Measuring the Deviation from the Linear and Deterministic Bias through Cosmic Gravitational Lensing Effects

Since gravitational lensing effects directly probe inhomogeneities of dark matter, lensing-galaxy cross-correlations can provide us important information on the relation between dark matter and galaxy distributions, i.e., the bias. In this paper, we propose a method to measure the stochasticity/nonlinearity of the galaxy bias through correlation studies of the cosmic shear and galaxy number fluctuations. Specifically, we employ the aperture mass statistics Map to describe the cosmic shear. We divide the foreground galaxy redshift zf < zs into several bins, where zs is the redshift of the source galaxies, and calculate the quantity < MapNg(zf ) > 2 / < N g (zf ) > for each redshift bin. Then the ratio of the summation of < MapNg(zf) > 2 / < N g (zf ) > over the bins to < M 2 ap > gives a measure of the nonlinear/stochastic bias. Here Ng(zf ) is the projected surface number density fluctuation of foreground galaxies at redshift zf , and Map is the aperture mass from the cosmic-shear analysis. We estimate that for a moderately deep weak-lensing survey with zs = 1, source galaxy surface number density nb = 30 gal/ arcmin 2 and a survey area of 25 deg, the effective r-parameter that represents the deviation from the linear and deterministic bias is detectable in the angular range of 1-10 if |r − 1| ∼ 10%. For shallow, wide surveys such as the Sloan Digital Sky Survey with zs = 0.5, nb = 5 gal/ arcmin , and a survey area of 10 deg, a 10% detection of r is possible over the angular range 1′−100′. Subject headings: cosmology: theory— dark matter —galaxy: cluster: general— gravitational lensing — large-scale structure of universe Department of Astronomy, Peking University, Beijing 100871, China Beijing Astrophysical Center, Chinese Academy of Science and Peking University, Beijing 100871, China Department of Astronomy and Astrophysics, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637