The Polytropic Index of Solar Coronal Plasma in Sunspot Fan Loops and Its Temperature Dependence

Abstract

Observations of slow magneto-acoustic waves have been demonstrated to possess a number of applications in coronal seismology. Determination of the polytropic index ( γ ) is one such important application. Analyzing the amplitudes of oscillations in temperature and density corresponding to a slow magneto-acoustic wave, the polytropic index in the solar corona has been calculated and, on the basis of the obtained value, it has been inferred that thermal conduction is highly suppressed in a very hot loop, in contrast to an earlier report of high thermal conduction in a relatively colder loop. In this study, using Solar Dynamics Observatory /AIA data, we analyzed slow magneto-acoustic waves propagating along sunspot fan loops from 30 different active regions and computed polytropic indices for several loops at multiple spatial positions. The obtained γ values vary from 1.04 ± 0.01 to 1.58 ± 0.12 and, most importantly, display a temperature dependence indicating higher γ at hotter temperatures. This behavior brings both the previous studies to agreement, and perhaps implies a gradual suppression of thermal conduction with increase in temperature of the loop. The observed phase shifts between temperature and density oscillations, however, are substantially larger than that expected from the classical Spitzer thermal conduction, and appear to be influenced by a line-of-sight integration effect on the emission measure.