The Jet Opening Angle and Event Rate Distributions of Short Gamma-Ray Bursts from Late-time X-Ray Afterglows

We present a comprehensive study of 29 short gamma-ray bursts (SGRBs) observed ≈0.8-60 days postburst using Chandra and XMM-Newton. We provide the inferred distributions of the SGRB jet opening angles and true event rates to compare against neutron star merger rates. We perform a uniform analysis and modeling of their afterglows, obtaining 10 opening angle measurements and 19 lower limits. We report on two new opening angle measurements (SGRBs 050724A and 200411A) and eight updated values, obtaining a median value of <θ _j> ≈ 6.°1 [-3.°2, +9.°3] (68% confidence on the full distribution) from jet measurements alone. For the remaining events, we infer θ _j ≳ 0.°5-26°. We uncover a population of SGRBs with wider jets of θ _j ≳ 10° (including two measurements of θ _j ≳ 15°), representing ~28% of our sample. Coupled with multiwavelength afterglow information, we derive a total true energy of <E _true,tot> ≈ 10⁴⁹-10⁵⁰ erg, which is consistent with magnetohydrodynamic jet launching mechanisms. Furthermore, we determine a range for the beaming-corrected event rate of ${{\mathfrak{R}}}_{{\rm{true}}}\approx 360-1800$ Gpc^-3 yr^-1, set by the inclusion of a population of wide jets on the low end, and the jet measurements alone on the high end. From a comparison with the latest merger rates, our results are consistent with the majority of SGRBs originating from binary neutron star mergers. However, our inferred rates are well above the latest neutron star-black hole merger rates, consistent with at most a small fraction of SGRBs originating from such mergers.