Three-dimensional Structure of Incomplete Carbon-Oxygen Detonations in Type Ia Supernovae

Carbon-oxygen (CO) detonation with reactions terminating either after burning of C$^{12}$ in the leading C$^{12}$ + C$^{12}$ reaction or after burning of C$^{12}$ and O$^{16}$ to Si-group elements may occur in the low-density outer layers of exploding white dwarfs and be responsible for the production of intermediate-mass elements observed in the outer layers of Type Ia supernovae. Basic one-dimensional properties of CO-detonations have been summarized in our previous work. This paper presents the results of two- and three-dimensional numerical simulations of low-density CO-detonations and discusses their multidimensional stability, cellular structure, and propagation through a constant low-density background. We find three-dimensional CO detonations to be strikingly different from their one-dimensional and two-dimensional counterparts. Three-dimensional detonations are significantly more robust and capable of propagating without decay compared to highly unstable and marginal one- and two- dimensional detonations. The detonation cell size and whether burning of C$^{12}$ in a three-dimensional detonation wave is followed by the subsequent O$^{16}$ burning is sensitive to both the background density and the initial C$^{12}$ to O$^{16}$ mass ratio. We also discuss the possible implications for understanding the observed early time bumps in light-curves.