# COSMOS: Stochastic Bias from Measurements of Weak Lensing and Galaxy Clustering

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- American Astronomical Society
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## Abstract

In the theory of structure formation, galaxies are biased tracers of the underlying matter density field. The statistical relation between galaxy and matter density field is commonly referred to as galaxy bias. In this paper, we test the linear bias model with weak-lensing and galaxy clustering measurements in the 2 deg^2 COSMOS field. We estimate the bias of galaxies between redshifts z = 0.2 and z = 1 and over correlation scales between R = 0.2 h^(–1) Mpc and R = 15 h^(–1) Mpc. We focus on three galaxy samples, selected in flux (simultaneous cuts I_(814W) < 26.5 and K_s < 24) and in stellar mass (10^9 < M_* < 10^(10) h^(–2) M_☉ and 10^(10) < M_* < 10^(11) h^(–2) M_☉). At scales R > 2 h^(–1) Mpc, our measurements support a model of bias increasing with redshift. The Tinker et al. fitting function provides a good fit to the data. We find the best-fit mass of the galaxy halos to be log (M_(200)/h^(–1) M_☉) = 11.7^(+0.6)_(–1.3) and log (M_(200)/h^(–1) M_☉) = 12.4^(+0.2)_(–2.9), respectively, for the low and high stellar-mass samples. In the halo model framework, bias is scale dependent with a change of slope at the transition scale between the one and the two halo terms. We detect a scale dependence of bias with a turndown at scale R = 2.3 ± 1.5 h^(–1) Mpc, in agreement with previous galaxy clustering studies. We find no significant amount of stochasticity, suggesting that a linear bias model is sufficient to describe our data. We use N-body simulations to quantify both the amount of cosmic variance and systematic errors in the measurement.

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