Radio, X-ray and γ-ray surface brightness profiles as powerful diagnostic tools for non-thermal SNR shells

Distributions of non-thermal surface brightness of supernova remnants (SNRs) contain important information about the properties of magnetic field and acceleration of charged particles. In the present paper, the synchrotron radio, X-ray, and inverse-Compton (IC) gamma-ray maps of adiabatic SNRs in uniform interstellar medium and interstellar magnetic field are modelled and their morphology is analysed, with particular emphasis on comparison of azimuthal and radial variations of brightness in radio, X-rays and gamma-rays. Approximate analytical formulae for the azimuthal and radial profiles of the synchrotron radio and X-ray as well as the IC gamma-ray brightness are derived. They reveal the main factors which influence the pattern of the surface brightness distribution due to leptonic emission processes in shells of SNRs and can account for some non-linear effects of acceleration if necessary. These approximations provide observers and theorists with a set of simple diagnostic tools for quick analysis of the non-thermal maps of SNRs.