Merging of a massive binary due to ejection of bound stars

From the results of numerical scattering experiments and simulations of a massive black hole binary in spherically symmetric and shallow cores it has been deduced that most likely the shrinking process stalls due to loss-cone depletion before emission of gravitational radiation becomes important. Here we follow a different approach and focus on the population of stars which is bound to the binary and so far has not received much attention. With simple assumptions which should not be sensitive to initial conditions we derive a lower limit for the mass of stars which needs to be ejected by the binary in order to coalesce. We also compute this mass in dependence on the steepness of the density profile according to which the stars are distributed. Our results are not as pessimistic as earlier conclusions and actually suggest that the BHs merge.