A new polarisation amplitude bias reduction method

TL;DR

This paper introduces a novel bias correction method for polarisation amplitude estimation that leverages known polarisation angles to significantly reduce bias, especially in low SNR regions.

Contribution

The paper presents the 'known-angle estimator', a new bias correction technique that improves polarisation amplitude estimates using angle information, applicable even with asymmetric uncertainties.

Findings

The estimator fully corrects bias when the angle is perfectly known.

It reduces residual bias compared to classical estimators in realistic scenarios.

It outperforms existing methods when angle information is incorporated.

Abstract

Polarisation amplitude estimation is affected by a positive noise bias, particularly important in regions with low signal-to-noise ratio (SNR). We present a new approach to correct for this bias in the case there is additional information about the polarisation angle. We develop the 'known-angle estimator' that works in the special case when there is an independent and high signal-to-noise ratio ($\gtrsim 2\sigma$) measurement of the polarisation angle. It is derived for the general case where the uncertainties in the Q,U Stokes parameters are not symmetric. This estimator completely corrects for the polarisation bias if the polarisation angle is perfectly known. In the realistic case, where the angle template has uncertainties, a small residual bias remains, but that is shown to be much smaller that the one left by other classical estimators. We also test our method with more realistic data, using the noise properties of the three lower frequency maps of WMAP. In this case, the known-angle estimator also produces better results than methods that do not include the angle information. This estimator is therefore useful in the case where the polarisation angle is expected to be constant over different data sets with different SNR.