# Features of Gaia DR3 Spectroscopic Binaries I. Tidal circularization of Main-Sequence Stars

**Authors:** Dolev Bashi, Tsevi Mazeh, Simchon Faigler  
**arXiv:** [2304.00043](https://arxiv.org/abs/2304.00043)  
**Date:** 2023-03-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.00043v1/

## Key points

- Tidal circularization theory is important for understanding the evolution of short-period binaries, close triple systems, cataclysmic binaries, and X-ray binaries.
- Tidal interaction could play a crucial role in the formation and evolution of exoplanets, hot Jupiters, and their orbit alignment with the stellar spin.
- Many observed samples of short-period binaries display a cutoff period ($P_{\rm cut}$) where almost all binaries with periods shorter than $P_{\rm cut}$ have circular orbits due to long-term circularization processes induced by tidal interaction between the two stars of each binary.
- Using MS spectroscopic orbits recently released by $\textit{Gaia}$, it has been found that $P_{\rm cut}$ does not depend on the stellar age but instead varies with stellar temperature. The cutoff period decreases linearly from 6.5 days at $T_{\rm eff}\sim 5700$ K to $\sim 2.5$ days at $6800$ K.
- A new algorithm was used to derive $P_{\rm cut}$ based on clear upper envelopes displayed in period-eccentricity diagrams which suggest that circularization likely took place during the pre-main sequence phase as suggested previously by Zahn and Bouchet (1989) and Khaluillin and Khaluillina (2011).
- Recent observational evidence has been presented for orbital decay of very close hot Jupiters based on precise timings of transits spanning over more than a decade which has exciting potential to further constrain the theory of tidal interaction when additional information is available.
- Understanding this theory has far-reaching implications for binary and exoplanet circularization, synchronization, and alignment; five observational avenues might be useful in order to deepen our understanding:
- comparing observational evidence with a realistic tidal model;
- studying primordial period-eccentricity distributions;
- examining planetary period decay in real-time;
- observing binary star systems; and
- analyzing X-ray binaries.

## Summary

The theory of tidal circularization is essential for understanding the evolution of short-period binaries, close triple systems, cataclysmic binaries, and X-ray binaries. Tidal interaction could also play a crucial role in the formation and evolution of exoplanets, hot Jupiters, and their orbit alignment with the stellar spin. Previous studies have pointed out that many observed samples of short-period binaries display a cutoff period, $P_{\rm cut}$, such that almost all binaries with periods shorter than $P_{\rm cut}$ have circular orbits. This feature is probably due to long-term circularization processes induced by tidal interaction between the two stars of each binary. It was previously thought that coeval main-sequence (MS) samples of open clusters display $P_{\rm cut}$ that depends on the sample age. However, using the unprecedentedly large sample of MS spectroscopic orbits recently released by $\textit{Gaia}$, it has been found that $P_{\rm cut}$ does not depend on the stellar age but instead varies with stellar temperature. The cutoff period decreases linearly from 6.5 days at $T_{\rm eff}\sim 5700$ K to $\sim 2.5$ days at $6800$ K.

The new algorithm used to derive $P_{\rm cut}$ relied on clear upper envelopes displayed in the period-eccentricity diagrams which suggest that circularization has likely taken place during the pre-main sequence phase as suggested already in 1989 by Zahn and Bouchet and later by Khaluillin and Khaluillina in 2011. Furthermore, recent observational evidence has been presented for orbital decay of very close hot Jupiters based on precise timings of transits spanning over more than a decade which has exciting potential to further constrain the theory of tidal interaction when additional information is available. Understanding this theory has far reaching implications for binary and exoplanet circularization, synchronization and alignment; five observational avenues might be useful in order to deepen our understanding: (1) comparing observational evidence with a realistic tidal model; (2) studying primordial period-eccentricity distributions; (3) examining planetary period decay in real time; (4) observing binary star systems; and (5) analyzing X-ray binaries.