Coronal seismology by slow waves in non-adiabatic conditions

Abstract

Slow magnetoacoustic waves represent an important tool for probing the solar coronal plasma. The majority of seismological methods with slow waves are based on a weakly non-adiabatic approach, which assumes the coronal energy transport has only weak effects on the wave dynamics. Despite it significantly simplifies the application of coronal seismology by slow waves, this assumption omits a number of important and confidently observed effects and thus puts strong limitations on the reliability of seismological estimations. We quantitatively assess the applicability of the weak thermal conduction theory to coronal seismology by slow waves. We numerically model the linear standing slow wave in a 1D coronal loop, with field-aligned thermal conduction κ‖ as a free parameter and no restrictions on its efficiency. The time variations of the perturbed plasma parameters, obtained numerically with full conductivity, are treated as potential observables and analysed with the standard data processing techniques. The slow wave oscillation period is found to increase with κ‖ by about 30%, indicating the corresponding modification in the effective wave speed, which is missing from the weak conduction theory. Phase shifts between plasma temperature and density perturbations are found to be well consistent with the approximate weakly conductive solution for all considered values of κ‖. In contrast, the comparison of the numerically obtained ratio of temperature and density perturbation amplitudes with the weak theory revealed relative errors up to 30–40%. We use these parameters to measure the effective adiabatic index of the coronal plasma directly as the ratio of the effective slow wave speed to the standard sound speed and in the polytropic assumption, which is found to be justified in a weakly conductive regime only, with relative errors up to 14% otherwise. The damping of the initial perturbation is found to be of a non-exponential form during the first cycle of oscillation, which could be considered as an indirect signature of entropy waves in the corona, also not described by weak conduction theory. The performed analysis and obtained results offer a more robust scheme of coronal seismology by slow waves, with reasonable simplifications and without the loss of accuracy.

Exact solution to the problem of slow oscillations in coronal loops and its diagnostic applications

“…For an illustration of the mentioned feature, we recommend to compare the results in Figures 1A,B. A similar sensitivity of the apparent entropy mode excitation to both the perturbation type and characteristic value of thermal conduction has been demonstrated numerically by Kolotkov (2022).…”

“…In particular, the assumptions of weak (Owen et al, 2009;Van Doorsselaere et al, 2011;Wang et al, 2015;Krishna Prasad et al, 2018;Prasad et al, 2022) or strong (Krishna Prasad et al, 2014;Duckenfield et al, 2021Duckenfield et al, ) impact of 10.3389/fspas.2023 thermal conduction are frequently used for this purpose. However, the results presented in Kolotkov (2022) show that by assuming that the thermal conductivity satisfies the value proposed by Spitzer, the dynamics of the fundamental slow-wave harmonic can be described with neither strong nor weak thermal conductivity limits (see Figure 2 in Kolotkov (2022) for details). In this case, the general description without limitation on the thermal conduction coefficient is required.…”