Characterizing proton polytropic indices inside near-Earth magnetic clouds and ICME sheaths

The thermodynamics of interplanetary coronal mass ejections (ICMEs) is often described using a polytropic process. Estimating the polytopic index ($\gamma$) allows us to quantify the expansion or compression of the ICME plasma arising from changes in the plasma temperature. In this study, we estimate $\gamma$ for protons inside the magnetic clouds (MCs), their associated sheaths, and ambient solar wind for a large sample of well-observed events observed by the Wind spacecraft at 1 AU. We find that $\gamma$ shows a high ($\approx 1.6$) - low ($\approx 1.05$) - high ($\approx 1.2$) behavior inside the ambient solar wind, sheath, and MCs, respectively. We also find that the proton polytropic index is independent of small-scale density fluctuations. Furthermore, our results show that the stored energy inside MC plasma is not expended in expanding its cross-section at 1 AU. The sub-adiabatic nature of MC plasma implies external heating - possibly due to thermal conduction from the corona. We find that the heating gradient per unit mass from the corona to the protons of MC at 1 AU is $\approx 0.21$ erg cm$^{-1}$ g$^{-1}$ which is in agreement with the required proton heating budget.