PROPAGATION OF TURBULENT FLAMES IN SUPERNOVAE

Turbulent thermonuclear burning is studied on scales relevant to the e xplosion of Type Ia supernovae. A scaling law is formulated for turbul ent burning in a uniform gravitational field. The steady state turbule nt flame speed is D-t = f(alpha)root gL in the regime where the Froude number F = D-l(2)/gL much less than 1; g, L, D-l, and alpha = rho(0)/ rho(1) > 1 are the acceleration, characteristic scale of the problem, normal speed of the laminar flame, and ratio of the densities ahead an d behind the flame, respectively; and f similar or equal to 1 is a uni versal function. In this regime, the turbulent flame speed does not de pend on the laminar speed D-l and on details of burning on scales much less than L. A flame-capturing technique for modeling turbulent burni ng is described. It is used to numerically study the transition to tur bulence and turbulent flame propagation in three dimensions. The resul ts confirm the scaling law. The self-regulating mechanism underlying t he scaling law is discussed. In Type Ia supernovae, steady state burni ng takes place on scales less than the radius of the flame, where the effects of spherical geometry and expansion are small. Larger scales i nfluenced by these effects need to be resolved explicitly. Direct, ab initio three-dimensional numerical simulations of deflagration in supe rnovae thus become feasible. Effects of spherical geometry and expansi on of matter on the propagation of turbulent flames are discussed. The expansion decreases large-scale turbulent motions and reduces the bul k rate of deflagration in a massive carbon-oxygen white dwarf. Results of a large-scale three-dimensional simulation of the deflagration exp losion of a Type Ia supernova are presented.