Refinements and improvements to a phenomenological model for the jet opening angles of gamma-ray bursts

Abstract

Long duration gamma-ray bursts (GRBs) are thought to originate from the core collapse of massive, rapidly rotating stars - events called "hypernovae." In this thesis, we improve upon a phenomenological model to determine [theta], the jet opening angle of GRBs. We assume that hypernova progenitors are massive stars in binary systems. We calculate [theta] by equating two expressions for the probability of a given GRB being detected - one based on the geometry of the beaming model and the other based on the observed and expected rates of long duration GRBs. These expressions give [theta] as a function of several key physical parameters. We estimate these parameters, perform a Monte Carlo simulation, and obtain the most probable value of [theta] for both single and double jet GRB models. In contrast to previous work, we allow the minimum mass of star-forming galaxies to vary between 10⁶Mo and 10⁷Mo, and we calculate the galactic number density separately for three subtypes of spiral galaxies. For single jet and double jet models, we find that [theta] = 2.8+³.²-¹.². deg and [theta] = 1.9+².²-⁰.⁸. deg respectively. These results are somewhat lower than the results obtained in the earlier stages of this project [15, 16], but are in agreement with values inferred from the observed properties of GRBs [4]. Our results therefore support the assumption that massive binary stars are the progenitors of hypernovae that produce long-duration GRBs.