The differential cosmic ray energy flux in the light of an ultrarelativistic generalized Lorentzian thermodynamics

Abstract

We apply the ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution to the energy spectrum of galactic cosmic ray fluxes. The inferred power law slopes contain a component which evolves with cosmic ray energy in steps of thirds, resembling the sequence of structure functions in fully developed Kolmogorov turbulence. Within the generalized thermodynamics the chemical potential can be estimated from the deviation of the fluxes at decreasing energy. Both may throw some light on the cosmic ray acceleration mechanism to very high energies.

Olbert’s Kappa Fermi and Bose Distributions

“…It has been demonstrated elsewhere [cf., e.g., 23,25,26,31,35] that T remains the real physical temperature in the classical case, a conclusion which is not violated in the quantum domain as its physical meaning is not changed by the transition from classical to quantum physics. For ideal nonrelativistic and relativistic gases, one in addition has s 5/2 and s 4 [12,35], respectively.…”

“…The kappa distribution occurred almost permanently when dealing with particle distributions in high-temperature plasmas encountered in space [4][5][6][7][8][9][10]. It was also inferred from cosmic ray [11] spectra [12], extended into the relativistic domain, in the solar wind [13][14][15][16][17], near shocks [18][19][20], and in the heliosphere in general [21]. Various applications to statistical probabilities in correlated systems have been reviewed as well [see Refs.…”

Lorentzian Entropies and Olbert's κ - Distribution

“…The independence of the exponential cut-off on temperature and β guaranties that, in all derivatives or integrals with respect to β, it appears as an energy dependent factor. An example has been given [15] by application to the Cosmic Ray energy spectrum, where the cut-off is, for quantum physical reasons, found in the GZ-energy spectral limit. Its inclusion, if necessary, does not cause any principal problems.…”

Olbertian Partition Function in Scalar Field Theory

“…Particle spectra in near-Earth space (e.g., see [1][2][3]) as well as in cosmic rays very frequently exhibit power law tails at high energies which since their introduction by [4] have been interpreted as Olbert distributions (κ-distributions). 1, Cosmic ray spectra in particular extend as power laws over many decades reminding of several ultra-relativistic Olbert distributions adding up continuously [5]. Olbert distributions have been inferred in plasma turbulence and many other occasions as for instance in front [6] and behind [7] collisionless shocks [8] as also, for example, in the heliosphere and its heliosheath [9,10], which may serve as the paradigm of a stellar wind that is terminated by its interaction with the interstellar galactic medium.…”