Comparison of algorithms for determination of rotation measure and Faraday structure I. 1100 - 1400 MHz

TL;DR

This study benchmarks various algorithms for determining Faraday rotation measures and structures using simulated data in the 1.1-1.4 GHz range, highlighting their strengths and limitations in different scenarios.

Contribution

It provides a comprehensive comparison of current algorithms for Faraday structure analysis, identifying their performance and failure modes with simulated data.

Findings

QU-fitting performs best for two Faraday thin components.

Most methods struggle with Faraday thick components due to narrow bandwidth.

No current method reliably resolves complex Faraday structures with the given data quality.

Abstract

(abridged) We run a Faraday structure determination data challenge to benchmark the currently available algorithms including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling and $QU$-fitting. The frequency set is similar to POSSUM/GALFACTS with a 300 MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: a) an average RM weighted by polarized intensity, RMwtd, b) the separation $\Delta\phi$ of two Faraday components and c) the reduced chi-squared. Based on the current test data of signal to noise ratio of about 32, we find that: (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found; (2) For two Faraday thin components, QU-fitting routines perform the best, with errors close to the theoretical ones for RMwtd, but with significantly higher errors for $\Delta\phi$. All other methods including standard Faraday synthesis frequently identify only one component when $\Delta\phi$ is below or near the width of the Faraday point spread function; (3) No methods, as currently implemented, work well for Faraday thick components due to the narrow bandwidth; (4) There exist combinations of two Faraday components which produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model.