MEASURING THE DEVIATION FROM THE LINEAR AND DETERMINISTIC BIAS THROUGH COSMIC GRAVITATIONAL LENSING EFFECTS

摘要

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 stochasticityonlinearity of the galaxy bias through correlation studies of the cosmic shear and galaxy number fluctuations. Specifically, we employ the aperture mass statistics M_(ap) to describe the cosmic shear. We divide the foreground-galaxy redshift z_f < z_s into several bins, where z_s is the redshift of the source galaxies, and calculate the quantity ~2/(N_g~2(z_f)> for each redshift bin. Then, the ratio of the summation of ~2/ over the bins to gives a measure of the nonlinear/stochastic bias. Here, N_g(z_f) is the projected surface number density fluctuation of foreground galaxies at redshift z_f, and M_(ap) is the aperture mass from the cosmic-shear analysis. We estimate that for a moderately deep weak-lensing survey with z_s = 1, source galaxy surface number density n_b = 30 galaxies arcmin~(-2), and a survey area of 25 deg~2, 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 | approx> 10%. For shallow, wide surveys such as the Sloan Digital Sky Survey with z_s = 0.5, n_b = 5 galaxies arcmin~(-2), and a survey area of 10~4 deg~2, a 10% detection of r is possible over the angular range l′-100′.