Critical Mass Transfer in Double-Degenerate Type Ia Supernovae

Doubly-degenerate binary systems consisting of two white dwarfs both composed of carbon and oxygen and close enough that mass is transferred from the less massive to the more massive are possible progenitors of type Ia supernovae. If the mass transfer rate is slow enough that the accreting white dwarf can reach a mass of 1.38M⊙ then it can ignite carbon degenerately at its centre. This can lead to a thermonuclear runaway and thence a supernova explosion. However if the accretion rate is too high the outer layers of the white dwarf heat up too much and carbon ignites there non-degenerately. A series of mild carbon flashes can then propagate inwards and convert the carbon to neon relatively gently. There is no thermonuclear runaway and no supernova. We examine the critical accretion rate at which ignition switches from the centre to the surface for a variety of white dwarfs and find it to be about two fifths of the Eddington rate. In a real binary star the mass transfer rate falls off as mass transfer proceeds and the system widens. Even if the initial transfer rate is high enough for carbon to ignite at the outer edge, if such rapid accretion were to persist, we find that it can extinguish if the rate drops sufficiently quickly. The interior of the white dwarf remains carbon rich and, if sufficient mass can still be transferred from the companion, it can eventually ignite degenerately at the centre. The primary white dwarf must be about 1.1M⊙ or above and the companion about 0.3M⊙. Though white dwarfs of such low mass are expected to be pure helium we note that a star of initial mass 2.5M⊙ has a CO core of about 0.3M⊙ when it begins to ascend the asymptotic giant branch. Alternatively if the accretion rate can be limited to a maximum of 0.46 of the Eddington rate then a 1.1M⊙ white dwarf accretes sufficiently slowly to explode from a companion white dwarf of any large enough mass.