Effect of Thermal Conductivity,Compressive Viscosity and Radiative Cooling on the Phase Shift of Propagating Slow Waves with andWithout Heating-Cooling Imbalance

摘要

We study the phase shifts of propagating slow magnetoacoustic waves in solar coronal loops invoking the effects of thermal conductivity,compressive viscosity,radiative losses,and heating-cooling imbalance.We derive the general dispersion relation and solve it to determine the phase shifts of density and temperature perturbations relative to the velocity and their dependence on the equilibrium parameters of the plasma such as the background density ρ_0 and temperature T_0.We estimate the phase difference ?φ between density and temperature perturbations and its dependence on ρ_0 and T_0.The role of radiative losses,along with the heating-cooling imbalance for an assumed specific heating function H(ρ,T ) ∝ ρ~(?0.5)T~(?3),in the estimation of the phase shifts is found to be significant for the high-density and low-temperature loops.Heating-cooling imbalance can significantly increase the phase difference (?φ ≈ 140?) for the low-temperature loops compared to the constant-heating case (?φ ≈ 30?).We derive a general expression for the polytropic index γ_(eff) using the linear MHD model.We find that in the presence of thermal conduction alone,γ_(eff) remains close to its classical value 5/3 for all the considered ρ_0 and T_0 observed in typical coronal loops.We find that the inclusion of radiative losses (with or without heating- cooling imbalance) cannot explain the observed polytropic index under the considered heating and cooling models.To make the expected γ_(eff) match the observed value of 1.1 ± 0.02 in typical coronal loops,the thermal conductivity needs to be enhanced by an order of magnitude compared to the classical value.However,this conclusion is based on the presented model and needs to be confirmed further by considering more realistic radiative functions. We also explore the role of different heating functions for typical coronal parameters and find that although the γ_(eff) remains close to 5/3,but the phase difference is highly dep