Photons from neutrinos: the gamma ray echo of a supernova neutrino burst

When a star undergoes core collapse, a vast amount of energy is released in a ~10 s long burst of neutrinos of all species. Inverse beta decay in the star's hydrogen envelope causes an electromagnetic cascade which ultimately results in a flare of gamma rays - an "echo" of the neutrino burst - at the characteristic energy of 0.511 MeV. We study the phenomenology and detectability of this flare. Its luminosity curve is characterized by a fast, seconds-long, rise and an equally fast decline, with a minute- or hour-long plateau in between. For a near-Earth star (distance D<1 kpc) the echo will be observable at near future gamma ray telescopes with an effective area of 10^3 cm^2 or larger. Its observation will inform us on the envelope size and composition. In conjunction with the direct detection of the neutrino burst, it will also give information on the neutrino emission away from the line of sight and will enable tests of neutrino propagation effects between the stellar surface and Earth.