Tidally Perturbed, Rotating Stellar Systems: Asynchronous Equilibria

TL;DR

This paper introduces a new family of analytical models for rotating, tidally perturbed stellar systems, capturing the combined effects of external tides and internal rotation, useful for studying globular clusters in galactic environments.

Contribution

It develops a three-parameter family of self-consistent equilibrium models incorporating asynchronous rotation and tidal effects using asymptotic expansion methods.

Findings

Models exhibit triaxial shapes with increased asymmetry at higher asynchronicity.

Structural and kinematic properties depend on the asynchronicity parameter.

Models provide a simplified analytical framework for studying tidal and rotational interplay.

Abstract

We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised description of globular clusters that rotate asynchronously with respect to their orbital motion around a host galaxy. Model construction proceeds by extension of the truncated King models, using a newly defined asynchronicity parameter to couple the tidal and rotational perturbations. The method of matched asymptotic expansion is used to derive a global solution to the free boundary problem posed by the corresponding set of Poisson-Laplace equations. We explore the relevant parameter space and outline the intrinsic properties of the resulting models, both structural and kinematic. Their triaxial configuration, characterised by extension in the direction of the galactic centre and flattening toward the orbital plane, is found to depart further from spherical symmetry for larger values of the asynchronicity parameter. We hope that these simplified analytical models serve as useful tools for investigating the interplay of tidal and rotational effects, providing an equilibrium description that complements, and may serve as a basis for, more realistic numerical simulations.