Polytropic Index of the Solar Wind Ions Near the Earth Calculated Using a Homogeneous Magnetohydrodynamic Bernoulli Integral

Abstract

Abstract This paper, using the data of Cluster during 2001–2010, studies the polytropic processes of solar wind ions near the Earth. We calculate the polytropic index of ions for different outward electromagnetic energy ratios δ E × B and entropy parameter changes δ entropy based on the approach of the homogeneous magnetohydrodynamic Bernoulli integral (MBI). Solar wind ions have a broad distribution of polytropic indices with multiple peaks in the range of [−7.0, 6.0]. The median polytropic indices are 1.264, 1.321, and 1.418 at δ entropy = 5% for δ E × B ≤ 5%, 3%, and 1% and 1.241 and 1.097 at δ E × B ≤ 5% for δ entropy ≤ 3% and 1%. In most of the dayside, the median polytropic index of the solar wind basically increases with increasing geocentric distance and has an obvious dawn–dusk asymmetry because of the solar wind–magnetosphere interaction. The polytropic indices near the bow shock are basically within the range from ∼−1.0 to ∼3.0, and their median values are between 0.5 and 1.3. Those polytropic indices of solar wind ions far away from the bow shock are basically in the range from ∼−2.0 to ∼6.0 and have median values between 1.6 and 2.2. Near the terminator, the median polytropic index has no obvious radial distribution, but it has an obvious dawn–dusk asymmetry. The above results suggest that polytropic indices in the solar wind become smaller after being scattered or rebounded by a fast shock wave. It is also found that the polytropic processes in the solar wind near the Earth are closely related to those in the magnetosheath.