Joint gravitational wave - gamma-ray burst detection rates in the aftermath of GW170817

The observational follow-up campaign of the gravitational wave (GW) multimessenger event GW170817/GRB170817A has shown that the prompt gamma-rays are consistent with a relativistic structured jet observed from a wide viewing angle greater than or similar to 20 degrees. We perform Bayesian inference using the data from early and late EM observations to determine the jet profile of GRB170817A assuming a structured jet model. We use the geometric dependence on the burst luminosity to produce a short-duration gamma-ray burst (sGRB) efficiency function with redshift, which folded in with binary neutron star detection rate, allows us to estimate the future joint GW/sGRB detection rates for LIGO and Virgo detectors. We show that if the jet structured profile of GRB170817A is a relatively common feature of sGRBs, then there is a realistic probability of another off-axis coincident detection during the third aLIGO/Virgo observing run (O3). We also find that up to 4 yr(-1) joint events may be observed during the advanced LIGO run at design sensitivity and up to 10 yr(-1) by the upgraded advanced LIGO configuration A+. We show that the detection efficiencies for wide-angled sGRB emissions will be limited by GRB satellites as the GW detection range increases through proposed upgrades. Therefore, although the number of coincident detections will increase with GW detector sensitivity, the relative proportion of detected binary neutron stars with gamma-ray counterparts will decrease; 11 per cent for O3 down to 2 per cent during A+.