The detection efficiency of on-axis short gamma-ray burst optical afterglows triggered by aLIGO/Virgo

Abstract

Assuming neutron star (NS) or neutron star/stellar-mass black hole (BH) mergers as progenitors of the short gamma ray bursts, we derive and demonstrate a simple analysis tool for modelling the efficiency of recovering on-axis optical afterglows triggered by a candidate gravitational wave event detected by the Advanced LIGO and Virgo network. The coincident detection efficiency has been evaluated for different classes of operating telescopes using observations of gamma ray bursts. We show how the efficiency depends on the luminosity distribution of the optical afterglows, the telescope features, and the sky localisation of gravitational wave triggers. We estimate a plausible optical afterglow and gravitational wave coincidence rate of 1 yr$^{-1}$ (0.1 yr$^{-1}$) for NS-NS (NS-BH), and how this rate is scaled down in detection efficiency by the time it takes to image the gravitational wave sky localization and the limiting magnitude of the telescopes. For NS-NS (NS-BH) we find maximum detection efficiencies of $>80%$ when the total imaging time is less than 200 min (80 min) and the limiting magnitude fainter than 20 (21). We show that relatively small telescopes $(m<18)$ can achieve similar detection efficiencies to meter class facilities $(m<20)$ with similar fields of view, only if the less sensitive instruments can respond to the trigger and image the field within 10-15 min. The inclusion of LIGO India into the gravitational wave observatory network will significantly reduce imaging time for telescopes with limiting magnitudes $\sim20$ but with modest fields of view. An optimal coincidence search requires a global network of sensitive and fast response wide field instruments that could effectively image relatively large gravitational-wave sky localisations and produce transient candidates for further photometric and spectroscopic follow-up.