Observations suggest that the properties of Type Ia supernovae (SNe Ia) may depend on environmental characteristics, such as the morphology, metallicity, and age of the host galaxies. The influence of these environmental properties on the resulting SNe Ia is studied in this Letter. First, it is shown that the carbon mass fraction X(C) in the C + O white dwarf SN Ia progenitors tends to be smaller for a lower metallicity environment and an older binary system. It is then suggested that the variation of X(C) causes the diversity in the brightness of SNe Ia: a smaller X(C) leads to a dimmer SN Ia. Further studies of the propagation of the turbulent flame are necessary to confirm this relation. Our model for the SN Ia progenitors then predicts that when the progenitors belong to an older population or to a low-metallicity environment, the number of bright SNe Ia is reduced, so that the variation in brightness among the SNe Ia is also smaller. Thus, our model can explain why the mean SN Ia brightness and its dispersion depend on the morphology of the host galaxies and on the distance of the SN from the center of the galaxy. It is further predicted that at higher redshift (z ≳ 1), both the mean brightness of SNe Ia and its variation should be smaller in spiral galaxies than in elliptical galaxies. These variations are within the range observed in nearby SNe Ia. Insofar as the variation in X(C) is the most important cause for the diversity among SNe Ia, the light-curve shape method that is currently used to determine the absolute magnitude of SNe Ia can also be applied to high-redshift SNe Ia.
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