Weak Lensing with Sloan Digital Sky Survey Commissioning Data: The Galaxy-Mass Correlation Function to 1 [CLC][ITAL]h[/ITAL][/CLC][TSUP]−1[/TSUP] M[CLC]pc[/CLC]

Abstract

(abridged) We present measurements of galaxy-galaxy lensing from 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 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. A variety of rigorous tests demonstrate the reality of the gravitational lensing signal and confirm the uncertainty estimates. We interpret our results by modeling the mass distributions of the foreground galaxies as approximately isothermal spheres characterized by a velocity dispersion and a truncation radius. The velocity dispersion is constrained to be 150-190 km/s at 95% confidence (145-195 km/s 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 $s>140^{\prime\prime}$, corresponding to a physical radius of $260h^{-1}$ kpc, implying that galaxy halos extend to very large radii. However, it is likely that this is being biased high by diffuse matter in the halos of groups and clusters. 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 foreground galaxies, making it possible to greatly improve the precision of these constraints, measure additional parameters such as halo shape, and measure the properties of dark matter halos separately for many different classes of galaxies.