Young stellar cluster dilution near supermassive black holes: the impact of Vector Resonant Relaxation on neighbour separation

TL;DR

This paper studies how vector resonant relaxation causes the orbital planes of young stars near supermassive black holes to lose their initial alignment over time, affecting the structure of stellar clusters.

Contribution

It introduces a Markovian model to efficiently predict orbital orientation dilution due to vector resonant relaxation near black holes, linking theory with observations.

Findings

Dilution efficiency depends on initial orientation spread and orbital diversity.

The model matches numerical simulations for predicting orientation evolution.

Vector resonant relaxation impacts stellar orientations on timescales comparable to stellar ages.

Abstract

We investigate the rate of orbital orientation dilution of young stellar clusters in the vicinity of supermassive black holes. Within the framework of vector resonant relaxation, we predict the time evolution of the two-point correlation function of the stellar orbital plane orientations as a function of their initial angular separation and diversity in orbital parameters (semi-major axis, eccentricity). As expected, the larger the spread in initial orientations and orbital parameters, the more efficient the dilution of a given set of co-eval stars, with a characteristic timescale set up by the coherence time of the background potential fluctuations. A Markovian prescription which matches numerical simulations allows us to efficiently probe the underlying kinematic properties of the unresolved nucleus when requesting consistency with a given dilution efficiency, imposed by the observed stellar disc within the one arcsecond of Sgr A*. As a proof of concept, we compute maps of constant dilution times as a function of the semi major axis cusp index and fraction of intermediate mass black holes in the old background stellar cluster. This computation suggests that vector resonant relaxation should prove useful in this context since it impacts orientations on timescales comparable to the stars' age.