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The evolution and stability of mass transfer of CO+He WD binaries are notwell understood. Observationally they may emerge as AM CVn binaries and areimportant gravitational wave (GW) emitters. In this work, we have modeled theevolution 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 thedetailed stellar evolution code MESA. We find that the evolution of binarieswith same donor masses but different accretor masses is very similar andbinaries with same accretor masses but larger He donor masses have largermaximum mass transfer rates and smaller minimum orbital periods. We alsodemonstrate that the GW signal from AM CVn binaries can be detected byspace-borne GW observatories, such as LISA, TianQin. And there is a linearrelation between the donor mass and gravitational wave frequency during masstransfer phase. In our calculation, all binaries can have dynamically stablemass transfer, which is very different from previous studies. The thresholddonor mass of Eddington-limited mass transfer for a given accretor WD mass islower than previous studies. Assuming that a binary may enter common envelopeif the mass transfer rate exceeds the maximum stable burning rate of He, weprovide a new criterion for double WDs surviving mass transfer, which is belowthe threshold of Eddington-limit. Finally, we find that some systems with ONeWDs in our calculation may evolve into detached binaries consisting of neutronstars (NSs) and extremely low mass He WDs and further ultra-compact X-raybinaries.

Evolution of AM CVn binaries with WD donors