On variations in the peak luminosity of Type Ia supernovae

We explore the idea that the observed variations in the peak luminosities of Type Ia supernovae (SNe Ia) originate in part from a scatter in metallicity of the main-sequence stars that become white dwarfs. Previous numerical studies have not self-consistently explored metallicities greater than solar. One-dimensional Chandrasekhar mass models of SNe Ia produce most of their Ni-56 in a burn to nuclear statistical equilibrium between the mass shells 0.2 and 0.8 M., for which the electron-to-nucleon ratio Ye is constant during the burn. We show analytically that under these conditions, charge and mass conservation constrain the mass of Ni-56 produced to depend linearly on the original metallicity of the white dwarf progenitor. Detailed postprocessing of W7-like models confirms this linear dependence. The effect that we have identified is most evident at metallicities larger than solar and is in agreement with previous self-consistent calculations over the metallicity range common to both calculations. The observed scatter in the metallicity (1/3-3 Z.) of the solar neighborhood is enough to induce a 25% variation in the mass of Ni-56 ejected by SNe Ia. This is sufficient to vary the peak V-band brightness by \DeltaM(V)\ approximate to 0.2. This scatter in metallicity is present out to the limiting redshifts of current observations (z less than or similar to 1). Sedimentation of Ne-22 can possibly amplify the variation in 56Ni mass to less than or similar to50%. Further numerical studies can determine if other metallicity-induced effects, such as a change in the mass of the Ni-56-producing region, offset or enhance the variation that we identify.