Models applied to a selected set of 40 gamma-ray bursts found that most had small off-axis ratios. Here, q is the observer's viewing angle divided by the jet angle. Under model 1, the mean q was 0.1851, and the viewing-angle distribution was approximately Gaussian in log space. The study presents that as a model-derived pattern in a selected sample.
The inferred q values differed between the two emission prescriptions. The researchers compared two top-hat jet models, one without high-latitude emission and one that included it. Model 1 gave a larger q in 26 of the 40 bursts. The median q1/q2 ratio was 1.24, while the mean q values were 0.1851 for model 1 and 0.1545 for model 2. A paired Wilcoxon test gave p = 0.048. Model 2's q posterior retained much of the prior shape, however, so q2 values were better treated as upper limits than as detections.
The estimate depends on the jet model
The fit statistics favored model 1 across the selected sample. For all 40 bursts, it had the lower reduced chi-squared and Bayesian information criterion, or BIC, with the BIC difference positive in every case. That preference is conditional on selection for sharp breaks, which penalized the smoother model 2. It does not show that model 1 is physically superior in general.
How the bursts were selected
The final sample contained 40 bursts, split evenly between 20 assigned to an interstellar medium, or ISM, environment and 20 assigned to a wind environment. The equal split was a consequence of selection rather than a balance imposed in advance. The analysis used Swift/XRT jet-break afterglow light curves and compared q across the two medium groups, between bursts with and without an X-ray plateau, and across redshift.
Candidate breaks were assessed with time-sliced X-ray spectra before and after the break. Events were retained as edge-effect breaks only when the change in photon index was consistent within uncertainty or less than 0.2. The quality screen excluded bursts if either model returned a q-posterior coefficient of variation above 0.7. Using 0.6 instead changed the sample by five bursts but left the aggregate statistics unchanged.
Each burst was fit with Markov chain Monte Carlo, or MCMC, a parameter-estimation method. The two models used exactly the same data points, fitting interval and Gaussian likelihood.
No clear split by environment or plateau
Within model 1, the mean q was 0.1858 in the ISM group and 0.1845 in the wind group. A Kolmogorov-Smirnov test of the q distributions gave D = 0.1500 and p = 0.9831, indicating no significant distribution difference. The comparison remains conditional because the medium assignment came from break sharpness rather than independent environmental measurements.
The q distributions also did not differ significantly by plateau status. Among the 36 bursts with reliable plateau classifications, 18 had an X-ray plateau and 18 did not. The K-S result was D = 0.2222 and p = 0.7810. The authors note that the comparison had limited power to detect modest differences.
A mixed pattern across redshift
The redshift analysis found negative associations for both the fitted jet angle and viewing angle, while q showed no significant redshift evolution. Within this top-hat analysis, the relative alignment therefore appeared stable across redshift even as the fitted angles changed. The jet-angle association remained detectable after controlling for the burst's isotropic-equivalent energy measure, Eγ,iso, with a partial Spearman p-value of 0.0002. The authors caution that the anti-correlation is partly a construction and selection artifact associated with explicit model terms and Malmquist bias.
What the estimate cannot settle
Several limits narrow the claim. Only 4 of the 40 bursts had sufficient optical coverage across the break, so multi-wavelength achromaticity was not imposed as a formal selection criterion. The alignment result should therefore be read as conditional on the selected sample and the adopted top-hat framework.
The work is a preprint manuscript and identifies the UK Swift Science Data Centre at the University of Leicester as the data source. It reports support from the Shandong Provincial Natural Science Foundation, the Natural Science Foundation of Jiangxi Province of China and the China Manned Space Project.
Paper data and sources
Original title: Constraining gamma-ray burst viewing angles with Swift/XRT afterglow light curves
Authors: Cheng-Jie Sun, Shuang-Xi Yi, Lin Zhou et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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