Where and When: Optimal Scheduling of the Electromagnetic Follow-up of Gravitational-wave Events Based on Counterpart Light-curve Models

The electromagnetic (EM) follow-up of a gravitational-wave (GW) event requires scanning a wide sky region, defined by the so-called "skymap," to detect and identify a transient counterpart. We propose a novel method that exploits the information encoded in the GW signal to construct a "detectability map," which represents the time-dependent ("when") probability of detecting 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 light curves is the basis for constructing 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 (∼1500 deg²). We construct observing strategies for optical, infrared, and radio facilities based on the detectability maps, taking VST, VISTA, and MeerKAT as prototypes. Assuming limiting fluxes of $r\sim 24.5$, $J\sim 22.4$ (AB magnitudes), and $500\mu Jy$ ($1.4GHz$) for ∼1000 s of exposure each, the afterglow and macronova emissions are successfully detected with a minimum observing time of 7, 15, and 5 hr respectively.