Table 4.
Fit quality with and without including systematic uncertainties.
w/o systematics | w/systematics | ||
---|---|---|---|
Data set | χ2 (sys. error) | Ndof | χ2 (sys. error) |
H.E.S.S. stereo (flux points) | 45.5 (none) | 35 | 33.6 (3%) |
H.E.S.S. mono (flux points) | 36.7 (none) | 13 | 12.1 (4%) |
Fermi-LAT (flux points) | 41.7 (none) | 26 | 27.7 (10%) |
Synchrotron (flux points) | 235.0 (5%) | 194 | 152.7 (7%) |
Fermi-LAT + H.E.S.S. (extension) | 121.5 (none) | 6 | 8.9 (see text) |
Synchrotron (extension) | 60.3 (n.a.) | 13 | 13.0 (8″) |
Notes. The χ2 values are calculated for the respective data set and the variable B-field model. For each data set, we conservatively estimate the number of degrees of freedom (Ndof) as the number of data points minus one. The magnitude of the systematic uncertainties (specified in parentheses) are chosen such that a good fit quality is obtained, that is, χ2 ∼ Ndof, and thus do not represent estimates of the actual systematic uncertainty of each data set. The first section of the table summarises the flux measurements, where the systematic uncertainty is specified as a relative error on the flux level. The extension uncertainty, given in the second section of the table, is increased by a constant error for each data set (see main text for details). We note that we still add a systematic uncertainty of 5% to the synchrotron flux points for the ‘w/o systematics’ case, as the χ2-value would otherwise increase to > 106, due to the small statistical uncertainties of some of the points. Similarly, the extension measurements in the synchrotron regime already contain systematic uncertainties, which are however not easily separable and thus not stated explicitly here (see Dirson & Horns 2023 for details).
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