Attributing the O'Connell effect in contact binaries to a cooling mass-transfer stream

TL;DR

This paper tackles the O'Connell effect observed in contact binaries by moving beyond spot-based explanations to a lateral mass- and energy-transfer (MT) stream from the hotter primary to the cooler secondary, implemented within PHOEBE with a variable stream heat capacity. It formalizes two ET models—internal mixing with a global $\mathcal{T}_{\rm eff}$ and a lateral transfer model with parameters $z_{\rm stream}$, $p$, and $s$—where the lateral model uses $T'_{\rm eff,2}(\vec{r}) = T_{\rm eff,2}(\vec{r})\big[1 + (\mathcal{T}_{\rm eff,1}/\mathcal{T}_{\rm eff,2} - 1) f(z) g(\phi)\big]$, $f(z)=(1 - |z|/z_{\rm stream})^p$, $g(\phi)=\left(\frac{\phi_{\max}-\phi}{\phi_{\max}-\phi_{\min}}\right)^s$, and $\phi = \arctan(y/x) + \pi$. Applying this to the Kepler system KIC 6223646 yields a best-fit with $q \approx 0.461$, $i \approx 60.2^{\circ}$, $F \approx 0.244$, $T_{\rm eff,2} \approx 6990$ K (vs. fixed $T_{\rm eff,1}=9000$ K), $z_{\rm stream} \approx 0.72$, $p \approx 0.88$, and $s \approx 1.06$, reproducing the strong O'Connell effect and producing notable temperature asymmetries: the secondary is cooler than the primary by roughly 2300 K at the photosphere. The work also documents significant model uncertainties and the need for broader application to large survey samples to constrain the ET process in W UMa binaries.

Abstract

Contact binaries are very short-period systems that are continuously interacting by transferring mass and energy. Obtaining large, statistical samples of contact binaries from photometric surveys can put valuable constraints on the various processes involved in their evolution. Modeling those systems however present some challenges. In some contact-binary light curves, the O'Connell effect is visible, where the maxima at both quarter phases are unequal. In the literature, this effect is typically attributed to magnetic spots on the surface of the binary. In this work, we model contact-binary surfaces using PHOEBE, and include a parametric prescription for a lateral mass- and energy-transfer stream that travels from the hotter primary to the cooler secondary. We allow this stream to have a variable heat capacity. We fit a system from the Kepler sample with a strong O'Connell effect, and show that a low-heat capacity stream can explain the unequal maxima. This suggests that, in such systems, surface flows can play a significant role in transferring heat between components. Our methods can be used on larger samples of contact binaries from OGLE, Kepler, or TESS to advance our understanding of contact binary structure and evolution.

Figures (6)

• Figure 1: PHOEBE meshes of different energy transfer modes where parameters $\mathcal{T}_{\rm eff, 1} = \qty{5500}{\kelvin}$, $\mathcal{T}_{\rm eff, 2} = \qty{4400}{\kelvin}$, $F = 0.5$ and $q = 0.5$ are used throughout. Panel (a): no mixing applied. Panel (b): internal mixing mode. Panel (c): Two quadratures of the lateral mixing mode. Note the different color scale in panel b.
• Figure 2: Light curves of the same binary system with lateral mixing of Fig. \ref{['fig:meshes']}, but viewed under different inclinations. The O'Connell effect is highlighted with dashed lines. The unit of the $y$ axis is arbitrary.
• Figure 3: Light curve for KIC 6223646 (blue), with the best-fit PHOEBE model with lateral mixing in red. The lower panel shows the residuals, which has a root-mean-squared value of 0.0035. For comparison, an equal-temperature model (by internal mixing) is shown in black.
• Figure 4: PHOEBE models of KIC 6223646 that include larger covariance than the original MCMC estimate in Table \ref{['tab:par6223646']}. The red line is the median of the 200 models from the rescaled distributions, while the shaded area is the 1-$\sigma$ flux range of these models.
• Figure 5: Posterior distribution densities of the MCMC chains that estimated the errors on the fit parameters in Table \ref{['tab:par6223646']}. The final row, $\sigma_{\rm lnf}$ is a numerical "fudge" parameter that estimates the fraction with which the errors on the data are underestimated.