  On March 2010, the symbiotic binary V407 Cyg erupted as a result of a nova
explosion. The event gave rise to a two-week long burst of >100MeV gamma-rays
detected by Fermi/LAT, a unique observation testifying to particle acceleration
in the system. The outburst can be considered a scaled-down supernova, with
short dynamical time scale, and thus can constitute a test case for theories of
the origin of galactic cosmic rays. We aim at determining the properties of the
accelerated particles and identifying the origin of the high-energy radiation.
We developed a model for diffusive shock acceleration and non-thermal emission
in V407 Cyg, complemented by an evaluation of the thermal emission from the
shocked plasma. We considered both leptonic and hadronic contributions to the
non-thermal processes, and investigated the effect of many binary and nova
parameters. The gamma-ray emission is mostly of leptonic origin and arises
predominantly from inverse-Compton scattering of the nova light. Upscattering
of the red giant photons is a minor contribution. Matching the light curve
requires gas accumulation in the vicinity of the white dwarf, as a consequence
of wind accretion, while the spectrum imposes particle scattering close to the
Bohm limit in the upstream equipartition magnetic field. The nova accelerated
protons (respectively electrons) with energies up to ~300GeV (respectively
~20GeV), for a total non-thermal energy 10^43 erg after two weeks, representing
~10% of the initial nova kinetic energy. The electron-to-proton ratio at
injection is 6%. The V407 Cyg eruption can be understood from the same
principles that are invoked for particle acceleration in supernova remnants,
although without the need for strong magnetic field amplification. The
population of novae in symbiotic systems is a negligible source of Galactic
cosmic rays, and most likely not a class of TeV-emitters.
