  Recent observations have revealed that Type Ia supernovae (SNe Ia) are not
perfect standard candles but show some variations in their absolute magnitudes,
light curve shapes, and spectra. The C/O ratio in the SNe Ia progenitors (C-O
white dwarfs) may be related to this variation. In this work, we systematically
investigate the effects of stellar mass (M) and metallicity (Z) on the C/O
ratio and its distribution in the C-O white dwarfs by calculating stellar
evolution from the main-sequence through the end of the second dredge-up for
M=3-9 Mo and Z=0.001-0.03. We find that the total carbon mass fraction just
before SN Ia explosion varies in the range 0.36 -- 0.5. We also calculate the
metallicity dependence of the main-sequence-mass range of the SN Ia progenitor
white dwarfs. Our results show that the maximum main-sequence mass to form C-O
white dwarfs decreases significantly toward lower metallicity, and the number
of SN Ia progenitors may be underestimated if metallicity effectis neglected.
We discuss the implications of these results on the variation of SNe Ia,
determination of cosmological parameters, luminosity function of white dwarfs,
and the galactic chemical evolution.
