  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 SNR's
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 SNR's evolution. The radio
flux is increasing throughout the SNR's lifetime and changes from a shell-like
to a more center-filled morphology later on.
