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

ABSTRACT 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 $\theta _\textrm {obs}$. 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 $\theta _\textrm {obs}$ to the jet’s core $\theta _\textrm {c}$. We adopt a power-law angular jet structure in both energy $E(\theta)\propto \theta ^{-a}$ and Lorentz factor $\Gamma (\theta)\propto \theta ^{-b}$ beyond the core. We find that either sGRBs are viewed within $\theta _\textrm {obs}/\theta _\textrm {c}\lt 1$ or the initial Lorentz factor of material in their jet’s core is extremely high ($\Gamma _0\gt 500$). If we consider tophat jets, we constrain 90 per cent of our sample to be viewed within $\theta _\textrm {obs}/\theta _\textrm {c}\lt 1.06$ and 1.15 for our canonical and conservative afterglow scenarios. For a subset of events with measurements of the jet break, we can constrain $\Gamma _0\theta _\textrm {c}\gtrsim 30$. 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.