Solar Modulation of Galactic Cosmic Rays
Abstract
Beginning with the equations of the convectiondiffusion model including energy losses, it is shown that the streaming of galactic cosmic rays in the solarwind cavity can be neglected above a few hundred MeV per nucleon. For the case in which the diffusion coefficient is separable into radially and rigidity dependent parts, an integral is derived which relates the intensity at points within the cavity to that at infinity through an energyloss parameter. This parameter is a function of energy; it is defined in terms of observable quantities and is identified, tentatively, as the mean energy lost by the cosmicray particles in moving into the interplanetary region. The integral is formally equivalent to that obtained by using Liouvilie's theorem. Experimental data for the modulation of protons and helium ions in 19631965 and electrons and protons in 19651966 are shown to behave as predicted, down to kinetic energies of a few hundred MeV per nucleon. The diffusion coefficient was proportional to the magnitude of the charge of the cosmicray species during these periods, and the analytical results are formally equivalent to those obtained for a heliocentric force field proportional to the magnitude of the charge of the cosmicray species. Making use of the observed lower limits of validity, it is shown that the efolding distance for the diffusion coefficient lies between 0.8 and 1.6 a.u., thus setting limits on the radial dependence of the scattering process. Estimates are given of the changes in energy loss in the periods 19631965 and 1965 1966 and of the energy loss at solar minimum
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1968
 DOI:
 10.1086/149822
 Bibcode:
 1968ApJ...154.1011G