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

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.

Significance of Bernoulli Integral Terms for the Solar Wind Protons at 1 au

“…This simplification is equivalent to using the Bernoulli integral expression for incompressible, non-magnetized plasmas, which is independent of γ. Although [22] argue that this approach is not appropriate, we support that when analyzing solar wind protons at 1 au, there is no apparent impact on the results if the cases with γ → 1 are properly treated or excluded from a large statistical sample.…”

Relationship between Polytropic Index and Temperature Anisotropy in Space Plasmas

“…However, there are rarer cases, where space plasmas have negative correlations between their density and temperature; these were found in the outer heliosphere (Elliott et al 2019), inner heliosheath (e.g., Livadiotis & McComas 2013), and the planetary magnetospheres, namely, terrestrial low latitude boundary layer (e.g., Sckopke et al 1981), central plasma sheet (e.g., Pang et al 2015), and bow shock (e.g., Pang et al 2020); Jovian ionosphere (Allegrini et al 2020), magnetosheath and boundary layer (e.g., Nicolaou et al 2014b;; and Saturnian magnetosphere (e.g., Dialynas et al 2018).…”

Spatial Distribution and Low-frequency Disturbance Modulation of Magnetosheath Ion Polytropic Index

“…In this paper, we, using the Cluster data from 2001 to 2010, studied spatial distribution of the ion polytropic index in the magnetosheath, and the modulation of the polytropic process by the low-frequency disturbances (4-18 mHz). We collect 303,283 identical quasi-static process samples in the magnetosheath to calculate their polytropic indices as in Pang et al (2016Pang et al ( , 2020. Each polytropic index is calculated for a streamline-tube experiencing the identical polytropic processes defined by the theory of homogenous MBI (Kartalev et al 2006;Nicolaou et al 2014;Pang et al 2015bPang et al , 2016Pang et al , 2020Livadiotis & Nicolaou 2021).…”

“…Only samples with p-value 0.05 and |R| max (0.4227, R N−2,0.05 ) and duration longer than 12 s (where N are more than four data points), where R N−2,0.05 is the critical value of the correlation coefficient with 95% confidence level, were selected in this work. Each polytropic index is calculated for a streamline-tube experiencing identical polytropic processes defined by the theory of the homogenous MHD Bernoulli integral (MBI; Kartalev et al 2006;Nicolaou et al 2014;Pang et al 2015bPang et al , 2016Pang et al , 2020.…”

“…During this diverting process, plasma flows are thermalized, which are assumed to be polytropic. The polytropic relation (polytropic equation of state) of plasma is determined by the polytropic index, which describes the relationship between plasma pressure p (or plasma temperature T) and number density n, i.e., p/n α = constant or T/n α−1 = constant (Pang et al 2015a(Pang et al , 2015b(Pang et al , 2016(Pang et al , 2020Livadiotis 2016;Livadiotis & Nicolaou 2021) in which the "constant" may be different for different streamline. Polytropic index α is extremely important in MHD theory and can provide key information on some internal plasma processes.…”