Three periodically variable stars have recently been discovered ( V407 Vul , P = 9.5 \min ; ES Cet , P = 10.3 \min ; RX J0806.3+1527 , P = 5.3 \min ) with properties that suggest that their photometric periods are also their orbital periods , making them the most compact binary stars known .
If true , this might indicate that close , detached , double white dwarfs are able to survive the onset of mass transfer caused by gravitational wave radiation and emerge as the semi-detached , hydrogen-deficient stars known as the AM CVn stars .
The accreting white dwarfs in such systems are large compared to the orbital separations .
This has two effects : first it makes it likely that the mass transfer stream can hit the accretor directly , and second it causes a loss of angular momentum from the orbit which can destabilise the mass transfer unless the angular momentum lost to the accretor can be transferred back to the orbit .
The effect of the destabilisation is to reduce the number of systems which survive mass transfer by as much as one hundred-fold .
In this paper we analyse this destabilisation and the stabilising effect of a dissipative torque between the accretor and the binary orbit .
We obtain analytic criteria for the stability of both disc-fed and direct impact accretion , and carry out numerical integrations to assess the importance of secondary effects , the chief one being that otherwise stable systems can exceed the Eddington accretion rate .
We show that to have any effect upon survival rates , the synchronising torque must act on a timescale of order 1000 years or less .
If synchronisation torques are this strong , then they will play a significant role in the spin rates of white dwarfs in cataclysmic variable stars as well .