The nature of carbon burning flames in Type Ia supernovae is explored as they interact with Kolmogorov turbulence. One-dimensional calculations using the Linear Eddy Model of Kerstein (1991) elucidate three regimes of turbulent burning. In the simple
st case, large scale turbulence folds and deforms thin laminar flamelets to produce a flame brush with a total burning rate given approximately by the speed of turbulent fluctuations on the integral scale, U_L. This is the regime where the supernova explosion begins and where most of its pre-detonation burning occurs. As the density declines, turbulence starts to tear the individual flamelets, making broader structures that move faster. For a brief time, these turbulent flamelets are still narrow compared to their spacing and the concept of a flame brush moving with an overall speed of U_L remains valid. However, the typical width of the individual flamelets, which is given by the condition that their turnover time equals their burning time, continues to increase as the density declines. Eventually, mixed regions almost as large as the integral scale itself are transiently formed. At that point, a transition to detonation can occur. The conditions for such a transition are explored numerically and it is estimated that the transition will occur for densities near 1 x 10**7 g/cm**3, provided the turbulent speed on the integral scale exceeds about 15% sonic. An example calculation shows the details of a detonation actually developing.
The evolution and explosion of metal-free stars with masses 10--100 solar masses are followed, and their nucleosynthetic yields, light curves, and remnant masses determined. When the supernova yields are integrated over a Salpeter initial mass functi
on, the resulting elemental abundance pattern is qualitatively solar, but with marked deficiencies of odd-Z elements with 7 <= Z <= 13. Neglecting the contribution of the neutrino wind from the neutron stars that they make, no appreciable abundances are made for elements heavier than germanium. The computed pattern compares favorably with what has been observed in metal-deficient stars with [Z] ~< -3. Most of the stars end their lives as blue supergiants and make supernovae with distinctive light curves resembling SN 1987A, but some produce primary nitrogen by dredge up and become red supergiants. A novel automated fitting algorithm is developed for determining optimal combinations of explosion energy, mixing, and initial mass function in the large model data base to agree with specified data sets. The model is applied to the low metallicity sample of Cayrel et al. (2004) and the two ultra-iron-poor stars HE0107-5240 and HE1327-2326. Best agreement with these low metallicity stars is achieved with very little mixing, and none of the metal-deficient data sets considered show the need for a high energy explosion component. To the contrary, explosion energies somewhat less than 1.2 B seem to be preferred in most cases. (abbreviated)
