Energetic constraints on electromagnetic signals from double black hole mergers

The possible Fermi detection of an electromagnetic counterpart to the double black hole merger GW150914 has inspired many theoretical models, some of which propose that the holes spiraled together inside a massive star. However, we show that the heat produced by the dynamical friction on such black hole orbits can exceed the stellar binding energy by a large factor, which means that this heat could destroy the star and thus make it difficult for enough gas to be near the holes at merger to produce detectable photons. These considerations must be taken into account when models are proposed for electromagnetic counterparts to the coalescence of two stellar-mass black holes. We find that only when the two black holes form very close to the center can the star avoid destruction. In that case, dynamical friction can make the black holes coalesce faster than they would in vacuum, which leads to a modification of the gravitational waveform that is potentially observable by advanced LIGO.