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 spiralled 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. The energy scale of the explosion and the terminal velocity of the gas can be much larger than those in conventional supernovae. If the star unbinds before the merger, it would be hard for enough gas to remain near the holes at the merger to produce a gamma-ray burst, and this consideration should 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 centre can the star certainly 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.