Concerning the Nature of the Cosmic Ray Power Law Exponents

TL;DR

This paper explores the theoretical origins of cosmic ray energy distribution exponents using thermodynamic models and quantum field theory, explaining their close match with experimental data through asymptotic freedom and parton structures.

Contribution

It introduces a thermodynamic quantum field theoretical approach employing gamma and zeta function regulation to explain cosmic ray power law exponents.

Findings

Theoretical exponents match experimental values with high accuracy.

Asymptotic freedom explains the spectral tail behavior.

Quantum chromodynamics models are applicable to cosmic ray sources.

Abstract

We have recently shown that the cosmic ray energy distributions as detected on earthbound, low flying balloon or high flying satellite detectors can be computed by employing the heats of evaporation of high energy particles from astrophysical sources. In this manner, the experimentally well known power law exponents of the cosmic ray energy distribution have been theoretically computed as 2.701178 for the case of ideal Bose statistics, 3.000000 for the case of ideal Boltzmann statistics and 3.151374 for the case of ideal Fermi statistics. By "ideal" we mean virtually zero mass (i.e. ultra-relativistic) and noninteracting. These results are in excellent agreement with the experimental indices of 2.7 with a shift to 3.1 at the high energy ~ PeV "knee" in the energy distribution. Our purpose here is to discuss the nature of cosmic ray power law exponents obtained by employing conventional thermal quantum field theoretical models such as quantum chromodynamics to the cosmic ray sources in a thermodynamic scheme wherein gamma and zeta function regulation is employed. The key reason for the surprising accuracy of the ideal boson and ideal fermion cases resides in the asymptotic freedom or equivalently the Feynman "parton" structure of the ultra-high energy tails of spectral functions.