The Formation and Evolution of Cataclysmic Variables
White dwarf-main sequence star (WD+MS) binaries allows us to investigate two major, poorly understood, paradigms of binary evolution. Firstly, the disrupted magnetic braking (DMB) model; a widely cited explanation for the paucity of observed cataclysmic variables (CVs) with orbital periods of between about 2 and 3 hours (coined the period gap). Secondly, common envelope (CE) evolution, which is thought to be a major formation mechanism of semi-detached, compact binaries. Despite the ubiquity of
... ite the ubiquity of these models in the literature, they have yet to be comprehensively tested with observations. To test the former paradigm, we exploit the model's main prediction: the existence of detached WD+MS binaries within the period gap that were CVs but ceased mass transfer as a result of DMB ('detached CVs'; dCVs). For a range of models describing the CE phase and magnetic braking, we employ population synthesis techniques to calculate the present day population of dCVs and detached WD+MS that have formed from a CE phase (post-common envelope binaries; PCEBs). We find that dCVs outnumber PCEBs with late spectral-type secondary stars within the period gap by a factor of between 4 and 13. This excess manifests as a prominent peak within the period gap of the combined PCEB and dCV orbital period distribution. If this feature is detected in the observed WD+MS orbital period distribution, it would strongly corroborate the DMB model. Our comprehensive analysis between the theoretical and observed PCEB populations shows that an αcE >0.1 and an initial mass ratio distribution favouring small mass ratios, q < 1, best reproduces the observed PCEB distribution, and the observed local space density. Finally, we reconstruct the CE phase for the observed PCEBs and investigate any dependence of αcE on the secondary mass and the orbital period of the PCEB. Indeed, this may shed light into the CE ejection mechanism.