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 θ_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 θ_obs to the jet’s core θ_c. We adopt a power-law angular jet structure in both energy E(θ) ∝ θ^−a and Lorentz factor Γ(θ) ∝ θ^−b beyond the core. We find that either sGRBs are viewed within θ_obs/θ_c < 1 or the initial Lorentz factor of material in their jet’s core is extremely high (Γ₀ > 500). If we consider tophat jets, we constrain 90 per cent of our sample to be viewed within θ_obs/θ_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 Γ₀θ_c ≿ 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.