Inward Propagation of Nuclear-Burning Shells in Merging C-O and He White Dwarfs

We have investigated the consequences of merging double white dwarf systems by calculating evolutionary models of accreting white dwarfs. We have considered two cases; a massive C-O white dwarf of∼ 1M⊙ accreting C-O mixture, and a low mass white dwarf with an initial mass of 0.4M⊙ accreting matter composed mostly of helium. The accretion rate of the C-O white dwarf is assumed to be 1 × 10M⊙y . After carbon burning is ignited at M r ∼ 1.04M⊙, the flame propagates inward due to heat conduction. By inserting enough grid points to resolve the structure of the flame, we have obtained almost steady burning in most phase of evolution, but we have found a new phenomenon that the strength of flame sometimes oscillates due to a thermal instability in early phase of the evolution. In calculating evolutionary models, we have occasionally employed a steady-burning approximation, in which the propagation speed of flame is given a priori. We have considered two extreme cases for the interior abundance of the massive white dwarf: XC = 0.5 and XC = 0.2. For XC = 0.5, the flame becomes very weak at M r ∼ 0.4M⊙ and the inward propagation stall there. But a few thousand years later, the flame is reactivated due to contraction and propagates to the center. For XC = 0.2, the flame propagates smoothly and reaches the center in ∼ 1000 years. In both cases the C-O mixture has been burned into an O-Ne-Mg mixture without causing an explosive phenomenon. For helium accreting low mass white dwarfs, we have considered accretion rates of 1 × 10 and 1 × 10M⊙y . After a fraction of M⊙ is accreted to the white dwarf, helium is ignited in the outer part and a shell flash occurs. Such a shell flash diminishes when about 10% of helium in the convective shell is burned into carbon and oxygen. The next shell flash occurs at a shell interior to the previously flashed shell. After less than 30 shell flashes, the helium ignition occurs at the center and steady burning begins. Thus, the merging produces a helium star which burns helium at the center. The mechanism of the propagation of the burning shell in this case is compressional