The effects of assembly bias on the inference of matter clustering from galaxy-galaxy lensing and galaxy clustering

The combination of galaxy-galaxy lensing and galaxy clustering is a promising route to measuring the amplitude of matter clustering and testing modified gravity theories of cosmic acceleration. Halo occupation distribution (HOD) modelling can extend the approach down to non-linear scales, but galaxy assembly bias could introduce systematic errors by causing the HOD to vary with the large-scale environment at fixed halo mass. We investigate this problem using the mock galaxy catalogs created by Hearin & Watson (2013, HW13), which exhibit significant assembly bias because galaxy luminosity is tied to halo peak circular velocity and galaxy colour is tied to halo formation time. The preferential placement of galaxies (especially red galaxies) in older haloes affects the cutoff of the mean occupation function ⟨N_cen(M_min)⟩ for central galaxies, with haloes in overdense regions more likely to host galaxies. The effect of assembly bias on the satellite galaxy HOD is minimal. We introduce an extended, environment-dependent HOD (EDHOD) prescription to describe these results and fit galaxy correlation measurements. Crucially, we find that the galaxy-matter cross-correlation coefficient, r_gm(r) ≡ ξ_gm(r) . [ξ_mm(r)ξ_gg(r)]^-1/2, is insensitive to assembly bias on scales r ≳ 1 h^-1 Mpc, even though ξ_gm(r) and ξ_gg(r) are both affected individually. We can therefore recover the correct ξ_mm(r) from the HW13 galaxy-galaxy and galaxy-matter correlations using either a standard HOD or EDHOD fitting method. For M_r ≤ -19 or M_r ≤ -20 samples the recovery of ξ_mm(r) is accurate to 2 per cent or better. For a sample of red M_r ≤ -20 galaxies, we achieve 2 per cent recovery at r ≳ 2 h^-1 Mpc with EDHOD modelling but lower accuracy at smaller scales or with a standard HOD fit. Most of our mock galaxy samples are consistent with r_gm = 1 down to r = 1 h^-1 Mpc, to within the uncertainties set by our finite simulation volume.