Analytic Detection Thresholds for Measurements of Linearly Polarized Intensity Using Rotation Measure Synthesis

TL;DR

This paper develops an analytic statistical framework for detecting and analyzing linearly polarized intensity in radio astronomy using rotation measure synthesis, enhancing the understanding of measurement significance and source complexity.

Contribution

It extends the formalism for linear polarization measurements to the rotation measure synthesis context, providing new statistical tools for detection and analysis.

Findings

Derived probability density function for Faraday-space polarization

Established relationships for polarization detection significance

Applicable to sources with multiple Faraday components

Abstract

A fully analytic statistical formalism does not yet exist to describe radio-wavelength measurements of linearly polarized intensity that are produced using rotation measure synthesis. In this work we extend the analytic formalism for standard linear polarization, namely that describing measurements of the quadrature sum of Stokes Q and U intensities, to the rotation measure synthesis environment. We derive the probability density function and expectation value for Faraday-space polarization measurements for both the case where true underlying polarized emission is present within unresolved Faraday components, and for the limiting case where no such emission is present. We then derive relationships to quantify the statistical significance of linear polarization measurements in terms of standard Gaussian statistics. The formalism developed in this work will be useful for setting signal-to-noise ratio detection thresholds for measurements of linear polarization, for the analysis of polarized sources potentially exhibiting multiple Faraday components, and for the development of polarization debiasing schemes.