Weak lensing study of galaxy biasing

We combine weak lensing measurements from the Red-Sequence Cluster Survey 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 9.3 h_{50}^{-1} Mpc 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 (\Omega_m=0.3,\Omega_\Lambda=0.7), we find b=0.71^+0.06_-0.04 on a scale of 1-2 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 1 Mpc). This suggests significant stochastic biasing and/or non-linear biasing. On scales larger than ~4 Mpc the value of r is consistent with a value of 1. In addition we use RCS data alone to measure the ratio b/r on scale ranging from 0.15 to 12.5 Mpc, 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.