Late-time Evolution of Afterglows from Off-Axis Neutron-Star Mergers

Gravitational-wave detected neutron star mergers provide an opportunity to investigate short gamma-ray burst (GRB) jet afterglows without the GRB trigger. Here we show that the post-peak afterglow decline can distinguish between an initially ultra-relativistic jet viewed off-axis and a mildly relativistic wide-angle outflow. Post-peak the afterglow flux will decline as $F_\nu \propto t^{-\alpha}$. The steepest decline for a jet afterglow is $\alpha>3p/4$ or $> (3p+1)/4$, for an observation frequency below and above the cooling frequency, respectively, where $p$ is the power-law index of the electron energy distribution. The steepest decline for a mildly relativistic outflow, with initial Lorentz factor $\Gamma_0\lesssim 2$, is $\alpha\lesssim(15p-19)/10$ or $\alpha\lesssim(15p-18)/10$, in the respective spectral regimes. If the afterglow from GW170817 fades with a maximum index $\alpha > 1.5$ then we are observing the core of an initially ultra-relativistic jet viewed off the central axis, while a decline with $\alpha\lesssim 1.4$ after $\sim 5$--10 peak times indicates that a wide-angled and initially $\Gamma_0\lesssim 2$ outflow is responsible. At twice the peak time, the two outflow models fall on opposite sides of $\alpha \approx 1$. So far, two post-peak X-ray data points at 160 and 260 days suggest a decline consistent with an off-axis jet afterglow. Follow-up observations over the next 1--2 years will test this model.