Evolution of low-mass helium stars in semidetached binaries

We systematically investigate the evolution of low-mass (0.35, 0.40, and 0.65 M _⊙) helium donors in semidetached binaries with white-dwarf accretors. The initial periods of the binaries are chosen in such a way that the helium abundance in the center of the models at the time of Roche lobe overflow varies between Y _c = 0.98 and Y _c ≃ 0.1. The results of our calculations can be used to analyze the formation scenarios and evolutionary status of AM CVn stars. We show that the minimum orbital periods of the semidetached binaries depend weakly on the total mass of the components and the evolutionary phase of the donor at the time of Roche lobe overflow and are 9 10 min. The differences in the mass transfer rates after P _orb reaches its minimum in the range P _orb ≈ 10 40 min do not exceed a factor of ∼2.5. For P _orb ≳ 20 min, the mass-losing stars are weakly degenerate homogeneous cooling objects; the He, C, N, O, and Ne abundances depend on the evolutionary phase at which Roche lobe overflow occurred. For the binaries that are currently believed to be the most probable candidates for AM CVn stars with helium donors, Y ≳ 0.4, X _C ≲ 0.3, X _O ≲ 0.25, and X _N ≲ 0.5 × 10^-2. In the binaries under consideration, once P _orb ≈ 40 min has been reached, the mass loss time scale begins to exceed the thermal time scale of the donors, the latter begin to contract, their matter becomes degenerate, and the populations of AMCVn stars with white-dwarf and helium-star progenitors of their donors probably merge together.