  Meng, Chen & Han (2009) comprehensively and systemically studied the WD + MS
system by detailed binary evolution calculations. Following their studies, we
have carried out a series of binary population synthesis studies about the
properties of the companions of SNe Ia for different metallicities $Z$. We
present the distributions of the masses, $M_{\rm 2}^{\rm SN}$, the radii,
$R_{\rm 2}^{\rm SN}$, of companions, and the periods, $P_{\rm SN}$, and the
ratios of separations to radii, $A/R_{\rm 2}^{\rm SN}$, of WD + MS systems for
various $Z$ at the moment of supernova explosion. These arameters can be
applied to constrain the numerical simulation of the interaction between the
ejecta of a supernova and its companion. We also show the distributions of some
integral properties of companions, i.e. the mass, the space velocity and the
surface gravity, for various $Z$ after the interaction. The distributions may
help to search companion in a supernova remnant. All the parameters above
significantly change with $Z$. Incorporating the simulation results of
interaction between supernovae ejecta and companions in Marietta et al. (2000)
and Kasen et al. (2004) into our binary population synthesis study, we found
that more than 75% of all supernovae have enough polarization signal which can
be detected by spectropolarimetric observations. We also found that 13 to 14
per cent SNe Ia belong to the supernovae like 1991T, which is consistent with
observations within errors. This may indicate that SNe 1991T-like have not any
special properties in physics except for the viewing angle of an observer.
