Thermal instability in coronal loops: Linking eigenvalue spectra to time-dependent evolution

Centre for mathematical Plasma-Astrophysics (CmPA), KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium

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Received: 18 March 2026
Accepted: 27 April 2026

Abstract

Context. Cool, dense condensations such as coronal rain and prominences suggest that coronal plasma can undergo runaway radiative cooling. Connecting this behaviour to linear thermal modes requires a fuller understanding of the deeper connection between eigenvalue spectra and actual time-dependent evolution.

Aims. We aim to clarify this intricate link for a simplified coronal-only model of a stratified coronal loop by combining spectral, linear initial value, and non-linear simulations of the same loop setup.

Methods. We studied waves and instabilities, as well as temporal evolutions for a 1D hydrostatic, thermally balanced loop with optically thin radiation and prescribed heating. The non-adiabatic spectrum of all the physically realisable eigenmodes was computed with our open-source code LEGOLAS. We demonstrate the capabilities of our newly developed boundary value–initial value solver called LEGOLAS-IVP, where linear evolutions are performed for controlled perturbations and fully equivalent non-linear runs are carried out with our generic software toolkit MPI-AMRVAC.

Results. The spectrum of the stratified 1D loop contains discrete acoustic modes and a thermally unstable branch consisting of thermal modes, including a thermal continuum. Linear initial-value experiments with isochoric, isobaric, and isentropic pulses highlight how the polarisation of the eigenmodes and the obtained evolution from specific perturbations demonstrate physically consistent behaviour expected from the eigenspectrum. Even in the linear stage, thermal imbalance drives siphon-like flows from the footpoints towards the cooling region. Growth rates measured from LEGOLAS-IVP agree with the spectral predictions and are reproduced in MPI-AMRVAC. The latter follows the condensation through runaway cooling to chromospheric temperatures, with the resulting cool dense blob sliding under gravity towards the loop footpoint.

Conclusions. The spectral–linear–non-linear investigation for the simple 1D loop demonstrates a direct link between thermal eigenmodes and time-dependent condensation dynamics and provides a basis for extending such mode-based interpretations to fully 3D magnetohydrodynamic models.