Beyond kappa distributions: Exploiting Tsallis statistical mechanicsin space plasmas

摘要

Empirically derived kappa distributions are becoming increasingly widespread inspace physics as the power law nature of various suprathermal tails is melded with moreclassical quasi-Maxwellian cores. Two different mathematical definitions of kappadistributions are commonly used and various authors characterize the power law nature ofsuprathermal tails in different ways. In this study we examine how kappa distributionsarise naturally from Tsallis statistical mechanics, which provides a solid theoreticalbasis for describing and analyzing complex systems out of equilibrium. This analysisexposes the possible values of kappa, which are strictly limited to certain ranges. Wealso develop the concept of temperature out of equilibrium, which differs significantlyfrom the classical equilibrium temperature. This analysis clarifies which of the kappadistributions has primacy and, using this distribution, the kinetic and physicaltemperatures become one, both in and out of equilibrium. Finally, we extract the generalrelation between both types of kappa distributions and the spectral indices commonly usedto parameterize space plasmas. With this relation, it is straightforward to compare bothspectral indices from various space physics observations, models, and theoretical studiesthat use kappa distributions on a consistent footing that minimizes the chances formisinterpretation and error. Now that the connection is complete between empiricallyderived kappa distributions and Tsallis statistical mechanics, the full strength andcapability of Tsallis statistical tools are available to the space physics community for-analyzing and understanding the kappa-like properties of the various particle and energydistributions observed in space.