One model to rule them all: magnetic braking from CVs to low-mass stars

We present the results of the study of the secular evolution of donor stars in cataclysmic variables (CVs) and AM Canum Venaticorum (AM CVn) stars with our double dynamo (DD) formalism of angular momentum loss (AML) by magnetic braking (MB). In our DD model, MB is driven by an interplay between two $\alpha-\Omega$ dynamos, one in the convective envelope and the other at the boundary of the radiative core and the convective envelope. We show that (1) our MB model reproduces the period gap ($2\lesssim P_\mathrm{orb}/\,\mathrm{hr}\lesssim3$) and the period minimum spike ($P_\mathrm{orb}\approx 80\, \mathrm{min}$) in the distribution of non-magnetic CVs, (2) evolved CVs, where the donor star commences Roche lobe overflow (RLOF) close to or just beyond the end of the main-sequence, populate the region in and beyond the period gap, and are more likely to be detected at $P_\mathrm{orb}\geq 5.5 \,\mathrm{hr}$. This likely contaminates the mass-radius fit of long-period CV donors. We show that (3) some of the evolved CVs become AM CVn stars with $10\lesssim P_\mathrm{orb}/\,\mathrm{min}\lesssim 65$. Their evolution, driven by $\mathrm{AML_{MB}}$ and AML by gravitational radiation (GR, $\mathrm{AML_{GR}}$), leaves them extremely H-exhausted to the point of being indistinguishable from AM CVn systems formed via the He-star and the White Dwarf (WD) channels in terms of the absence of H in their spectra. We further show that (4) owing to the presence of a significant radiative region, intermediate-mass giants/sub-giants, which are progenitors of AM~CVn stars formed through the He-star channel, may undergo common envelope evolution that does not behave classically, (5) several AM CVn systems with extremely bloated donors, such as Gaia14aae, ZTFJ1637+49 and SRGeJ045359.9+622444 do not match any modelled trajectories if these systems are modelled only with $\mathrm{AML_{GR}}$ without incorporating $\mathrm{AML_{MB}}$, (6) the uncertainties in MB estimates greatly affect modelling results. This, in turn, affects our efforts to distinguish between different AM CVn formation channels and their relative importance. Finally, we find that (7) a similar MB prescription also explains the spin-down of single, low-mass stars.