Carbon-oxygen white dwarf accreting CO-rich matter. II. Self-regulating accretion process up to the explosive stage

We investigate the effect of rotation on the evolution of double-degenerate white dwarf systems, which are possible progenitors of Type Ia supernovae. We assume that prior to merging, the two white dwarfs rotate synchronously at the orbital frequency and that in the merger process, the lighter white dwarf is transformed into a thick disk from which the more massive white dwarf initially accretes at a very high rate (similar to10(-5) M-. yr(-1)). Because of the lifting effect of rotation, the accreting white dwarf expands until the gravitational acceleration and centripetal acceleration required for binding at the surface become equal, initiating a Roche instability. The white dwarf continues to accrete matter from the disk, but at a rate that is determined by the balance between two competing processes operating in outer layers: ( 1) heating, expansion, and spin-up due to accretion and (2) cooling and contraction due to thermal diffusion. The balance produces an accretion rate such that the angular velocity of the white dwarf omega(WD) and the break-up angular velocity omega(cr) remain equal. Because of the deposition of angular momentum by accreted matter and the contraction of the accreting star, omega(WD) increases continuously until the rotational energy reaches about 14% of the gravitational binding energy; then, another instability sets in: the structure is forced to adopt an elliptical shape and emit gravitational waves. Thereafter, a balance between the rate of deposition of angular momentum by accreted matter and the rate of loss of angular momentum by gravitational waves produces a nearly constant or plateau'' accretion rate of similar to 4 x 10(-7) M-. yr(-1). The mass of the accreting white dwarf can increase up to and beyond the Chandresekhar mass limit for nonrotating white dwarfs before carbon ignition occurs. Independent of the initial value of the accretion rate, the physical conditions suitable for carbon ignition are achieved at the center of the accreting white dwarf and, because of the high electron degeneracy, the final outcome is an event of SN Ia proportions. Our results apply to merged binary white dwarf systems which, at the onset of explosive carbon ignition, have a total mass in the range 1.4 - 1.5M(.).