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Gravitational recoil: effects on massive black hole occupation fraction over cosmic time

We assess the influence of massive black hole (MBH) ejections from galaxy centres, due to the gravitational radiation recoil, along the cosmic merger history of the MBH population. We discuss the 'danger' of the recoil for MBHs as a function of different MBH spin/orbit configurations and of the host halo cosmic bias, and on how that reflects on the 'occupation fraction' of MBHs. We assess ejection probabilities for mergers occurring in a gas-poor environment, where the MBH binary coalescence is driven by stellar dynamical processes, and the spin/orbit configuration is expected to be isotropically distributed. We contrast this case with the 'aligned' case. The latter is the most realistic situation for 'wet', gas-rich mergers, which are the expectation for high-redshift galaxies. We find that if all halos at z>5-7 host a MBH, the probability of the Milky Way (or similar size galaxy) to host a MBH today is less than 50%, unless MBHs form continuously in galaxies. The 'occupation fraction' of MBHs, intimately related to halo bias and MBH formation efficiency, plays a crucial role in increasing the retention fraction. Small halos, with shallow potential wells and low escape velocities, have a high ejection probability, but the MBH merger rate is very low along their galaxy formation merger hierarchy: MBH formation processes are likely inefficient in such shallow potential wells. Recoils can decrease the overall frequency of MBHs in small galaxies to ~60%, while they have little effect on the frequency of MBHs in large galaxies (at most a 20% effect).