On Combining Galaxy Clustering and Weak Lensing to Unveil Galaxy Biasing via the Halo Model

Understand

We formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics.

• Using two-point statistics in projection, we define the galaxy bias function, b_g(r_p), and the galaxy-dark matter cross-correlation function, R_{gm}(r_p), where r_p is the projected distance.
• We use the analytical halo model to predict how the scale dependence of b_g and R_{gm}, over the range 0.1 Mpc/h < r_p < 30 Mpc/h, depends on the non-linearity and stochasticity in halo occupation models.
• In particular we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo, and the Poisson character of the probability to have a certain number of satellite galaxies in a halo of a certain mass.