Model for the origin and properties of the cosmic‐ray rigidity spectrum

Abstract

We propose a model to explain a number ooe oeeatures of the differential rigidity spectra ooe the nuclear component ooe the primary cosmic radiation. A supernova explosion is assumed to result in the acceleration of nuclei to a pure power law rigidity spectrum and • composition relatively rich in heavy and medium weight nuclei. The supernova remnant into which these particles are injected is characterized as a large-scMe trapping region resulting from predominantly closed magnetic field lines that partially isolate the region from the surrounding galactic space. This oeeature of the supernova region is represented by a dipole-like field. We assume that, superimposed on this field, magnetic irregularities produce a certain amount of distortion of the field lines in the interior of the source, and that irregularities along the periphery of the source lead to local distortions of the field and, hence, a mixing of galactic and source field lines in the neighborhood of these irregularities.The observed large-scale regularit•; of the magnetic field in the Crab leads us to treat the particle motion within the source region in the guiding center approximation (except at very high rigidities), so that these particles are capable ooe guiding outward to the source boundary and returning inward to the interior along the source's predominantly closed magnetic lines ooe force. The well defined inward field gradient and field curvature, however, cause the particles to drift longitudinally as they spiral along the periphery of the source region, and accordingly they have a certain probability ooe drifting into a neighborhood of field mixing and onto a galactic field line which guides them out of the source region.During their confinement within the source region, the particles necessarily undergo nuclear interactions and ionization loss, and, therefore, the differential rigidity spectrum of particles escaping from the source boundary into the galaxy is jointly determined by their injection spectrum, their escape probability, and the extent to which they suffer loss processes. A continuity equation combining these various processes is constructed and then averaged over the entirety of active sources in the galaxy. The solutions of the averaged continuity equation for each charge group then give us the differential rigidity spectra with which the cosmic radiation is injected into the galactic medium.The additional effects of intragalactic motion on the cosmic-ray spectrum are treated in the approximation that the particles escaping from source regions undergo magnetic diffusion in the galactic volume with a rigidity independent scattering mean oeree path. The differential rigidity spectra of the various charge groups incident on the solar system are thereby obtained. The effects of solar modulation on the galactic cosmic-ray spectrum are treated in accordance with the solar wind theory. The resulting differential rigidity spectra are derived and compared with data taken near solar minimum, and it is found that the calculated spect...

Particles and fields: Significant achievements

“…Galactic cosmic rays have been studied for several decades, but we are only now beginning to obtain the detailed data that should eventually permit a quantitative understanding of cosmic-ray sources and of modifications of their atomic composition and energy spectra during their propagation through space. A treatmen• of the over-all problem, with the objective of explaining the observed rigidity spectra, was prepared by Kaplon and Skadron [1966]. In arriving at the observed spectra, however, a number of assumptions had to be made that may not be correct in every detail.…”

Propagation of cosmic rays in the galaxy

“…result from acceleration and storage by the magnetic fields in the source region (Kaplon and Skadron, 1966); (ii) the shockwave acceleration in supernovae can lead to a power law in kinetic energy per nucleon (Colgate, 1968);and (iii) the Fermi-type of acceleration (Fermi, 1949) can lead to a power law in total energy per nucleon. We shall now attempt to bring out the merits and demerits of these three source spectra as we analyze the observed spectra of nuclei.…”