Adiabatic Mass Loss in Binary Stars. IV. Low- and Intermediate-mass Helium Binary Stars

The unstable mass transfer situation in binary systems will asymptotically cause the adiabatic expansion of the donor star and finally lead to the common envelope phase. This process could happen in helium binary systems once the helium donor star fills its Roche-lobe. We have calculated the adiabatic mass-loss model of naked helium stars with a mass range of 0.35 M _⊙–10 M _⊙, and every mass sequence evolved from the helium-zero-age main sequence to the cooling track of white dwarf or carbon ignition. In consideration of the influence of stellar wind, massive helium stars are not considered in this paper. Comparing the stellar radius with the evolution of the Roche-lobe under the assumption of conservative mass transfer, we give the critical mass ratio q _crit = M _He/M _accretor as the binary stability criteria of low- and intermediate-mass helium binary stars. On the helium main sequence, the result shows 1.0 < q _crit < 2.6, which is more unstable than the classical result of polytropic model q _crit = 3. After the early helium Hertzsprung Gap, the q _crit quickly increases even larger than 10 (more stable compared with the widely used result of q _crit = 4), which is dominated by the expansion of the radiative envelope. Our result could be useful for these quick mass transfer binary systems such as AM CVns, ultra-compact X-ray binaries, and helium novae, and it could guide the binary population synthesis for the formation of special objects such as type Ia supernova and gravitational wave sources.