A Phenomenological Approach to the Solar Modulation of Cosmic Rays

Abstract

The interstellar electron spectrum is derived from the Galactic non thermal radio volume emissivity. Comparison with the electron spectrum observed near the Earth yields the magnitude of the modulation K(R, rE, 1968) at the Earth in 1968. We apply K(R, r5, 1968) to the proton and a-particle spectra observed in 1968 using the simple diffusion-convection theory. The use of this theory at R > 0.5 GV is justified by the characteristics of the simultaneous intensity variations of electrons, protons, and aparticles. The demodulated proton and a-particle spectra are compared with interstellar equilibrium spectra calculated for injection spectra, following power laws in kinetic energy T, total energy I , or rigidity R. The fit between the demodulated spectra and the equilibrium spectra from the rigidity power4aw injection spectra is good for protons as well as a-particles with a kinetic energy above 100 MeV per nucleon. The fit is equally good if we assume source spectra for protons and -partides similar to the derived electron spectrum, taking the rigidity as the appropriate parameter. The deviations occurring below a kinetic energy of 100 MeV per nucleon are attributed either to local components present in the observations near the Earth or to energy4oss processes complicating the modulation at these energies. The rigidity dependence of K(R, rE, 1968) below 2 GV differs significantly from the rigidity depen dence of the variations of the cosmic rays at the Earth. Hence the cosmic-ray diffusion coefficient D cannot be a separable function of R and heliocentric distance r instead, we propose a new model for D(R, r), which is based on a decrease of the magnetic bending power in the average magnetic irregularity present in the solar wind with increasing r. An observational justification of this basis is discussed in some detail. This new model implies that (1) the time variations of the cosmic rays near the Earth arise mainly from changes in the conditions in local interplanetary space; (2) the rigidity dependence of the time variations reflects the rigidity dependence of the local scattering mean free path x5, which has a transition rigidity R0 below which XE is independent of R and above which XE R; (3) R0 is a decreasing function of r. With this model a satisfactory match of the rigidity dependences of K(R, r5, 1968) and the time variations is obtained. The specific r-dependence of R0 and X, which reconciles the observed rigidity dependences suggests that X for R <Ro(r) is not only independent of R but also independent of r. The numerical values of the various parameters required in this model are in good agreement with the current estimates.