The effect of the magnetic field on the damping of slow waves in the solar corona

Abstract

Context. Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona, and they are usually seen to damp rapidly. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and the magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and the magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave. Aims. This effect of heating and cooling misbalance has previously been studied in the infinite magnetic field approximation in a plasma whose thermal equilibrium is comprised of optically thin radiative losses and field-aligned thermal conduction, balanced by an (unspecified) heating process. In this work we extend this analysis by considering a non-zero β plasma. The importance of the effect of the magnetic field in the rapid damping of slow waves in the solar corona is evaluated and compared to the effects of thermal conduction. Methods. A linear perturbation under the thin flux tube approximation is considered, and a dispersion relation describing the slow magnetoacoustic modes is found. The dispersion relation’s limits of strong non-adiabaticity and weak non-adiabaticity are studied. The characteristic timescales were calculated for plasma systems with a range of typical coronal densities, temperatures, and magnetic field strengths. Results. The number of timescales characterising the effect of the misbalance is found to remain at two, as with the infinite magnetic field case. In the non-zero β case, these two timescales correspond to the partial derivatives of the combined heating and cooling function with respect to constant gas pressure and with respect to constant magnetic pressure. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10–100 min, coinciding with the wave periods and damping times observed. Moreover, the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. The change in damping with plasma-β is complex and depends on the coronal heating function’s dependence on the magnetic field in particular. Nonetheless, we show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than approximately 10 G for quiescent loops and plumes, and 100 G for hot and dense loops. Conclusions. A thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between the observations and theory relying on compressive viscosity and thermal conduction alone.