Nucleosynthesis in Chandrasekhar Mass Models for Type Ia Supernovae and Constraints on Progenitor Systems and Burning-Front Propagation

We calculate explosive nucleosynthesis in Chandrasekhar mass models for Type Ia Supernovae(SNe Ia) to obtain new constraints on the rate of matter accretion onto the progenitor white dwarf and on the ignition density of central carbon deflagration. The calculated abundance of the Fe-group neutron-rich nuclei is highly sensitive to the electron captures taking place in the central layers. The yields obtained from a slow central deflagration, and from a fast deflagration or delayed detonation in the outer layers, are combined and put to comparison with solar isotopic abundances. We found that (1) to avoid too large ratios of $^{54}$Cr/$^{56}$Fe and $^{50}$Ti/$^{56}$Fe, the ignition density should be as low as \ltsim 2 \e9 \gmc, and that (2) to avoid the overproduction of $^{58}$Ni and $^{54}$Fe, either the flame speed should not exceed a few % of the sound speed in the central low $Y_e$ layers, or the progenitor star has to be metal-poor compared with solar. Such low central densities can be realized by a rapid accretion as fast as $\dot M$ \gtsim 1 $\times$ 10$^{-7}$M$_\odot$ yr$^{-1}$. In order to reproduce the solar abundance of $^{48}$Ca, one also needs progenitor systems that undergo ignition at higher densities. We also found that the total amount of $^{56}$Ni, the Si-Ca/Fe ratio, and the abundance of elements like Mn and Cr (incomplete Si-burning ashes), depend on the density of the deflagration-detonation transition in delayed detonations. Our nucleosynthesis results favor transition densities slightly below 2.2$\times 10^7$ g cm$^{-3}$.