  We explore the idea that the observed variations in the peak luminosities of
Type Ia supernovae 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 56Ni
in a burn to nuclear statistical equilibrium between the mass shells 0.2 and
0.8 solar masses, for which the electron to nucleon ratio is constant during
the burn. We show analytically that, under these conditions, charge and mass
conservation constrain the mass of 56Ni produced to depend linearly on the
original metallicity of the white dwarf progenitor. Detailed post-processing of
W7-like models confirms this linear dependence. The effect that we identify 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 times solar) of
the solar neighborhood is enough to induce a 25% variation in the mass of 56Ni
ejected by Type Ia supernovae. This is sufficient to vary the peak V-band
brightness by approximately 0.2. This scatter in metallicity is present out to
the limiting redshifts of current observations (z < 1). Sedimentation of 22Ne
can possibly amplify the variation in 56Ni mass up to 50%. Further numerical
studies can determine if other metallicity-induced effects, such as a change in
the mass of the 56Ni-producing region, offset or enhance this variation.
