Properties of Deflagration Fronts and Models for Type Ia Supernovae

Detailed models of the explosion of a white dwarf that include self-consistent calculations of the light curve and spectra provide 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, the 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 provide a new and better understanding of the physics. Several new descriptions for flame propagation have been proposed by Khokhlov et al. and Niemeyer et al. Using various descriptions 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 first propagates 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 from the transition to detonation differ almost by a factor of 2. 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 to 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 burning front changes by less than 3%, and the expansion velocity changes by less than 10%. The burning conditions are very close to previous calculations which used a constant deflagration velocity. Based on a comparison with observations, those required low deflagration speeds (≈2%-3% of the speed of sound). Exceptions to the similarity are the innermost layers of ≈0.03-0.05 M☉. Still, nuclear burning is in nuclear statistical equilibrium, but the rate of electron capture is larger for the new descriptions of the flame propagation. Consequently, the production of very neutron-rich isotopes is increased. In our example, close to the center Ye is about 0.44, compared to 0.46 in the model with constant deflagration speed. This increases the 48Ca production by more than a factor of 100 to 3.E-6 M☉. Conclusions from previous analyses of light curves and spectra on the properties of the WD and the explosions will not change, and even with the new descriptions, the delayed detonation scenario is consistent with the observations. Namely, the central density results with respect to the chemical structure of the progenitor and the transition density from deflagration to detonation do not change. The reason for this similarity is the fact that the total amount of burning during the long deflagration phase determines the restructuring of the WD prior to the detonation. Therefore, we do not expect that the precise, microphysical prescription for the speed of a subsonic burning front has a significant effect on the outcome. However, at the current level of uncertainties for the burning front, the relation between properties of the burning front and of the initial white dwarf cannot be obtained from a comparison between observation and theoretical predictions by one-dimensional models. Multidimensional calculations are needed (1) to get inside the relations between model parameters such as central density and properties of the deflagration front and its relation to the transition density between deflagration and detonation and (2) to make use of information on asphericity that is provided by polarization measurements. These questions are essential to test, estimate, and predict some of the evolutionary effects of SNe Ia and their use as cosmological yardsticks.