Formation of the Black Holes in the Highest Redshift Quasars

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The recent discovery of luminous quasars up to a redshift z=6.43 has renewed interest in the formation of black holes massive enough to power quasars. If black holes grow by Eddington-limited gas accretion with a radiative efficiency of at least 10%, the time required to grow from a stellar black hole to ~10^9 msun is ~10^9 years, close to the age of the universe at z=6. Black hole mergers may accelerate the rate of mass growth, but can also completely eject black holes from halo centers owing to the gravitational wave recoil effect. Recently, Haiman concluded that black hole ejections likely do not allow black holes to grow to ~10^9 msun by z=6.43. We reexamine this problem and show that, by using a different halo escape velocity, accounting for the dependence of the recoil velocity on the black hole binary mass ratio and spins, and allowing seed black holes to form in all halos down to virial temperatures of 2000 K, black hole masses may reach ~10^9 msun as early as z=9 starting from stellar seeds, without super-Eddington accretion. In this particular case, we find that these massive black holes form from the merger of ~10^4 stellar black holes formed in low-mass halos at z~20, which must all grow close to the maximum Eddington rate over most of the time available from their birth to z~6. The alternative is that black holes can grow more rapidly by super-Eddington accretion.