Effect of the central gravitational field on self-accelerating outward propagating flames subjected to the Rayleigh-Taylor instability: Transition to detonation

Within the Boussinesq approximation an elementary model for the deflagration-to-detonation transition triggered by self-acceleration of an expanding flame in a central gravitational field is formulated and explored numerically. 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. The present study is an extension of the preceding models dealing with constant gravitational fields.