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

Abstract

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 MapM_{ap} to describe the cosmic shear. We divide the foreground galaxy redshift zf<zsz_f<z_s into several bins, where zsz_s is the redshift of the source galaxies, and calculate the quantity 2/^2/ for each redshift bin. Then the ratio of the summation of 2/<Ng2(zf)>^2/< N_g^2(z_f)> over the bins to gives a measure of the nonlinear/stochastic bias. Here Ng(zf)N_g(z_f) is the projected surface number density fluctuation of foreground galaxies at redshift zfz_f, and MapM_{ap} is the aperture mass from the cosmic-shear analysis. We estimate that for a moderately deep weak-lensing survey with zs=1z_s=1, source galaxy surface number density nb=30gal/arcmin2n_b=30 \hbox {gal}/\hbox {arcmin}^2 and a survey area of 25deg225 \hbox {deg}^2, the effective rr-parameter that represents the deviation from the linear and deterministic bias is detectable in the angular range of 1'-10' if |r-1|\gsim 10%. For shallow, wide surveys such as the Sloan Digital Sky Survey with zs=0.5z_s=0.5, nb=5gal/arcmin2n_b=5 \hbox {gal}/\hbox {arcmin}^2, and a survey area of 104deg210^4 \hbox {deg}^2, a 10% detection of rr is possible over the angular range 1β€²βˆ’100β€²1'-100'.Comment: ApJ in pres

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    Last time updated on 03/01/2020