Observational constraints on the structure of gamma-ray burst jets

Motivated by GW170817, we examine constraints that observations put on the angular structure of long gamma-ray burst (GRB) jets. First, the relatively narrow observed distribution of E_X/E_γ (the isotropic equivalent 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 high. Specifically, the Lorentz factor of gamma-ray emitting material cannot drop rapidly with angle, and must be Γ(θ) ≳ 50 even if there are angles for which the gamma-ray received energy is lower by three orders of magnitude compared to the jet core. Secondly, jets with an angular structure of the gamma-ray emission that overproduce 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 is not sufficiently steep and the Lorentz factor distribution is not sufficiently shallow. Finally, models with a steep structure (e.g. Gaussian) that are detected away from the jet core generate afterglow light curves that were never observed. We conclude that even if the jet kinetic energy distribution drops continuously with latitude, efficient gamma-ray emission seems to be restricted to material with Γ ≳ 50 and is most likely confined to a narrow region around the core. While our study is confined to long GRBs, where the observed sample is larger and more complete, there are indications that similar conclusions may be applicable also to short GRBs. We discuss the possible implications to the gamma-rays observed in GRB 170817A.