A stochastic approach to Galactic proton propagation: Influence of the spiral arm structure

•SDE code for multidimensional Fokker–Planck-type equations.•Applied to Galactic propagation of energetic protons.•Diffusion coefficient reflects spiral arm structure.•New diffusion coefficient leads to non-negligible effects on the spectrum.•And to enhance flux ratios between inarm and interarm regions.

A newly developed numerical code solving Fokker–Planck type transport equations in currently four dimensions (space plus momentum or energy) and time by means of stochastic differential equations (SDEs) is applied to the Galactic propagation of Cosmic Ray protons, where the paths of pseudo particles originating in spiral arms and in the interarm region are traced back to a distribution of point sources. The transport equation in this first, simplified approach includes scalar spatial diffusion and catastrophic energy losses. In a first step we validate the code by obtaining results being consistent with previous ones obtained with finite-difference methods, revealing lower spectra with less variations in the interarm region compared to the inarm region. While Effenberger et al. (2012) used this approach to study the effects of a fully anisotropic diffusion tensor, we concentrate here on a diffusion coefficient taking into account the spiral arm structure. Such a variable diffusion coefficient is of importance e.g. for the long-scale time-variation of the Cosmic Ray flux at Earth related to spiral arm crossings. For our choice of parameters, we find that a diffusion coefficient reflecting the spiral arm structure leads to a clearly enhanced flux ratio between the inarm and interarm regions. The strength of this effect depends, however, on the parameters chosen.