A New Derivation of GRB Jet Opening Angles from the Prompt Gamma-Ray Emission

The jet opening angle of gamma-ray bursts (GRBs) is an important parameter for determining the characteristics of the progenitor, and the information contained in the opening angle gives insight into the relativistic outflow and the total energy that is contained in the burst. Unfortunately, a confident inference of the jet opening angle usually requires broadband measurement of the afterglow of the GRB, from the X-ray down to the radio and from minutes to days after the prompt gamma-ray emission, which may be difficult to obtain. For this reason, very few of all detected GRBs have constrained jet angles. We present an alternative approach to derive jet opening angles from the prompt emission of the GRB, given that the GRB has a measurable Epeak and fluence, and which does not require any afterglow measurements. We present the distribution of derived jet opening angles for the first two years of the Fermi Gamma-ray Burst Monitor (GBM) operation, and we compare a number of our derived opening angles to the reported opening angles using the traditional afterglow method. We derive the collimation-corrected gamma-ray energy, E_{\gamma}, for GRBs with redshift and find that some of the GRBs in our sample are inconsistent with a proto-magnetar progenitor. Finally, we show that the use of the derived jet opening angles results in a tighter correlation between the rest-frame Epeak and E_{\gamma} than has previously been presented, which places long GRBs and short GRBs onto one empirical power law.