Relationship between Polytropic Index and Temperature Anisotropy in Space Plasmas

The paper develops a theoretical relationship between the polytropic index and the temperature anisotropy that may characterize space plasmas. The derivation is based on the correlation among the kinetic energies of particles with velocities described by anisotropic kappa distributions. The correlation coefficient depends on the effective dimensionality of the velocity distribution, which is determined by the temperature anisotropy caused by the ambient magnetic field; on the other hand, the effective dimensionality is directly dependent on the polytropic index. This analysis leads to the connection between the correlation coefficient, effective dimensionality of the velocity space, and the polytropic index, with the temperature anisotropy. Moreover, a data and statistical analysis is performed to test the developed model in the solar wind proton plasma near 1 au. The derived theoretical relationship is in good agreement with observations, showing that the lowest and classical value of the adiabatic polytropic index occurs in the isotropic case, while higher values of the adiabatic index characterize more anisotropic plasmas. Finally, possible extensions of the theory considering (i) nonadiabatic polytropic behavior and (ii) more general distributions, are further discussed.