Modeling of the Polytropic Index and Temperature Anisotropy in the Solar Wind

Abstract

The polytropic index is a fundamental physical parameter related to the thermodynamic processes present in space and astrophysical plasmas. This paper investigates the theoretical relationship between the polytropic index and the temperature anisotropy for flow parameters relevant to space plasmas. The derivation is based on the Chew–Goldberger–Low double-adiabatic equations of state and the finite Larmor radius correction. On the basis of this, we present the polytropic index relation, taking into account the temperature anisotropy, flow speed, and magnetic field of the plasma. This relation was further analyzed for the limit of the quasi-parallel and quasi-transversal cases. The quasi-transversal limit gives a polytropic index as a function of the anisotropic temperature γ = 1 + 2[2T ⊥ − T ∥]/[2T ⊥ + T ∥]. Using this result, we analyze the polytropic index for the bulk proton parameters derived from Ulysses spacecraft data spanning the interval from 1992 January 1 to 2009 June 30, and we find an average polytropic index of γ ∼ 1.43. This value is close to that of recently published results. However, unlike previous statistical studies, this research computes the polytropic index without relying on power-law fitting, and its variation is now associated with the anisotropic temperature.