Testing the Predictions of the Universal Structured GRB Jet Model

The two leading models for the structure of GRB jets are (1) the uniform jet model, where the energy per solid angle, $\epsilon$, is roughly constant within some finite half-opening angle, $\theta_j$, and sharply drops outside of $\theta_j$, and (2) the universal structured jet (USJ) model, where all GRB jets are intrinsically identical, and $\epsilon$ drops as the inverse square of the angle from the jet axis. The simplicity of the USJ model gives it a strong predictive power, including a specific prediction for the observed GRB distribution as a function of both the redshift $z$ and the viewing angle $\theta$ from the jet axis. We show that the current sample of GRBs with known $z$ and estimated $\theta$ does not agree with the predictions of the USJ model. This can be best seen for a relatively narrow range in $z$, in which the USJ model predicts that most GRBs should be near the upper end of the observed range in $\theta$, while in the observed sample most GRBs are near the lower end of that range. Since the current sample is very inhomogeneous (it involves many different detectors), it should be taken with care and cannot be used to rule out the USJ model. Nevertheless, this sample strongly disfavors the USJ model. Comparing the prediction for the observed GRB distribution both in $\theta$ and in $z$, with a larger and more homogeneous GRB sample, like the one expected from Swift, would either clearly rule out the USJ model, or alternatively, provide a strong support for it. Finally, we stress that the test presented here is general, and can be used to test any model that predicts both a luminosity function and a luminosity-angle relation.