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 $M_{ap}$ 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 $<M_{ap}{N}_g(z_f){>}^2/<N_g^2(z_f)>$ for each redshift bin. Then the ratio of the summation of $<M_{ap}{N}_g(z_f){>}^2/<N_g^2(z_f)>$ over the bins to $<M_{ap}^2>$ 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 $n_b=30gal/{arcmin}^2$ 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 $|r-1|\gsim 10%$. For shallow, wide surveys such as the Sloan Digital Sky Survey with $z_s=0.5$, $n_b=5gal/{arcmin}^2$, and a survey area of $10^4{deg}^2$, a 10% detection of $r$ is possible over the angular range $1^{\prime }-100^{\prime }$.

ApJ in press

References in corpus (6)

• Virial masses of galactic halos from galaxy-galaxy lensing: theoretical modeling and application to SDSS
• Likelihood Analysis of Cosmic Shear on Simulated and VIRMOS-DESCART Data
• Weak lensing study of galaxy biasing
• Lensing by galaxies in CNOC2 fields
• Measurement of the bias parameter from weak lensing
• Wide-field cosmic shear surveys

Cited by in corpus (6)

• Cosmology with cosmic shear observations: a review
• Self calibration of gravitational shear-galaxy intrinsic ellipticity correlation in weak lensing surveys
• Beating Lensing Cosmic Variance with Galaxy Tomography
• Weak lensing reconstruction through cosmic magnification I: a minimal variance map reconstruction
• Time evolution of the stochastic linear bias of interacting galaxies on linear scales
• Improving three-dimensional mass mapping with weak gravitational lensing using galaxy clustering