Where and when: optimal scheduling of the electromagnetic follow-up of gravitational-wave events based on counterpart lightcurve models

The electromagnetic (EM) follow-up of a gravitational wave (GW) event requires to scan a wide sky region, defined by the so called "skymap", for the detection and identification of a transient counterpart. We propose a novel method that exploits information encoded in the GW signal to construct a "detectability map", which represents the time-dependent ("when") probability to detect the transient at each position of the skymap ("where"). Focusing on the case of a neutron star binary inspiral, we model the associated short gamma-ray burst afterglow and macronova emission, using the probability distributions of binary parameters (sky position, distance, orbit inclination, mass ratio) extracted from the GW signal as inputs. The resulting family of possible lightcurves is the basis to construct the detectability map. As a practical example, we apply the method to a simulated GW signal produced by a neutron star merger at 75 Mpc whose localization uncertainty is very large (about 1500 square degrees). We construct observing strategies based on the detectability maps for optical, infrared and radio facilities, taking VST, VISTA and MeerKAT as prototypes. Assuming limiting fluxes of r ~ 24.5, J ~ 22.4 (AB magnitudes) and 500 uJy @ 1.4 GHz for ~ 1000 s of exposure each, the afterglow and macronova emissions are successfully detected with a minimum observing time of 7, 15 and 5 hours respectively.