Effect of the diffusion parameters on the observed gamma-ray spectrum of sources and their contribution to the local all-electron spectrum: the EDGE code

Abstract

The positron excess measured by PAMELA and AMS can only be explained if there is one or several sources injecting them. Moreover, at the highest energies, it requires the presence of nearby ($\sim$hundreds of parsecs) and middle age (maximum of $\sim$hundreds of kyr) sources. Pulsars, as factories of electrons and positrons, are one of the proposed candidates to explain the origin of this excess. To calculate the contribution of these sources to the electron and positron flux at the Earth, we developed EDGE (Electron Diffusion and Gamma rays to the Earth), a code to treat the propagation of electrons and compute their diffusion from a central source with a flexible injection spectrum. Using this code, we can derive the source's gamma-ray spectrum, spatial extension, the all-electron density in space, the electron and positron flux reaching the Earth and the positron fraction measured at the Earth. We present in this paper the foundations of the code and study how different parameters affect the gamma-ray spectrum of a source and the electron flux measured at the Earth. We also studied the effect of several approximations usually performed in these studies.