The 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 (WDs). Based on the single-degenerate scenario and assuming that the WDs would differentially rotate when the accretion ratė M > 3 × 10 −7 M yr −1 , we performed the numerical calculations for ∼1000 binary systems consisting of a He star and a CO WD with Eggleton's stellar evolution code. We present the initial parameters in the orbital period − helium star-mass plane (for WD masses of 1.0 M and 1.2 M , respectively), which lead to super-Chandrasekhar mass SNe Ia. Our results indicate that for an initially massive WD of 1.2 M , a large number of SNe Ia may result from super-Chandrasekhar mass WDs. The highest mass of the WD at the moment of the SNe Ia explosion is 1.81 M , but very massive (>1.85 M ) WDs cannot be formed. However, when the initial mass of WDs is 1.0 M , the explosive masses of SNe Ia are nearly uniform, which is consistent with the rareness of super-Chandrasekhar mass SNe Ia in observations.

Context. Ultracompact cataclysmic variables (CVs) of the AM CVn type are deemed to be important verification sources for the future space gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). Aims. We model the present-day Galactic population of AM CVn stars with He-star donors. Such a population has long expected to exist, though only a couple of candidates are known. Methods. We applied the hybrid method of binary population synthesis (BPS) which combines a simulation of the population of immediate precursors of AM CVn stars by a fast BPS code with subsequent tracking of their evolution by a full evolutionary code.Results. The model predicts that the present birthrate of He-donor AM CVn stars in the Galaxy is 4.6 × 10 −4 yr −1 and the Galaxy may harbour 112 000 objects of this class which have orbital periods P < ∼ 42 − 43 min. The foreground confusion limit and instrumental noise of LISA prevent the discovery of longer periods systems in gravitational waves. We find that about 500 He-star AM CVns may be detected by LISA with signal-to-noise ratio (S/N)>5 during a 4 yr mission. Within 1 Kpc from the Sun, there may exist up to 130 He-star AM CVns with the periods in the same range, which may serve as verification binaries, if detected in the electromagnetic spectrum. In the Milky Way, there are also 14 800 immediate precursors of AM CVn stars. They are detached systems with a stripped low-mass He-star and a white dwarf companion, out of which about 75 may potentially be observed by LISA during its mission.