Evolution of Low-Mass Helium Stars in Semidetached Binaries

We present results of a systematic investigation of the evolution of low-mass (0.35, 0.40, and 0.65 solar mass) helium donors in semidetached binaries with accretors - white dwarfs. In the initial models of evolutionary sequences abundance of helium in the center is between $\simeq 0.1$ and 0.98. Results of computations may be applied to the study of the origin and evolutionary state of AM CVn stars. It is shown that the minimum orbital periods of the systems only weakly depend on the total mass of the system and evolutionary state of the donor at RLOF and are equal to 9-11 min. The scatter in the mass-exchange rates at a given orbital period in the range between period minimum and about 40 min. does not exceed $\sim 2.5$. At orbital periods exceeding about 20 min. mass-losing stars are weakly degenerate homogeneous cooling objects and abundances of He, C, N, O, Ne in the matter lost by them depend on the extent of He-depletion at RLOF. For the systems which are currently considered as the most probable model candidates for AM CVn stars with helium donors these abundances are, approximately, Y$>$0.4, X_C$<$0.3, X_O$<$0.25, X_N$<$0.005. At orbital periods greater than about 40 min. the timescale of mass-loss begins to exceed thermal time-scale of the donors, the latter begin to contract, they become more degenerate and, apparently, "white-dwarf" and "helium-star" populations of AM CVn stars merge.