Toward an optimal search strategy of optical and gravitational wave emissions from binary neutron star coalescence

Observations of an optical source coincident with gravitational wave emission detected from a binary neutron star coalescence will improve the confidence of detection, provide host galaxy localisation, and test models for the progenitors of short gamma ray bursts. We employ optical observations of three short gamma ray bursts, 050724, 050709, 051221, to estimate the detection rate of a coordinated optical and gravitational wave search of neutron star mergers. Model R-band optical afterglow light curves of these bursts that include a jet-break are extrapolated for these sources at the sensitivity horizon of an Advanced LIGO/Virgo network. Using optical sensitivity limits of three telescopes, namely TAROT (m=18), Zadko (m=21) and an (8-10) meter class telescope (m=26), we approximate detection rates and cadence times for imaging. We find a median coincident detection rate of 4 yr^{-1} for the three bursts. GRB 050724 like bursts, with wide opening jet angles, offer the most optimistic rate of 13 coincident detections yr^{-1}, and would be detectable by Zadko up to five days after the trigger. Late time imaging to m=26 could detect off-axis afterglows for GRB 051221 like bursts several months after the trigger. For a broad distribution of beaming angles, the optimal strategy for identifying the optical emissions triggered by gravitational wave detectors is rapid response searches with robotic telescopes followed by deeper imaging at later times if an afterglow is not detected within several days of the trigger.