Supernova remnants (SNRs) are known to accelerate particles to relativistic energies, on account of their nonthermal emission. The observational progress from radio to gamma-ray observations reveals more and more morphological features that need to be accounted for when modeling the emission from those objects. We use our time-dependent acceleration code RATPaC to study the formation of extended gamma-ray halos around supernova remnants and the morphological implications that arise when the high-energetic particles start to escape from the SNRs. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma. Our simulations span 25,000 years, thus covering the free-expansion and the Sedov-Taylor phase of the SNRs evolution. We find a strong difference in the morphology of the gamma-ray emission from SNRs at later stages dependent on the emission process. At early times, both the inverse-Compton and the Pion-decay morphology are shell-like. However, as soon as the maximum-energy of the freshly accelerated particles starts to fall, the inverse-Compton morphology starts to become center-filled, whereas the Pion-decay morphology keeps its shell-like structure. Escaping high-energy electrons start to form an emission halo around the SNR at this time. There are good prospects for detecting this spectrally hard emission with the future Cerenkov Telescope Array, as there are for detecting variations in the gamma-ray spectral index across the interior of the SNR. Further, we find a constantly decreasing nonthermal X-ray flux that makes a detection of X-ray unlikely after the first few thousand years of the SNRs evolution. The radio flux is increasing throughout the SNRs lifetime and changes from a shell-like to a more center-filled morphology later on.
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