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

Technical Summary: "A modest change in magnetic braking at the fully convective boundary explains cataclysmic variable evolution"

Problem Statement
For decades, the standard model of Cataclysmic Variable (CV) evolution has relied on the assumption that magnetic braking (MB) undergoes a drastic "disruption" (a reduction in efficiency by factors of 30–100) when the donor star becomes fully convective. This assumption was necessary to explain the "orbital period gap" (a lack of CVs between ~2 and ~3 hours) and the observed mass-radius relation of CV donors.

However, this standard scenario faces two major contradictions:

1. Outdated Prescriptions: Traditional MB laws (e.g., Rappaport et al. 1983) do not account for "saturation," where MB efficiency plateaus for rapidly rotating stars. Recent observations of single stars and close binaries suggest MB saturates, yet previous CV studies incorporating saturation still required extreme disruption factors ($\eta \gtrsim 30-100$).
2. Single Star Discrepancy: Observations of single M-dwarfs indicate that angular momentum loss increases (by ~1.5x) across the fully convective boundary, contradicting the CV model which requires a sharp decrease.

Methodology
The authors employed state-of-the-art stellar evolution simulations using the Modules for Experiments in Stellar Astrophysics (MESA) code (v24.03.1) to re-evaluate CV evolution with a revised magnetic braking prescription. Key methodological steps included:

1. Recalibration of Saturation Thresholds:

   • Instead of using semi-empirical approximations for convective turnover time ($\tau_c$) from Wright et al. (2011), the authors calculated $\tau_c$ directly within MESA using the Kim & Demarque (1996) integral equation.
   • This recalculation yielded a significantly lower critical Rossby number for saturation: $Ro_{crit} \approx 0.04$ (compared to the previously used 0.13).
   • The critical rotation period was redefined as $P_{crit} = 0.04 \times \tau_c$, removing dependence on solar parameters ($P_\odot, \tau_\odot$) which introduce inconsistencies.

2. Implementation of the Revised SBD Law:

   • The authors adopted the saturated MB prescription from Matt et al. (2015), which depends on stellar mass, radius, and convective turnover time, but is independent of convective turnover time in the saturated regime.
   • They integrated two modification factors previously proposed for CVs:
     • Boosting ($K$): Enhances MB for stars with radiative cores.
     • Disruption ($\eta$): Reduces MB for fully convective stars.
   • The total angular momentum loss rate ($\dot{J}_{SBD}$) was defined as $K \cdot \dot{J}_{SAT}$ for partially convective stars and $(K \cdot \dot{J}_{SAT}) / \eta$ for fully convective stars.

3. Simulation Parameters:

   • Simulated CVs with an initial donor mass of $0.8 M_\odot$ and initial orbital period of 1.0 day.
   • Assumed a constant white dwarf mass of $0.83 M_\odot$ and included Consequential Angular Momentum Loss (CAML) for low-mass white dwarfs.
   • Explored parameter spaces: $K \in [10, 100]$ and $\eta \in [1, 20]$.

Key Contributions

• Direct Calculation of $\tau_c$: The study demonstrates that using internally calculated convective turnover times rather than approximations significantly alters the saturation threshold, leading to stronger magnetic braking in the saturated regime (by a factor of ~4).
• Revised Disruption Factor: The paper challenges the long-standing dogma that magnetic braking must be almost entirely switched off at the fully convective boundary to explain CV observations.

Results

1. Moderate Disruption is Sufficient:

   • To reproduce the upper and lower boundaries of the orbital period gap and the period minimum, a disruption factor of $\eta \approx 2-3$ is sufficient.
   • This is a drastic reduction from the previously required factors of 30–100.
   • A boosting factor of $K \approx 20$ was found to best reproduce the upper edge of the period gap.

2. Mass-Radius Relation:

   • The observed mass-radius relation for CV donors is well-reproduced even without disruption ($\eta=1$), but the fit improves statistically ($\chi^2_{red} \approx 18$) with $\eta = 2-3$.
   • The model predicts mass transfer rates above the period gap that are slightly higher than those derived from white dwarf temperatures, suggesting potential overestimation of MB or unaccounted stellar bloating.

3. Angular Momentum Loss:

   • The recalibrated model shows that magnetic braking remains significantly stronger in the saturated regime than previously assumed, reducing the need for extreme "disruption" to match observational data.

Significance and Implications

• Dynamo Theory: The finding that only a modest reduction ($\sim 2-3\times$) in MB efficiency is required at the fully convective boundary suggests that the dynamo mechanism does not undergo a catastrophic change or complete cessation in fully convective stars, as previously hypothesized. This aligns better with the observed increase in angular momentum loss in single stars across this boundary.
• Unified Prescription: The results move the field closer to a unified magnetic braking prescription that can explain both single star spin-down and CV evolution without invoking extreme, unphysical parameters.
• Stellar Structure: The authors suggest that the remaining tension between model predictions and observations (e.g., donor radii) may be resolved by accounting for magnetically induced stellar bloating (up to 20%) rather than solely attributing radius inflation to angular momentum loss.
• Future Work: The authors plan to conduct population synthesis studies incorporating internal angular momentum redistribution and updated donor star radii to fully validate these findings.