ar X iv : a st ro - p h / 99 08 20 4 v 1 1 8 A ug 1 99 9 1 Properties of Deflagration Fronts and Models for Type Ia Supernovae

Detailed models of the explosion of a white dwarf, which include self-consistent calculations of the light curve and spectra, proved a link between observational quantities and the underlying explosion model. These calculations assume spherical geometry and are based on parameterized descriptions of the burning front. Recently, first multidimensional calculations for nuclear burning fronts have been performed. Although a fully consistent treatment of the burning fronts is beyond the current state of the art, these calculations provided a new and better understanding of the physics. Several new descriptions for the flame propagation have been proposed by Khokhlov et al. and Niemeyer et al.. Using various description for the propagation of a nuclear deflagration front, we have studied the influence on the results of previous analyses of Type Ia Supernovae, namely, the nucleosynthesis and structure of the expanding envelope. Our calculations are based on a set of delayed detonation models with parameters that give a good account of the optical and infrared light curves, and of the spectral evolution. In this scenario, the burning front propagates first in a deflagration mode and, subsequently, turns into a detonation. The explosions and light curves are calculated using a one-dimensional Lagrangian radiation-hydro code, including a detailed nuclear network. We find that the results of the explosion are rather insensitive to details of the description of the deflagration front, even if its speed and the time till the transition to detonation differ by almost a factor of two. For a given white dwarf (WD) and a fixed transition density, the total production of elements changes by less than 10 %, and the distribution in the velocity space changes by less than 7 %. Qualitatively, this insensitivity of the final outcome of the explosion on the details of the flame propagation during the (slow) deflagration phase can be understood as follows: For plausible variations in the speed of the turbulent deflagration, the duration of this phase is several times longer than the sound crossing time in the initial WD. Therefore, the energy produced during the early nuclear burning can be redistributed over the entire WD causing a slow preexpansion. In this intermediate state the WD is still bound but its binding energy is reduced by the amount of nuclear energy. The expansion ratio depends mainly on the total amount of burning during the deflagration phase. Consequently, the conditions are very similar under which nuclear burning takes place during the subsequent detonation phase. In our example, the density and temperature at the the burning front changes by less than 3 % , and the expansion velocity changes by less than 10 % . The burning