On the evolution of rapidly rotating massive white dwarfs towards supernovae or collapses

A recent study by Yoon & Langer (2004a) indicated that the inner cores of rapidly accreting (Mdot > 10^{-7} M_sun/yr) CO white dwarfs may rotate differentially, with a shear rate near the threshold value for the onset of the dynamical shear instability. Such differentially rotating white dwarfs obtain critical masses for thermonuclear explosion or electron-capture induced collapse which significantly exceed the canonical Chandrasekhar limit. Here, we construct two-dimensional differentially rotating white dwarf models with rotation laws resembling those of the one-dimensional models of Yoon & Langer (2004a). We derive analytic relations between the white dwarf mass, its angular momentum, and its rotational-, gravitational- and binding energy. We show that these relations are applicable for a wide range of angular velocity profiles, including solid body rotation. We demonstrate that pre-explosion and pre-collapse conditions of both, rigidly and differentially rotating white dwarfs are well established by the present work, which may facilitate future multi-dimensional simulations of Type Ia supernova explosions and studies of the formation of millisecond pulsars and gamma-ray bursts from collapsing white dwarfs.Our results lead us to suggest various possible evolutionary scenarios for progenitors of Type Ia supernovae, leading to a new paradigm of a variable mass of exploding white dwarfs, at values well above the classical Chandrasekhar mass. Based on our 2D-models, we argue for the supernova peak brightness being proportional to the white dwarf mass, which could explain various aspects of the diversity of Type Ia supernovae, such as their variation in brightness, the dependence of their mean luminosity on the host galaxy type, and the weak correlation between ejecta velocity and peak brightness.