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Register a new userCreep Tide Model for the 3-Body Problem. The rotational evolution of a circumbinary planet
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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 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.
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We present a self-consistent model for the tidal evolution of circumbinary planets. Based on the weak-friction model, we derive expressions of the resulting forces and torques considering complete tidal interactions between all the bodies of the system. Although the tidal deformation suffered by each extended mass must take into account the combined gravitational effects of the other two bodies, the only tidal forces that have a net effect on the dynamic are those that are applied on the same body that exerts the deformation, as long as no mean-motion resonance exists between the masses. We apply the model to the Kepler-38 binary system. The evolution of the spin equations shows that the planet reaches a stationary solution much faster than the stars, and the equilibrium spin frequency is sub-synchronous. The binary components evolve on a longer timescale, reaching a super-synchronous solution very close to that derived for the 2-body problem. After reaching spin stationarity, the eccentricity is damped in all bodies and for all the parameters analyzed here. A similar effect is noted for the binary separation. The semimajor axis of the planet, on the other hand, may migrate inwards or outwards, depending on the masses and orbital parameters. In some cases the secular evolution of the system may also exhibit an alignment of the pericenters, requiring to include additional terms in the tidal model. Finally, we derived analytical expressions for the variational equations of the orbital evolution and spin rates based on low-order elliptical expansions in the semimajor axis ratio and the eccentricities. These are found to reduce to the 2-body case when one of the masses is taken equal to zero. This model allow us to find a close and simple analytical expression for the stationary spin rates of all the bodies, as well as predicting the direction and magnitude of the orbital migration.
Determining habitable zones in binary star systems can be a challenging task due to the combination of perturbed planetary orbits and varying stellar irradiation conditions. The concept of dynamically informed habitable zones allows us, nevertheless, to make predictions on where to look for habitable worlds in such complex environments. Dynamically informed habitable zones have been used in the past to investigate the habitability of circumstellar planets in binary systems and Earth-like analogs in systems with giant planets. Here, we extend the concept to potentially habitable worlds on circumbinary orbits. We show that habitable zone borders can be found analytically even when another giant planet is present in the system. By applying this methodology to Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64, Kepler-413, Kepler-453, Kepler-1647 and Kepler-1661 we demonstrate that the presence of the known giant planets in the majority of those systems does not preclude the existence of potentially habitable worlds. Among the investigated systems Kepler-35, Kepler-38 and Kepler-64 currently seem to offer the most benign environment. In contrast, Kepler-16 and Kepler-1647 are unlikely to host habitable worlds.
It has been established theoretically that atmospheric thermal tides on rocky planets can lead to significant modifications of rotational evolution, both close to synchronous rotation and at faster rotations if certain resonant conditions are met. Here it is demonstrated that the normally considered dissipative gravitational tidal evolution of rocky planet rotation could, in principle, be stalled by thermal tide resonances for Earth-analog worlds in the liquid water orbital zone of stars more massive than ~0.3 Msolar. The possibility of feedback effects between a planetary biosphere and the planetary rotational evolution are examined. Building on earlier studies, it is suggested that atmospheric oxygenation, and ozone production could play a key role in planetary rotation evolution, and therefore represents a surprising but potent form of biological imprint on astronomically accessible planetary characteristics.
Kepler-16 is an eccentric low-mass eclipsing binary with a circumbinary transiting planet. Here we investigate the angular momentum of the primary star, based on Kepler photometry and Keck spectroscopy. The primary stars rotation period is 35.1 +/- 1.0 days, and its projected obliquity with respect to the stellar binary orbit is 1.6 +/- 2.4 degrees. Therefore the three largest sources of angular momentum---the stellar orbit, the planetary orbit, and the primarys rotation---are all closely aligned. This finding supports a formation scenario involving accretion from a single disk. Alternatively, tides may have realigned the stars despite their relatively wide separation (0.2 AU), a hypothesis that is supported by the agreement between the measured rotation period and the pseudosynchronous period of tidal evolution theory. The rotation period, chromospheric activity level, and fractional light variations suggest a main-sequence age of 2-4 Gyr. Evolutionary models of low-mass stars can match the observed masses and radii of the primary and secondary stars to within about 3%.
We report the discovery and confirmation of a transiting circumbinary planet (PH1b) around KIC 4862625, an eclipsing binary in the Kepler field. The planet was discovered by volunteers searching the first six Quarters of publicly available Kepler data as part of the Planet Hunters citizen science project. Transits of the planet across the larger and brighter of the eclipsing stars are detectable by visual inspection every ~137 days, with seven transits identified in Quarters 1-11. The physical and orbital parameters of both the host stars and planet were obtained via a photometric-dynamical model, simultaneously fitting both the measured radial velocities and the Kepler light curve of KIC 4862625. The 6.18 +/- 0.17 Earth radii planet orbits outside the 20-day orbit of an eclipsing binary consisting of an F dwarf (1.734 +/- 0.044 Solar radii, 1.528 +/- 0.087 Solar masses) and M dwarf (0.378+/- 0.023 Solar radii, 0.408 +/- 0.024 Solar masses). For the planet, we find an upper mass limit of 169 Earth masses (0.531 Jupiter masses) at the 99.7% confidence level. With a radius and mass less than that of Jupiter, PH1b is well within the planetary regime. Outside the planets orbit, at ~1000 AU,a previously unknown visual binary has been identified that is likely bound to the planetary system, making this the first known case of a quadruple star system with a transiting planet.
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