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The Sloan Digital Sky survey detected luminous quasars at very high redshift, z>6. Follow-up observations indicated that at least some of these quasars are powered by supermassive black holes (SMBHs) with masses in excess of billion solar masses. SMBHs, therefore, seem to have already existed when the Universe was less than 1 Gyr old, and the bulk of galaxy formation still has to take place. We investigate in this paper to which extent accretion and dynamical processes influence the early growth of SMBHs. We assess the impact of (i) black hole mergers, (ii) the influence of the merging efficiency and (iii) the negative contribution due to dynamical effects which can kick black holes out of their host halos (gravitational recoil). We find that if accretion is always limited by the Eddington rate via a thin disc, the maximum radiative efficiency allowed to reproduce the LF at z=6 is of order 12%, when the adverse effect of the gravitational recoil is taken into consideration. Dynamical effects cannot be neglected in studies of high-redshift SMBHs. If black holes can accrete at super-critical rate during an early phase, reproducing the observed SMBH mass values is not an issue, even in the case that the recoil velocity is in the upper limits range, as the mass ratios of merging binaries are skewed towards low values, where the gravitational recoil effect is very mild. We propose that SMBH growth at early times is very selective, and efficient only for black holes hosted in high density peak halos.
Volonteri et al. (Wed,) studied this question.