Extreme recoils: impact on the detection of gravitational waves from massive black hole binaries

Recent numerical simulations of the coalescence of highly spinning massive black hole binaries (MBHBs) suggest that the remnant can suffer a recoil velocity of the order of few thousand kms(-1). We study here, by means of dedicated simulations of black hole build-up, how such extreme recoils could affect the cosmological coalescence rate of MBHBs, placing a robust lower limit for the predicted number of gravitational wave (GW) sources detectable by future space-borne missions (such as the Laser Interferometer Space Antenna, LISA). We consider two main routes for black hole formation: one where seeds are light remnants of Population III stars (similar or equal to 10(2)M circle dot), and one where seeds are much heavier (>= 10(4)M circle dot), formed via the direct gas collapse in primordial nuclear discs. We find that extreme recoil velocities do not compromise the efficient MBHB detection by LISA. If seeds are already massive and/or relatively rare, the detection rate is reduced by only similar to 15 per cent. The number of detections drops substantially (by similar to 60 per cent) if seeds are instead light and abundant, but in this case the number of predicted coalescences is so high that at least similar to 10 sources in a three-year observation are guaranteed.