Recent discovery of several overluminous type Ia supernovae (SNe Ia) indicates that the explosive masses of white dwarfs may significantly exceed the canonical Chandrasekhar mass limit. Rapid differential rotation may support these massive white dwarfs. Based on the single-degenerate scenario, and assuming that the white dwarfs would differentially rotate when the accretion rate $dot{M}>3times 10^{-7}M_{odot}rm yr^{-1}$, employing Eggletons stellar evolution code we have performed the numerical calculations for $sim$ 1000 binary systems consisting of a He star and a CO white dwarf (WD). We present the initial parameters in the orbital period - helium star mass plane (for WD masses of $1.0 M_{odot}$ and $1.2 M_{odot}$, respectively), which lead to super-Chandrasekhar mass SNe Ia. Our results indicate that, for an initial massive WD of $1.2 M_{odot}$, a large number of SNe Ia may result from super-Chandrasekhar mass WDs, and the highest mass of the WD at the moment of SNe Ia explosion is 1.81 $M_odot$, but very massive ($>1.85M_{odot}$) WDs cannot be formed. However, when the initial mass of WDs is $1.0 M_{odot}$, the explosive masses of SNe Ia are nearly uniform, which is consistent with the rareness of super-Chandrasekhar mass SNe Ia in observations.
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