Loaded layer-cake model for cosmic ray interaction around exploding super-giant stars making black holes

The experiment AMS on the International Space-Station has produced accurate cosmic ray spectra for many chemical elements, both primaries like He, C, O, Fe, other cosmic ray (CR) primaries like Ne, Mg, and Si, secondaries like Li, Be, B, and of mixed provenance, like N, Na, and Al. The AMS spectra demonstrate that interaction is seriously diminishing fluxes up to a rigidity of about 100 GV, and so the existing models for CR interaction have to be re-examined. Based on earlier well-established ideas a model is proposed here that focusses on the cosmic ray interaction first in the wind shock shell of super giant stars, when the supernova driven shock races through, and second in the OB-Superbubble surrounding the SN: These stars include both red super-giant stars and blue super-giant stars; both produce black holes in their explosion, and drive winds and jets with electric currents. Variability of these winds or jets gives rise to temporary electric fields, as has recently been demonstrated, and discharge (so lightning) acceleration gives steep spectra, with synchrotron losses to $p^{-5}$ in momentum $p$; these spectra are typically observed in both Galactic and some extragalactic radio filaments. Analogous hadron spectra $p^{-4}$ excite a flat spectrum of magnetic irregularities in the bubble zone, which in turn yields a steep dependence of residence time versus energy, with power $-5/3$. This spectrum is indicated by the AMS data and appears to be required to explain the CR spectra below 100 GV. The emphasis in this paper is to work out the interaction of the freshly accelerated cosmic ray particles. In the model presented here the interaction is derived as a function of time, and then integrated, or developed to long times. The model gives a rigidity dependence of the secondary/primary ratio of slope $-1/3$ as well as the strong reduction of the primary fluxes below a rigidity of about 100 GV, relative to a power-law injection spectrum, with slope $+2$. The two key aspects based on blue super-giant stars and a magnetic irregularity spectrum in the bubble zone given by lightning are (i) a much larger column of interaction, allowed because of heavy element enrichment of the interaction zone, and (ii) even He, C, and O may have a small secondary contribution, as the difference to the Fe spectrum suggests; this small secondary component is visible in the ${}^3$He/${}^4$He ratio. The model may also explain the spectrum of CR anti-protons, the gamma-ray spectra of the Galaxy and the high energy neutrino spectrum of our Galaxy, including also red super-giant stars as sources. ISM-SNe, i.e. SN Ia and neutron-star SNe, contribute to CR protons and CR He nuclei.