Entropy-mode imprints in the solar corona: non-exponential damping and phase shifts of compressive oscillations

Abstract

Magnetohydrodynamic (MHD) waves in coronal loops provide key seismological diagnostics through their characteristic time signatures. While fast and slow magnetoacoustic modes are routinely exploited, the entropy mode, despite being another eigenmode of the system, remains largely inaccessible due to its non-propagating and non-oscillatory nature. We identify possible observable time-domain signatures of the entropy mode and its indirect effects. Our approach exploits the intrinsically non-adiabatic conditions of the solar corona, under which the entropy mode is closely linked to the compressive slow mode. We consider a one-dimensional coronal loop model with field-aligned thermal conduction, where standing slow and entropy modes are simultaneously excited. We show that the entropy mode leaves distinct imprints on the total loop temperature and density perturbations. Specifically, its rapid decay relative to the slow mode produces a non-exponential damping profile during the initial oscillation cycles and introduces a pronounced asymmetry between the upper and lower temperature and density envelopes. These effects arise naturally from the superposition of two exponentially decaying components with different damping timescales. Furthermore, deviations from the canonical quarter-period phase shift between temperature/density and velocity perturbations in the standing slow mode are explained by the entropy-mode effect. We conclude that the entropy mode may be detected through its impact on compressive oscillations. Revealing its role in non-exponential damping, envelope asymmetry, and phase shifts of compressive oscillations makes the entropy mode potentially accessible to observations and lays the foundation for solar and stellar seismological applications.