Legolas: a modern tool for magnetohydrodynamic spectroscopy

TL;DR

Legolas is an open-source numerical tool that calculates the full spectrum of magnetohydrodynamic waves and instabilities in astrophysical plasma configurations, incorporating complex physics and geometries.

Contribution

It introduces a versatile, high-resolution code for MHD spectroscopy that handles various physical effects and geometries, advancing the analysis of plasma stability and wave modes.

Findings

Validated against known MHD wave modes in stratified atmospheres

Revealed new spectral regions with high resolution

Analyzed instabilities like Kelvin-Helmholtz and resistive tearing modes

Abstract

Magnetohydrodynamic (MHD) spectroscopy is central to many astrophysical disciplines, ranging from helio- to asteroseismology, over solar coronal (loop) seismology, to the study of waves and instabilities in jets, accretion disks, or solar/stellar atmospheres. MHD spectroscopy quantifies all linear (standing or travelling) wave modes, including overstable (i.e. growing) or damped modes, for a given configuration that achieves force and thermodynamic balance. Here, we present Legolas, a novel, open-source numerical code to calculate the full MHD spectrum of one-dimensional equilibria with flow, that balance pressure gradients, Lorentz forces, centrifugal effects and gravity, enriched with non-adiabatic aspects like radiative losses, thermal conduction and resistivity. The governing equations use Fourier representations in the ignorable coordinates, and the set of linearised equations are discretised using Finite Elements in the important height or radial variation, handling Cartesian and cylindrical geometries using the same implementation. A weak Galerkin formulation results in a generalised (non-Hermitian) matrix eigenvalue problem, and linear algebraic algorithms calculate all eigenvalues and corresponding eigenvectors. We showcase a plethora of well-established results, ranging from p- and g-modes in magnetised, stratified atmospheres, over modes relevant for coronal loop seismology, thermal instabilities and discrete overstable Alfv\'en modes related to solar prominences, to stability studies for astrophysical jet flows. We encounter (quasi-)Parker, (quasi-)interchange, current-driven and Kelvin-Helmholtz instabilities, as well as non-ideal quasi-modes, resistive tearing modes, up to magneto-thermal instabilities. The use of high resolution sheds new light on previously calculated spectra, revealing interesting spectral regions that have yet to be investigated.