From galaxy-galaxy lensing to cosmological parameters

Galaxy-galaxy lensing uses the weak distortion of background sources to measure the mean excess surface density profile, Delta Sigma(r), around a sample of foreground lensing galaxies. We develop a method for combining Delta Sigma(r) with the galaxy-galaxy correlation function xi(gg)(r) to constrain the matter density parameter Omega(m) and the matter fluctuation amplitude sigma(8), going beyond the linear biasing model to reach the level of accuracy demanded by current and future measurements. We adopt the halo occupation distribution ( HOD) framework and test its applicability to this problem by examining the effects of replacing satellite galaxies in the halos of a smoothed particle hydrodynamics (SPH) simulation with randomly selected dark matter particles from the same halos. After accounting for the slight differences between the predicted radial profile of dark matter and satellite galaxies, the residual effects of individual subhalos around satellite galaxies and environmental dependence of the HOD at fixed halo mass are less than or similar to 5% in Delta Sigma(r) for 0.1 h(-1) Mpc < r < 15 h(-1) Mpc. We develop an analytic approximation for calculating Delta Sigma(r), improving on previous work with more accurate treatments of halo bias and halo exclusion. We demonstrate its accuracy at the few percent level with tests against a suite of populated N-body simulations. We use the analytic model to investigate the dependence of Delta Sigma(r) and the galaxy-matter correlation function xi(gm)(r) on Omega(m) and sigma(8), once HOD parameters for a given cosmological model are pinned down bymatching xi(gg)(r). The linear bias prediction that xi(gm)(r)/xi(gg)(r) constant is accurate for r greater than or similar to 2 h(-1) Mpc but fails at the 30% - 50% level on smaller scales. The linear bias prediction that Delta Sigma(r) proportional to Omega(m)sigma(8) breaks down at r < 10 h(-1) Mpc. We present predictions of Delta Sigma(r) for SDSS galaxy samples with M-r <= 20 and -21. These can be combined with future lensing measurements for these samples to constrain Omega(m) and sigma(8).