A modest change in magnetic braking at the fully convective boundary explains cataclysmic variable evolution

Abstract

Context. For decades, reproducing the orbital period distribution of non-magnetic Cataclysmic Variables (CVs) seemed to require a drastic decrease, usually termed disruption, of angular momentum loss through magnetic braking at the fully convective boundary, which argued for a change in the dynamo mechanism operating in fully and partially convective stars. However, recent studies showed that the magnetic braking prescription traditionally used in CV evolution theory is clearly outdated as saturation, that is, a weak period dependence for rapidly rotating stars, is not included. Aims. Here we test an updated version of a saturated magnetic braking prescription that has been developed to explain the spin-down of single stars in the context of CV evolution. This prescription contains a boosting and a disruption parameter that represent the change in the strength of magnetic braking at the fully convective boundary. Methods. We performed state of the art MESA simulations for CVs with the revised saturated magnetic braking prescription. Results. As in previous studies, we found that magnetic braking needs to be stronger in close binaries than in single stars and that, in contrast to what is observed in single stars, magnetic braking needs to be reduced at the fully convective boundary. However, in contrast to previous studies of CV evolution, only a moderate disruption by a factor of 2 - 3 is sufficient to explain key features of the CV orbital period distribution and the measured mass-radius relation for CV donors. Conclusions. The relatively small decrease of the efficiency of magnetic braking at the fully convective boundary might have implications for our understanding of dynamo models for fully and partially convective stars.

Figures (2)

• Figure 1: A new saturation threshold appears naturally from fitting observational data using calculated turnover times. The global convective turnover time is very different to frequently used approximations wrightetal11, especially around and below the fully convective boundary (left panel). A lower threshold ($0.04$) for the Rossby number separating the saturated from the non-saturated regime is derived from fitting observations using the calculated global convective turnover time (middle panel). This causes magnetic braking to be stronger in the saturated regime as we keep the strength and slope of magnetic braking in the unsaturated regime unchanged (right panel).
• Figure 2: Mass transfer rates (left) and angular momentum loss rates (middle) as a function of orbital period as well as the mass-radius relation (right) predicted by our model for a fixed value of the boosting parameter ($K=20$) and different values for disruption ($1\leq\eta\leq20$). The tracks have been calculated assuming typical parameters, that is, initial donor mass and period of $M_{2} = 0.8 \, \rm{M_{\odot}}$ and $P_{\rm orb} = 1$ day, respectively, and a constant white dwarf mass of $M_{\rm WD} = 0.83 \, \rm{M_{\odot}}$. The mass-radius relation derived from observations mcallisteretal19-1 is reasonably well reproduced independent of the value of $\eta$ (right) but the fit improves for $\eta=2-3$ according to a $\chi^2$ test (see text). Such a moderate disruption is also required to generate a detached phase as an explanation for the orbital period gap kniggeetal11-1schreiberetal24-1. These values of $\eta$ also predict a period minimum similar to that derived from observations kniggeetal11-1mcallisteretal19-1. Such a mild disruption is very different to (almost) fully turning magnetic braking off as assumed in the standard scenario of CV evolution. By fitting the mass-radius relation (right panel) we predict mass transfer rates above the gap that, on average, exceed those measured from white dwarf temperatures palaetal22-1.