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Taking into account the rotation of mass-accreting white dwarfs (WDs) whosemasses exceed the Chandrasekhar mass, we extend our new single degenerate modelfor the progenitors of Type Ia supernovae (SNe Ia), accounting for two types ofbinary 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 Msun. These progenitor models areassigned to various types of SNe Ia. A lower mass range of WDs (1.38 Msun <M_WD <~ 1.5 Msun), which are supported by rigid rotation, correspond to normalSNe Ia. A variety of spin-down time may lead to a variation of brightness. Ahigher mass range of WDs (M_WD >~ 1.5 Msun), which are supported bydifferential rotation, correspond to brighter SNe Ia such as SN 1991T. In thiscase, a variety of the WD mass may lead to a variation of brightness. We alsoshow the evolutionary states of the companion stars at SN Ia explosions andpose 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 thespin-down phase before the SN Ia explosions. In such a case, we do not expectany prominent signature of the companion immediately before and after theexplosion. We also compare our new models with the recent stringent constraintson the unseen progenitors of SNe Ia such as SN 2011fe.

Final Fates of Rotating White Dwarfs and Their Companions in the Single Degenerate Model of Type Ia Supernovae