Carbon Ignition in Type Ia Supernovae: An Analytic Model

The observable properties of a Type Ia supernova are sensitive to how thenuclear runaway ignites in a Chandrasekhar mass white dwarf - at a single pointat its center, off-center, or at multiple points and times. We present a simpleanalytic model for the runaway based upon a combination of stellarmixing-length theory and recent advances in understanding Rayleigh-Benardconvection. The convective flow just prior to runaway is likely to have astrong dipolar component, though higher multipoles may contribute appreciablyat the very high Rayleigh number (10$^{25}$) appropriate to the white dwarfcore. A likely outcome is multi-point ignition with an exponentially increasingnumber of ignition points during the few tenths of a second that it takes therunaway to develop. The first sparks ignite approximately 150 - 200 km offcenter, followed by ignition at smaller radii. Rotation may be important tobreak the dipole asymmetry of the ignition and give a healthy explosion.Comment: 14 pages, 0 figures, submitted to ApJ, corrected typo in first author's nam