The apparent and cosmic event rate densities of short gamma-ray bursts

The short gamma-ray burst (sGRB), GRB 170817A, is often considered a rare event. However, its inferred event rate density,O(100s) Gpc⁻³ yr⁻¹, exceeds cosmic sGRB rate estimates from high-redshift samples by an order of magnitude. This discrepancy can be explained by geometric effects related to the structure of the relativistic jet. We first illustrate how adopting a detector flux threshold point estimate rather than an efficiency function can lead to a large variation in rate estimates. Simulating the Fermi-Gamma-ray Burst Monitor sGRB detection efficiency, we then show that for a given universal structured jet profile, one can model a geometric bias with redshift. Assuming different jet profiles, we show that a geometrically scaled rate of GRB 170817A is consistent with the cosmic beaming uncorrected event rate density estimates of sGRBs and that geometry can boost observational rates within O(100s) Mpc. We find an apparent GRB 170817A rate of 304−300+1590​ Gpc⁻³yr⁻¹, which when corrected for geometry yields 5.94−5.86+30.7​ Gpc⁻³yr⁻¹ and 3.34−3.3+17.2​ Gpc⁻³yr⁻¹ for two different jet profiles, consistent with pre-2017 estimates of the isotropic sGRB rate. Our study shows how jet structure can impact rate estimations and could allow one to test structured jet profiles. We finally show that modelling the maximum structured jet viewing angle with redshift can transform a cosmic beaming uncorrected rate to a representative estimate of the binary neutron star merger rate. We suggest this framework can be used to demonstrate parity with merger rates or to yield estimates of the successful jet fraction of sGRBs.