Evolution of AM CVn binaries with WD donors

The evolution and stability of mass transfer of CO+He WD binaries are not well understood. Observationally they may emerge as AM CVn binaries and are important gravitational wave (GW) emitters. In this work, we have modeled the evolution of double WD binaries with accretor masses of $0.50 - 1.30\;M_{\odot}$ and donor masses of $0.17\; - 0.45\;M_{\odot}$ using the detailed stellar evolution code MESA. We find that the evolution of binaries with same donor masses but different accretor masses is very similar and binaries with same accretor masses but larger He donor masses have larger maximum mass transfer rates and smaller minimum orbital periods. We also demonstrate that the GW signal from AM CVn binaries can be detected by space-borne GW observatories, such as LISA, TianQin. And there is a linear relation between the donor mass and gravitational wave frequency during mass transfer phase. In our calculation, all binaries can have dynamically stable mass transfer, which is very different from previous studies. The threshold donor mass of Eddington-limited mass transfer for a given accretor WD mass is lower than previous studies. Assuming that a binary may enter common envelope if the mass transfer rate exceeds the maximum stable burning rate of He, we provide a new criterion for double WDs surviving mass transfer, which is below the threshold of Eddington-limit. Finally, we find that some systems with ONe WDs in our calculation may evolve into detached binaries consisting of neutron stars (NSs) and extremely low mass He WDs and further ultra-compact X-ray binaries.