Determination of the Total Solar Modulation Factors in the Heliosphere For Cosmic Ray Protons and Electrons by Comparing Interstellar Spectra Deduced from Voyager Measurements and PAMELA Spectra of These Particles at the Earth

TL;DR

This study derives interstellar spectra of cosmic ray protons and electrons using Voyager and PAMELA data, then quantifies the solar modulation effects at various energies, finding similar modulation factors for both particles.

Contribution

It provides a novel comparison of interstellar and Earth-measured cosmic ray spectra to determine total solar modulation factors for protons and electrons.

Findings

Total modulation factors range from ~400 at 0.1 GV to ~3.3 at 1 GV.

Protons and electrons experience nearly identical modulation at the same rigidity.

A simple force field model can approximate the modulation for protons, while electrons require more detailed parameters.

Abstract

We have determined the interstellar spectra of cosmic ray protons and electrons from a few MeV to ~10 GeV. These interstellar spectra are based on Voyager data and a normalization of specific galactic propagation model calculations of both protons and electrons to PAMELA data at the Earth at 10 GeV, where the solar modulation is small. These resulting interstellar spectra are then compared with spectra of protons and electrons measured at lower energies at the Earth by PAMELA in 2009. The total amount of modulation at lower rigidities (energies) is found to be nearly the same at the same rigidity for both protons and electrons and ranges in magnitude from a factor ~400 at 0.1 GV for electrons, to a factor ~15 at 0.44 GV (100 MeV for protons), to a factor ~3.3 at 1 GV for both components. The magnitude of this total modulation of both components are the same to within + 10% from ~0.3 to ~3 GV in rigidity. The observed total modulation for protons can be matched quite closely using a simple spherically symmetric modulation picture involving a force field model for the modulation and a constant energy loss at all energies. The electrons require a set of parameters to calculate more detailed features of the modulation using the diffusion coefficient and its variation with rigidity and radius at rigidities less than few GV.