the WD could reach $M_{\rm Ch}$ by several evolutionary paths, either by a mass-transfer from a binary giant/main-sequence companion (single degenerate scenario; e.g., Whelan & Iben 1973; Nomoto 1982) or as a result of merging with a binary degenerate WD companion (double degenerate scenario; e.g., Iben & Tutukov 1984; Webbink 1984). As the WD has accreted a sufficient amount of material, the central density of the WD increases and the heating rate by the carbon fusion exceeds the cooling rate by neutrino emission. The evolution is then followed by a simmering phase with convective carbon burning, lasting for about a century. At the end of this simmering phase, the temperature rises to the point where convection can no longer efficiently transport away the energy produced by the carbon burning. This is a stage where the burning becomes dynamical, initiating a thermonuclear flame that propagates outward and disrupts the WD, i.e., a supernova explosion (Nomoto et al. 1984; Woosley & Weaver 1986).

Once the thermonuclear flame is ignited, there are two possible modes of the propagation: subsonic deflagration and supersonic detonation. A prompt ignition of the detonation flame is disfavored because the resulting nucleosynthesis yield conflicts with Galactic chemical evolution (Arnett 