On the reliability of polarization estimation using Rotation Measure Synthesis

TL;DR

This paper evaluates the reliability of Rotation Measure synthesis for polarization estimation, comparing it with traditional methods, and introduces a Bayesian approach to assess solution correctness based on noise and signal properties.

Contribution

It provides a first-principles statistical framework and Bayesian method to quantify the reliability of RM synthesis polarization estimates under noise.

Findings

RM synthesis can estimate polarization at lower S/N with bounded RMs.

Reliable estimates of sources with unusual RMs require higher S/N and unconstrained solutions.

The Bayesian model accurately predicts the probability of correct RM solutions based on amplitude and noise.

Abstract

We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. (2009). The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower S/N if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrainted solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically-derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.