Abstract
Within the Boussinesq approximation, an elementary model for the deflagration-to-detonation transition triggered by self-acceleration of an expanding flame is formulated and explored. The self-acceleration is sustained by the intrinsic Rayleigh–Taylor instability until the Deshaies–Joulin deflagrability threshold is reached, followed by an abrupt transition to detonation. Emergence of the threshold is caused by positive feedback between the accelerating flame and the flame-driven pressure shock that results in the thermal runaway when the flame speed reaches a critical level. The model offers a simple mechanism that may be responsible for the transition to detonation in thermonuclear supernovae.
Highlights
Understanding supernovae explosions is a fundamental astrophysical issue that has frustrated theorists since the effect was first clearly identified by Zwicky in 1933, and it is still commonly regarded as an unsolved problem (Röpke [1])
There is a general consensus that the Type Ia supernova explosion of a degenerate carbon white dwarf star is a manifestation of the deflagration-to-detonation transition (DDT) triggered by an outward-propagating thermonuclear flame subjected to Darrieus–Landau (DL)
The present study offers an elementary model of the DDT event by synthesizing a weakly nonlinear equation of the RT-instability with the Deshaies–Joulin (DJ) theory of thermal runaway [3]
Summary
Understanding supernovae explosions is a fundamental astrophysical issue that has frustrated theorists since the effect was first clearly identified by Zwicky in 1933, and it is still commonly regarded as an unsolved problem (Röpke [1]). There is a general consensus that the Type Ia supernova explosion of a degenerate carbon white dwarf star is a manifestation of the deflagration-to-detonation transition (DDT) triggered by an outward-propagating thermonuclear flame subjected to Darrieus–Landau (DL). The crucial point of the DJ approach is that at the DDT threshold the corrugated flame may stay perfectly subsonic (see [8,9,10]). This premise allows one to deal with the small (yet nonzero) Mach number approximation with all the technical advantages it provides. The ability of a subsonic flame to trigger the transition challenges the common view that to ensure DDT the flame should cross the threshold of the DJ-deflagration
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