Determining the jet opening-angle of gamma-ray bursts

Abstract

There is growing scientific agreement that at least some cosmic gamma-ray bursts (GRBs) coincide with the deaths of rapidly rotating massive stars - dubbed "hyper-novae." In 1987, a supernova (SN 1987A) was detected in the Large Magellanic Cloud - its progenitor was a blue, rapidly rotating supergiant that was probably a member of a binary system that underwent merger prior to the supernova event [1]. Was SN 1987A a (possibly failed) hypernova? Although no accompanying GRB was detected, there is evidence [2] that one may have occurred but was beamed in a direction away from the earth. If so, are massive binary systems the progenitors of hypernovae and, in turn, of GRBs? In this thesis, we use a phenomenological model to determine [theta], the opening angle of the beams of GRBs. Our basic underlying assumption is that objects like SN 1987A are hypernovae, i.e., that they produce certain GRBs. We calculate [theta] by deriving two expressions for the probability that a given GRB is detected, one based on the solid geometry implied by the beaming model and the other based on the number of GRBs observed over time. These expressions give the probability as a function of a few key physical variables. By obtaining realistic estimates of the physical variables, equating the two expressions, and performing a Monte-Carlo simulation, we obtain an estimate of the most probable value of [theta]. We find that [theta] = 6.203⁰ ± 1.620⁰. Because this result is well in agreement with values inferred from the observed properties of GRBs [3]; and with values calculated based on the structured jet model of GRBs [4], we conclude that our underlying assumption - that SN 1987A was a hypernova - is at the very least plausible.