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 Alfvn 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.

磁流体动力学 (MHD) 光谱是许多天体物理学学科的核心，从日震学到星震学、日冕（环）地震学，到研究喷流、吸积盘或太阳/恒星大气中的波和不稳定性。对于实现力和热力学平衡的给定配置，MHD 光谱量化了所有线性（驻波或行波）波模式，包括过稳定（即增长）或阻尼模式。在这里，我们呈现莱戈拉斯，一种新颖的开源数字代码，用于计算具有流动、平衡压力梯度、洛伦兹力、离心效应和重力的一维平衡的完整 MHD 谱，并丰富了非绝热方面，如辐射损失、热传导和电阻率. 控制方程在可忽略坐标中使用傅立叶表示，并且线性化方程组在重要的高度或径向变化中使用有限元进行离散化，使用相同的实现处理笛卡尔和圆柱几何。弱伽辽金公式导致广义（非厄米）矩阵特征值问题，线性代数算法计算所有特征值和相应的特征向量。我们展示了大量公认的结果，范围从p和磁化分层大气中的g模式，与日冕环地震学、热不稳定性和与日珥相关的离散超稳定 Alfvn 模式相关的模式，以及天体物理射流的稳定性研究。我们遇到（准）帕克、（准）交换、电流驱动和开尔文-亥姆霍兹不稳定性，以及非理想准模式、电阻撕裂模式，直至磁热不稳定性。高分辨率的使用为先前计算的光谱提供了新的线索，揭示了尚未研究的有趣光谱区域。