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 \mathrm { M } _ { \odot } 
and accretion of carbon-oxygen rich matter at rates of 3 \dots 10 \times 10 ^ { -7 } M _ { \odot } / 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 \mathrm { M } _ { \odot } .
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 \dots 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 .