The Myriad‐Source Model of Cosmic Rays. I. Steady State Age and Path Length Distributions

Abstract

We have developed a source model for calculating the age and path length distributions of cosmic rays reaching the solar system as the summation of the diffusive contributions of a myriad of spatially and temporally discrete sources. This new model enables us to consider the spatial distribution of Galactic OB associations and their subsequent supernovae, which appear to be the major shock energy for cosmic-ray acceleration, together with the Galactic spatial distribution of the multiphase interstellar medium. With this model we can explicitly study the local cosmic-ray path length distributions, essential to understanding the recent Advanced Composition Explorer (ACE) measurements. In this paper we apply the myriad-source model only to the spatially and temporally averaged source distribution in order to compare the resulting cosmic-ray age and path length distributions with those determined in the and standard steady state models. These average source calculations also provide a basis for comparison of the effects of the spatial and temporal clustering of Galactic supernovae on the local cosmic rays, which we explore in our next paper. Here we also use these average age and path length distributions to calculate the secondary- to primary-abundance ratios of key stable and radioactive nuclei in the local cosmic rays. Comparisons of these calculated ratios with recent ACE and other measurements enable us to greatly constrain the range of viable diffusion mean free paths and effective escape boundaries. We find that the resulting cosmic-ray path length distributions calculated with this model are very different from the simple exponential distributions of the common leaky box model.