Slow Mode Oscillations and Damping of Hot Solar Coronal Loops

The effect of temperature inhomogeneity on the periods, their ratios (fundamental vs. first overtone), and the damping times of the standing slow modes in gravitationally stratified solar coronal loops are studied. The effects of optically thin radiation, compressive viscosity, and thermal conduction are considered. The linearized one-dimensional magnetohydrodynamic (MHD) equations (under low-$\beta$ condition) were reduced to a fourth--order ordinary differential equation for the perturbed velocity. The numerical results indicate that the periods of non-isothermal loops (i.e. temperature increases from the loop base to apex) are smaller compared to those of isothermal loops. In the presence of radiation, viscosity, and thermal conduction, an increase in the temperature gradient is followed by a monotonic decrease in the periods (compared with the isothermal case), while the period ratio turns out to be a sensitive function of the gradient of the temperature and the loop lengths. We verify that radiative dissipation is not a main cooling mechanism of both isothermal and non-isothermal hot coronal loops and has a small effect on the periods. Thermal conduction and compressive viscosity are primary mechanisms in the damping of slow modes of the hot coronal loops. The periods and damping times in the presence of compressive viscosity and/or thermal conduction dissipation are consistent with the observed data in specific cases. By tuning the dissipation parameters, the periods and the damping times could be made consistent with the observations in more general cases.