Abstract Type Ia supernovae (SNe Ia) play an important role in the study of cosmic evolution, especially in cosmology. There are several progenitor models for SNe Ia proposed in the past years. By considering the effect of accretion disk instability on the evolution of white dwarf (WD) binaries, we performed detailed binary evolution calculations for the WD + red-giant (RG) channel of SNe Ia, in which a carbon-oxygen WD accretes material from a RG star to increase its mass to the Chandrasekhar mass limit. According to these calculations, we mapped out the initial and final parameters for SNe Ia in the orbital period-secondary mass (log Pi -Mi2) plane for various WD masses for this channel. We discussed the influence of the variation of the duty cycle value on the regions for producing SNe Ia. Similar to previous studies, this work also indicates that the long-period dwarf novae offer possible ways for producing SNe Ia. Meanwhile, we find that the surviving companion stars from this channel have a low mass after the SN explosion, which may provide a means for the formation of the population of single low-mass WDs (<0.45M⊙).

Keywords stars: evolution — supernovae: general — binaries: close — white dwarfs

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