Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in Coronal Loops with and Without Heating–Cooling Imbalance

Abstract

In the present article, we derive a new dispersion relation for slow magnetoacoustic waves invoking the effect of thermal conductivity, compressive viscosity, radiation, and an unknown heating term along with the consideration of heating–cooling imbalance from linearized MHD equations. We solve the general dispersion relation to understand the role of compressive viscosity and thermal conductivity in the damping of slow waves in coronal loops with and without heating–cooling imbalance. We have analyzed the wave damping for the range of loop length $L=50\,\text{--}\,500~\text{Mm}$, temperature $T=5\,\text{--}\,30~\text{MK}$, and density $\rho=10^{-11}\,\text{--}\,10^{-9}~\text{kg}\,\text{m}^{-3}$. It was found that the inclusion of compressive viscosity along with thermal conductivity significantly enhances the damping of the fundamental mode oscillations in shorter (e.g. $L=50~\text{Mm}$) and super-hot ($T>10~\text{MK}$) loops. However, the role of viscosity in the damping is insignificant in longer (e.g. $L=500~\text{Mm}$) and hot loops ($T\leq 10~\text{MK}$) where, instead, thermal conductivity along with the presence of heating–cooling imbalance plays a dominant role. For shorter loops at a super-hot regime of temperature, the increment in the loop density substantially enhances the damping of the fundamental modes due to thermal conductivity when viscosity is absent, however, when the compressive viscosity is added the increase in density substantially weakens the damping. Thermal conductivity alone is found to play a dominant role in longer loops at lower temperatures ($T\leq10~\text{MK}$), while compressive viscosity dominates the damping at super-hot temperatures ($T>10~\text{MK}$) in shorter loops. The predicted scaling law between damping time ($\tau$) and wave period ($P$) is found to better match the observed SUMER (Solar Ultraviolet Measurements of Emitted Radiation) oscillations when the heating–cooling imbalance is taken into account in addition to thermal conductivity and compressive viscosity for the damping of the fundamental slow mode oscillations.