How to augment cosmic shear measurements with radio polarimetry of galaxies?

TL;DR

This paper develops an unbiased, minimal-variance statistical framework for cosmic shear measurement using radio galaxy polarization, improving accuracy and robustness over previous methods.

Contribution

It introduces a new likelihood-based estimator that jointly estimates gravitational shear, intrinsic shape alignment, and polarization rotation, addressing biases and uncertainties.

Findings

Derived analytically unbiased estimators for shear and polarization effects.

Estimates are robust with few galaxies or poor polarization-shape alignment.

Framework minimizes uncertainties in power spectrum estimation.

Abstract

The integral polarization of spiral galaxies in the radio band has been proposed as a new tracer of the intrinsic galaxy shape that augments lensing shear measurements. We revisit the method of shear estimation in this context. We introduce a new statistical model in which galaxy shape and polarization are Gaussian random variables with their covariance characterizing the quality of polarization-shape alignment. Applying the principle of likelihood maximization, we then analytically derive unbiased, minimal-variance estimators, which allow to simultaneously estimate gravitational shear, intrinsic shape alignment and line-of-sight polarization rotation, all at once and accurate to first order in these three effects. New to the literature, our estimators have the merits of being free of biases, robust in situations of few galaxies or poor polarization-shape alignment, allowing analytic reconstruction noise covariance, and minimizing uncertainties in power spectrum estimation, thus resolving conceptual issues of the existing estimation methods. This new analytic framework is generally applicable to future research that exploits the polarization-shape alignment effect of galaxies.