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We simulate recoiling black hole trajectories from $z=20$ to $z=0$ in darkmatter halos, quantifying how parameter choices affect escape velocities. Thesechoices include the strength of dynamical friction, the presence of stars andgas, the accelerating expansion of the universe (Hubble acceleration), hosthalo accretion and motion, and seed black hole mass. $\Lambda$CDM haloaccretion increases escape velocities by up to 0.6 dex and significantlyshortens return timescales compared to non-accreting cases. Other parameterschange orbit damping rates but have subdominant effects on escape velocities;dynamical friction is weak at halo escape velocities, even for extremeparameter values. We present formulae for black hole escape velocities as afunction of host halo mass and redshift. Finally, we discuss how these findingsaffect black hole mass assembly as well as minimum stellar and halo massesnecessary to retain supermassive black holes.

Recoiling Supermassive Black Hole Escape Velocities from Dark Matter Halos