Luminosity function and jet structure of Gamma-Ray Burst

The structure of gamma-ray burst (GRB) jets impacts on their prompt and afterglow emission properties. The jet of GRBs could be uniform, with constant energy per unit solid angle within the jet aperture, or it could be structured, namely with energy and velocity that depend on the angular distance from the axis of the jet. We try to get some insight about the still unknown structure of GRBs by studying their luminosity function. We show that low (1046-48 erg s-1) and high (i.e. with L ≥ 1050 erg s-1) luminosity GRBs can be described by a unique luminosity function, which is also consistent with current lower limits in the intermediate luminosity range (1048-50 erg s-1). We derive analytical expressions for the luminosity function of GRBs in uniform and structured jet models and compare them with the data. Uniform jets can reproduce the entire luminosity function with reasonable values of the free parameters. A structured jet can also fit adequately the current data, provided that the energy within the jet is relatively strongly structured, i.e. Eαθ-k with k ≥ 4. The classical Eαθ-2 structured jet model is excluded by the current data.