Recoiling Supermassive Black Hole Escape Velocities from Dark Matter
  Halos
  We simulate recoiling black hole trajectories from $z=20$ to $z=0$ in dark
matter halos, quantifying how parameter choices affect escape velocities. These
choices include the strength of dynamical friction, the presence of stars and
gas, the accelerating expansion of the universe (Hubble acceleration), host
halo accretion and motion, and seed black hole mass. $\Lambda$CDM halo
accretion increases escape velocities by up to 0.6 dex and significantly
shortens return timescales compared to non-accreting cases. Other parameters
change orbit damping rates but have subdominant effects on escape velocities;
dynamical friction is weak at halo escape velocities, even for extreme
parameter values. We present formulae for black hole escape velocities as a
function of host halo mass and redshift. Finally, we discuss how these findings
affect black hole mass assembly as well as minimum stellar and halo masses
necessary to retain supermassive black holes.
