It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudospectral code Dedalus. Because the flame propagation timescale is $\sim 10^5$ times longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a turbulent chemical diffusivity produced by the convection as a function of height, $D_t(z)$. Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, $D_t$, is shorter than the flame propagation timescale, set by the thermal diffusivity, $\kappa$, i.e., when $D_t>\kappa$. However, we find $D_t<\kappa$ for most of the flame because convective plumes are not dense enough to penetrate into the flame. This implies that convective mixing cannot stall a carbon flame and that “hybrid carbon-oxygen-neon” white dwarfs are not a typical product of stellar evolution.
D. Lecoanet, J. Schwab, E. Quataert, et. al.
Thu, 31 Mar 16
Comments: Submitted to ApJL