A recent study by Yoon & Langer ( [ 2004a ] ) indicated that the inner cores of rapidly accreting ( \dot { M } > 10 ^ { -7 } ~ { } \mathrm { M _ { \odot } ~ { } yr ^ { -1 } } ) 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 .
Taken at a central density of 2 \times 10 ^ { 9 } ~ { } \mathrm { g~ { } cm ^ { -3 } } they specify initial models for the thermonuclear explosion of rotating CO white dwarfs .
At \rho _ { \mathrm { c } } = 10 ^ { 10 } ~ { } \mathrm { g~ { } cm ^ { -3 } } and 4 \times 10 ^ { 9 } ~ { } \mathrm { g~ { } cm ^ { -3 } } , they give criteria for the electron-capture induced collapse of rotating CO and ONeMg white dwarfs , respectively .
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 .