2007ApJ...662L..95B

Helium that accretes onto a carbon/oxygen white dwarf in double white dwarf AM Canum Venaticorum (AM CVn) binaries undergoes unstable thermonuclear flashes when the orbital period is in the 3.5-25 minute range. At the shortest orbital periods (and highest accretion rates, M{dot}>10^–7 M_☉/yr), the flashes are weak and likely lead to the helium equivalent of classical nova outbursts. However, as the orbit widens and M{dot} drops, the mass required for the unstable ignition increases, leading to progressively more violent flashes up to a final flash with helium shell mass ~0.02-0.1 M_☉. The high pressures of these last flashes allow the burning to produce the radioactive elements ⁴⁸Cr, ⁵²Fe, and ^ 56^Ni that power a faint (M_V=-15 to -18) and rapidly rising (few days) thermonuclear supernova. Current galactic AM CVn space densities imply one such explosion every 5,000-15,000 years in 10¹¹ M_☉ of old stars (~2%-6% of the Type Ia rate in E/SO galaxies). These ``.Ia'' supernovae (one-tenth as bright for one-tenth the time as a Type Ia supernovae) are excellent targets for deep (e.g., V=24) searches with nightly cadences, potentially yielding an all-sky rate of 1000 per year.