EBLM XVII - Tidal Synchronization and Circularization in Tight Stellar Binaries

Abstract

Tidal interactions in close stellar binaries are central to their orbital and rotational evolution, making observational tests of theoretical predictions essential for our understanding of the evolution of these, as well as close exoplanetary systems. Such tests require precise measurements of the orbital eccentricity and stellar rotation. The EBLM (Eclipsing Binary Low Mass) survey delivers a homogeneous sample of eclipsing binaries, composed of F/G/K primaries and M-dwarf (or low-mass K-dwarf) secondaries. We analyze 68 unequal mass binaries ($0.1 \leq q \leq 0.6$, where $q$ is the mass ratio), with measurable primary star rotation rates from TESS, and over a decade of radial velocity observations. This sample probes the critical regime where tidal effects are expected to transition between being efficient and inefficient. We find that ~75% of our sample has circularized, with eccentric systems confined to $P_{\rm orb} \gtrsim 3$ days, with modest eccentricities (e < 0.25). Roughly ~78% of our sample is synchronized, with nearly all binaries within a 3-day orbital period residing in a well-defined "synchronization zone". Beyond this, a minority of asynchronous systems persist, which cannot be easily explained by our application of current tidal mechanisms or by differential rotation.

Figures (5)

• Figure 1: Histogram showing the orbital period distribution of binaries from the EBLM catalog. The three histograms are stacked vertically for clarity. The top histogram represents EBLMs for which no rotational signature was detected, the middle one highlights the systems for which 2024MNRAS.529.4442S measured rotation periods from TESS light curves exhibiting out-of-eclipse variability due to starspots, and the bottom histogram shows the ellipsoidal variables discovered by 2024MNRAS.529.4442S.
• Figure 2: Eccentricity distribution of systems in our sample. Eccentricities are taken from 2017AA...EBLM4, which reports values with a median precision of 0.0025. Circular systems are shown as circles, and eccentric systems as star symbols. Left: Marker colors indicate the tidal circularization timescales derived in this study due to dissipation in the primary (more massive) star. Right: Marker colors indicate the minimum of the two circularization timescales due to dissipation in either the primary or the secondary star, whichever yields the shorter timescale.
• Figure 3: Period–ratio diagram for our sample. The solid red line at $P_{\rm orb}/P_{\rm rot} = 1$ marks the synchronization line, with systems clustered around it identified as tidally locked. Circular EBLMs are shown as purple circles, while eccentric EBLMs are shown as star symbols, color-coded by eccentricity. Since most systems with $P_{\rm orb} \lesssim 3$ days are synchronized, this region is labeled the “Synchronization Zone”, whereas longer-period region consists of binaries showing larger deviations from synchronization and is labeled as the “Transition Zone”. An approximate best-fit straight line, representing the boundary defined by the most subsynchronous systems is shown as a dashed red line and referred to as the “subsynchronization slope”.
• Figure 4: Dependence of the degree of synchronization on key system parameters. All three panels show period–ratio diagrams ($P_{\rm orb}/P{\rm rot}$ vs. $P_{\rm orb}$): (top) color-coded by synchronization timescale, (middle) by mass ratio ($q$), and (bottom) by primary mass ($M_{\rm A}$).
• Figure 5: Convective Rossby number ($\mathrm{Ro}_c$) distribution for the systems in our sample. The blue-shaded region corresponds to $\mathrm{Ro}_c < 1$ and the red-shaded region to $\mathrm{Ro}_c > 1$. Eccentric binaries are denoted by stars, like in other plots. Binaries with the primary star in the blue region are expected to exhibit primarily solar-type differential rotation (faster at the equator), whereas those in the red region are expected to primarily exhibit antisolar-type differential rotation (faster at the poles).