A Possible Approach to Three‐Dimensional Cosmic‐Ray Propagation in the Galaxy. I. Stable Nuclei without Energy Change

Abstract

We present an analytical solution of the three-dimensional cosmic-ray propagation in our Galaxy, adopting a more realistic structure of the Galaxy than conventional propagation studies. We assume that there is no boundary in both longitudinal distance r from the disk center and the latitudinal distance z from the Galactic plane and that the three critical parameters, the diffusion coefficient D, the gas density n, and the cosmic-ray source density Q, depend on r in the form of D(r) = D0 exp[r/rD + |z|/zD], n(r) = n0 exp[-(r/rn + |z|/zn)], and Q(r) = Q0 exp[-(r/rQ + |z|/zQ)], respectively. We derive analytically the path length distribution P(x) and its mean value , based on the present solution of the cosmic-ray density. Both simple exponential-type and the truncated-type distributions are reproduced by assuming three adequate scale heights, zD, zn, and zQ. Anisotropy amplitudes are also given on the basis of the present model and found to be compatible with the experimental data if we assume adequate scale heights, as well as the diffusion coefficient D0 at the Galactic center. We present empirical formulae for the fragmentation cross sections, reproducing well the accelerator data, with which we perform numerical calculations for several observables. We compare our numerical results with recent experimental data on the stable nuclei, particularly on the energy spectrum of primary components such as protons, helium nuclei, etc., and on the secondary-to-primary ratios such as B/C and sub-Fe/Fe. We find a good agreement between our calculations and experimental data by assuming an adequate set of the scale heights and the ratio of the diffusion coefficient to the gas density at the Galactic center, D0/n0, while we need additional data other than the stable nuclei in order to obtain unique numerical values for the parameters we have introduced.