TeV Neutrinos and GeV Photons from Shock Breakout in Supernovae

We show that as a Type II supernova shock breaks out of its progenitor star, it becomes collisionless and may accelerate protons to energies >10 TeV. Inelastic nuclear collisions of these protons produce a ~1 hr long flash of TeV neutrinos and 10 GeV photons, about 10 hr after the thermal (10 MeV) neutrino burst from the cooling neutron star. A Galactic supernova in a red supergiant star would produce a photon and neutrino flux of ~10^{-4} erg/cm^2 s. A km^2 neutrino detector will detect ~100 muons, thus allowing to constrain both supernova models and neutrino properties.