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(50)(-1) Mpc (which correspond to aperture radii of 1.'5-45') at a lens redshift z similar or equal to 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(-0.04)(+0.06) (68% confidence) on a scale of 1-2 h(50)(-1) Mpc, increasing to similar to1 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 similar to 0.57(-0.07)(+0.08) (at 1 h(50)(-1) Mpc; 68% confidence). This suggests significant stochastic biasing and/or nonlinear biasing. On scales larger than similar to4 h(50)(-1) 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(50)(-1) 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.