  Recent studies have shown that during their coalescence, binary supermassive
black holes (SMBHs) experience a gravitational recoil with velocities of 100
km/s < v(kick) < 600 km/s. These velocities exceed the escape velocity v(esc)
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 SMBHs, with
inferred masses in excess of 10^9 M(sun), powering the bright quasars
discovered in the Sloan Digital Sky Survey at z>6. We assume that these SMBHs
grew via a combination of accretion and mergers between pre-existing seed BHs
in individual progenitor halos, and that mergers between progenitors with
v(esc) < v(kick) disrupt the BH growth process. Our results suggest that under
these assumptions, the z=6 SMBHs had a phase during which gained mass
significantly more rapidly than under an Eddington-limited exponential growth
rate.
