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

Recent numerical simulations of coalescences of highly spinning massive black hole binaries (MBHBs) suggest that the remnant can suffer a recoil velocity of the order of few thousands km/s. We study here, by means of dedicated simulations of black holes 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 LISA). We consider two main routes for black hole formation: one where seeds are light remnants of Population III stars (~10^2 \msun), and one where seeds are much heavier (>~10^4 \msun), formed via the direct gas collapse in primordial nuclear disks. 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 ~15%. The number of detections drops substantially (by ~60%) if seeds are instead light and abundant, but in this case the number of predicted coalescences is so high that at least ~10 sources in a three year observation are guaranteed.