Cosmic ray diffusion at energies of 1 MeV to 105 GeV

Abstract

A supernova remnant accelerates cosmic rays to energies somewhat above 106 GeV by the time that the free expansion phase of its evolution has come to an end. As the remnant’s outer shock slows, these highest energy cosmic rays diffuse away from the shock along a magnetic flux tube with a radius comparable to that of the remnant at the end of its free expansion phase and which eventually (over a distance of the order of a kiloparsec) bends into the Galactic halo. A similarity solution exists for the temporal and spatial variations, in such a tube, of both the number density for these ∼ 105 GeV cosmic rays and the energy density of the waves on which they resonantly scatter. Wave-wave interactions probably do not dominate the evolution of the energy density of these lowest frequency waves, but we assume that they do establish a Kraichnan wave spectrum at higher wavenumber. Although we cannot rigorously justify this assumption, it does receive some support from the analysis of pulsar signals. There is a large body of observations to which such a model can be applied, yielding constraints that must be met. With the model that we develop here we obtain the following results: 1 The local intensity of ∼ 105 GeV cosmic rays implies that the flux tube which currently surrounds the Solar System last contained a remnant in the free expansion phase several times 107 years ago. We comment on the rough agreement between this age and that inferred from Be10 data. 2 The theoretical value of the cosmic ray diffusion coefficient at ∼ 1 GeV in the tube corresponding to that time is in harmony with the value of the diffusion coefficient inferred from cosmic ray composition and synchrotron measurements.