On the Origin of Polytropic Behavior in Space and Astrophysical Plasmas

It is shown that the polytropic behavior-a specific power-law relationship among the thermal plasma moments-restricts the functional form of the distribution of particle velocities and energies. Surprisingly, the polytropic behavior requires the statistical mechanics of the plasma particles to obey the framework of kappa distributions. An already known interesting property of these distributions is that they can lead to the polytropic relationship. New results show that the reverse derivation is also true, thus, the polytropic behavior has the role of a mechanism generating kappa distributions. Ultimately, an observation of a polytropic behavior in plasma particle populations constitutes a possible indirect observation of kappa velocity or energy distributions. Finally, it is discussed how the derived equivalence between the polytropic behavior and the kappa distribution function can be used in further modeling and data analyses in space and astrophysical plasmas.