Linear response of rotating and flattened stellar clusters: the oblate Kuzmin-Kutuzov St\"ackel family

TL;DR

This study analyzes the linear response of spheroidal stellar clusters with varying flattening and rotation, using a matrix method to identify instabilities and eigenmodes, and provides a public code for further research.

Contribution

It extends the analysis of stellar cluster stability to a family of models with continuous flattening and rotation, using an efficient matrix method.

Findings

Identified two types of bi-symmetric instabilities: bending and bar-growing modes.

Confirmed that increased rotation leads to flatter configurations in less unstable models.

Replicated growth modes from previous N-body simulations.

Abstract

This paper investigates the linear response of a series of spheroidal stellar clusters, the Kuzmin-Kutuzov St\"ackel family, which exhibit a continuous range of flattening and rotation, extending from an isochrone sphere to a Toomre disk. The method successfully replicates the growing modes previously identified in published $N$-body simulations. It relies on the efficiency of the matrix method to quantify systematically the effects of rotation and flattening on the eigenmodes of the galaxy. We identify two types of bi-symmetric instabilities for the flatter models - the so-called bending and bar-growing modes - the latter of which persists even for very round models. As anticipated, in its least unstable configurations, the system becomes flatter as its rotational speed increases. More realistic equilibria will be required to achieve a better match to the main sequence of fast-slow rotators. The corresponding code is made public.