Constraining deflagration models of type Ia supernovae through intermediate-mass elements

Abstract

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 × 107 g cm-3 down to 2 × 106 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, XIME, of these elements to estimate the total amount of IMEs synthesized during the deflagration of a massive white dwarf. Using XIME 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, τc ≥ 0.2 s, and high turbulent intensities. According to our results, it could be difficult to produce much more than 0.2 M☉ 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.