Predicting Short-duration GRB Rates in the Advanced LIGO Volume

Abstract

Starting with models for the compact object merger event rate, the short-duration Gamma-ray Burst (sGRB) luminosity function, and the Swift/BAT detector, we calculate the observed Swift sGRB rate and its uncertainty. Our probabilistic sGRB world model reproduces the observed number distributions in redshift and flux for 123 Swift/BAT detected sGRBs and can be used to predict joint sGRB/LIGO detection rates. We discuss the dependence of the rate predictions on the model parameters and explore how they vary with increasing experimental sensitivity. In particular, the number of bursts in the LIGO volume depends strongly on the parameters that govern sGRB beaming. Our results suggest that nearby sGRBs should be observed to have broader jets on average ($\theta_{\rm jet}\gtrsim 30$ degrees), as compared to the narrowly-beamed appearance of cosmological sGRBs due to detection selection effect driving observed jet angle. Assuming all sGRBs are due to compact object mergers, within a $D < 200$ Mpc aLIGO volume, we predict $0.18^{+0.19}_{-0.08}$ sGRB/GW associations all-sky per year for on-axis events at Swift sensitivities, increasing to $1.2^{+1.9}_{-0.6}$ with the inclusion of off-axis events. We explore the consistency of our model with GW170817/GRB~170817A in the context of structured jets. Predictions for future experiments are made.