Recent discoveries of several transiting planets with clearly non-zero eccentricities and some large inclinations started changing the simple picture of close-in planets having circular and well-aligned orbits. Two major scenarios to form such planets are planet migration in a disk, and planet--planet interactions combined with tidal dissipation. The former scenario can naturally produce a circular and low-obliquity orbit, while the latter implicitly assumes an initially highly eccentric and possibly high-obliquity orbit, which are then circularized and aligned via tidal dissipation. We investigate the tidal evolution of transiting planets on eccentric orbits. We show that the current and future orbital evolution of these systems is likely dominated by tidal dissipation, and not by a more distant companion. Although most of these close-in planets experience orbital decay all the way to the Roche limit, there are two characteristic evolution paths for them, depending on the relative efficiency of tidal dissipation inside the star and the planet. We point out that the current observations may be consistent with one of them. Our results suggest that at least some of the close-in planets with non-zero orbital eccentricity may have been formed by tidally circularizing an initially eccentric orbit. We also find that even when the stellar spin-orbit misalignment is observed to be small at present, some systems could have had a highly misaligned orbit in the past. Finally, we also re-examine the recent claim by Levrard et. al., who found that all orbital and spin parameters evolve on a similar timescale to orbital decay.
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant planets, as a function of core size and mass. We demonstrate that in general …
Star-planet tidal interactions play a significant role in the dynamical evolution of close-in planetary systems. We investigate the propagation and dissipation of tidal inertial waves in a stellar/planetary convective region. We take into account a latitudinal differential rotation for the background flow, similar to what is observed in the envelope of low-mass stars like the Sun. Previous works have shown that differential rotation significantly alters the propagation and dissipation properties of inertial waves. In particular, when the Doppler-shifted tidal frequency vanishes in the fluid, a…
Tidal dissipation is known as one of the main drivers of the secular evolution of planetary systems. It directly results from dissipative mechanisms that occur in planets and stars' interiors and strongly depends on the structure and dynamics of the bodies. This work focuses on the mechanism of viscous friction in stars and planetary layers. A local model is used to study tidal dissipation. It provides general scaling laws that give a qualitative overview of the different possible behaviors of fluid tidal waves. Furthermore, it highlights the sensitivity of dissipation to the tidal frequency a…
The planet formation process and subsequent planet migration may lead to configurations resulting in strong dynamical interactions among the various planets. Well-studied possible outcomes include collisions between planets, scattering events that eject one or more of the planets, and a collision of one or more of the planets with the parent star. In this work we consider one other possibility that has seemingly been overlooked in the various scattering calculations presented in the literature: the tidal capture of two planets which leads to the formation of a binary planet (or binary brown dw…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints are now obtained both in the Solar and exoplanetary systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this letter, we compute separately the contributions of the potential dense rocky/icy core and the convective fluid envelope of gaseous giant p…
The occurrence distribution of the shortest period giant exoplanets as found by Kepler show a drop-off that is a remarkable match to the drop-off expected by taking migration due to tides in the star. We present a comparison that can show the level of tidal dissipation (friction) as a function of the distribution of the ages of the star and planet system, with known dependencies on basic star and planet parameters. Use of this relation enables constraints to be put on the value of the tidal dissipation, constraints that will be improved as the distribution of the ages are determined. For the g…
Astrophysical fluid bodies that orbit close to one another induce tidal distortions and flows that are subject to dissipative processes. The spin and orbital motions undergo a coupled evolution over astronomical timescales, which is relevant for many types of binary star, short-period extrasolar planetary systems and the satellites of the giant planets in the solar system. I review the principal mechanisms that have been discussed for tidal dissipation in stars and giant planets in both linear and nonlinear regimes. I also compare the expectations based on theoretical models with recent observ…
Planets in close-in orbits interact magnetically and tidally with their host stars. These interactions lead to a net torque that makes close-in planets migrate inward or outward depending on their orbital distance. We compare systematically the strength of magnetic and tidal torques for typical observed star-planet systems (T-Tauri & hot Jupiter, M dwarf & Earth-like planet, K star & hot Jupiter) based on state-of-the-art scaling-laws. We find that depending on the characteristics of the system, tidal or magnetic effects can dominate. For very close-in planets, we find that both torques can ma…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints are now obtained both in the Solar and exoplanetary systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant …
In a multi-planet system, a gradual change in one planet's semi-major axis will affect the eccentricities of all the planets, as angular momentum is distributed via secular interactions. If tidal dissipation in the planet is the cause of the change in semi-major axis, it also damps that planet's eccentricity, which in turn also contributes to the evolution of all the eccentricities. Formulae quantifying the combined effects on the whole system due to semi-major axis changes, as well as eccentricity damping, are derived here for a two-planet system. The CoRoT 7 system is considered as an exampl…
The presence of a massive close-in planet with an orbital period of a few days or less around a low-mass star can possibly results in a strong variation of the properties of the central star. Indeed, star-planet tidal interactions generate exchanges of angular momentum that can results in tidal spin-up. This effect could then lead to gyrochronological ages biased towards younger ages. Aims. This article provides the community with TATOO, a standalone tool based on tidal-chronology, to estimate the age of a massive close-in planetary system by only using its observed properties: mass of the pla…
We hypothesise that planets are made by tidal downsizing of migrating giant planet embryos. The proposed scheme for planet formation consists of these steps: (i) a massive young protoplanetary disc fragments at R ~ several tens to hundreds of AU on gaseous clumps with masses of a few Jupiter masses; (ii) the clumps cool and contract, and simultaneously migrate closer in to the parent star; (iii) as earlier suggested by Boss (1998), dust sediments inside the gas clumps to form terrestrial mass solid cores; (iv) if the solid core becomes more massive than ~ 10 Earth masses, a massive gas atmosph…
The tidal evolution of planets orbiting brown dwarfs (BDs) presents an interesting case study because BDs' terrestrial planet forming region is located extremely close-in. In fact, the habitable zones of BDs range from roughly 0.001 to 0.03 AU and for the lowest-mass BDs are located interior to the Roche limit. In contrast with stars, BDs spin up as they age. Thus, the corotation distance moves inward. This has important implications for the tidal evolution of planets around BDs. We used a standard equilibrium tidal model to compute the orbital evolution of a large ensemble of planet-BD system…
Recent analysis suggests that the faint optical point source observed around Fomalhaut from 2004-2014 (Fomalhaut b) is gradually fading and expanding, supporting the case that it may be a dispersing dust cloud resulting from the sudden disruption of a planetesimal. These types of disruptions may arise from catastrophic collisions of planetesimals, which are perturbed from their original orbits in the Fomalhaut dust ring by nearby giant planets. However, disruptions can also occur when the planetesimals pass within the tidal disruption field of the planet(s) that perturbed them in the first pla…
Tidal interaction between an exoplanet and its host star is a possible pathway to transfer angular momentum between the planetary orbit and the stellar spin. In cases where the planetary orbital period is shorter than the stellar rotation period, this may lead to angular momentum being transferred into the star's rotation, possibly counteracting the intrinsic stellar spin-down induced by magnetic braking. Observationally, detecting altered rotational states of single, cool field stars is challenging, as precise ages for such stars are rarely available. Here we present an empirical investigatio…
A large fraction of known exoplanets have short orbital periods where tidal excitation of gravity waves within the host star causes the planets' orbits to decay. We study the effects of tidal resonance locking, in which the planet locks into resonance with a tidally excited stellar gravity mode. Because a star's gravity mode frequencies typically increase as the star evolves, the planet's orbital frequency increases in lockstep, potentially causing much faster orbital decay than predicted by other tidal theories. Due to nonlinear mode damping, resonance locking in Sun-like stars likely only op…
Over the last two decades, a large population of close-in planets has been detected around a wide variety of host stars. Such exoplanets are likely to undergo planetary migration through magnetic and tidal interactions. We aim to follow the orbital evolution of a planet along the structural and rotational evolution of its host star by taking into account simultaneously tidal and magnetic torques, in order to explain some properties of the distribution of observed close-in planets. We rely on a numerical model of a coplanar circular star-planet system taking into account stellar structural chan…
Stellar insolation has been used as the main constraint on a planet's habitability. However, as more Earth-like planets are discovered around low-mass stars (LMSs), a re-examination of the role of tides on the habitability of exoplanets has begun. Those studies have yet to consider the misalignment between a planet's rotational axis and the orbital plane normal, i.e. the planetary obliquity. We apply two equilibrium tide theories to compute the obliquity evolution of terrestrial planets orbiting in the habitable zones around LMSs. The time for the obliquity to decrease from an Earth-like obliq…
We investigate how the evolution of the stellar spin rate affects, and is affected by, planets in close orbits, via star-planet tidal interactions. To do this, we used a standard equilibrium tidal model to compute the orbital evolution of single planets orbiting both Sun-like stars and 0.1 M\odot M-dwarfs. We tested two stellar spin evolution profiles, one with fast initial rotation (P=1.2 day) and one with slow initial rotation (P=8 day). We tested the effect of varying the stellar and planetary dissipation and the planet's mass and initial orbital radius. Conclusions: Tidal evolution allows …
Since 1995, numerous close-in planets have been discovered around low-mass stars (M to A-type stars). These systems are susceptible to be tidally evolving, in particular the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and also shape the orbital architecture of the surrounding planetary system. Recent theoretical studies have shown that the amplitude of the stellar dissipation can vary over several orders of magnitude as the star evolves, and that it also depends on the stellar mass and rotation. We present here one of the first studies …
Observational evidence of white dwarf planetary systems is dominated by the remains of exo-asteroids through accreted metals, debris discs, and orbiting planetesimals. However, exo-planets in these systems play crucial roles as perturbing agents, and can themselves be perturbed close to the white dwarf Roche radius. Here, we illustrate a procedure for computing the tidal interaction between a white dwarf and a near-spherical solid planet. This method determines the planet's inward and/or outward drift, and whether the planet will reach the Roche radius and be destroyed. We avoid constant tidal…
A gas giant planet which survives the giant branch stages of evolution at a distance of many au and then is subsequently perturbed sufficiently close to a white dwarf will experience orbital shrinkage and circularization due to star-planet tides. The circularization timescale, when combined with a known white dwarf cooling age, can place coupled constraints on the scattering epoch as well as the active tidal mechanisms. Here, we explore this coupling across the entire plausible parameter phase space by computing orbit shrinkage and potential self-disruption due to chaotic f-mode excitation and…
In recent years it has been shown that the tidal coupling between extrasolar planets and their stars could be an important mechanism leading to orbital evolution. Both the tides the planet raises on the star and vice versa are important and dissipation efficiencies ranging over four orders of magnitude are being used. In addition, the discovery of extrasolar planets extremely close to their stars has made it clear that the estimates of the tidal quality factor, Q, of the stars based on Jupiter and its satellite system and on main sequence binary star observations are too low, resulting in life…
It is well accepted that 'hot Jupiters' did not form in situ, as the temperature in the protoplanetary disc at the radius at which they now orbit would have been too high for planet formation to have occurred. These planets, instead, form at larger radii and then move into the region in which they now orbit. The exact process that leads to the formation of these close-in planets is, however, unclear and it seems that there may be more than one mechanism that can produce these short-period systems. Dynamical interactions in multiple-planet systems can scatter planets into highly eccentric orbit…
This is an erratum for the publication Bolmont & Mathis 2016 (Celestial Mechanics and Dynamical Astronomy, 126, 275-296, https://doi.org/10.1007/s10569-016-9690-3). There was a small mistake for the spin integration of our code which we corrected and we take advantage of this erratum to investigate a bit further the influence of a planet on the spin of its host star.
Tidal force plays an important role in the evolution of the planet-moon system. The tidal force of a moon can excite seismic waves in the planet it is orbiting. A tidal-seismic resonance is expected when a tidal force frequency matches a free-oscillation frequency of the planet. Here we show that when the moon is close to the planet, the tidal-seismic resonance can cause large-amplitude seismic waves, which can change the shape of the planet and in turn exert a negative torque on the moon to cause it to fall rapidly toward the planet. We postulate that the tidal-seismic resonance may be an imp…
Unveiling the fate of ultra-short period (USP) planets may help us understand the qualitative agreement between tidal theory and the observed exoplanet distribution. Nevertheless, due to the time-varying interchange of spin-orbit angular momentum in star-planet systems, the expected amount of tidal friction is unknown and depends on the dissipative properties of stellar and planetary interiors. In this work, we couple structural changes in the star and the planet resulting from the energy released per tidal cycle and simulate the orbital evolution of USP planets and the spin-up produced on the…
With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star-planet interactions and how such systems evolve. We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introdu…
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 a…
While the number of detected planets is continuously increasing since 1995, their impact on their central star still remain poorly understood. Yet, the presence of a massive close-in planet can strongly modify the surface angular velocity evolution of the star. In these circumstances, age estimation techniques based on rotation, such as the gyrochronology, can't be applied to stars that experienced significant star-planet magnetic and tidal interactions during their evolution. With the use of a numerical model that combines an angular momentum evolution and an orbital evolution code, we invest…
In a multiplanet system, tides acting on the inner planet can significantly affect the orbital evolution of the entire system. While tides usually damp eccentricities, a novel mechanism identified by Correia et al. (2012) tends to raise eccentricities as a result of the tides' effect on the inner planet's rotation. Our analytical description of this spin-driven tidal (SDT) effect shows that, while the inner planet's eccentricity undergoes pumping, the process is more completely described by an exchange of strength between the two eigenmodes of the dynamical system. Our analysis allows derivati…
We suggest that tidal destruction of Earth-like and icy planets near a white dwarf (WD) might lead to the formation of one or more low-mass - Earth-like and lighter - planets in tight orbits around the WD. The formation of the new WD planetary system starts with a tidal break-up of the parent planet to planetesimals near the tidal radius of about 1Rsun. Internal stress forces keep the planetesimal from further tidal break-up when their radius is less than about 100km. We speculate that the planetesimals then bind together to form new sub-Earth - daughter-planets at a few solar radii around the…
Recent observational results show that very low mass stars and brown dwarfs are able to host close-in rocky planets. Low-mass stars are the most abundant stars in the Galaxy and the formation efficiency of their planetary systems is relevant in the computation of a global probability of finding Earth-like planets inside habitable zones. Tidal forces and relativistic effects are relevant in the latest dynamical evolution of planets around low-mass stars and their effect on the planetary formation efficiency still needs to be addressed. Our goal is to evaluate the impact of tidal forces and rela…
We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semi-major axis. We perform the largest-yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances and semi-major axes between 3 AU and 150 AU. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as …
Since twenty years, a large population of close-in planets orbiting various classes of low-mass stars (from M to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, the stellar rotation evolution strongly impacts angular momentum exchan…
Star-planet interactions must be taken into account in stellar models to understand the dynamical evolution of close-in planets. The dependence of the tidal interactions on the structural and rotational evolution of the star is of peculiar importance and should be correctly treated. We quantify how tidal dissipation in the convective envelope of rotating low-mass stars evolves from the pre-main sequence up to the red-giant branch depending on the initial stellar mass. We investigate the consequences of this evolution on planetary orbital evolution. We couple the tidal dissipation formalism des…
Age estimation techniques such as gyrochronology and magnetochronology can't be applied to stars that exchanged angular momentum with their close environment. This is especially true for massive close-in planetary companion (with a periods of few days or less), which could have been strongly impacted the rotational evolution of the host star, along the stellar evolution, through the star-planet tidal interaction. We showed that the interaction of a close-in massive planet with its host star can strongly modify the surface rotation rate of this latter, in most of the cases associated to a plane…
It has been suggested that tidal interaction is important for shaping the orbital configurations of close orbiting giant planets. The excitation of propagating waves and normal modes (dynamical tide) will be important for estimating time scales for orbital evolution. We consider the tidal interaction of a Jupiter mass planet orbiting a solar type primary. Tidal and rotational frequencies are assumed comparable making the effect of rotation important. Although centrifugal distortion is neglected, Coriolis forces are fully taken into account. We focus in detail on the potentially resonant excita…
We study the evolution of the orbit of a planetary companion as the primary star evolves during the red giant branch phase. Our aim is to determine a prescription for the capture radius and capture timescales for companions in a wide range of masses, from planet to star, including the effect of a non constant f parameter. Our initial results reproduce past findings. According to our study the mass-loss during the red giant branch does not significantly affect the semi major axis of the planet and for a 1.5 M star the capture radius is approximately 300 R or 1.4 AU.
Turbulent friction in convective regions in stars and planets is one of the key physical mechanisms that drive the dissipation of the kinetic energy of tidal flows in their interiors and the evolution of their systems. This friction acts both on the equilibrium/non-wave like tide and on tidal inertial waves in these layers. It is thus necessary to obtain a robust prescription for this friction. In the current state-of-the-art, it is modeled by a turbulent eddy-viscosity coefficient, based on mixing-length theory, applied on velocities of tides. However, none of the current prescriptions take i…
With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, the correct treatment of tidal interactions is becoming necessary. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeed the result of tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets, which can then be responsible for volcanism and/or surface deformation. In the majority of studies to estimate the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology…
A large number of observed exoplanets are part of multiple planet systems. Most of these systems are sufficiently close-in to be tidally evolving. In such systems, there is a competition between the excitation caused by planet-planet interactions and tidal damping. Using as an example two multiple planet systems, which host planets in the surface liquid water habitable zone (HZ): Kepler-62 and Kepler-186, we show the importance and effect of both planetary and stellar tides on the dynamical evolution of planets and on the climate of the HZ planets.
Tidal Downsizing (TD) is a recently developed planet formation theory that supplements the classical Gravitational disc Instability (GI) model with planet migration inward and tidal disruptions of GI fragments in the inner regions of the disc. Numerical methods for a detailed population synthesis of TD planets are presented here. As an example application, the conditions under which GI fragments collapse faster than they migrate into the inner $a\sim$ few AU disc are considered. It is found that most gas fragments are tidally or thermally disrupted unless (a) their opacity is $\sim 3$ orders o…
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Tidal dissipation inside the fluid layers of celestial bodies are intrinsically linked to the dynamics and the physical properties of the latter. This complex dependence must be characterized. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Car…
The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2 Jupiter-mass planet in Kepler 1625 puts interesting constraints on the formation of the system. In particular, the relatively wide orbit of the moon around the planet, at ~40 planetary radii, is hard to reconcile with planet formation theories. We demonstrate that the observed characteristics of the system can be explained from the tidal capture of a secondary planet in the young system. After a quick phase of tidal circularization, the lunar orbit, initially much tighter than 40 planetary radii, subsequently gradually…
Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability -- the elliptical instability. It has been proposed that this instability might drive enough energy dissipation to solve the long-standing problem of the origin of tidal dissipation in stars and planets. But the nonlinear outcome of the elliptical instability has yet to be investigated in the parameter regime of interest, and the resulting turbulent energy dissipation has not yet been quantified. We do so by performing three dimensional hydrodynamical simulations of a small patch of a tida…
