How Many CVs are Crossing the Period Gap? A Test for the Disruption of Magnetic Braking

We apply population synthesis techniques to calculate the present day number of two types of white dwarf-main sequence star (WDMS) binaries within the cataclysmic variable 2 to 3 hour period gap. The first are post-common envelope binaries with secondary stars that have masses 0.17 ≤ M2/M⊙ ≤ 0.36 (gPCEBs), such that they will commence mass transfer within the period gap. The second type are systems that were CVs at some point in their past, but detached once they evolved down in orbital period to ≈ 3 h as a consequence of disrupted magnetic braking, and are crossing the period gap via gravitational radiation (dCVs). Full population synthesis calculations are performed where we assume either constant, global values of the common envelope ejection efficiency, αCE, or consider αCE as a function of secondary mass. Several forms of magnetic braking are also considered. We predict an excess of dCVs over gPCEBs within the period gap of ∼4 to ∼13 assuming αCE = 0.1−0.6, and an initial mass ratio distribution of the form n(q) = 1. This excess is revealed as a prominent peak at the location of the period gap in the orbital period distribution of the combined gPCEB and dCV population. We suggest that if such a feature is observed in the orbital period distribution of an observed sample of short orbital period WDMS binaries, this would strongly corroborate the disruption of magnetic braking.