Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars

The stability of binary mass transfer is a critical problem for binary evolution. We systematically calculate the adiabatic mass-loss model for naked helium stars with masses ranging from 10$M_{\odot}$ to 80$M_{\odot}$ to study the critical mass ratio ($q_\textrm{crit}$) of Wolf-Rayet binaries. We set up two prescriptions about Wolf-Rayet stellar wind and consider the isotropic re-emission effect during adiabatic mass loss. Results of the critical mass ratio for conserved dynamically unstable mass transfer show that most of the no-wind helium stars on the main sequence (HeMS) have $0.7<q_\textrm{crit}<3.0$ and on the Hertzsprung gap (HeHG) have $1.5<q_\textrm{crit}<27$. With the Wolf-Rayet star wind effect, the $q_\textrm{crit}$ gets lower on a certain evolutionary stage. With the isotropic re-emission effect, the $q_\textrm{crit}$ gets larger for early-evolutionary stage helium stars and lower for late-evolutionary stage helium stars. Based on fully non-conserved mass transfer, the criteria for HeMS stars are $1.0<q_\textrm{crit}<2.8$ and HeHG stars are $1.5<q_\textrm{crit}<5.0$. Compared with the widely used criterion $q_\textrm{crit}=3$ (HeMS) and $q_\textrm{crit}=4$ (HeHG), our result becomes more unstable for the HeMS stars and more stable for the HeHG stars. Our work could be applied to the binary mass transfer stage of massive helium binaries, such as Wolf-Rayet star binaries and high mass X-ray binaries with Wolf-Rayet star companions. It can be applied to the binary population synthesis studies for the formation of special objects, such as double black hole mergers.