Forecasting Gamma-Ray Bursts using Gravitational Waves

We explore the intriguing possibility of employing future ground-based gravitational-wave interferometers to detect the inspiral of binary neutron stars sufficiently early to alert electromagnetic observatories so that a gamma-ray burst (GRB) can be observed in its entirety from its very beginning. We quantify the ability to predict a GRB by computing the time a binary neutron star (BNS) system takes to inspiral from its moment of detection to its final merger. We define the moment of detection to be the instant at which the interferometer network accumulates a signal-to-noise ratio of 15. For our computations, we specifically consider BNS systems at luminosity distances of (i) $D\le200\,$Mpc for the three-interferometer Advanced-LIGO-Virgo network of 2020, and (ii) $D\le 1000\,$Mpc for Einstein Telescope's B and C configurations. In the case of Advanced LIGO-Virgo we find that we may at best get a few minutes of warning time, thus we expect no forecast of GRBs in the 2020s. On the other hand, Einstein Telescope will provide us with advance warning times of more than five hours for $D\le 100$Mpc. Taking one hour as a benchmark advance warning time, we obtain a corresponding range of roughly 600 Mpc for the Einstein Telescope C configuration. Using current BNS merger event rates within this volume, we show that Einstein C will forecast $\gtrsim\mathcal{O}(10^2)$ GRBs in the 2030s. We reapply our warning-time computation to black hole - neutron star inspirals and find one to three tidal disruption events to be forecast by the same detector. This is a pedagogical introduction to gravitational-wave astronomy written at a level accessible to PhD students, advanced undergraduates, and colleagues in astronomy/astrophysics who wish to learn more about the underlying physics. Though many of our results may be known to the experts, they might nonetheless find this article motivating and exciting.