6 Conclusions

We study the formation of AM CVn stars from (i) close detached double white dwarfs which become semi-detached and (ii) helium stars that transfer matter to a white dwarf and stop burning helium due to mass loss and become dim and semi-degenerate.

We find that, with our assumptions, in all cases where a double white dwarf potentially can form an AM CVn star no accretion disk will be formed in the initial phase of mass transfer. Normally the disk provides the feedback of angular momentum to the orbit, stabilising the mass transfer. In absence of a disk, the stability of the mass transfer in the semi-detached white dwarf binary depends critically on the efficiency of the coupling between the accretor and the donor. If this coupling is not efficient most systems merge, and the formation rate of AM CVn stars from double white dwarfs becomes very low. In this case it is possible that magnetically coupled systems are almost the only ones to survive. RX J1914.4+245 may be such a system.

In the second channel the formation of AM CVn stars may be prevented by explosive burning of the accumulated helium layer which may cause detonation of the CO white dwarf accretor and the disruption of the system.

We combine our population synthesis results into two models, an "efficient'' model in which the stability of mass transfer is not affected by the absence of an accretion disk and the explosive helium burning disrupting the system happens when 0.3 ${M}_{\odot }$ is accumulated and an "inefficient'' model in which the absence of an accretion disk is very important and the explosive helium disrupting the system happens already when 0.15  ${M}_{\odot }$ is accumulated. Applying very simple selection effects we estimate that in the "inefficient'' model only one in 30 potentially observed systems descends from double white dwarfs. In the "efficient'' model both families produce comparable numbers of observable systems. The observed systems fall roughly in the expected range of periods for a magnitude limited sample.

We conclude that to learn more about the AM CVn population both theory (stability of the mass transfer and helium accretion disks) and observations (especially the distances and the completeness of the sample) need to be improved.

Acknowledgements

We thank the referee Jan-Erik Solheim for valuable comments. LRY and SPZ acknowledge the warm hospitality of the Astronomical Institute "Anton Pannekoek''. This work was supported by NWO Spinoza grant 08-0 to E. P. J. van den Heuvel, RFBR grant 99-02-16037, the "Astronomy and Space Research Program'' (project 1.4.4.1) and by NASA through Hubble Fellowship grant HF-01112.01-98A awarded (to SPZ) by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS5-26555.