A lesson from GW170817: most neutron star mergers result in tightly collimated successful GRB jets

Abstract

The joint detection of gravitational waves (GWs) and $\\gamma$-rays from a\nbinary neutron-star (NS) merger provided a unique view of off-axis GRBs and an\nindependent measurement of the NS merger rate. Comparing the observations of\nGRB170817 with those of the regular population of short GRBs (sGRBs), we show\nthat an order unity fraction of NS mergers result in sGRB jets that breakout of\nthe surrounding ejecta. We argue that the luminosity function of sGRBs, peaking\nat $\\approx 2\\times 10^{52}\\, \\mbox{erg s}^{-1}$, is likely an intrinsic\nproperty of the sGRB central engine and that sGRB jets are typically narrow\nwith opening angles $\\theta_0 \\approx 0.1$. We perform Monte Carlo simulations\nto examine models for the structure and efficiency of the prompt emission in\noff axis sGRBs. We find that only a small fraction ($\\sim 0.01-0.1$) of NS\nmergers detectable by LIGO/VIRGO in GWs is expected to be also detected in\nprompt $\\gamma$-rays and that GW170817-like events are very rare. For a NS\nmerger rate of $\\sim 1500$ Gpc$^{-3}$ yr$^{-1}$, as inferred from GW170817, we\nexpect within the next decade up to $\\sim 12$ joint detections with off-axis\nGRBs for structured jet models and just $\\sim 1$ for quasi-spherical cocoon\nmodels where $\\gamma$-rays are the result of shock breakout. Given several\njoint detections and the rates of their discoveries, the different structure\nmodels can be distinguished. In addition the existence of a cocoon with a\nreservoir of thermal energy may be observed directly in the UV, given a\nsufficiently rapid localisation of the GW source.\n