On the surface brightness radial profile of the extended γ-ray sources

The morphology of the extended $\gamma$-ray source is governed by propagation process parent relativistic particles. In this paper, we investigate surface brightness radial profile sources illuminated cosmic ray protons and electrons, considering radiation mechanisms, projection effects, response instruments. We found that particle species can cause considerable differences in observed profiles. Thus, be used as a unique tool to identify mechanism addition, also discuss possible implications regarding latest discoveries from very/ultra-high energy instruments like LHAASO HAWC.