The authors explore the possible evolution of one component in a close binary system when it is assumed that this component fills its Roche lobe after it has become a giant with a degenerate helium core of mass ≡0.3 M_sun;. The model experiences two hydrogen shell flashes which begin when the envelope is compact and which force the model to again fill its Roche lobe. The second flash is due to the diffusion of hydrogen inward to regions of high temperature. After all nuclear burning has ceased and all explicitly calculated mass-loss episodes are completed, the total mass of hydrogen remaining near the surface of the model is about 1.4×10⁻⁴M_sun;. A modest radiative wind could remove the surface layer of hydrogen, transforming the model into a non-DA white dwarf. The radius of the model remains significantly larger than that of a zero-temperature model until well over 5×10⁹yr of cooling have elapsed. Using the cooling curve, the authors construct a number-magnitude distribution function for helium dwarfs.
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Icko et al. (1986) studied this question.