Fluxes of cosmic rays: a delicately balanced stationary state

Abstract

The analysis of cosmic rays fluxes as a function of energy reveals a knee slightly below 1016 eV and an ankle close to 1019 eV. Their physical origins remain up to now quite enigmatic; in particular, no elementary process is known which occurs at energies close to 1016 eV. We propose a phenomenological approach along the lines of nonextensive statistical mechanics, a formalism which contains Boltzmann–Gibbs statistical mechanics as a particular case. The knee then appears as a crossover between two fractal-like thermal regimes, the crossover being caused by process occurring at energies ten million times lower than that of the knee, in the region of the quark hadron transition (≃109 eV). This opens the door to an unexpected standpoint for further clarifying the phenomenon.