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 (BH) 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 the unfavorable location of Fermi-GBM. Here we answer the following question: if GW150914 and GW150914-GBM were associated, how many LIGO-Virgo binary BH mergers would Fermi-GBM have to follow up to detect a second source? To answer this question, we perform simulated observations of binary BH mergers with LIGO-Virgo and adopt different scenarios for gamma-ray emission from the literature. We calculate the ratio of simulated binary BH mergers detected by LIGO-Virgo to the number of gamma-ray counterpart detections by Fermi-GBM, the BBH-to-GRB ratio. A large majority of the models considered here predict a BBH-to-GRB ratio in the range of 5-20, but for optimistic cases it can be as low as 2, while for pessimistic assumptions it can be as high as 700. Hence, we expect that the third observing run, with its high rate of binary BH detections and assuming the absence of a joint detection, will provide strong constraints on the presented models.