Obtaining nonlinear galaxy bias constraints from galaxy-lensing phase differences

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 deg(2) 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.