The single-degenerate channel for the progenitors of type Ia supernovae ( SNe Ia ) are currently accepted , in which a carbon-oxygen white dwarf ( CO WD ) accretes hydrogen-rich material from its companion , increases its mass to the Chandrasekhar mass limit , and then explodes as a SN Ia .
Incorporating the prescription of Hachisu et al .
( 30 ) for the accretion efficiency into Eggleton ’ s stellar evolution code and assuming that the prescription is valid for all metallicities , we performed binary stellar evolution calculations for more than 25,000 close WD binaries with metallicities Z = 0.06 , 0.05 , 0.04 , 0.03 , 0.02 , 0.01 , 0.004 , 0.001 , 0.0003 and 0.0001 .
For our calculations , the companions are assumed to be unevolved or slightly evolved stars ( WD + MS ) .
As a result , the initial parameter spaces for SNe Ia at various Z are presented in orbital period-secondary mass ( \log P _ { i } ,M _ { 2 } ^ { i } ) planes .
Our study shows that both the initial mass of the secondary and the initial orbital period increase with metallicity .
Thus , the minimum mass of the CO WD for SNe Ia decreases with metallicity Z .
The difference of the minimum mass may be as large as 0.24 M _ { \odot } for different Z .

Adopting the results above , we studied the birth rate of SNe Ia for various Z via a binary population synthesis approach .
If a single starburst is assumed , SNe Ia occur systemically earlier and the peak value of the birth rate is larger for a high Z .
The Galactic birth rate from the WD + MS channel is lower than ( but comparable to ) that inferred from observations .
Our study indicates that supernovae like SN2002ic would not occur in extremely low-metallicity environments , if the delayed dynamical-instability model in Han & Podsiadlowski ( 48 ) is appropriate .