The importance of off-jet relativistic kinematics in gamma -ray burst jet models

Gamma-Ray Bursts (GRBs) are widely thought to originate from collimated jets of material moving at relativistic velocities. Emission from such a jet should be visible even when viewed from outside the angle of collimation. I summarize recent work on the special relativistic transformation of the burst quantities Eiso and E peak as a function of viewing angle, where Eiso is the isotropic-equivalent energy of the burst and E peak is the peak of the burst spectrum in the power nuF nu. The formulae resulting from this work serve as input for a Monte Carlo population synthesis method, with which I investigate the importance of off-jet relativistic kinematics as an explanation for a class of GRBs termed "X-ray Flashes" (XRFs). I do this in the context of several top-hat shaped variable opening-angle jet models. I find that such models predict a large population of off-jet bursts that are observable and that lie away from the Epeak ∝ E1/2iso relation. The predicted burst populations are not seen in current datasets. I investigate the effect of the bulk gamma value upon the properties of this population of off-jet bursts, as well as the effect of including an O 0-Egamma correlation to jointly fit the Epeak ∝ E1/2iso and Epeak ∝ Ebg relations, where O0 is the opening solid angle of the GRB jet. I find that the XRFs seen by HETE-2 and BeppoSAX cannot be easily explained as classical GRBs viewed off-jet. I also find that an inverse correlation between gamma and O0 has the effect of greatly reducing the visibility of off-jet events. Therefore, unless gamma > 300 for all bursts or unless there is a strong inverse correlation between gamma and O0, top-hat variable opening-angle jet models produce a significant population of bursts away from the Epeak ∝ E1/2iso and Epeak ∝ Ebg relations, in contradiction of current observations.