TP-24

On the Luminosity Function of GRBs Associated with Supernovae

Haihong Che

If Gamma-ray Bursts (GRBs) are generally associated with supernovae, a relatively wide intrinsic luminosity function is implied, which indicates the existence of a large amount of undetected dim bursts, and a much higher event-rate than is often estimated. If it is assumed that the intrinsic luminosity function of GRBs is a power-law: ${\phi (L)} \propto {L^{-\beta}}$ ($\beta > 0$, $L_{min} \leq L \leq L_{max}$), data from the BATSE 4B catalog can be used to constrain slope index $\beta$ and the dynamic range width $Log {L_{max}\over L_{min}}$. Using a K-S test comparison with the observational Log N - Log P, we find constraints on the GRB fireball model, GRB jets, and the possible GRB contribution to cosmic gamma-ray background. Our results show that the fireball model is not inconsistent with GRBs following the supernovae rate. Our studies also show that the luminosity function provided by a purely special relativistic effect on a jet is outside of a K-S test acceptable range, which indicates that the emission direction of GRBs is not random in the jet's comoving frame.