Nonthermal and suprathermal distributions as a consequence of superstatistics

We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. They are perceived as a consequence of typical temperature fluctuations. We show that the suprathermal distribution is generated by the Γ distribution of the inverse temperature, in the same way as the Tsallis q statistics. The nonthermal distribution also follows from the χ² distribution, with a small variance. Our contribution provides a possible physical meaning for these ad hoc distributions.