Constraints on the Electron Injection Spectrum from Di use Gamma - Ray Observations

We perform a propagation calculation for cosmic ray electrons and positrons using a three-dimensional di usion model, and use the resulting interstellar total electron spectrum to obtain the galactic di use photon spectrum due to inverse Compton, synchrotron and bremsstrahlung interactions consistently from radio to PeV energies. By considering the observed galactic non-thermal emission, we constrain the injection spectrum of electrons at acceleration. This contrasts with our earlier work (Porter & Protheroe 1997) which only utilised a simple one-dimensional model for the electron propagation, and did not consider constraints imposed by the observed non-thermal radio spectrum. We nd that, if the electron injection spectrum is very at, electrons with energies higher than 20 TeV cannot be accelerated in sources located within the disk of the Galaxy. We discuss our results in terms of recent models for shock acceleration in shell-type supernova remnants.