Comparing Short Gamma-Ray Burst Jet Structure Models

TL;DR

This paper compares different models of gamma-ray burst jet structures using simulated gravitational wave and gamma-ray data, demonstrating that the correct model can be identified with high confidence after fewer than 100 events.

Contribution

It introduces a Bayesian model comparison framework for jet structures in binary neutron star mergers, enabling model discrimination and parameter constraints with future observations.

Findings

Correct jet structure models can be distinguished with a log Bayes factor >5 after <100 events.

Jet core width can be constrained to within ~4-9 degrees after 25-100 events.

Gaussian jet width can be constrained to within ~1.6-2.8 degrees.

Abstract

A structured gamma-ray burst jet could explain the dimness of the prompt emission observed from GRB$\,170817$A but the exact form of this structure is still ambiguous. However, with the promise of future joint gravitational wave and gamma-ray burst observations, we shall be able to examine populations of binary neutron star mergers rather than a case-by-case basis. We present an analysis that considers gravitational wave triggered binary neutron star events both with and without short gamma-ray burst counterparts assuming that events without a counterpart were observed off-axis. This allows for Bayes factors to be calculated to compare different jet structure models. We perform model comparison between a Gaussian and power-law apparent jet structure on simulated data to demonstrate that the correct model can be distinguished with a log Bayes factor of $>5$ after less than 100 events. Constraints on the apparent structure jet model parameters are also made. After 25(100) events the angular width of the core of a power-law jet structure can be constrained within a $90\%$ credible interval of width $ \sim9.1(4.4)^{\circ} $, and the outer beaming angle to be within $\sim19.9(8.5)^{\circ}$. Similarly we show the width of a Gaussian jet structure to be constrained to $\sim2.8(1.6)^{\circ}$.