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 ^ { 56 } \mathrm { Ni } in a burn to nuclear statistical equilibrium between the mass shells 0.2 M _ { \odot } and 0.8 M _ { \odot } , for which the electron to nucleon ratio Y _ { e } is constant during the burn .
We show analytically that , under these conditions , charge and mass conservation constrain the mass of ^ { 56 } \mathrm { Ni } 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 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 ( ⅓ Z _ { \odot } –3 Z _ { \odot } ) of the solar neighborhood is enough to induce a 25 % variation in the mass of ^ { 56 } \mathrm { Ni } ejected by Type Ia supernova .
This is sufficient to vary the peak V -band brightness by | \Delta M _ { V } | \approx 0.2 .
This scatter in metallicity is present out to the limiting redshifts of current observations ( z \lesssim 1 ) .
Sedimentation of ^ { 22 } \mathrm { Ne } can possibly amplify the variation in ^ { 56 } \mathrm { Ni } mass to \lesssim 50 \% .
Further numerical studies can determine if other metallicity-induced effects , such as a change in the mass of the ^ { 56 } \mathrm { Ni } -producing region , offset or enhance the variation we identify .