X-ray afterglow limits on the viewing angles of short gamma-ray bursts

The behaviour of a short gamma-ray burst (sGRB) afterglow light curve can reveal the angular structure of the relativistic jet and constrain the observer's viewing angle theta obs. The observed deceleration time of the jet, and, therefore, the time of the afterglow peak, depends on the observer's viewing angle. A larger viewing angle leads to a later peak of the afterglow and a lower flux at peak. We utilize the earliest afterglow detections of 58 sGRBs detected with the Neil Gehrels Swift Observatory X-ray Telescope to constrain the ratio of the viewing angle theta obs to the jet's core theta c. We adopt a power-law angular jet structure in both energy E(theta)proportional to theta-a and Lorentz factor Gamma(theta)proportional to theta-b beyond the core. We find that either sGRBs are viewed within theta obs/theta c<1 or the initial Lorentz factor of material in their jet's core is extremely high (Gamma 0>500). If we consider tophat jets, we constrain 90 per cent of our sample to be viewed within theta obs/theta c<1.06 and 1.15 for our canonical and conservative afterglow scenarios. For a subset of events with measurements of the jet break, we can constrain Gamma 0 theta c greater than or similar to 30. This confirmation that cosmological sGRBs are viewed either on-axis or very close to their jet's core has significant implications for the nature of the prompt gamma-ray production mechanism and for the rate of future sGRB detections coincident with gravitational waves, implying that they are extremely rare.