Hydrogen-atmosphere hot-spot models fit the X-ray spectrum of HESS J1731-347 as well as carbon-atmosphere models

Re-assessed after the geometric-exclusion subclaim received its first assessment. The verdict is unchanged; the change sharpens the against-argument without touching the claim as worded.

The claim rests directly on the fit reports of the primary papers of both camps. Suleimanov, Klochkov, Poutanen and Werner (2017, A&A 600, A43, arxiv.org/abs/1701.06417) tested hydrogen hot-spot alternatives against the XMM-Newton data: the free fit implies an unrealistically low mass and small radius at 3.2 kpc, but fixing M = 1.5 solar masses and R = 12 km still yields a formally acceptable fit with a hot component covering about 2.3 percent of the surface. Alford and Halpern (2023, ApJ 944, 36) report the degeneracy in both directions: unpulsed central compact objects, including this source, are fitted as well by two-temperature blackbody or hydrogen models as by uniform carbon atmospheres, and the pulsed CCOs that certainly have hot spots can also be fitted with carbon atmospheres. The supporting generalization that phase-averaged spectra cannot discriminate the two model families↗︎ stands supported (credence 0.88).

The subclaim that the pulsed-fraction upper limits exclude most hot-spot viewing geometries↗︎ is now verified (credence 0.92): the roughly 7 to 10 percent pulsed-fraction limits exclude about 92 percent of randomly oriented hot-spot geometries by Suleimanov et al.'s own light-bending calculation, a figure accepted by both sides. This firms up the pulsation-absence objection, whose premises were previously partly unassessed. It is not material to the verdict, because the exclusion bears on whether a hot-spot configuration is physically probable for this source, not on the chi-squared quality of the hydrogen fits, which both camps report as acceptable. The claim as canonically worded is about fit quality, and no source disputes the fit parity; the dispute is entirely about which interpretation the parity plus the pulsation limits favor. The residual single-source probability of order 8 percent and the aligned-spot caveat are now reflected in the assessment prose so readers see what the geometric penalty does and does not establish.

The assumed comparator, that the spectrum is well described by a uniform-temperature carbon atmosphere↗︎, stands verified. What would change the conclusion: a formal model-comparison analysis of the same XMM-Newton data showing the hydrogen hot-spot fits significantly worse than the carbon fits, or a retraction or failed reproduction of the Alford and Halpern fits. Residual uncertainty: this assessment relies on the papers' own reported fit statistics rather than an independent re-fit of the data.