The Fermi LAT discovery that classical novae produce >100 MeV gamma-rays establishes that shocks and relativistic particle acceleration are key features of these events. These shocks are likely to be radiative due to the high densities of the nova ejecta at early times coincident with the gamma-ray emission. Thermal X-rays radiated behind the shock are absorbed by neutral gas and reprocessed into optical emission, similar to Type IIn (interacting) supernovae. Gamma-rays are produced by collisions between relativistic protons with the nova ejecta (hadronic scenario) or Inverse Compton/bremsstrahlung emission from relativistic electrons (leptonic scenario), where in both scenarios the efficiency for converting relativistic particle energy into LAT gamma-rays is at most a few tens of per cent. The ratio of gamma-ray and optical luminosities, L_gam/L_opt, thus sets a lower limit on the fraction of the shock power used to accelerate relativistic particles, e_nth. The measured values of L_gam/L_opt for two classical novae, V1324 Sco and V339 Del, constrains e_nth > 1e-2 and > 1e-3, respectively. Inverse Compton models for the gamma-ray emission are disfavored given the low electron acceleration efficiency, e_nth ~ 1e-4-1e-3, inferred from observations of Galactic cosmic rays and particle-in-cell (PIC) numerical simulations. A fraction > 100(0.01/e_nth) and > 10(0.01/e_nth) per cent of the optical luminosity is powered by shocks in V1324 Sco and V339 Del, respectively. Such high fractions challenge standard models that instead attribute all nova optical emission to the direct outwards transport of thermal energy released near the white dwarf surface.
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