The Thermonuclear Explosion of Chandrasekhar Mass White Dwarfs

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Abstract
The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities, the combination of which determines the observational characteristics of the explosion. We briefly review these instabilities and discuss the length scales for which each dominates. Their cumulative effect is to accelerate the speed of the flame beyond its laminar value, but that acceleration has uncertain time and angle dependence which has allowed numerous solutions to be proposed (e.g., deflagration, delayed detonation, pulsational deflagration, and pulsational detonation). We discuss the conditions necessary for each of these events and the attendant uncertainties. A grid of critical masses for detonation in the range 107-2 × 109 g cm-3 is calculated and its sensitivity to composition explored. The conditions for prompt detonation are discussed. Such explosions are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. "Active turbulent combustion" and multipoint ignition are presented as two plausible ways of doing this. A deflagration that moves at the "Sharp-Wheeler" speed, 0.1geff t, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if fuel can be efficiently burned behind a front that moves with the speed of the fastest floating bubbles generated by the nonlinear Rayleigh-Taylor instability. The relevance of the transition to the "distributed regime" of turbulent nuclear burning is discussed for delayed and pulsational detonations. This happens when the flame speed has slowed to the point that turbulence can actually penetrate the flame thickness and may be advantageous for producing the high fuel temperatures and gentle temperature gradients necessary for detonation. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate-mass elements, and warrants further study. The other two leading models, simple deflagration and pulsational detonation, are mutually exclusive.
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