Legolas: A Modern Tool for Magnetohydrodynamic Spectroscopy

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 traveling) 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, balancing pressure gradients, Lorentz forces, centrifugal effects, and gravity, and enriched with nonadiabatic aspects like radiative losses, thermal conduction, and resistivity. The governing equations use Fourier representations in the ignorable coordinates, and the set of linearized equations is discretized 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 generalized (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 magnetized, stratified atmospheres, over modes relevant for coronal loop seismology, thermal instabilities, and discrete overstable Alfven 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 nonideal quasi-modes, resistive tearing modes, up to magnetothermal instabilities. The use of high resolution sheds new light on previously calculated spectra, revealing interesting spectral regions that have yet to be investigated.