The structure of steady detonation waves in Type Ia supernovae: pathological detonations in C-O cores

The structure of steady, one-dimensional detonation waves in C-O is investigated for initial densities in the range 2x10⁷ to 1x10⁹gcm^-3. At these and greater densities, the self-supporting detonation wave is of the pathological type. For such waves the detonation speed is an eigenvalue of the steady equations, and the reaction zone contains an internal frozen sonic point where the thermicity vanishes. The self-supporting flow downstream of this singular point is supersonic, and is very different from that in supported (overdriven) detonations. A method for determining the structure of pathological detonation waves is described. These waves are examined, and the self-sustaining wave is compared with and contrasted to the supported detonations considered previously by Khokhlov. We show that the thickness of the self-sustaining detonation is a few times the thickness of supported detonations, and that the self-sustaining detonation produces more of the iron-peak and less of the intermediate mass elements than do supported detonations. Implications for the cellular detonation instability are also discussed.