A statistical theory of cosmic ray propagation from discrete galactic sources

Abstract

Assuming that the sources of primary cosmic radiation are discrete and distributed at random but according to a given probability distribution throughout the Galaxy, statistical quantities of interest (e.g., means, variances, and two-point correlations) are calculated analytically for the density, flux (anistropy), and age distribution of both secondaries and primaries in terms of a Green's function describing galactic propagation from a monoenergetic discrete source. Also presented is the probability distribution for the density of primary cosmic rays at a given position when the spacetime source volume and number of sources increase without limit. For illustrative purposes, detailed results are presented for one species of primary and secondary nuclei within a version of the standard ''leaky box'' propagation model assuming supernova sources. The importance of the theory lies in its unification of all models of galactic cosmic ray propagation involving discrete sources within a single framework.