approximately isothermal spheres characterized by a velocity dispersion σ _v and a truncation radius s. The velocity dispersion is constrained to be σ _v = 150-190 km s ^-1 at 95% confidence (145-195 km s ^-1 including systematic uncertainties), consistent with previous determinations but with smaller error bars. Our detection of shear at large angular radii sets a 95% confidence lower limit s > 140″, corresponding to a physical radius of 260 h _-1 kpc, implying that the dark halos of typical luminous galaxies extend to very large radii. However, it is likely that this is being systematically biased to large value by diffuse matter in the halos of groups and clusters of galaxies. We also present a preliminary determination of the galaxy-mass correlation function, finding a correlation length similar to the galaxy autocorrelation function and consistency with a low matter density universe with modest bias. The full SDSS will cover an area 44 times larger and provide spectroscopic redshifts for the fore-ground galaxies, making it possible to improve greatly the precision of these constraints, to measure additional parameters such as halo shape and halo concentration, and to measure the properties of dark matter halos separately for many different classes of galaxies.