The AM Canum Venaticorum stars are rare interacting white dwarf binaries , whose formation and evolution are still poorly known .
The Sloan Digital Sky Survey provides , for the first time , a sample of 6 AM CVn stars ( out of a total population of 18 ) that is sufficiently homogeneous that we can start to study the population in some detail .

We use the Sloan sample to ‘ calibrate ’ theoretical population synthesis models for the space density of AM CVn stars .
We consider optimistic and pessimistic models for different theoretical formation channels , which yield predictions for the local space density that are more than two orders of magnitude apart .
When calibrated with the observations , all models give a local space density \rho _ { 0 } = 1 - 3 \times 10 ^ { -6 } pc ^ { -3 } , which is lower than expected .

We discuss the implications for the formation of AM CVn stars , and conclude that at least one of the dominant formation channels ( the double-degenerate channel ) has to be suppressed relative to the optimistic models .
In the framework of the current models this suggests that the mass transfer between white dwarfs usually can not be stabilized .
We furthermore discuss evolutionary effects that have so far not been considered in population synthesis models , but which could be of influence for the observed population .
We finish by remarking that , with our lower space density , the expected number of Galactic AM CVn stars resolvable by gravitational-wave detectors like LISA should be lowered from current estimates , to about 1 , 000 for a mission duration of one year .