Cell-based theoretical criteria on the onset and stability limit of thermonuclear detonation

One of the key unresolved problems in thermonuclear explosions of white dwarfs (WDs), including type Ia supernovae, is the condition for ignition and propagation of thermonuclear flame. Given the limitation of hydrodynamic simulations in resolving the flame front involved in the explosion process, theoretical considerations for these criteria merit accurate prediction of the onset of deflagration and detonation (deflagration-to-detonation transition or direct initiation) and subsequent stable propagation. Application of cell-based theories, which are originally designed for terrestrial detonation incorporating the size of the cellular structure, to pure-helium detonation in a WD envelope was proven to be powerful. In the present work, we extend this for detonation in helium-carbon and carbon-oxygen mixtures, both of which are associated with the double-detonation model for type Ia supernovae. Comparing with previous hydrodynamic studies in terms of the minimum initiation energy and critical stellar mass for stable propagation, the agreement is satisfactory. For the helium-carbon detonation, it is theoretically substantiated that even an extremely low-mass WD envelope about 10-3 M can accommodate stable detonation. For the carbon-oxygen detonation, the oxygen-scale cell width is shown to be a good diagnosing indicator. In addition, it is indicated that direct initiation of the carbon-oxygen detonation is only available for a WD heavier than 0.6 M. The findings of this study enable first-order calibration of the explosion model by a simple calculation through the analogy between astrophysical and terrestrial burning, the latter of which can be tested and observed in a laboratory-scale experiment.