Tidal damping of the mutual inclination in hierarchical systems

Correia, A. C. M.; Boué, G.; Laskar, Jacques; Morais, M. H. M.

doi:10.1051/0004-6361/201220482

Cited by 22 publications

(20 citation statements)

References 48 publications

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“…As a simplified model, we only consider the dominating conservative terms of the secular hamiltonian (after averaging over the mean anomalies), namely the quadrupolar interaction with general relativity corrections (e.g., Correia et al 2013):…”

Section: Phase Portraitsmentioning

confidence: 99%

Dynamical evolution of triple-star systems by Lidov–Kozai cycles and tidal friction

Bataille

Libert

Correia

2018

Monthly Notices of the Royal Astronomical Society

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Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with tidal friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and nonuniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" h = (1 − e 2 ) cos i in the dynamical evolution of triple-star systems, by showing that phase portraits at given h-values unveil different evolution paths.

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Section: Phase Portraitsmentioning

confidence: 99%

Dynamical evolution of triple-star systems by Lidov–Kozai cycles and tidal friction

Bataille

Libert

Correia

2018

Monthly Notices of the Royal Astronomical Society

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“…we can use a quadrupolar approximation to study its secular dynamics (e.g. Kozai 1962;Correia et al 2013). As a result, the orbital evolution becomes integrable and easy to understand.…”

Section: Dynamical Evolutionmentioning

confidence: 99%

“…As a consequence, in the frame of a quadrupolar model the tidal evolution can be delayed to a maximum of 1.5 Gyr. However, this is not very realistic, because near the separatrix the inner orbit becomes chaotic, and the planet becomes a hot Jupiter in a few Myr (see Correia et al 2013).…”

Section: Dynamical Evolutionmentioning

confidence: 99%

SOPHIE velocimetry ofKeplertransit candidates

Santerne¹,

Hébrard²,

Deleuil³

et al. 2014

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In this paper we report a new transiting warm giant planet: KOI-1257 b. It was first detected in photometry as a planet-candidate by the Kepler space telescope and then validated thanks to a radial velocity follow-up with the SOPHIE spectrograph. It orbits its host star with a period of 86.647661 d ± 3 s and a high eccentricity of 0.772 ± 0.045. The planet transits the main star of a metal-rich, relatively old binary system with stars of mass of 0.99 ± 0.05 M and 0.70 ± 0.07 M for the primary and secondary, respectively. This binary system is constrained thanks to a self-consistent modelling of the Kepler transit light curve, the SOPHIE radial velocities, line bisector and full-width half maximum (FWHM) variations, and the spectral energy distribution. However, future observations are needed to confirm it. The PASTIS fully-Bayesian software was used to validate the nature of the planet and to determine which star of the binary system is the transit host. By accounting for the dilution from the binary both in photometry and in radial velocity, we find that the planet has a mass of 1.45 ± 0.35 M , and a radius of 0.94 ± 0.12 R , and thus a bulk density of 2.1 ± 1.2 g cm −3 . The planet has an equilibrium temperature of 511 ± 50 K, making it one of the few known members of the warm-Jupiter population. The HARPS-N spectrograph was also used to observe a transit of KOI-1257 b, simultaneously with a joint amateur and professional photometric follow-up, with the aim of constraining the orbital obliquity of the planet. However, the Rossiter-McLaughlin effect was not clearly detected, resulting in poor constraints on the orbital obliquity of the planet.

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“…The results showed that the inclusion of the R 4C term gives results that are worst than the ones given by the R 3C term, but the inclusion of the R 5C term corrects the problem. Correia et al (2013) shows that the effects of the tides combined with gravitational interactions helped to reduce the initial mutual inclination to small values on time scales. This effect is not a direct consequence of the tides on the orbits, but results from a secular forcing of the inner planet's flattening.…”

Section: Introductionmentioning

confidence: 98%

“…The choice of the small parameter (α) is made because, in general, the hierarchical systems have highly eccentric orbits which makes it difficult the expansion of the perturbation in series of the eccentricity. It is more convenient to use the ratio of the semi-major axis of the planet (a 1 ) and the disturbing star (a 2 ), because exact expressions can be computed for the secular system (see Correia et al 2013). The orbit of the disturbing star is considered to be elliptical, planar and fixed in space.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the orbital evolution of exoplanets

et al. 2015

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An exoplanet, or extrasolar planet, is a planet that does not orbit the Sun, but is around a different star, stellar remnant, or brown dwarf. Up to now, about 1900 exoplanets were discovered. To better understand the dynamics of these exoplanets, a study with respect to possible collisions of the planet with the central star is shown here. We present an expanded model in a small parameter that takes into account up to the fifth order to analyze the effect of this potential in the orbital elements of the extrasolar planet. Numerical simulations were also performed using the N-body simulations, using the software Mercury, to compare the results with the ones obtained by the analytical model. The numerical simulations are presented in two stages: one considering the celestial bodies as point masses and the other one taking into account their dimensions. This analysis showed that the planet collided with the central star in the moment of the first inversion for orbits with high inclinations in various situations. The results of the simulations of the equations developed in this study are consistent with the N-body numerical simulations. We analyze also the flip of the inclination taking into account the coupling of the perturbations of the third body, effect due to the precession of periastron and the tide effect. In general, we find that such perturbations combined delay the time of first inversion, but do not keep the planet in a prograde or retrograde orbit.

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Tidal damping of the mutual inclination in hierarchical systems

Cited by 22 publications

References 48 publications

Dynamical evolution of triple-star systems by Lidov–Kozai cycles and tidal friction

Dynamical evolution of triple-star systems by Lidov–Kozai cycles and tidal friction

SOPHIE velocimetry ofKeplertransit candidates

Analysis of the orbital evolution of exoplanets

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