  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 simulate the accretion of matter and angular momentum from a quasi-Keplerian
accretion disk. 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. 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 Msun. 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.

Astrophysics