Nucleosynthesis in multi-dimensional SN Ia explosions

We present the results of nucleosynthesis calculations based on multi-dimensional (2D and 3D) hydrodynamical simulations of the thermonuclear burning phase in type la supernovae (hereafter SN la). The detailed nucleosynthetic yields of our explosion models are calculated by post-processing the ejecta, using passively advected tracer particles. The nuclear reaction network employed in computing the explosive nucleosynthesis contains 383 nuclear species, ranging from neutrons, protons, and alpha-particles to Mo-98. Our models follow the common assumption that SN la are the explosions of white dwarf's that have approached the Chandrasekhar mass (M-ch similar to 1.39), and are disrupted by thermonuclear fusion of carbon and oxygen. But in contrast to 1D models which adjust the burning speed to reproduce lightcurves and spectra, the thermonuclear burning model applied in this paper does not contain adjustable parameters. Therefore variations of the explosion energies and nucleosynthesis yields are dependent on changes of the initial conditions only. Here we discuss the nucleosynthetic yields obtained in 2D and 3D models with two different choices of ignition conditions (centrally ignited, in which the spherical initial flame geometry is perturbated with toroidal rings, and bubbles, in which multi-point ignition conditions are simulated), but keeping the initial composition of the white dwarf unchanged. Constraints imposed on the hydrodynamical models from nucleosynthesis as well as from the radial velocity distribution of the elements are discussed in detail. We show that in our simulations unburned C and O varies typically from similar to40% to similar to50% of the total ejected material. Some of the unburned material remains between the flame plumes and is concentrated in low velocity regions at the end of the simulations. This effect is more pronounced in 2D than in 3D and in models with a small number of (large) ignition spots. The main differences between all our models and standard 1D computations are, besides the higher mass fraction of unburned C and O, the C/O ratio (in our case is typically a factor of 2.5 higher than in 1D computations), and somewhat lower abundances of certain intermediate mass nuclei such as S, Cl, Ar, K, and Ca, and of Ni-56. We also demonstrate that the amount of Ni-56 produced in the explosion is a very sensitive function of density and temperature. Because explosive C and O burning may produce the iron-group elements and their isotopes in rather different proportions one can get different Ni-56-fractions (and thus supernova luminosities) without changing the kinetic energy of the explosion. Finally, we show that we need the high resolution multi-point ignition (bubbles) model to burn most of the material in the center (demonstrating that high resolution coupled with a large number of ignition spots is crucial to get rid of unburned material in a pure deflagration SN la model).