## Abstract

Galaxy-galaxy lensing uses the weak distortion of background sources to measure the mean excess surface density profile, ΔΣ(r), around a sample of foreground lensing galaxies. We develop a method for combining ΔΣ(r) with the galaxy-galaxy correlation function ξ_{gg}(r) to constrain the matter density parameter Ω_{m} and the matter fluctuation amplitude σ_{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 sub-halos around satellite galaxies and environmental dependence of the HOD at fixed halo mass are ≲5% in ΔΣ(r) for 0.1 h^{-1} Mpc < r < 15 h^{-1} Mpc. We develop an analytic approximation for calculating ΔΣ(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 ΔΣ(r) and the galaxy-matter correlation function ξ_{gm}(r) on Ω_{m} and σ_{8}, once HOD parameters for a given cosmological model are pinned down by matching ξ_{gg}(r). The linear bias prediction that ξ_{gm}(r)/ ξ_{gg}(r) = constant is accurate for r ≳ 2 h^{-1} Mpc but fails at the 30%-50% level on smaller scales. The linear bias prediction that Δσ(r) ∝ Ω_{m}σ_{8} breaks down at r < 10 h^{-1} Mpc. We present predictions of ΔΣ(r) for SDSS galaxy samples with Mr ≤ -20 and -21. These can be combined with future lensing measurements for these samples to constrain Ω_{m} and σ_{8}.

Original language | English |
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Pages (from-to) | 26-42 |

Number of pages | 17 |

Journal | Astrophysical Journal |

Volume | 652 |

Issue number | 1 I |

DOIs | |

Publication status | Published - 20 Nov 2006 |

## Keywords

- Cosmology: Theory
- Dark matter
- Galaxies: Halos
- Gravitational lensing
- Large-scale structure of universe