Obtaining non-linear galaxy bias constraints from galaxy-lensing phase differences. (arXiv:2009.03256v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Manera_M/0/1/0/all/0/1">Marc Manera</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bacon_D/0/1/0/all/0/1">David Bacon</a>

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.

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.

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