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

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 chi-squared 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.