Population synthesis for double white dwarfs. II. Semi-detached systems: AM CVn stars

We study two models for AM CVn stars: white dwarfs accreting (i) from a helium white dwarf companion and (ii) from a helium-star donor. We show that in the first model possibly no accretion disk forms at the onset of mass transfer. The stability and the rate of mass transfer then depend on the tidal coupling between the accretor and the orbital motion. In the second model the formation of AM CVn stars may be prevented by detonation of the CO white dwarf accretor and the disruption of the system. With the most favourable conditions for the formation of AM CVn stars we find a current Galactic birth rate of 6.8 10^{-3} yr^{-1}. Unfavourable conditions give 1.1 10^{-3} yr^{-1}. The expected total number of the systems in the Galaxy is 9.4 10^{7} and 1.6 10^{7}, respectively. We model very simple selection effects to get some idea about the currently expected observable population and discuss the (quite good) agreement with the observed systems.