Deflagration-to-detonation transition by amplification of acoustic waves in type Ia supernovae

Aims. We study a new mechanism for deflagration-to-detonation transition in thermonuclear supernovae (SNe Ia), based on the formation of shocks by amplification of sound waves in the steep density gradients of white dwarfs envelopes. We characterise, in terms of wavelength and amplitude, the perturbations which will ignite a detonation after their amplification. Methods. This study was performed using the well tested HERACLES code, a conservative hydrodynamical code, validated in the present specific application by an analytical description of the propagation of sound waves in white dwarfs. Thermonuclear combustion of the carbon oxygen fuel was treated with the α-chain nuclear reactions network. Results. In planar geometry we found the critical parameter to be the height of shock formation. When it occurs in the inner dense regions (ρ > 106 g cm−3) detonation is inevitable but can take an arbitrarily long time. We found that ignition can be achieved for perturbation as low as Mach number: M ∼ 0.005, with heating times compatible with typical explosion time scale (a few seconds). On the opposite no ignition occurs when shocks initiated by small amplitude or large wavelength form further away in less dense regions. We show finally that ignition is also achieved in a spherical self-gravitating spherical model of cold C+O white dwarf of 1.430 M , but due to the spherical damping of sound waves it necessitates stronger perturbation (M ∼ 0.02). Small perturbations (M ∼ 0.003) could still trigger detonation if a small helium layer is considered. In the context of SNe Ia, one has to consider further the initial expansion of the white dwarf, triggered by the deflagration, prior to the transition to detonation. As the star expands, gradients get flatter and ignition requires increasingly strong perturbations.