The SDSS Coadd: Cross-Correlation Weak Lensing and Tomography of Galaxy Clusters

The shapes of distant galaxies are sheared by intervening galaxy clusters. We examine this effect in Stripe 82, a 275 square degree region observed multiple times in the Sloan Digital Sky Survey and coadded to achieve greater depth. We obtain a mass-richness calibration that is similar to other SDSS analyses, demonstrating that the coaddition process did not adversely affect the lensing signal. We also propose a new parameterization of the effect of tomography on the cluster lensing signal which does not require binning in redshift, and we show that using this parameterization we can detect tomography for stacked clusters at varying redshifts. Finally, due to the sensitivity of the tomographic detection to accurately marginalizing over the effect of the cluster mass, we show that tomography at low redshift (where dependence on exact cosmological models is weak) can be used to constrain mass profiles in clusters.