Fermi GBM follow-up of LIGO-Virgo binary black hole mergers -- detection prospects

Fermi-Gamma-ray Burst Monitor observed a 1 s long gamma-ray signal (GW150914-GBM) starting 0.4 s after the first gravitational wave detection from the binary black hole merger GW150914. GW150914-GBM is consistent with a short gamma-ray burst origin; however, no unambiguous claims can be made as to the physical association of the two signals due to a combination of low gamma-ray flux and unfavorable location for Fermi-GBM. Here we answer the following question: if GW150914 and GW150914-GBM were associated, how many LIGO-Virgo binary black hole mergers would Fermi-GBM have to follow up to detect a second source? To answer this question, we perform simulated observations of binary black hole mergers with LIGO-Virgo and adopt different scenarios for gamma-ray emission from the literature. We calculate the ratio of simulated binary black hole mergers detected by LIGO-Virgo to the number of gamma-ray counterpart detections by Fermi-GBM, BBH-to-GRB ratio. A large majority of the models considered here predict a BBH-to-GRB ratio in the range of 5 to 20, but for optimistic cases can be as low as 2 or for pessimistic assumptions as high as 700. Hence we expect that the third observing run, with its high rate of binary black hole detections and assuming the absence of a joint detection, will provide strong constraints on the presented models.