A Nonextensive Entropy Approach to Kappa-Distributions

Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use of these distributions has been unjustly criticized because of a perceived lack of theoretical justification. We show that distributions very close to kappa-distributions are a consequence of the generalized entropy favored by non extensive statistics, which provides the missing link for power-law models of non-thermal features from fundamental physics. With regard to the physical basis supplied by the Tsallis nonextensive entropy formalism we propose that this slightly modified functional form, qualitatively similar to the traditional kappa-distribution, be used in fitting particle spectra in the future.