A Robust Analysis of QU-fitting Behavior for 800-1088 MHz and 1296-1440 MHz

Abstract QU-fitting is a powerful tool for interpreting spectro-polarimetric radio continuum observations by linking them to physical models, enabling estimates of the magnetic fields in, for example, the Milky Way, galaxy clusters, and radio jets. We present a comprehensive investigation into the effectiveness and limitations of QU-fitting within the ASKAP POSSUM survey frequency ranges (800–1088 MHz and 1296–1440 MHz) with projections to other spectro-polarimetric radio observations. We simulate different physical polarization sources: Faraday simple, Burn slab, internal turbulence, external turbulence, and two-component models in the POSSUM frequencies, and assess their observational degeneracies and fit accuracies. Our results highlight the model-dependent nature of reliable fitting and identify specific regions of parameter space where model selection, and therefore characterization of the physical medium, becomes ambiguous. For QU-fitting we find the Bayes factor, computed using the marginal likelihood, outperforms more traditionally used goodness-of-fit metrics such as Bayesian Information Criterion (BIC), Akaike Information Criterion (AIC), and χ2 for model selection. We provide empirical relationships to delineate the boundaries where model distinguishability is impossible. Finally, we evaluate how accurately QU-fitting recovers model parameters and their associated uncertainties, thereby assessing its ability to correctly characterize the Faraday-rotating medium in both point and extended sources in Faraday depth space.