Comprehensive modulation potential for the solar modulation of Galactic cosmic rays

Abstract

The concept of the modulation potential being utilized to describe the solar modulation of galactic cosmic rays is calculated based on the full three-dimensional Parker transport equation. This is in sharp contrast to the force-field approach, which is based on a series of approximations of this equation and where traditionally all the physical processes are condensed into a single parameter without knowing their relative contribution. In our comprehensive approach to the modulation potential, the contribution of all the different physical processes is given explicitly as derived directly from the parameters of Parker's transport equation. We use the stochastic differential equations approach to study the effects of each of these different physical modulation processes thoroughly and then also determine the rigidity and mass-to-charge-ratio ($A/Z$) of these processes for the first time in the context of a modulation potential. It is found that: (1) This comprehensive modulation potential for galactic cosmic particles with a given rigidity at the Earth is a random variable, which can be fit by an inverse Gaussian distribution; (2) the rigidity and $A/Z$ dependence of this modulation potential can be divided into three categories based on the index value of power law diffusion; (3) the modulation caused by convection becomes weaker with increased rigidity and eventually dissipates, leading to a larger modulation potential for particles with a larger $A/Z$; (4) particle drift significantly reduces this modulation potential and its variation with changes in the tilt angle of the heliospheric current sheet has a distinct pattern for each of the two solar magnetic field polarities.