ON silicon group elements ejected by supernovae type ia

There is evidence that the peak brightness of a Type Ia supernova is affected by the electron fraction Y _e at the time of the explosion. The electron fraction is set by the aboriginal composition of the white dwarf and the reactions that occur during the pre-explosive convective burning. To date, determining the makeup of the white dwarf progenitor has relied on indirect proxies, such as the average metallicity of the host stellar population. In this paper, we present analytical calculations supporting the idea that the electron fraction of the progenitor systematically influences the nucleosynthesis of silicon group ejecta in Type Ia supernovae. In particular, we suggest the abundances generated in quasi-nuclear statistical equilibrium are preserved during the subsequent freeze-out. This allows potential recovery of Y _e at explosion from the abundances recovered from an observed spectra. We show that measurement of ²⁸Si, ³²S, ⁴⁰Ca, and ⁵⁴Fe abundances can be used to construct Y _e in the silicon-rich regions of the supernovae. If these four abundances are determined exactly, they are sufficient to recover Y _e to 6%. This is because these isotopes dominate the composition of silicon-rich material and iron-rich material in quasi-nuclear statistical equilibrium. Analytical analysis shows the ²⁸Si abundance is insensitive to Y _e , the ³²S abundance has a nearly linear trend with Y _e , and the ⁴⁰Ca abundance has a nearly quadratic trend with Y _e . We verify these trends with post-processing of one-dimensional models and show that these trends are reflected in the model's synthetic spectra.