From Galaxy‐Galaxy Lensing to Cosmological Parameters

Galaxy-galaxy lensing measures the mean excess surface density DS(r) around asample of lensing galaxies. We develop a method for combining DS(r) with thegalaxy correlation function xi_gg(r) to constrain Omega_m and sigma_8, goingbeyond the linear bias model to reach the level of accuracy demanded by currentand future measurements. We adopt the halo occupation distribution (HOD)framework, and we test its applicability to this problem by examining theeffects of replacing satellite galaxies in the halos of an SPH simulation withrandomly selected dark matter particles from the same halos. The differencebetween dark matter and satellite galaxy radial profiles has a ~10% effect onDS(r) at r<1 Mpc/h. However, if radial profiles are matched, the remainingimpact of individual subhalos around satellite galaxies and environmentaldependence of the HOD at fixed halo mass is <5% in DS(r) for 0.12 Mpc/h, but it fails at the 30-50% level on smaller scales. Thescaling of DS(r) ~ Omega_m^a(r) sigma_8^b(r) approaches the linear biasexpectation a=b=1 at r>10 Mpc/h, but a(r) and b(r) vary from 0.8 to 1.6 atsmaller r. We calculate a fiducial DS(r) and scaling indices a(r) and b(r) fortwo SDSS galaxy samples; galaxy-galaxy lensing measurements for these samplescan be combined with our predictions to constrain Omega_m and sigma_8.Comment: 18 pages, 10 figures, accepted for publication in The Astrophysical Journa