Weak Lensing Study of Galaxy Biasing

We combine weak lensing measurements from the Red-Sequence Cluster Survey (RCS) and the VIRMOS-DESCART survey and present the first direct measurements of the bias parameter b and the galaxy-mass cross-correlation coefficient r on scales ranging from 0.2 to 9.3h^-1₅₀ Mpc (which correspond to aperture radii of 1.5‧-45^') at a lens redshift z~=0.35. We find strong evidence that both b and r change with scale for our sample of lens galaxies (19.5<R_C<21), which have luminosities around L_*. For the currently favored cosmology (Ω_m=0.3,Ω_Λ=0.7), we find b=0.71^+0.06_-0.04 (68% confidence) on a scale of 1-2h^-1₅₀ Mpc, increasing to ~1 on larger scales. The value of r has only minimal dependence on the assumed cosmology. The variation of r with scale is very similar to that of b and reaches a minimum value of r~0.57^+0.08_-0.07 (at 1h^-1₅₀ Mpc; 68% confidence). This suggests significant stochastic biasing and/or nonlinear biasing. On scales larger than ~4h^-1₅₀ Mpc, the value of r is consistent with a value of r=1. In addition, we use RCS data alone to measure the ratio b/r on scale ranging from 0.15 to 12.5h^-1₅₀ Mpc (1^'-60^') and find that the ratio varies somewhat with scale. We obtain an average value of b/r=1.090+/-0.035, in good agreement with previous estimates. A (future) careful comparison of our results with models of galaxy formation can provide unique constraints, as r is linked intimately to the details of galaxy formation.