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 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.

Figures (16)

• Figure 1: The parameter selection maps for the POSSUM low-band (800-1088 MHz) Burn slab population when fit with the Faraday simple model as the alternative model. These three maps are defined by S:N (y-axis) and three of the four model parameters (x-axes). From left to right they are fractional polarization, initial polarization angle, rotation measure of the uniform foreground. Each bin is colored by the median ln(BF) of the sources within ($\sim$ 25 sources per bin). See the text for explanation of the high S:N outlier bins.
• Figure 2: Top: The parameter selection maps are shown for the POSSUM low-band (800-1088 MHz) Burn slab population fitted with both the Burn slab and Faraday simple models. Both maps are defined by the S:N and the $\text{RM}_{{\textnormal{src}}}$. Each bin is colored by the median ln(BF) of the sources within ($\sim$ 25 sources per bin). Top Left: Bins are coloured according to the raw median values. Top Right: The same quantity is shown, but using a colour scale that reflects the relative confidence in each bin (Table \ref{['tab:binning']}). The larger the value, the higher the confidence that the sources in that bin are Burn slabs. The green line defines the boundary between confident correct and incorrect selections (Equation \ref{['FSBSrelation']}). Bottom: The four spectra (black) are sources taken from the corresponding lettered positions in the parameter space. The red solid lines show the Burn slab fit and the red dashed lines show the simple fit. Spectrum [a] is a thin slab that QU-fitting prefers to fit as FS, spectrum [b] is a source where the BS model is preferred, spectra [c] and [d] are sources that are in regions where the nulls of the spectra have aligned with the frequency range and so QU-fitting has elevated confidence in the FS fit.
• Figure 3: The parameter selection map for the POSSUM low-band (800-1088 MHz) two-component source population when the Burn slab model is the alternate. This map is defined by an estimated signal-to-noise for the first component and $\Delta \text{RM}_{{\textnormal{screen}}}$. We are marginalizing over the S:N for the second component, only including sources that have S:N > 5 for the second component. Each bin is colored by the median ln(BF) value and the color bar is scaled according to Table \ref{['tab:binning']}.
• Figure 4: Top: The parameter selection map for the POSSUM low-band (800-1088 MHz) Burn slab population when fitted with the internal turbulence model as the alternate. The map is defined by the true $\text{RM}_{{\textnormal{src}}}$ and S:N. Bottom: The parameter selection map for the low-band internal turbulence source populations when the Burn slab is the alternate model. The map is defined by the true $\text{RM}_{{\textnormal{src}}}$ and $\sigma_{{\textnormal{RM, src}}}$. For the true internal turbulence population experiment only sources with S:N > 8 are considered. Each bin is colored by the median ln(BF) value and the color bar is scaled according to Table \ref{['tab:binning']}.
• Figure 5: Top: The parameter selection map for the true internal turbulence POSSUM low-band (800-1088 MHz) population when fit with the external turbulence model as the alternative model. This map's space is defined by the slab width ($\text{RM}_{{\textnormal{src}}}$) and small-scale RM dispersion parameter ($\sigma_{{\textnormal{RM, src}}}$). Sources with S:N < 7 were removed from this map. Bottom: Parameter selection map for the true external turbulence low-band population with the internal turbulence model as the alternative model. This map is defined with the S:N and small-scale foreground RM dispersion ($\sigma_{{\textnormal{RM, FG}}}$). Each bin is colored by the median ln(BF) value and the color bar is scaled according to Table \ref{['tab:binning']}