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

The joint detection of gravitational waves (GWs) and $\gamma$-rays from a binary neutron-star (NS) merger provided a unique view of off-axis GRBs and an independent measurement of the NS merger rate. Comparing the observations of GRB170817 with those of the regular population of short GRBs (sGRBs), we show that an order unity fraction of NS mergers result in sGRB jets that breakout of the surrounding ejecta. We argue that the luminosity function of sGRBs, peaking at $\approx 2\times 10^{52}\, \mbox{erg s}^{-1}$, is likely an intrinsic property of the sGRB central engine and that sGRB jets are typically narrow with opening angles $\theta_0 \approx 0.1$. We perform Monte Carlo simulations to examine models for the structure and efficiency of the prompt emission in off axis sGRBs. We find that only a small fraction ($\sim 0.01-0.1$) of NS mergers detectable by LIGO/VIRGO in GWs is expected to be also detected in prompt $\gamma$-rays and that GW170817-like events are very rare. For a NS merger rate of $\sim 1500$ Gpc$^{-3}$ yr$^{-1}$, as inferred from GW170817, we expect within the next decade up to $\sim 12$ joint detections with off-axis GRBs for structured jet models and just $\sim 1$ for quasi-spherical cocoon models where $\gamma$-rays are the result of shock breakout. Given several joint detections and the rates of their discoveries, the different structure models can be distinguished. In addition the existence of a cocoon with a reservoir of thermal energy may be observed directly in the UV, given a sufficiently rapid localisation of the GW source.