(Ehud Nakar, Maria Petropoulou, Rodolfo Barniol Duran, Dimitrios Giannios)
Motivated by GW170817 we examine observational constraints on the angular structure of gamma-ray burst (GRB) jets. First, the relatively narrow observed distribution of the early X-ray afterglow to prompt gamma-ray energy ratio implies that at any angle that gamma-rays are emitted the Lorentz factor must be large. Specifically, the Lorentz factor of gamma-ray emitting material cannot drop rapidly with angle, and must be Gamma(theta)>50 even if there are angles for which the gamma-ray emitted energy is lower by three orders of magnitude compared to the jet core. Second, jets with an angular structure of the gamma-ray emission that over-produce events with a gamma-ray luminosity below the peak of the observed luminosity function are ruled-out. This eliminates models in which the gamma-ray energy angular distribution isn't sufficiently steep and the Lorentz factor distribution isn't sufficiently shallow. Furthermore, models with a steep structure (e.g. Gaussian) which are detected away from the jet core generate afterglow light-curves that were never observed. Thus even if the jet kinetic energy distribution drops continuously with latitude, efficient gamma-ray emission seems to be restricted to material with Gamma>50 and is most likely confined to a narrow region around the core. Comparing GRB170817 with 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, that their luminosity function must be intrinsically peaked and that sGRB jets are typically narrow with opening angles ~ 0.1 rad. Finally, 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, 0.01-0.1, of NS mergers detectable by LIGO/VIRGO in GWs is expected to be also detected in prompt gamma-rays, and GW170817-like events are very rare.