MUSIC for Faraday Rotation Measure Synthesis

TL;DR

This paper introduces a novel RM synthesis deconvolution method called RM-MUSIC, which outperforms traditional approaches in resolving closely spaced Faraday components, especially at high to moderate S/N ratios.

Contribution

The paper extends the MUSIC algorithm for Faraday RM synthesis, enabling better resolution of closely spaced components compared to existing methods like RM-CLEAN.

Findings

RM-MUSIC accurately recovers Faraday depths of closely spaced components.

RM-MUSIC outperforms RM-CLEAN at high to moderate S/N ratios.

Both methods perform similarly at low S/N ratios.

Abstract

Faraday Rotation Measure (RM) synthesis requires the recovery of the Faraday Dispersion Function (FDF) from measurements restricted to limited wavelength ranges, which is an ill-conditioned deconvolution problem. Here, we propose a novel deconvolution method based on an extension of the MUltiple SIgnal Classification (MUSIC) algorithm. The complexity and speed of the method is determined by the eigen-decomposition of the covariance matrix of the observed polarizations. We show numerically that for high to moderate Signal to Noise (S/N) cases the RM-MUSIC method is able to recover the Faraday depth values of closely spaced pairs of thin RM components, even in situations where the peak response of the FDF is outside of the RM range between the two input RM components. This result is particularly important because the standard deconvolution approach based on RM-CLEAN fails systematically in such situations, due to its greedy mechanism used to extract the RM components. For low S/N situations, both the RM-MUSIC and RM-CLEAN methods provide similar results.