Obtaining non-linear galaxy bias constraints from galaxy-lensing phase differences

TL;DR

This paper introduces a new phase difference statistic between galaxy and lensing fields, demonstrating its effectiveness in constraining the second-order galaxy bias parameter with competitive accuracy.

Contribution

The paper presents a novel phase difference statistic for galaxy bias analysis and shows its potential to improve constraints on second-order bias parameters using galaxy-lensing data.

Findings

Phase differences are sensitive to the second-order bias parameter c2.

The method can recover c2 with an error of about 0.1 for large surveys.

The approach provides constraints comparable to traditional power spectrum and bispectrum methods.

Abstract

We demonstrate the utility and constraining power of a new statistic for investigating galaxy bias: the galaxy-lensing phase difference. The statistic consists in taking the differences of the phases of the harmonic wave-modes between the weak lensing convergence field and the galaxy count field. We use dark matter simulations populated with galaxies up to redshift $z=1$ to test the performance of this estimator. We find that phase differences are sensitive to the absolute value of the second order bias ($c_2=b_2/b_1$), and demonstrate why this is the case. For a $\sim$1500 sq. deg. galaxy survey we recover $c_2$ with an error of approximately $0.1$ for a wide range of $c_2$ values; current constraints from redshift surveys have errors of 0.1-0.6 depending on redshift. This new statistic is therefore expected to provide constraints for $c_2$ which are complementary and competitive with constraining power by the conventional estimators from the power spectrum and bispectrum. For the Dark Energy Survey (DES), we predict leading measurements of second-order bias.