Constraints from gravitational recoil on the growth of supermassive black holes at high redshift

Recent studies have suggested that during their coalescence, binary supermassive black holes (SMBHs) experience typical gravitational recoil velocities that may be as large as ≳100 km s^-1. These velocities exceed the escape velocity vesc from typical dark matter (DM) halos at high redshift (z ≳ 6), and therefore put constraints on scenarios in which early SMBHs grow at the centers of DM halos. Here we quantify these constraints for the most distant known SMBH, with an inferred mass in excess of 10^9 M☉, powering the bright quasar SDSS J1148+5251 discovered in the Sloan Digital Sky Survey at z = 6.43. We assume that this SMBH grew via a combination of accretion and mergers between preexisting seed BHs in individual progenitor halos, and that mergers between progenitors with vesc < vkick disrupt the BH growth process. Our results suggest that under these assumptions, the z ≈ 6 SMBHs had a phase during which they gained mass vary rapidly. In particular, typical z ≈ 3 quasars with luminosities similar to that of SDSS J1148+5251 have recently been inferred to have an average radiative efficiency of epsilon ≈ 20%. The growth rate of the SMBH in SDSS J1148+5251 must have significantly exceeded the Eddington accretion rate with this efficiency.