A self-consistent weak friction model for the tidal evolution of circumbinary planets

Zoppetti, F. A.; Beaugé, C.; Leiva, A. M.; Folonier, H.

doi:10.1051/0004-6361/201935849

Cited by 6 publications

(46 citation statements)

References 19 publications

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“…It may also be possible to reduce the binary eccentricity through tidal interaction with the planet after the disc has been dispersed. Thereby, the low eccentric binaries may have been more eccentric during the planet formation phase and only lost the eccentricity after the planets reached stable orbits and were thus undisturbed by the outer disc (Zoppetti et al 2019).…”

Section: Discussion and Summarymentioning

confidence: 99%

Parking planets in circumbinary discs

Penzlin

Kley

Nelson

2021

A&A

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The Kepler space mission has discovered about a dozen planets orbiting around binary stars systems. Most of these circumbinary planets lie near their instability boundaries, at about three to five binary separations. Past attempts to match these final locations through an inward migration process were only shown to be successful for the Kepler-16 system. Here, we study ten circumbinary systems and attempt to match the final parking locations and orbital parameters of the planets with a disc-driven migration scenario. We performed 2D locally isothermal hydrodynamical simulations of circumbinary discs with embedded planets and followed their migration evolution using different values for the disc viscosity and aspect ratio. We found that for the six systems with intermediate binary eccentricities (0.1 ≤ ebin ≤ 0.21), the final planetary orbits matched the observations closely for a single set of disc parameters, specifically, a disc viscosity of α = 10−4 and an aspect ratio of H∕r ~ 0.04. For these systems the planet masses are large enough to open at least a partial gap in their discs as they approach the binary, forcing the discs to become circularised and allowing for further migration towards the binary – ultimately leading to a good agreement with the observed planetary orbital parameters. For systems with very small or large binary eccentricities, the match was not as good as the very eccentric discs and the large inner cavities in these cases prevented close-in planet migration. In test simulations with higher than observed planet masses, a better agreement was found for those systems. The good agreement for six out of the ten modelled systems, where the relative difference between observed and simulated final planet orbit is ≤10% strongly supports the idea that planet migration in the disc brought the planets to their present locations.

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Section: Discussion and Summarymentioning

confidence: 99%

Parking planets in circumbinary discs

Penzlin

Kley

Nelson

2021

A&A

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“…In Zoppetti et al (2019) we presented a self-consistent tidal model for the planar and non-oblique 3BP, using a weak friction Constant Time Lag (CTL) model based on the expressions of the tidal forces and torques of the classical work of Mignard (1979). We applied the model to the circumbinary (CB) case and found that for systems like those discovered by the Kepler mission, the planet acquired stationary spin rates on timescales of approximately millions of years (depending on the dissipation factor Q 2 ) and, curiously, in subsynchronous solutions (Zoppetti et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Creep tide model for the three-body problem

Zoppetti

Folonier

Leiva

et al. 2021

A&A

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We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into account. Based on the creep tide theory, we present a set of differential equations that describes the rotational evolution of each body, in a formalism that is easily extensible to the N tidally interacting body problem. We apply our model to the case of a circumbinary planet and use a Kepler-38 like binary system as a working example. We find that, in this low planetary eccentricity case, the most likely final stationary rotation state is the 1:1 spin–orbit resonance, considering an arbitrary planetary viscosity inside the estimated range for the Solar System planets. The timescales for reaching the equilibrium state are expected to be approximately millions of years for stiff bodies but can be longer than the age of the system for planets with a large gaseous component. We derive analytical expressions for the mean rotational stationary state, based on high-order power series of the ratio of the semimajor axes a1∕a2 and low-order expansions of the eccentricities. These are found to very accurately reproduce the mean behaviour of the low-eccentric numerical integrations for arbitrary planetary relaxation factors, and up to a1∕a2 ~ 0.4. Our analytical model is used to predict the stationary rotation of the Kepler circumbinary planets and we find that most of them are probably rotating in a subsynchronous state, although the synchrony shift is much less important than our previous estimations. We present a comparison of our results with those obtained with the Constant Time Lag and find that, as opposed to the assumptions in our previous works, the cross torques have a non-negligible net secular contribution, and must be taken into account when computing the tides over each body in an N-extended-body system from an arbitrary reference frame. These torques are naturally taken into account in the creep theory. In addition to this, the latter formalism considers more realistic rheology that proved to reduce to the Constant Time Lag model in the gaseous limit and also allows several additional relevant physical phenomena to be studied.

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“…We focused our habitability analysis on orbital evolution, but many other factors might be important and could be included in future work. CBP rotation rates may reach a stationary solution analogous to tidal locking (Zoppetti et al 2019;Zoppetti et al 2020), which could significantly affect climates (see e.g., Pierrehumbert 2011;Yang et al 2013;Del Genio et al 2019). The planets of M dwarf stars, such as those in Figs.…”

Section: Discussionmentioning

confidence: 99%

“…Fleming et al (2018) dubbed their model the "Stellar-Tidal Evolution Ejection of Planets" (STEEP). We note that Zoppetti et al (2019) showed that outward-then-inward evolution of the binary orbit can occur even when one ignores the stellar evolution.…”

Section: Introductionmentioning

confidence: 88%

Orbital evolution of potentially habitable planets of tidally interacting binary stars

Graham

Fleming

Barnes

2021

A&A

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We simulate the coupled stellar and tidal evolution of short-period binary stars (orbital period P orb < ∼ 8 days) to investigate the orbital oscillations, instellation cycles, and orbital stability of circumbinary planets (CBPs). We consider two tidal models and show that both predict an outward-then-inward evolution of the binary's semi-major axis a bin and eccentricity e bin. This orbital evolution drives a similar evolution of the minimum CBP semi-major axis for orbital stability. By expanding on previous models to include the evolution of the mass concentration, we show that the maximum in the CBP orbital stability limit tends to occur 100 Myr after the planets form, a factor of 100 longer than previous investigations. This result provides further support for the hypothesis that the early stellar-tidal evolution of binary stars has removed CBPs from short-period binaries. We then apply the models to Kepler-47 b, a CBP orbiting close to its host stars' stability limit, to show that if the binary's initial e bin > ∼ 0.24, the planet would have been orbiting within the instability zone in the past and probably wouldn't have survived. For stable, hypothetical cases in which the stability limit does not reach a planet's orbit, we find that the amplitudes of a bin and e bin oscillations can damp by up to 10% and 50%, respectively. Finally, we consider equal-mass stars with P orb = 7.5 days and compare the HZ to the stability limit. We find that for stellar masses < ∼ 0.12M , the HZ is completely unstable, even if the binary orbit is circular. For e bin < ∼ 0.5, that limit increases to 0.17M , and the HZ is partially destabilized for stellar masses up to 0.45M. These results may help guide searches for potentially habitable CBPs, as well as characterize their evolution and likelihood to support life after they are found.

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A self-consistent weak friction model for the tidal evolution of circumbinary planets

Cited by 6 publications

References 19 publications

Parking planets in circumbinary discs

Parking planets in circumbinary discs

Creep tide model for the three-body problem

Orbital evolution of potentially habitable planets of tidally interacting binary stars

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