On Silicon Group Elements Ejected by Supernovae Type Ia
  There is compelling evidence that the peak brightness of a Type Ia supernova
is affected by the electron fraction Ye 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 freezeout. This allows one to potential
recovery of Ye 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 Ye in the silicon rich regions of the supernovae. If these
four abundances are determined exactly, they are sufficient to recover Ye to 6
percent. This is because these isotopes dominate the composition of
silicon-rich material and iron rich material in quasi nuclear statistical
equilibrium. Analytical analysis shows that the 28Si abundance is insensitive
to Ye, the 32S abundance has a nearly linear trend with Ye, and the 40Ca
abundance has a nearly quadratic trend with Ye. We verify these trends with
post-processing of 1D models and show that these trends are reflected in model
synthetic spectra.
