Taking into account the rotation of mass-accreting white dwarfs ( WDs ) whose masses exceed the Chandrasekhar mass , we extend our new single degenerate model for the progenitors of Type Ia supernovae ( SNe Ia ) , accounting for two types of binary systems , those with a main sequence companion and those with a red-giant ( RG ) companion .
We present a mass distribution of WDs exploding as SNe Ia , where the WD mass ranges from 1.38 to 2.3 ~ { } M _ { \sun } .
These progenitor models are assigned to various types of SNe Ia .
A lower mass range of WDs ( 1.38 ~ { } M _ { \sun } < M _ { WD } \lesssim 1.5 ~ { } M _ { \sun } ) , which are supported by rigid rotation , correspond to normal SNe Ia .
A variety of spin-down time may lead to a variation of brightness .
A higher mass range of WDs ( M _ { WD } \gtrsim 1.5 ~ { } M _ { \sun } ) , which are supported by differential rotation , correspond to brighter SNe Ia such as SN 1991T .
In this case , a variety of the WD mass may lead to a variation of brightness .
We also show the evolutionary states of the companion stars at SN Ia explosions and pose constraints on the unseen companions .
In the WD+RG systems , in particular , most of the RG companions have evolved to helium/carbon-oxygen WDs in the spin-down phase before the SN Ia explosions .
In such a case , we do not expect any prominent signature of the companion immediately before and after the explosion .
We also compare our new models with the recent stringent constraints on the unseen progenitors of SNe Ia such as SN 2011fe .