Observational implications of lowering the LIGO-Virgo alert threshold

Abstract: The recent detection of the binary-neutron-star merger associated with GW170817 by both LIGO-Virgo and the network of electromagnetic-spectrum observing facilities around the world has made the multi-messenger detection of gravitational-wave events a reality. These joint detections allow us to probe gravitational-wave sources in greater detail and provide us with the possibility of confidently establishing events that would not have been detected in gravitational-wave data alone. In this paper, we explore the prospects of using the electromagnetic follow-up of low-significance gravitational-wave event candidates to increase the sample of confident detections with electromagnetic counterparts. We find that the gravitational-wave alert threshold change that would roughly double the number of detectable astrophysical events would increase the false-alarm rate by more than 5 orders of magnitude from 1 per 100 years to more than 1000 per year. We find that the localization costs of following-up low-significance candidates are marginal, as the same changes to false-alarm rate only increase distance/area localizations by less than a factor of 2 and increase volume localization by less than a factor of 4. We argue that EM follow-up thresholds for low-significance candidates should be set on the basis of alert purity ($P_\text{astro}$) and not false-alarm rate. Ideally, such estimates of $P_\text{astro}$ would be provided by LIGO-Virgo, but in their absence we provide estimates of the average purity of the gravitational-wave candidate alerts issued by LIGO-Virgo as a function of false-alarm rate for various LIGO-Virgo observing epochs.