Predicting the linear response of self-gravitating stellar spheres and discs with LinearResponse.jl

TL;DR

LinearResponse.jl is a Julia library that efficiently computes the linear response of self-gravitating stellar systems, enabling analysis of their stability and mode structures across different models.

Contribution

It introduces a versatile, validated Julia library for calculating the linear response of spherical and disc stellar systems, extending to kinetic theory applications.

Findings

Validated against known models like isochrone and Mestel discs.

Successfully simulated modes in the spherical Plummer model.

Can scan the complex frequency plane for stability analysis.

Abstract

We present LinearResponse.jl, an efficient, versatile public library written in julia to compute the linear response of self-gravitating (3D spherically symmetric) stellar spheres and (2D axisymmetric razor-thin) discs. LinearResponse.jl can scan the whole complex frequency plane, probing unstable, neutral and (weakly) damped modes. Given a potential model and a distribution function, this numerical toolbox estimates the modal frequencies as well as the shapes of individual modes. The libraries are validated against a combination of previous results for the spherical isochrone model and Mestel discs, and new simulations for the spherical Plummer model. Beyond linear response theory, the realm of applications of LinearResponse.jl also extends to the kinetic theory of self-gravitating systems through a modular interface.