摘要：Aims. There exists inevitable scatter in the intrinsic luminosity of gamma-ray bursts (GRBs). If there is relativistic beaming in the source, viewing angle variation necessarily introduces variation in the intrinsic luminosity function (ILF). Scatter in the ILF can cause selection bias where sources detected at distance have a greater median luminosity than those detected close by. Median luminosity divides any given population into equal halves. When the functional form of a distribution is unknown, it can be a more robust diagnostic than those that use trial functional forms. Method. In this work, we employ a statistical test based on median luminosity and use it to test a class of models for GRBs. We assume that the GRB jet has a finite opening angle and that the orientation of the GRB jet is random relative to the observer. We calculate Lmedian as a function of redshift by simulating GRBs empirically and theoretically, and use the luminosity-vs.-redshift Swift data in order to compare the theoretical results with the observed ones. The method accounts for the fact that there may be GRBs that go undetected at some redshifts. Results. We find that Lmedian is extremely insensitive to the on-axis (i.e., maximal) luminosity of the jet.
