The Rigidity Dependence of the Diffusion Coefficient in the Heliosheath and an Explanation of the Extreme Solar Modulation Effects for Cosmic Ray Electrons from 3-60 MeV Observed at Voyager 1

TL;DR

This paper analyzes Voyager 1 data to understand how the diffusion coefficient's rigidity dependence explains extreme solar modulation effects on cosmic ray electrons and protons in the heliosheath.

Contribution

It introduces a two-regime model of the diffusion coefficient's rigidity dependence, explaining observed solar modulation effects for electrons and protons.

Findings

Diffusion coefficient depends on rigidity with two distinct regimes.

Electron modulation is independent of rigidity below a certain rigidity.

Proton modulation varies linearly with the modulation potential.

Abstract

We believe that the extreme solar modulation of 3-60 MeV Galactic electrons measured by Voyager in the heliosheath and the interpretation of this new data in terms of the rigidity dependence of the diffusion coefficient at low rigidities presented in this paper represents a major step in understanding diffusion theory as it applies to energetic particles. This description uses electron spectra measured at 5 different epochs and distances within the heliosheath. The diffusion dependence needed to explain the remarkable solar modulation effects observed for both electrons and higher rigidity protons as one progresses from the heliopause inward by ~25 AU to the termination shock really has two distinct rigidity regimes. Above a rigidity ~Pc the diffusion coefficient has a dependence ~beta P, the modulation is ~P and its magnitude increases linearly with radius in AU according to the integral of dr/K. This integral defines a potential, beta, called the modulation potential, thus explaining the proton variations. At rigidities <Pc, the diffusion coefficient is ~beta and independent of rigidity. The modulation is also independent of rigidity but its magnitude depends on the modulation potential, thus explaining the electron modulation. One needs both electron and proton observations, together, to recognize the physical description of the solar modulation process. For the first time we have been able, using proton data at high rigidities and electron data at low rigidities, to put together a picture of the high and low rigidity diffusion coefficients and how they affect energetic particles in an astrophysical scale environment.