Cosmic ray diffusion at energies of 1 MeV to 105 GeV

A supernova remnant accelerates cosmic rays to energies somewhat above 10⁵ 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.

In the light of our inhomogeneous cosmic ray acceleration/propagation model we re-examine our earlier work on the evidence for second order acceleration in a very old remnant. Such evidence is provided by the molecular compositions along several lines of sight to the Perseus OB2 association. We find as a third significant result that the model value of the diffusion coefficient at energies in the range of 1 MeV agrees within about an order of magnitude with that which we infer from the molecular data.