  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.
