Observations suggest that the properties of Type Ia supernovae (SNe Ia) may
depend on environmental characteristics, such as the morphology, metallici
ty, and age of the host galaxies. The influence of these environmental prop
erties on the resulting SNe Ia is studied in this Letter. First, it is show
n that the carbon mass fraction X(C) in the C + O white dwarf SN Ia progeni
tors tends to be smaller for a lower metallicity environment and an older b
inary system. It is then suggested that the variation of X(C) causes the di
versity 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 t
o 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-metalli
city environment, the number of bright SNe Ia is reduced, so that the varia
tion in brightness among the SNe Ia is also smaller. Thus, our model can ex
plain why the mean SN Ia brightness and its dispersion depend on the morpho
logy 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 greater than
or similar to 1), both the mean brightness of SNe Ia and its variation sho
uld be smaller in spiral galaxies than in elliptical galaxies. These variat
ions are within the range observed in nearby SNe Ia. Insofar as the variati
on 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 m
agnitude of SNe Ia can also be applied to high-redshift SNe Ia.