At what Rigidity does the Solar Modulation of Galactic Cosmic Rays begin?

TL;DR

This paper investigates the onset of solar modulation of galactic cosmic rays across a range of rigidities using a stochastic differential equations model, providing insights into how modulation varies from high to low energies.

Contribution

It introduces a stochastic differential equations approach that does not require predefined boundary conditions to determine the level of cosmic ray modulation across rigidities.

Findings

Modulation begins at lower rigidities than previously assumed.

The percentage modulation varies significantly across the energy spectrum.

The model accurately captures the modulation trend from 100 MeV to 250 GeV.

Abstract

Observationally, it is difficult to establish at what rigidity the modulation of galactic cosmic rays (CRs) actually begins in the heliosphere. It should be possible to do if the relevant local interstellar CR spectra were known and reliable measurements were made between 10 GV and about 200 GV, inside and outside the heliosphere. Numerical models for solar modulation studies are based on simply assuming that CR modulation begins at a given spatial boundary and at rigidities between 30 to 50 GV, usually handled as an initial condition. The Stochastic Differential Equations approach to numerical modelling presents the opportunity to determine the level of modulation from high to low rigidities because an initial condition at a prescribed high rigidity is not required. We present the results of such an approach and show the percentage modulation of CR protons as a function of kinetic energy between 100 MeV and 250 GeV.