Accretion disc models for AM Canum Venaticorum systems

Using a model of the vertical structure of accretion discs, we calculate disc spectra across a range of system parameters for the helium-rich AM CVn cataclysmic variables, and investigate thermal instabilities in their discs. Applying a χ²-minimisation technique, predicted HeI and HI continuum and line profiles are compared with those observed for two such systems, AM CVn and CR Boo, to estimate several system parameters. We find: - mean accretor masses close to, but somewhat higher than, the 0.7-0.8M_⊙ range predicted by present population synthesis studies; - typical helium-to-hydrogen number density ratios of 10²-10⁴, consistent with a helium-degenerate donor surrounded by a helium-rich envelope; and - mass-transfer rates of about 10¹⁷gs^-1, which may place the systems in the region of potential disc instability. S-curves calculated for the best-fit models are consistent with a thermally-stable disc in AM CVn, and a thermally unstable disc in CR Boo.