Evolved cataclysmic variables as progenitors of AM CVn stars

Abstract

We model cataclysmic variables (CVs) with solar metallicity donors ($X=0.7,\:Z=0.02$) that evolve to form AM CVn stars through the Evolved CV formation channel using various angular momentum loss mechanisms by magnetic braking ($\mathrm{AML_{MB}}$). We find that the time-scale for $\mathrm{AML_{MB}}$ in our double-dynamo (DD) model is shorter than that of previously used empirical formulae. Owing to the shorter time-scales, a larger parameter space of initial conditions evolves to form AM CVn stars with the DD model than with other models. We perform an analysis of the expected number of AM CVn stars formed through the Evolved CV channel and find about $3$ times as many AM CVn stars as reported before. We evolve these systems in detail with the Cambridge stellar evolution code (STARS) and show that evolved CVs populate a region with orbital period $P_\mathrm{orb}\geq5.5\,\mathrm{hr}$. We evolve our donors beyond their orbital period minimum and find that a significant number become extremely H-exhausted systems. This makes them indistinguishable from systems evolved from the He-star and the White Dwarf (WD) channels in terms of the absence of H in their spectra. We also compare the masses, mass-transfer rates of the donor, and the orbital period with observations. We find that the state of the donor and the absence of H in systems such as YZ LMi and V396 Hya match with our modelled trajectories, while systems such as CR Boo and HP Lib match with our modelled tracks if their actual donor mass lies on the lower-end of the observed mass range.