Contact-binary evolution with energy transfer and saturated magnetic braking

TL;DR

This work investigates how magnetic braking and energy transfer shape the evolution of low-mass contact binaries (W UMa). Using analytic estimates and MESA-based binary evolution, it contrasts classical (Skumanich-like) magnetic braking with a saturated MB prescription and incorporates energy transfer across the common envelope. The results show that only saturated MB combined with energy transfer can produce long-lived contact phases and mass-ratio evolution away from unity, consistent with observed low-$q$ systems and TRO behavior; classical MB yields rapid mergers, while ET can moderate angular-momentum loss by reducing convection-driven magnetic activity during TROs. These findings support a weaker-than-Skumanich MB framework in contact binaries and underscore the need to model ET accurately to understand W UMa demographics and their evolutionary pathways.

Abstract

The evolution of low-mass contact binaries is influenced by angular-momentum loss, mass and energy transfer, and the nuclear evolution of the components. They have periods shorter than one day, and we expect their period evolution to be dominated by magnetic braking. Evidence for saturated magnetic braking was presented by studying the period distribution of detached eclipsing binaries. This means the strength of magnetic braking likely does not cause a steep period-shrinking relation derived from the widely used Skumanich law. We find further evidence for saturated magnetic braking by considering evolutionary models of low-mass contact binaries. We also show that energy transfer must play an important role over a wide parameter range in producing the observed low mass ratios of contact binaries.

Figures (10)

• Figure 1: Volume-equivalent-radius ratio of the ${\rm L_2}$ and Roche Lobe equipotentials as a function of the mass ratio. This function is discontinuous at $q = 1$ because the location of ${\rm L_2}$ moves from the far side of $M_2$ to the near size of $M_1$.
• Figure 2: Mass-transfer rate, radius, and mass-ratio evolution of the $M_{\rm 1, init}=\qty{0.9}{\Msun}$, $p_{\rm init} = \qty{0.67}{}$, $q_{\rm init} = 0.75$ models without ET under the different MB laws. We note that the saturated MB model has its total lifetime as well as its time in binary interaction increased by about an order of magnitude.
• Figure 3: Mass-transfer rate, radius and mass-ratio evolution of the $M_{\rm 1, init}=\qty{0.9}{\Msun}$, $p_{\rm init} = \qty{0.67}{}$, $q_{\rm init} = 0.75$, with saturated MB, with ET (red curves) and without ET (blue curves). Without ET, the system merges at mass ratio of unity after MT is engaged, while the model with ET evolves away from mass ratio unity, and develops TROs (see inset).
• Figure 4: Termination of the $q=0.75$ models of our grids as function of initial primary mass $M_{1, \rm init}$ and initial period $p$. Termination conditions are listed in Sect. \ref{['ssec:termination']}. We note that only the combination of ET and saturated MB allows for models over a large parameter range that experience TROs.
• Figure 5: Lifetimes of the contact phases of the models with $q_{\rm init} = 0.75$. We confirm our estimates from Sect. \ref{['sec:analytic']} that models using the classical MB law have an lifetime of only $\qty{e7}{}$, while saturated MB allows for lifetimes larger than $\qty{e8}{}$. The fact that the ET and no-ET models have largely the same lifetime is coincidental. For the models undergoing TROs (see Fig. \ref{['fig:termination']}), the lifetimes reported here are lower limits.