Core-halo distribution functions: A natural equilibrium state in generalized thermostatistics

Space observations provide a clear signature of non-Maxwellian core-halo electron and ion-velocity distribution functions as an ubiquitous and persistent feature of astrophysical plasma environments. In particular, the detected suprathermal halo populations are accurately represented by the family of kappa-distributions, a power law in particle speed. Contrary to observations, the physical relevance of kappa-distributions has frequently been criticized because of a lack of theoretical justification. We show that these distributions turn out as consequence of an entropy generalization based on nonextensive thermostatistics, thus providing the missing link for power-law models from fundamental physics. Moreover, upon clarifying that the full nonextensive formalism is also compatible with negative values of the spectral index kappa, we demonstrate that core-halo structures are a natural element within pseudoadditive entropy. As a consequence, pronounced core-halo patterns can be generated adiabatically, following density conservation out of a Maxwellian equilibrium state. The physical significance of the proposed nonextensive double-kappa distribution family is analyzed with regard to nonthermal entropy evolution and tested on typical core-halo characteristics of observed interplanetary electron and ion velocity space structures, originating as a natural equilibrium state within the generalized entropy concept. The peak separation scale of interplanetary double-humped proton distributions is found to obey a maximum entropy condition.