Radio-emitting electrons and cosmic ray confinement

Abstract

The propagation of cosmic ray electrons in the framework of the Disk-Halo diffusion model in which the diffusion coefficientD ∝ z ^δ E ^μ (where z is the distance from the galactic plane and E is the energy), and the magnetic field H∝z ^{- ξ} has been examined by making use of the recently available radio data up to 8 GHz toward the anticenter (A) and halo minimum (M). The following inferences are then made. From the difference in the frequency at which steepening occurs in the radio spectra toward A and H, it is found that the observations are consistent with the magnetic field decreasing with z such that ξ=0.24-0.37. An electron injection spectrum with a single power law down to energies well below 1 GeV cannot explain satisfactorily the observed radio spectra. All observations, however, can be understood in a self consistent way if the observed steepening of the radio spectra, and hence the interstellar electron spectrum, is due partly to the deviation in the power law electron injection spectrum below a few GeV and partly to the first break arising from electron energy losses occurring in the same energy region. In this case, using the value of ξ obtained above and a value of μ=0.3-0.6, it is found that the spectral index γ ₀ of the injected electrons above a few GeV has a value between 1.9 and 2.3 and the index δ a value between 0.5 and 1. Further, if the electrons and protons have the same spectral shape at injection, then γ ₀=2.1-2.3.