Creep Tide Model for the 3-Body Problem. The rotational evolution of a circumbinary planet

Abstract

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 the 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. We derive analytical expressions for the mean rotational stationary state, based on high-order power series of the semimajor axes ratio a1 /a2 and low-order expansions of the eccentricities. These are found to reproduce very accurately the mean behaviour of the low-eccentric numerical integrations for arbitrary planetary relaxation factors, and up to a1/a2 \sim 0.4. Our analytical model is used to predict the stationary rotation of the Kepler circumbinary planets and find that most of them are probably rotating in a sub-synchronous state, although the synchrony shift is much less important than the one estimated in Zoppetti et al. (2019, 2020). We present a comparison of our results with those obtained with the Constant Time Lag and find that, unlike what we assumed 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.

References in corpus (24)

• Long-Term Stability of Planets in Binary Systems
• Kepler-16: A Transiting Circumbinary Planet
• The Transiting Circumbinary Planets Kepler-34 and Kepler-35
• Kepler-47: A Transiting Circumbinary Multi-Planet System
• Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited
• Planet Hunters: A Transiting Circumbinary Planet in a Quadruple Star System
• The Neptune-Sized Circumbinary Planet Kepler-38b
• Kepler-413b: a slightly misaligned, Neptune-size transiting circumbinary planet
• Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths
• Increased Tidal Dissipation Using Advanced Rheological Models: Implications for Io and Tidally Active Exoplanets
• Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
• Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach
• No pseudosynchronous rotation for terrestrial planets and moons
• The Planetary Mass-Radius Relation and its Dependence on Orbital Period as Measured by Transit Timing Variations and Radial Velocities
• Tidal Evolution of Asteroidal Binaries. Ruled by Viscosity. Ignorant of Rigidity
• Secular and tidal evolution of circumbinary systems
• Kepler-1661 b: A Neptune-sized Kepler Transiting Circumbinary Planet around a Grazing Eclipsing Binary
• Tidal synchronization of close-in satellites and exoplanets. II. Spin dynamics and extension to Mercury and exoplanets host stars
• The flattenings of the layers of rotating planets and satellites deformed by a tidal potential
• Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus
• The small and large lags of the elastic and anelastic tides. The virtual identity of two rheophysical theories
• A self-consistent weak friction model for the tidal evolution of circumbinary planets
• Rotation and figure evolution in the creep tide theory. A new approach and application to Mercury
• Tidal evolution of circumbinary systems with arbitrary eccentricities: applications for Kepler systems