Nonlinear tidal flows in short-period planets

I discuss two related nonlinear mechanisms of tidal dissipation that require finite tidal deformations for their operation: the elliptical instability and the precessional instability. Both are likely to be important for the tidal evolution of short-period extrasolar planets. The elliptical instability is a fluid instability of elliptical streamlines, such as in tidally deformed non-synchronously rotating or non-circularly orbiting planets. I summarise the results of local and global simulations that indicate this mechanism to be important for tidal spin synchronisation, planetary spin-orbit alignment and orbital circularisation for the shortest period hot Jupiters. The precessional instability is a fluid instability that occurs in planets undergoing axial precession, such as those with spin-orbit misalignments (non-zero obliquities). I summarise the outcome of local MHD simulations designed to study the turbulent damping of axial precession, which suggest this mechanism to be important in driving tidal evolution of the spin-orbit angle for hot Jupiters. Avenues for future work are also discussed.

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Effects of magnetic braking and tidal friction on hot Jupiters

Proceedings of the International Astronomical Union ◽

10.1017/s1743921309030634 ◽

2008 ◽

Vol 4 (S259) ◽

pp. 295-302

Author(s):

Adrian J. Barker ◽

Gordon I. Ogilvie

Keyword(s):

Evolution Equations ◽

Phase Plane Analysis ◽

Spin Orbit ◽

Tidal Evolution ◽

Tidal Friction ◽

Hot Jupiters ◽

Secular Evolution ◽

Orbit Evolution ◽

Short Period ◽

Magnetic Braking

AbstractTidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction (Eggleton et al. 1998), we analyse the effects of the inclusion of stellar magnetic braking on the evolution of such systems. A phase-plane analysis of a simplified system of equations, including only the stellar tide together with a model of the braking torque proposed by Verbunt & Zwaan (1981), is presented. The inclusion of stellar magnetic braking is found to be extremely important in determining the secular evolution of such systems, and its neglect results in a very different orbital history. We then show the results of numerical integrations of the full tidal evolution equations, using the misaligned spin and orbit of the XO-3 system as an example, to study the accuracy of simple timescale estimates of tidal evolution. We find that it is essential to consider coupled evolution of the orbit and the stellar spin in order to model the behaviour accurately. In addition, we find that for typical Hot Jupiters the stellar spin-orbit alignment timescale is of the same order as the inspiral time, which tells us that if a planet is observed to be aligned, then it probably formed coplanar. This reinforces the importance of Rossiter-McLaughlin effect observations in determining the degree of spin-orbit alignment in transiting systems.

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Constraining Planetary Migration Mechanisms in Systems of Giant Planets

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313009046 ◽

2013 ◽

Vol 8 (S299) ◽

pp. 386-390

Author(s):

Rebekah I. Dawson ◽

Ruth A. Murray-Clay ◽

John Asher Johnson

Keyword(s):

Giant Planet ◽

Giant Planets ◽

Tidal Dissipation ◽

Hot Jupiters ◽

Short Period ◽

Pile Up ◽

Planetary Migration ◽

Multi Body ◽

Host Stars

AbstractIt was once widely believed that planets formed peacefully in situ in their proto-planetary disks and subsequently remain in place. Instead, growing evidence suggests that many giant planets undergo dynamical rearrangement that results in planets migrating inward in the disk, far from their birthplaces. However, it remains debated whether this migration is caused by smooth planet-disk interactions or violent multi-body interactions. Both classes of model can produce Jupiter-mass planets orbiting within 0.1 AU of their host stars, also known as hot Jupiters. In the latter class of model, another planet or star in the system perturbs the Jupiter onto a highly eccentric orbit, which tidal dissipation subsequently shrinks and circularizes during close passages to the star. We assess the prevalence of smooth vs. violent migration through two studies. First, motivated by the predictions of Socrates et al. (2012), we search for super-eccentric hot Jupiter progenitors by using the “photoeccentric effect” to measure the eccentricities of Kepler giant planet candidates from their transit light curves. We find a significant lack of super- eccentric proto-hot Jupiters compared to the number expected, allowing us to place an upper limit on the fraction of hot Jupiters created by stellar binaries. Second, if both planet-disk and multi-body interactions commonly cause giant planet migration, physical properties of the proto-planetary environment may determine which is triggered. We identify three trends in which giant planets orbiting metal rich stars show signatures of planet-planet interactions: (1) gas giants orbiting within 1 AU of metal-rich stars have a range of eccentricities, whereas those orbiting metal- poor stars are restricted to lower eccentricities; (2) metal-rich stars host most eccentric proto-hot Jupiters undergoing tidal circularization; and (3) the pile-up of short-period giant planets, missing in the Kepler sample, is a feature of metal-rich stars and is largely recovered for giants orbiting metal-rich Kepler host stars. These two studies suggest that both disk migration and planet-planet interactions may be widespread, with the latter occurring primarily in metal-rich planetary systems where multiple giant planets can form. Funded by NSF-GRFP DGE-1144152.

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Tidal evolution of the Pluto–Charon binary

Astronomy and Astrophysics ◽

10.1051/0004-6361/202038858 ◽

2020 ◽

Vol 644 ◽

pp. A94

Author(s):

Alexandre C. M. Correia

Keyword(s):

3D Model ◽

Central Star ◽

Initial System ◽

The Sun ◽

Spin Orbit ◽

Tidal Evolution ◽

Tidal Dissipation ◽

Two Bodies ◽

Initial Orbit

A giant collision is believed to be at the origin of the Pluto–Charon system. As a result, the initial orbit and spins after impact may have substantially differed from those observed today. More precisely, the distance at periapse may have been shorter, subsequently expanding to its current separation by tides raised simultaneously on the two bodies. Here we provide a general 3D model to study the tidal evolution of a binary composed of two triaxial bodies orbiting a central star. We apply this model to the Pluto–Charon binary, and notice some interesting constraints on the initial system. We observe that when the eccentricity evolves to high values, the presence of the Sun prevents Charon from escaping because of Lidov-Kozai cycles. However, for a high initial obliquity for Pluto or a spin-orbit capture of Charon’s rotation, the binary eccentricity is damped very efficiently. As a result, the system can maintain a moderate eccentricity throughout its evolution, even for strong tidal dissipation on Pluto.

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Three short-period Jupiters from TESS

Astronomy and Astrophysics ◽

10.1051/0004-6361/202037941 ◽

2020 ◽

Vol 639 ◽

pp. A76 ◽

Cited By ~ 1

Author(s):

L. D. Nielsen ◽

R. Brahm ◽

F. Bouchy ◽

N. Espinoza ◽

O. Turner ◽

...

Keyword(s):

Stellar System ◽

Phase Curve ◽

Mass Determination ◽

Tidal Dissipation ◽

Giant Star ◽

Hot Jupiters ◽

Short Period ◽

Host Stars ◽

Interesting System

We report the confirmation and mass determination of three hot Jupiters discovered by the Transiting Exoplanet Survey Satellite (TESS) mission: HIP 65Ab (TOI-129, TIC-201248411) is an ultra-short-period Jupiter orbiting a bright (V = 11.1 mag) K4-dwarf every 0.98 days. It is a massive 3.213 ± 0.078 MJ planet in a grazing transit configuration with an impact parameter of b = 1.17−0.08+0.10. As a result the radius is poorly constrained, 2.03−0.49+0.61RJ. The planet’s distance to its host star is less than twice the separation at which it would be destroyed by Roche lobe overflow. It is expected to spiral into HIP 65A on a timescale ranging from 80 Myr to a few gigayears, assuming a reduced tidal dissipation quality factor of Qs′ = 107 − 109. We performed a full phase-curve analysis of the TESS data and detected both illumination- and ellipsoidal variations as well as Doppler boosting. HIP 65A is part of a binary stellar system, with HIP 65B separated by 269 AU (3.95 arcsec on sky). TOI-157b (TIC 140691463) is a typical hot Jupiter with a mass of 1.18 ± 0.13 MJ and a radius of 1.29 ± 0.02 RJ. It has a period of 2.08 days, which corresponds to a separation of just 0.03 AU. This makes TOI-157 an interesting system, as the host star is an evolved G9 sub-giant star (V = 12.7). TOI-169b (TIC 183120439) is a bloated Jupiter orbiting a V = 12.4 G-type star. It has a mass of 0.79 ±0.06 MJ and a radius of 1.09−0.05+0.08RJ. Despite having the longest orbital period (P = 2.26 days) of the three planets, TOI-169b receives the most irradiation and is situated on the edge of the Neptune desert. All three host stars are metal rich with [Fe / H] ranging from 0.18 to0.24.

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Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters

Monthly Notices of the Royal Astronomical Society ◽

10.1111/j.1365-2966.2012.20893.x ◽

2012 ◽

Vol 423 (1) ◽

pp. 486-492 ◽

Cited By ~ 86

Author(s):

Dong Lai

Keyword(s):

Spin Orbit ◽

Tidal Dissipation ◽

Hot Jupiters

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Characterizing the Eccentricities of Transiting Extrasolar Planets with Kepler and CoRoT

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308026306 ◽

2008 ◽

Vol 4 (S253) ◽

pp. 111-119

Author(s):

Eric B. Ford ◽

Knicole D. Colón

Keyword(s):

Radial Velocity ◽

Extrasolar Planets ◽

Giant Planets ◽

Physical Parameters ◽

Tidal Dissipation ◽

Transiting Planets ◽

Photometric Observations ◽

Short Period ◽

Photometric Measurements ◽

Rocky Planets

AbstractRadial velocity planet searches have revealed that many giant planets have large eccentricities, in striking contrast with the giant planets in the solar system and prior theories of planet formation. The realization that many giant planets have large eccentricities raises a fundamental question: Do terrestrial-size planets of other stars typically have significantly eccentric orbits or nearly circular orbits like the Earth? While space-based missions such as CoRoT and Kepler will be capable of detecting nearly Earth-sized planets, it will be extremely challenging to measure their eccentricities using radial velocity observations. We review several ways that photometric measurements of transit light curves can constrain the eccentricity of transiting planets. In particular, photometric observations of transit durations can be used to characterize the distribution of orbital eccentricities for various populations of transiting planets (e.g., nearly Earth-sized planets in the habitable zone) without relying on radial velocity measurements. Applying this technique to rocky planets to be found by CoRoT and Kepler will enable constraints on theories for the excitation of eccentricities and tidal dissipation. We also remind observers that several short-period transiting planets are known to have significant eccentricities and caution that assuming they are on a circular orbit can reduce the probability of detecting transits, impact planning for follow-up observations, and adversely affect measurements of the physical parameters of the star and planet.

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Tidal evolution of close-in extra-solar planets

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308016591 ◽

2007 ◽

Vol 3 (S249) ◽

pp. 187-196

Author(s):

Brian Jackson ◽

Richard Greenberg ◽

Rory Barnes

Keyword(s):

Evolution Equations ◽

Theoretical Models ◽

Physical Models ◽

Tidal Evolution ◽

Tidal Dissipation ◽

Thermal Budget ◽

Hot Jupiters ◽

The Past ◽

Tidal Heating

AbstractThe distribution of eccentricities e of extra-solar planets with semi-major axes a > 0.2 AU is very uniform, and values for e are generally large. For a < 0.2 AU, eccentricities are much smaller (most e < 0.2), a characteristic widely attributed to damping by tides after the planets formed and the protoplanetary gas disk dissipated. We have integrated the classical coupled tidal evolution equations for e and a backward in time over the estimated age of each planet, and confirmed that the distribution of initial e values of close-in planets matches that of the general population for reasonable tidal dissipation values Q, with the best fits for stellar and planetary Q being ∼ 105.5 and ∼ 106.5, respectively. The current small values of a were only reached gradually due to tides over the lifetimes of the planets, i.e., the earlier gas disk migration did not bring all planets to their current orbits. As the orbits tidally evolved, there was substantial tidal heating within the planets. The past tidal heating of each planet may have contributed significantly to the thermal budget that governed the planet's physical properties, including its radius, which in many cases may be measured by observing transit events. Here we also compute the plausible heating histories for a few planets with anomalously large measured radii, including HD 209458 b. We show that they may have undergone substantial tidal heating during the past billion years, perhaps enough to explain their large radii. Theoretical models of exoplanet interiors and the corresponding radii should include the role of large and time-variable tidal heating. Our results may have important implications for planet formation models, physical models of “hot Jupiters”, and the success of transit surveys.

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Tidal evolution of star-planet systems

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311020242 ◽

2010 ◽

Vol 6 (S276) ◽

pp. 238-242

Author(s):

Rosemary A. Mardling

Keyword(s):

Binary Star ◽

Spin Orbit ◽

Tidal Evolution ◽

Tide Model ◽

Orbital Decay ◽

Short Period

AbstractThe equilibrium tide model in the weak friction approximation is used by the binary star and exoplanet communities to study the tidal evolution of short-period systems, however, each uses a slightly different approach which potentially leads to different conclusions about the timescales on which various processes occur. Here we present an overview of these two approaches, and show that for short-period planets the circularization timescales they predict differ by at most a factor of a few. A discussion of the timescales for orbital decay, spin-orbit synchronization and spin-orbit alignment is also presented.

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