tokens: and one, two, or three Faraday-thin components, each with a contribution to the polarized emission as given in equation ( 4 ), approximated to be independent of frequency over our band. We did not fit for any models with Faraday-thick components, as LOFAR HBA is minimally sensitive to these: from equation ( 3c ), the maximum scale recoverable is φ max-scale = 0.46 rad m −2 , so any polarized source with Faraday thickness exceeding this would not be properly recovered, although the edges in its Faraday spectrum might be visible if they were sufficiently sharp (Van Eck et al. 2017 ). In order to evaluate the quality of the fits across the knot and the lobe we calculate for each pair of models the Bayes factor, K , which is given by where each model M i is defined in terms of parameters θ i , is assigned a prior Pr(θ i | M i ), fits the data with likelihood Pr( D |θ i , M i ), and is supported by Bayesian evidence Pr( D | M i ). Following Kass Raftery ( 1995 ), we evaluate the Bayes factor based on the derived value 2ln K : a positive value supports model 2, constituting weak (values 2), positive (2–6), strong (6–10), or very strong (>10) evidence. Negative values of 2ln K , similarly, support model 1. Fig. 15 shows the results for the model with one Faraday-thin source. The evidence of the models with two or three Faraday-thin sources is less than the evidence for all other tested models and so is not shown. Fig. 15(a) shows the Faraday depth found for the one-source model for each pixel, where it is favoured over the null hypothesis with K > 1. Fig. 15(b) shows 2ln K > 2, where white to blue (2ln K > 2) indicates support for the one-source model and red (2ln K 2) indicates support for the null hypothesis. We find an average Faraday depth in the knot of −50.8 rad m −2 . Despite the fact that there is a significant polarized region detected at 5σ in the Faraday spectrum of the lobe, only 10 pixels are detected in the lobe with the presence of a source favoured over the null hypothesis with K > 1. The average Faraday depth of these pixels is −53.6 rad m −2 , in agreement with that measured from the Faraday spectra, with a standard deviation of 0.7 rad m −2 . The difference of 2.8 rad m −2 between the Faraday depths in the knot and the lobe is significant against this uncertainty. Figure 15. Results of the QU fitting. (a) shows the Faraday depth of the component found for a single Faraday-thin screen plus instrumental polarization. (b) The Bayes factor when comparing the fits for a single thin screen plus instrumental polarization with just instrumental polarization. Red indicates support for the null hypothesis while blue indicates support for the single Faraday-thin screen. White indicates inconclusive. There are small variations in Faraday depth of order Δφ ∼ 0.2 rad m −2 . Fig. 16 shows the distribution of the Faraday depths in the knot. The variance in the Faraday depth is rad 2 m −4 . If the variation in Faraday depth is due solely to
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