Cosmic rays IX. Interactions and transport of cosmic rays in the Galaxy

We propose that cosmic rays interact mostly near their sources of origin. To be specific, we differentiate the various supernovae by their mass of the progenitor star along the zero age main sequence. Stars between about 8 and 15 solar masses explode into the interstellar medium, and accelerate cosmic rays, as discussed by many for some time. From about 15 to 25 solar masses stars explode into their own stellar wind; this wind has built up a thin shell of both wind material and interstellar medium material in the red and blue giant phases preceding the supernova event. The shock accelerating cosmic ray particles races through that wind, gets loaded up with energetic particles, interacts while it goes, and finally smashes into the shell. While the shock goes out, it snowplows the entire wind into the pre-existing shell to form a composite shell. We propose that for the mass range 15 to 25 solar masses this composite shell is immediately broken up so that the time scale for interaction is caused by the breakup and so is convective. We note that the wind material for this range of zero age masses is a approximately half helium, and half hydrogen. The interactions in the composite wind-shell and the immediate environment produce positrons, gamma emission, but only few secondary nuclei, because for this mass range the enrichment in heavier elements is still minor. The energy spectrum of the gamma emission and the positrons produced corresponds then to the source spectrum. In contrast, from about 25 solar masses and up the wind is strongly enriched in heavy elements, and the wind shell is massive, comprising most of the initial zero age star's mass, as well as a good part of the local interstellar medium. We propose that for the interaction of the cosmic ray particles carried out by the shock in the snow-plow through the wind to the shell the interaction is diffusive, and calculate the diffusion coefficient. This leads to a leakage time energy dependence of E^-5/9 in the relativistic limit. This then gives an energy dependence of secondary nuclei, that matches the observations. There is a second component of positrons, and also gamma emission, but then at moderate energies all with the steeper energy dependence; spatial and velocity constraints give both a lower as well as an upper rigidity limit to the diffusion approximation. One important element in such a picture is the steady mixing of newly enriched material throughout the star before the explosion, induced by Voigt-Eddington circulation caused by rotation. The mixed material is then ejected through the wind, which at the end provides the source material for cosmic ray injection. This means that by the time the nuclei are subject to acceleration, they should have decayed already to final states, an effect which may be measureable in cosmic ray isotope ratios. Therefore, considering the history of the travel of cosmic rays through the normal interstellar medium, we can readily explain the ratio of secondaries to primaries, and at the same time use a spectrum of turbulence in the interstellar medium, a Kolmogorov spectrum, which is consistent with all other observational evidence. The escape time from the Galaxy is then proportional to E^-1/3 in the relativistic range of particle energies. Translating this result into the language common in the literature, this means that interaction path as measured in gm/cm² and escape time can not be used synonymously.