Finite element modelling of perturbed stellar systems

TL;DR

This paper develops a finite element method for modeling self-gravitating stellar systems, allowing for flexible potential and density profiles, and applies it to stability analysis and disturbance studies of stellar discs.

Contribution

It introduces a general FEM framework for stellar systems that handles complex profiles and non-axisymmetric features, advancing computational modeling in astrophysics.

Findings

FEM effectively analyzes stability of the Mestel disc.

Successfully models disturbances from satellite galaxies.

Demonstrates adaptability to various potential and density profiles.

Abstract

I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and suitable interpolating functions. General expressions are then introduced for the Hamiltonian and phase space distribution functions of the stars that visit a given element. Using the weighted residual form of Poisson's equation, I derive the Galerkin projection of the perturbed collisionless Boltzmann equation, and assemble the global evolutionary equations of nodal distribution functions. The FEM is highly adaptable to all kinds of potential and density profiles, and it can deal with density clumps and initially non-axisymmetric systems. I use ring elements of non-uniform widths, choose linear and quadratic interpolation functions in the radial direction, and apply the FEM to the stability analysis of the cutout Mestel disc. I also integrate the forced evolutionary equations and investigate the disturbances of a stable stellar disc due to the gravitational field of a distant satellite galaxy. The performance of the FEM and its prospects are discussed.