  There is growing evidence from gamma-ray observations at high and very high
energies that particle escape is a key aspect shaping the morphological
properties of pulsar wind nebulae (PWNe) at various evolutionary stages. We aim
to provide a simple model for the gamma-ray emission from these objects
including the transport of particles across the different components of the
system. We applied it to sources HESS J1809-193 and HESS J1825-137. We
developed a multi-zone framework applicable to dynamically young PWNe, taking
into account the diffusive escape of relativistic electron-positron pairs out
of the nebula into the parent supernova remnant (SNR) and their confinement
downstream of the magnetic barrier of the forward shock until an eventual
release into the surrounding interstellar medium (ISM). For a wide range of
turbulence properties in the nebula, the GeV-TeV inverse-Compton radiation from
pairs that escaped into the remnant can be a significant if not dominant
contribution to the emission from the system. It may dominate the pion-decay
radiation from cosmic rays accelerated at the forward shock and advected
downstream of it. In the TeV-PeV range, the contribution from particles escaped
into the ISM can exceed by far that of the SNR+PWN components. Applied to HESS
J1809-193 and HESS J1825-137, we found that spatially extended GeV-TeV emission
components can be accounted for mostly from particles escaped into the ISM,
while morphologically more compact components above 50-100TeV are ascribed to
the PWNe. In these two cases, the model suggests high turbulence in the nebula
and a forward shock accelerating cosmic rays up to ~100TeV at most. The model
provides the temporal and spectral properties of the flux of particles
originally energized by the pulsar wind and ultimately released in the ISM.
(Abridged).
