Propagation of the First Flames in Type Ia Supernovae

We consider the competition of the different physical processes that canaffect the evolution of a flame bubble in a Type Ia supernovae -- burning,turbulence and buoyancy. Even in the vigorously turbulent conditions of aconvecting white dwarf, thermonuclear burning that begins at a point near thecenter (within 100 km) of the star is dominated by the spherical laminarexpansion of the flame, until the burning region reaches kilometers in size.Consequently flames that ignite in the inner ~20 km promptly burn through thecenter, and flame bubbles anywhere must grow quite large--indeed, resolvable bylarge-scale simulations of the global system--for significant motion ordeformation occur. As a result, any hot-spot that successfully ignites into aflame can burn a significant amount of white dwarf material. This potentiallyincreases the stochastic nature of the explosion compared to a scenario where asimmering progenitor can have small early hot-spots float harmlessly away.Further, the size where the laminar flame speed dominates other relevantvelocities sets a characteristic scale for fragmentation of larger flamestructures, as nothing--by definition--can easily break the burning region intosmaller volumes. This makes possible the development of semi-analyticdescriptions of the earliest phase of the propagation of burning in a Type Iasupernovae, which we present here. Our analysis is supported by fully resolvednumerical simulations of flame bubbles.Comment: 33 pages, 14 figures, accepted for publication in Ap