Teamwork Makes the Dream Work: Optimizing Multi-Telescope Observations of Gravitational-Wave Counterparts.

The ever-increasing sensitivity of the network of gravitational-wave detectors has resulted in the accelerated rate of detections from compact binary coalescence systems in the third observing run of Advanced LIGO and Advanced Virgo. Not only has the event rate increased, but also the distances to which phenomena can be detected, leading to a rise in the required sky volume coverage to search for counterparts. Additionally, the improvement of the detectors has resulted in the discovery of more compact binary mergers involving neutron stars, revitalizing dedicated follow-up campaigns. While significant effort has been made by the community to optimize single telescope observations, using both synoptic and galaxy-targeting methods, less effort has been paid to coordinated observations in a network. This is becoming crucial, as the advent of gravitational-wave astronomy has garnered interest around the globe, resulting in abundant networks of telescopes available to search for counterparts. In this paper, we extend some of the techniques developed for single telescopes to a telescope network. We describe simple modifications to these algorithms and demonstrate them on existing network examples. These algorithms are implemented in the open-source software \texttt{gwemopt}, used by some follow-up teams, for ease of use by the broader community.