# The evolution of kicked stellar-mass black holes in star cluster environments II. Rotating star clusters

## TL;DR

This study investigates how rotating star clusters influence the trajectories and orbital decay of kicked stellar-mass black holes, revealing that rotation extends decay times and affects binary formation prospects.

## Contribution

It introduces an analytic framework and N-body simulations to analyze the impact of cluster rotation on the evolution of kicked black holes, highlighting the effects on orbital circularization and decay times.

## Key findings

- Rotating clusters cause black holes to gain angular momentum and circularize their orbits.
- Orbital decay times are longer in rotating clusters compared to non-rotating ones.
- Circularization increases the likelihood of tidal capture and binary formation.

## Abstract

In this paper, we continue our study on the evolution of black holes (BHs) that receive velocity kicks at the origin of their host star cluster potential. We now focus on BHs in rotating clusters that receive a range of kick velocities in different directions with respect to the rotation axis. We perform N-body simulations to calculate the trajectories of the kicked BHs and develop an analytic framework to study their motion as a function of the host cluster and the kick itself. Our simulations indicate that for a BH that is kicked outside of the cluster's core, as its orbit decays in a rotating cluster the BH will quickly gain angular momentum as it interacts with stars with high rotational frequencies. Once the BH decays to the point where its orbital frequency equals that of local stars, its orbit will be circular and dynamical friction becomes ineffective since local stars will have low relative velocities. After circularization, the BH's orbit decays on a longer timescale than if the host cluster was not rotating. Hence BHs in rotating clusters will have longer orbital decay times. The timescale for orbit circularization depends strongly on the cluster's rotation rate and the initial kick velocity, with kicked BHs in slowly rotating clusters being able to decay into the core before circularization occurs. The implication of the circularization phase is that the probability of a BH undergoing a tidal capture event increases, possibly aiding in the formation of binaries and high-mass BHs.