Although Type Ia supernovae (SNe Ia) play very important roles in many astrophysical fields, the exact nature of the progenitors of SNe Ia is still unclear. At present, the single degenerate (SD) model is a very likely one. Following the comprehensive SD model developed by Meng & Yang (2010), we show the properties of SNe Ia companions at the moment of the supernova explosion. The results may provide help in searching for companion stars in supernova remnants. We compared our results with the companion candidate Tycho G of Tycho's supernova and found that integral properties of the star (mass, space velocity, radius, luminosity and effective temperature) are all consistent with those predicted from our SD model with the exception of the rotational velocity. If Tycho G was the companion star of Tycho's supernova, an interaction between supernova ejecta and the rotational companion might be a key factor to solve the confliction, and then it could be encouraged to do a detailed numerical simulation about the interaction.
We calculated a grid of evolutionary tracks of rotating models with masses between 1.0 and 3.0 M⊙ and resolution δM 〈 0.02 M⊙, which can be used to study the effects of rotation on stellar evolution and on the characteristics of star clusters. The value of ～ 2.05 Me is a critical mass for the effects of rotation on stellar struc- ture and evolution. For stars with M 〉 2.05 Me, rotation leads to an increase in the convective core and prolongs their lifetime on the main sequence （MS）; rotating mod- els evolve more slowly than non-rotating ones; the effects of rotation on the evolution of these stars are similar to those of convective core overshooting. However for stars with 1.1 〈 M/M⊙ 〈 2.05, rotation results in a decrease in the convective core and shortens the duration of the MS stage; rotating models evolve faster than non-rotating ones. When the mass has values in the range ～ 1.7 - 2.0 M⊙, the mixing caused by rotationally induced instabilities is not efficient; the hydrostatic effects dominate pro- cesses associated with the evolution of these stars. For models with masses between about 1.6 and 2.0 M⊙, rotating models always exhibit lower effective temperatures than non-rotating ones at the same age during the MS stage. For a given age, the lower the mass, the smaller the change in the effective temperature. Thus rotations could lead to a color spread near the MS turnoff in the color-magnitude diagram for intermediate-age star clusters.
