Presupernova evolution of accreting white dwarfs with rotation

We discuss the effects of rotation on the evolution of accreting carbon-oxygen white dwarfs, with the emphasis on possible consequences in Type Ia supernova (SN Ia) progenitors. Starting with a slowly rotating white dwarf, we consider the accretion of matter and angular momentum from a quasi-Keplerian accretion disk. Numerical simulations with initial white dwarf masses of 0.8, 0.9 and 1.0 M⊙ and accretion of carbon-oxygen rich matter at rates of 3 . . . 10 × 10 M⊙/yr are performed. The models are evolved either up to a ratio of rotational to potential energy of T/W = 0.18 — as angular momentum loss through gravitational wave radiation will become important for T/W < 0.18 — or to central carbon ignition. The role of the various rotationally induced hydrodynamic instabilities for the transport of angular momentum inside the white dwarf is investigated. We find that the dynamical shear instability is the most important one in the highly degenerate core, while Eddington Sweet circulation, Goldreich-Schubert-Fricke instability and secular shear instability are most relevant in the non-degenerate envelope. Our results imply that accreting white dwarfs rotate differentially throughout, with a shear rate close to the threshold value for the onset of the dynamical shear instability. As the latter depends on the temperature of the white dwarf, the thermal evolution of the white dwarf core is found to be relevant for the angular momentum redistribution. As found previously, significant rotation is shown to lead to carbon ignition masses well above 1.4 M⊙. Our models suggest a wide range of white dwarf explosion masses, which could be responsible for some aspects of the diversity observed in SNe Ia. We analyze the potential role of the bar-mode and the r-mode instability in rapidly rotating white dwarfs, which may impose angular momentum loss by gravitational wave radiation. We discuss the consequences of the resulting spin-down for the fate of the white dwarf, and the possibility to detect the emitted gravitational waves at frequencies of 0.1 . . . 1.0 Hz in nearby galaxies with LISA. Possible implications of fast and differentially rotating white dwarf cores for the flame propagation in exploding white dwarfs are also briefly discussed.