Constraining Deflagration Models of Type Ia Supernovae through Intermediate-Mass Elements

The physical structure of a nuclear flame is a basic ingredient of the theory of Type Ia supernovae (SNe Ia). Assuming an exponential density reduction with several characteristic times, we have followed the evolution of a planar nuclear flame in an expanding background from an initial density of 6.6×10 7 g cm -3 down to 2×10 6 g cm -3 . The total amount of synthesized intermediate-mass elements (IMEs), from silicon to calcium, was monitored during the calculation. We have used the computed mass fractions, X IME , of these elements to estimate the total amount of IMEs synthesized during the deflagration of a massive white dwarf. Using X IME and adopting the usual hypothesis that the relevant flame speed is actually the turbulent speed on the integral length scale, we have built a simple geometrical approach to model the region where IMEs are thought to be produced. It turns out that a healthy production of IMEs involves the combination of not-too-short expansion times, τ c >=0.2 s, and high turbulent intensities. According to our results, it could be difficult to produce much more than 0.2 M solar of intermediate-mass elements within the standard deflagrative paradigm. The calculations also suggest that the mass of the IMEs scales with the mass of the Fe-peak elements, making it difficult to reconcile energetic explosions with low ejected nickel masses, as in the well-observed supernova SN 1991bg or in SN 1998de. Thus, a large production of Si-peak elements, especially in combination with a low or moderate production of iron, could be better addressed either by the delayed detonation route in standard Chandrasekhar-mass models or, perhaps, by the off-center helium detonation in the sub-Chandrasekhar-mass scenario.