Late-time evolution of afterglows from off-axis neutron star mergers

Abstract

Gravitational-wave detected neutron star mergers provide an opportunity to\ninvestigate short gamma-ray burst (GRB) jet afterglows without the GRB trigger.\nHere we show that the post-peak afterglow decline can distinguish between an\ninitially ultra-relativistic jet viewed off-axis and a mildly relativistic\nwide-angle outflow. Post-peak the afterglow flux will decline as $F_\\nu \\propto\nt^{-\\alpha}$. The steepest decline for a jet afterglow is $\\alpha>3p/4$ or $>\n(3p+1)/4$, for an observation frequency below and above the cooling frequency,\nrespectively, where $p$ is the power-law index of the electron energy\ndistribution. The steepest decline for a mildly relativistic outflow, with\ninitial Lorentz factor $\\Gamma_0\\lesssim 2$, is $\\alpha\\lesssim(15p-19)/10$ or\n$\\alpha\\lesssim(15p-18)/10$, in the respective spectral regimes. If the\nafterglow from GW170817 fades with a maximum index $\\alpha > 1.5$ then we are\nobserving the core of an initially ultra-relativistic jet viewed off the\ncentral axis, while a decline with $\\alpha\\lesssim 1.4$ after $\\sim 5$--10 peak\ntimes indicates that a wide-angled and initially $\\Gamma_0\\lesssim 2$ outflow\nis responsible. At twice the peak time, the two outflow models fall on opposite\nsides of $\\alpha \\approx 1$. So far, two post-peak X-ray data points at 160 and\n260 days suggest a decline consistent with an off-axis jet afterglow. Follow-up\nobservations over the next 1--2 years will test this model.\n