Recoiling Supermassive Black Hole Escape Velocities from Dark Matter Halos

TL;DR

This study models the trajectories of recoiling supermassive black holes in dark matter halos from early to present times, revealing how various parameters influence escape velocities and black hole retention.

Contribution

It provides new simulation-based formulae for black hole escape velocities considering dark matter halo growth and other factors, enhancing understanding of black hole retention.

Findings

Dark matter halo accretion raises escape velocities by up to 0.6 dex.

Hubble acceleration and other parameters have subdominant effects on escape velocities.

Dynamical friction is weak at halo escape velocities, even under extreme conditions.

Abstract

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.