# Recoiling supermassive black holes in analytical and numerical galaxy potential

## TL;DR

This paper compares analytical and numerical models of galaxy mergers to study recoiling supermassive black holes, revealing that numerical models show lower escape velocities and more spatially-offset active galactic nuclei than analytical models.

## Contribution

It demonstrates that numerical models provide a more realistic depiction of SMBH recoil dynamics during galaxy mergers, highlighting differences from static analytical models.

## Key findings

- Numerical models show up to 25% lower escape velocities than analytical models.
- Recoiling SMBHs reach larger galactocentric distances in numerical models.
- Numerical models predict more spatially-offset active galactic nuclei.

## Abstract

We follow trajectories of recoiling supermassive black holes (SMBHs) in analytical and numerical models of galaxy merger remnants with masses of $10^{11} \rm{M_{sun}}$ and $10^{12} \rm{M_{sun}}$. We construct various merger remnant galaxies in order to investigate how the central SMBH mass and the mass ratio of progenitor galaxies influence escape velocities of recoiling SMBHs. Our results show that static analytical models of major merger remnant galaxies overestimate the SMBHs escape velocities. During major mergers violent relaxation leads to the decrease of galaxy mass and lower potential at large remnant radii. This process is not depicted in static analytical potential but clearly seen in our numerical models. Thus, the evolving numerical model is a more realistic description of dynamical processes in galaxies with merging SMBHs. We find that SMBH escape velocities in numerical major merger remnant galaxies can be up to 25 per cent lower compared to those in analytical models. Consequently, SMBHs in numerical models generally reach greater galactocentric distances and spend more time on bound orbits outside of the galactic nuclei. Thus, numerical models predict a greater number of spatially-offset active galactic nuclei (AGNs).