Maximizing the Probability of Detecting an Electromagnetic Counterpart of Gravitational-wave Events

Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors such as advanced LIGO and advanced Virgo. These are among the most promising sources for joint detection of electromagnetic (EM) and gravitational-wave (GW) emission. To maximize the science performed with these objects, it is essential to undertake a followup observing strategy that maximizes the likelihood of detecting the EM counterpart. We present a follow-up strategy that maximizes the counterpart detection probability, given a fixed investment of telescope time. We show how the prior assumption on the luminosity function of the electro-magnetic counterpart impacts the optimized followup strategy. Our results suggest that if the goal is to detect an EM counterpart from among a succession of GW triggers, the optimal strategy is to perform long integrations in the highest likelihood regions, with a time investment that is proportional to the $2/3$ power of the surface density of the GW location probability on the sky. In the future, this analysis framework will benefit significantly from the 3-dimensional localization probability.