2001) and the sub-sequent detections of SN1006

Abstract. In a recent paper Pohl and Esposito (1998) demonstrated that if the sources of cosmic-rays are discrete, as are Supernova Remnants (SNR), then the spectra of cosmic-ray electrons largely vary with location and time and the locally measured electron spectrum may not be representative of the electron spectra elsewhere in the Galaxy, which could be substantially harder than the local one. They have shown that the observed excess of γ-ray emission above 1 GeV can in fact be partially explained as a correspondingly hard inverse Compton component, provided the bulk of cosmic-ray electrons is produced in SNR. As part of a program to model the Galactic γ-ray foreground we have continued the earlier studies by investigating the impact of the star forming region Gould's Belt on the local electron spectrum. If the electron sources in Gould's Belt were continous, the local electron spectrum would be slightly hardened. If the electron sources are discrete, which is the more probable case, the variation in the local electron spectrum found by Pohl & Esposito persists. The local cosmic-ray electron spectrum The recent detections of non-thermal X-ray synchrotron radiation from the supernova remnants SN1006 The Galactic distribution and spectrum of cosmic-ray electrons are intimately linked to the distribution and nature of their sources. Supernovae and hence their remnants are tranCorrespondence to: M. Pohl (mkp@tp4.ruhr-uni-bochum.de) sient features, which happen stochastically in space and time. Therefore steady-state models of cosmic-ray electron propagation in the Galaxy may be inadequate and time-dependent transport calculation seem to be required. Because effects of the discreteness of sources show up only at higher particle energy, at which the electron energy loss time is short, we may describe the propagation of cosmicray electrons at energies higher than a few GeV by a simplified, time-dependent transport equation where we consider continous energy losses by synchrotron radiation and inverse Compton scattering, a diffusion coefficient D E a dependent on energy, and a source term Q. The Green's function for this problem can be found in the literature In case of discrete sources the injection term Q is a sum over all sources. For an individual source showing up at time t 0 and injecting for a time period τ we can write Without loss of generality we can set t = 0 and obtain wher