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The path length distribution of Galactic cosmic rays (GCRs) is thefundamental ingredient for modeling the propagation process of GCRs based onthe so-called weighted slab method. We try to derive this distributionnumerically by taking into account the discreteness in both space and time ofoccurrences of supernova explosions where GCRs are suspected to be born. Wesolve numerically the stochastic differential equations equivalent to theParker diffusion-convection equation which describes the propagation process ofGCR in the Galaxy. We assume the three-dimensional diffusion is an isotropicone without any free escape boundaries. We ignore any energy change of GCRs andthe existence of the Galactic wind for simplicity. We also assume axisymmetricconfigurations for the density distributions of the interstellar matter and forthe surface density of supernovae. We have calculated age and path length ofGCR protons arriving at the solar system with this stochastic method. Theobtained age is not the escape time of GCRs from the Galaxy as usually assumed,but the time spent by GCRs during their journey to the solar system from thesupernova remnants where they were born. The derived age and path length show adistribution spread in a wide range even for GCR protons arriving at the solarsystem with the same energy. The distributions show a cut-off at a lower rangein age or path length depending on the energy of GCRs. These cut-offs clearlycome from the discreteness of occurrence of supernovae. The mean age of GeVparticles obtained from the distributions is consistent with the age obtainedby direct observation of radioactive secondary nuclei. The energy dependence ofthe B/C ratio estimated with the path length distribution reproduces reliablythe energy dependence of B/C obtained by recent observations in space.

astronomy and astrophysics

A stochastic simulation of the propagation of Galactic cosmic rays  reflecting the discreteness of cosmic ray sources. Age and path length  distribution