Cosmic Rays, III. The CR spectrum between 1 GeV and 10^4 GeV and the radio emission from supernova remnants

TL;DR

This paper develops a comprehensive theory for the cosmic ray spectrum between 1 GeV and 10^4 GeV, incorporating shock acceleration, diffusion, and magnetic field effects, to explain observed spectral features and composition.

Contribution

It introduces a detailed model of cosmic ray acceleration and propagation that accounts for spectral shape and elemental energy limits, extending previous work in the series.

Findings

Cosmic ray spectrum follows an E^-2.75 power law due to galactic leakage.

Higher Z elements are predicted to reach higher maximum energies.

The ratio of electrons to protons is influenced by expansion and cooling processes.

Abstract

We develop a theory to account for the cosmic ray spectrum between 1 GeV and 10^4 GeV following the earlier papers of this series. We use the basic concept that the cosmic ray particles are accelerated in a supernova shock that travels through the interstellar medium. Physically important ingredients besides the presence of a strong shock are diffusion, drifts, convection, adiabatic cooling, the injection history, and the topology of the magnetic field, here assumed for simplicity to be homogeneous in the interstellar medium. The result is a spectrum, which for strong shocks in a gas with adiabatic index 5/3 yields a spectrum of E^-2.42. Interstellar turbulence with a Kolmogorov spectrum then leads by leakage from the galactic disk to a spectrum which is E^-2.75, as observed. We argue that the ratio of cosmic ray electrons to protons is determined by the amount of expansion which takes place from the cessation of electron injection to the break-up of the shell by cooling instabilities. Since the highest particle energy reached derives from geometrical arguments, it depends on the charge of the nucleus and so higher Z elements are predicted to reach higher energies.