On the behavior of double degenerate binaries associated with Type I supernovae

An analytical investigation is performed of the evolution of double degenerate dwarf binary systems into Type I supernovae. The discussion is limited to systems consisting of carbon-oxygen and oxygen-neon-magnesium dwarfs and those composed of two carbon-oxygen dwarfs. The companions spiral together and the secondary, with a mass more than about 0.6 solar mass, fills its Roche lobe. The radius of the secondary increases faster than the Roche lobe due to mass overflow, which becomes unstable. The instability can lead to a Type I explosion and may or may not cause the formation of a neutron star. If a neutron star forms, the secondary, reduced to below 0.6 solar mass, will spiral inward to the primary and eventually be absorbed by the neutron star. If a white dwarf remnant remains after the supernova explosion of the overflow radius, then a second supernova explosion can occur.