Tidal interactions and planet evaporation processes impact the evolution of close-in star-planet systems. We study the impact of stellar rotation on these processes. We compute the time evolution of star-planet systems consisting of a planet with initial mass between 0.02 and 2.5 M$_{ Jup}$ (6 and 800 M$_{ Earth}$), in a quasi-circular orbit with an initial orbital distance between 0.01 and 0.10 au, around a solar-type star evolving from the Pre-Main-Sequence (PMS) until the end of the Main-Sequence (MS) phase. We account for the evolution of: the stellar structure, the stellar angular momentum due to tides and magnetic braking, the tidal interactions (equilibrium and dynamical tides in stellar convective zones), the mass-evaporation of the planet, and the secular evolution of the planetary orbit. We consider that at the beginning of the evolution, the proto-planetary disk has fully dissipated and planet formation is complete. Both a rapid initial stellar rotation, and a more efficient angular momentum transport inside the star, in general, contribute toward the enlargement of the domain which is devoid of planets after the PMS phase, in the plane of planet mass vs. orbital distance. Comparisons with the observed distribution of exoplanets orbiting solar mass stars, in the plane of planet mass vs. orbital distance (addressing the "Neptunian desert" feature), show an encouraging agreement with the present simulations, especially since no attempts have been made to fine-tune initial parameters of the models to fit the observations. We also obtain an upper limit for the orbital period of bare-core planets, that agrees with observations of the "radius valley" feature in the plane of planet radius vs. orbital period. The two effects, tides and planet evaporation, should be accounted for simultaneously and in a consistent way, with a detailed model for the evolution of the star.
When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium ti…
Temperate terrestrial planets orbiting low-mass stars are subject to strong tidal forces. The effects of gravitational tides on the solid planet and that of atmospheric thermal tides have been studied, but the direct impact of gravitational tides on the atmosphere itself has so far been ignored. We first develop a simplified analytic theory of tides acting on the atmosphere of a planet. We then implement gravitational tides into a general circulation model of a static-ocean planet in a short-period orbit around a low-mass star -- the results agree with our analytic theory. Because atmospheric …
The TRAPPIST-1 system is sufficiently closely packed that tides raised by one planet on another are significant. We investigate whether this source of tidal heating is comparable to eccentricity tides raised by the star. Assuming a homogeneous body with a Maxwell rheology, we find that energy dissipation from stellar tides always dominates over that from planet-planet tides across a range of viscosities. TRAPPIST-1 g may experience the greatest proportion of planet-planet tidal heating, where it can account for between 2% and 20% of the total amount of tidal heating, for high ($10^{21}$ Pa s) …
Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, and these are still not well understood. We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation by the quality factor Q, as is commonly done. We consider here the simplest case where t…
We provide an 'effective theory' of tidal dissipation in extrasolar planet systems by empirically calibrating a model for the equilibrium tide. The model is valid to high order in eccentricity and parameterised by two constants of bulk dissipation - one for dissipation in the planet and one for dissipation in the host star. We are able to consistently describe the distribution of extrasolar planetary systems in terms of period, eccentricity and mass (with a lower limit of a Saturn mass) with this simple model. Our model is consistent with the survival of short-period exoplanet systems, but not…
The star TRAPPIST-1 hosts a system of seven transiting, terrestrial exoplanets apparently in a resonant chain, at least some of which are in or near the Habitable Zone. Many have examined the roles of tides in this system, as tidal dissipation of the orbital energy of the planets may be relevant to both the rotational and orbital dynamics of the planets, as well as their habitability. Generally, tides are calculated as being due to the tides raised on the planets by the star, and tides raised on the star by the planets. I write this research note to point out a tidal effect that may be at leas…
Massive exoplanets on extremely tight orbits, such as WASP-12 b, induce equilibrium tides in their host stars. Following the orbital motion of the planet, the tidal fluid flow in the star can be detected with the radial velocity method. Its signature manifests as the second harmonics of the orbital frequency that mimics a non-zero orbital eccentricity. Using the new radial velocity measurements acquired with the HARPS-N spectrograph at the Telescopio Nazionale Galileo and combining them with the literature data, we show that the apparent eccentricity of WASP-12 b's orbit is non-zero at a 5.8 s…
All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that th…
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 …
Hot Jupiters on extremely short-period orbits are expected to be unstable to tidal dissipation and spiral toward their host stars. That is because they transfer the angular momentum of the orbital motion through tidal dissipation into the stellar interior. Although the magnitude of this phenomenon is related to the physical properties of a specific star-planet system, statistical studies show that tidal dissipation might shape the architecture of hot Jupiter systems during the stellar lifetime on the main sequence. The efficiency of tidal dissipation remains poorly constrained in star-planet s…
We present an analytic description of tides raised on a star by a small orbiting body. In particular, we highlight the disproportionate effect of eccentricity and thus the scope for using these tides to detect and characterise the orbits of exoplanets and brown dwarfs. The tidal distortions of the star produced by an eccentric orbit are, in comparison to a circular orbit, much richer in detail, and potentially visible from any viewing angle. The magnitude of these variations is much larger than that in a circular orbit of the same semi-major axis. These variations are visible in both photometr…
We have investigated i) the formation of gravitationally bounded pairs of gas-giant planets (which we call "binary planets") from capturing each other through planet-planet dynamical tide during their close encounters and ii) the following long-term orbital evolution due to planet-planet and planet-star {\it quasi-static} tides. For the initial evolution in phase i), we carried out N-body simulations of the systems consisting of three jupiter-mass planets taking into account the dynamical tide. The formation rate of the binary planets is as much as 10% of the systems that undergo orbital cross…
The competition between the torques induced by solid and thermal tides drives the rotational dynamics of Venus-like planets and super-Earths orbiting in the habitable zone of low-mass stars. The tidal responses of the atmosphere and telluric core are related to their respective physical properties and strongly depend on the tidal frequency. The resulting torque determines the possible equilibrium states of the planet's spin. We compute here an analytic expression for the total tidal torque exerted on a Venus-like planet. This expression is used to characterize the equilibrium rotation of the b…
A number of Kepler planet pairs lie just wide of first-order mean motion resonances (MMRs). Tides have been frequently proposed to explain these pileups, but it is still an ongoing discussion. We contribute to this discussion by calculating an optimistic theoretical estimate on the minimum initial eccentricity required by Kepler planets to explain the current observed spacing, and compliment these calculations with N-body simulations. In particular, we investigate 27 Kepler systems having planets within 6% of the 2:1 MMR, and find that the initial eccentricities required to explain the observe…
Planet--Planet scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, it can also explain close--in giant planets on circularized and potentially misaligned orbits. We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits.In our modeling we exploit a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides and two--bod…
Context. With the detection of thousands of exoplanets, characterising their dynamical evolution in detail represents a key step in the understanding of their formation. Studying the dissipation of tides occurring both in the host star and in the planets is of great relevance in order to investigate the distribution of the angular momentum occurring among the objects populating the system and to studying the evolution of the orbital parameters. From a theoretical point of view, the dissipation of tides throughout a body may be studied by relying on the so-called phase or time-lag equilibrium t…
Atmospheric tides can have a strong impact on the rotational dynamics of planets. They are of most importance for terrestrial planets located in the habitable zone of their host star, where their competition with solid tides is likely to drive the body towards non-synchronized rotation states of equilibrium, as observed in the case of Venus. Contrary to other planetary layers, the atmosphere is sensitive to both gravitational and thermal forcings, through a complex dynamical coupling involving the effects of Coriolis acceleration and characteristics of the atmospheric structure. These key phys…
Planets with masses between 0.1 - 10 M_earth are believed to host dense atmospheres. These atmospheres can play an important role on the planet's spin evolution, since thermal atmospheric tides, driven by the host star, may counterbalance gravitational tides. In this work we study the long-term spin evolution of Earth-sized exoplanets. We generalize previous works by including the effect of eccentric orbits and obliquity. We show that under the effect of tides and core-mantle friction, the obliquity of the planets evolve either to 0 or 180 degrees. The rotation of these planets is also expecte…
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…
Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the tidal deformation of the body, but considers the deformation as a low-Reynolds-number flow. The evolution under tidal forces is ruled by an approximate solution of the Navier-Stokes equation depending on the body's viscosity with no ad hoc assumptions on its shape and orientation. It reproduces closely the results of Darwinian theories in the case of gaseous pl…
The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new i…
The population of giant planets on short-period orbits can potentially be explained by some flavours of high-eccentricity migration. In this paper we investigate one such mechanism involving "secular chaos", in which secular interactions between at least three giant planets push the inner planet to a highly eccentric orbit, followed by tidal circularization and orbital decay. In addition to the equilibrium tidal friction, we incorporate dissipation due to dynamical tides that are excited inside the giant planet. Using the method of Gaussian rings to account for planet-planet interactions, we e…
We present a new empirical calibration of equilibrium tidal theory for extrasolar planet systems, extending a prior study by incorporating detailed physical models for the internal structure of planets and host stars. The resulting strength of the stellar tide produces a coupling that is strong enough to reorient the spins of some host stars without causing catastrophic orbital evolution, thereby potentially explaining the observed trend in alignment between stellar spin and planetary orbital angular momentum. By isolating the sample whose spins should not have been altered in this model, we a…
From its discovery, the WASP-18 system with its massive transiting planet on a tight orbit was identified as a unique laboratory for studies on tidal planet-star interactions. In an analysis of Doppler data, which include five new measurements obtained with the HIRES/Keck-I instrument between 2012 and 2018, we show that the radial velocity signal of the photosphere following the planetary tidal potential can be distilled for the host star. Its amplitude is in agreement with both theoretical predictions of the equilibrium tide approximation and an ellipsoidal modulation observed in an orbital p…
Semidiurnal atmospheric thermal tides are important for terrestrial exoplanets in the habitable zone of their host stars. With solid tides, they torque these planets, thus contributing to determine their rotation states as well as their climate. Given the complex dynamics of thermal tides, analytical models are essential to understand its dependence on the structure and rotation of planetary atmospheres and the tidal frequency. In this context, the state of the art model proposed in the 60's by Lindzen and Chapman explains well the properties of thermal tides in the asymptotic regime of Earth-…
We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. Then, we calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared.
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…
Planets are born from the gas and dust discs surrounding young stars. Energetic radiation from the central star can drive thermal outflows from the discs atmospheres, strongly affecting the evolution of the discs and the nascent planetary system. In this context several numerical models of varying complexity have been developed to study the process of disc photoevaporation from their central stars. We describe the numerical techniques, the results and the predictivity of current models and identify observational tests to constrain them.
High-eccentricity migration is an important channel for the formation of hot Jupiters (HJs). In particular, Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant planetary or stellar companion, combined with tidal friction, have been shown to produce HJs on Gyr timescales, provided that efficient tidal dissipation operates in the planet. We re-examine this scenario with the inclusion of dynamical tides. When the planet's orbit is in a high-eccentricity phase, the tidal force from the star excites oscillatory f-modes and r-modes in the planet. For sufficiently l…
Recent analyses have revealed a mystery. The orbital period of the highly inflated hot Jupiter, WASP-12b, is decreasing rapidly. The rate of inspiral, however, is too fast to be explained by either eccentricity tides or equilibrium stellar tides. While dynamical stellar tides are possible, they require a subgiant structure for the star, whereas stellar models point toward a main sequence host. Here, we show that these hitherto irreconcilable observations might be explained by planetary obliquity tides if planet b's spin vector is trapped in a high-obliquity state maintained by a secular spin-o…
We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotati…
Asynchronous rotation and orbital eccentricity lead to time-dependent irradiation of the close-in gas giant exoplanets -- the hot Jupiters. This time-dependent surface heating gives rise to fluid motions which propagate throughout the planet. We investigate the ability of this "thermal tide" to produce a quadrupole moment which can couple to the stellar gravitational tidal force. While previous investigations discussed planets with solid surfaces, here we focus on entirely fluid planets in order to understand gas giants with small cores. The Coriolis force, thermal diffusion and self-gravity o…
The discovery of many giant planets in close-in orbits and the effect of planetary and stellar tides in their subsequent orbital decay have been extensively studied in the context of planetary formation and evolution theories. Planets orbiting close to their host stars undergo close encounters, atmospheric photoevaporation, orbital evolution, and tidal interactions. In many of these theoretical studies, it is assumed that the interior properties of gas giants remain static during orbital evolution. Here we present a model that allows for changes in the planetary radius as well as variations in…
The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution II: The effect of tides in the misaligned case
Quantification of Tides in Giant Planets from Observations
IMCCE, Observatoire de Paris, PSL Research University, Sorbonne Université, CNRS, Univ. Lille（IMCCE，巴黎天文台，PSL研究大学，索邦大学，CNRS，里尔大学）；Dipartimento di Ingegneria Industriale, Alma Mater Studiorum - Università di Bologna（工业工程系，博洛尼亚大学）；Institut Polytechnique des Sciences Avancées IPSA（高级科学理工学院）；Observatoire de la Côte d’Azur, UniCA, Laboratoire Lagrange CNRS UMR 7293（蔚蓝海岸天文台，尼斯大学，拉格朗日实验室）
Some transiting extrasolar giant planets have measured radii larger than predicted by the standard theory. In this paper, we explore the possibility that an earlier episode of tidal heating can explain such radius anomalies and apply the formalism we develop to HD 209458b as an example. We find that for strong enough tides the planet's radius can undergo a transient phase of inflation that temporarily interrupts canonical, monotonic shrinking due to radiative losses. Importantly, an earlier episode of tidal heating can result in a planet with an inflated radius, even though its orbit has nearl…
Earth-scale planets in the classical habitable zone (HZ) are more likely to be habitable if they possess active geophysics. Without a constant internal energy source, planets cool as they age, eventually terminating tectonic activity and rendering the planet sterile to life. However, for planets orbiting low-mass stars, the presence of an outer companion could generate enough tidal heat in the HZ planet to prevent such cooling. The range of mass and orbital parameters for the companion that give adequate long-term heating of the inner HZ planet, while avoiding very early total desiccation, is …
In close two-body astrophysical systems, such as binary stars or Hot Jupiter systems, tidal interactions often drive dynamical evolution on secular timescales. Many host stars and presumably giant gaseous planets feature a convective envelope. Tidal flows generated therein by the tidal potential of the companion can be dissipated through viscous friction, leading to the redistribution and exchange of angular momentum within the convective shell and with the companion, respectively. In the tightest systems, nonlinear effects are likely to have a significant impact on the tidal dissipation and t…
Stellar radiation has conservatively been used as the key constraint to planetary habitability. We review here the effects of tides, exerted by the host star on the planet, on the evolution of the planetary spin. Tides initially drive the rotation period and the orientation of the rotation axis into an equilibrium state but do not necessarily lead to synchronous rotation. As tides also circularize the orbit, eventually the rotation period does equal the orbital period and one hemisphere will be permanently irradiated by the star. Furthermore, the rotational axis will become perpendicular to th…
In this work, we investigate the influence of planetary tidal interactions on the transit-timing variations of short-period low-mass rocky exoplanets. For such purpose, we employ the recently-developed creep tide theory to compute tidally-induced TTVs. We implement the creep tide in the recently-developed Posidonius N-body code, thus allowing for a high-precision evolution of the coupled spin-orbit dynamics of planetary systems. As a working example for the analyses of tidally-induced TTVs, we apply our version of the code to the K2-265 b planet. We analyse the dependence of tidally-induced TT…
Atmospheric tides can strongly affect the rotational dynamics of planets. In the family of Earth-like planets, such as Venus, this physical mechanism coupled with solid tides makes the angular velocity evolve over long timescales and determines the equilibrium configurations of their spin. Contrary to the solid core, the atmosphere is submitted to both tidal gravitational potential and insolation flux coming from the star. The complex response of the gas is intrinsically linked to its physical properties. This dependence has to be characterized and quantified to study the large variety of extr…
Planets in the habitable zone of lower-mass stars are often assumed to be in a state of tidally synchronized rotation, which would considerably affect their putative habitability. Although thermal tides cause Venus to rotate retrogradely, simple scaling arguments tend to attribute this peculiarity to the massive Venusian atmosphere. Using a global climate model, we show that even a relatively thin atmosphere can drive terrestrial planets' rotation away from synchronicity. We derive a more realistic atmospheric tide model that predicts four asynchronous equilibrium spin states, two being stable…
Layered semi-convection is a possible candidate to explain Saturn's luminosity excess and the abnormally large radius of some hot Jupiters. In giant planet interiors, it could lead to the creation of density staircases, which are convective layers separated by thin stably stratified interfaces. We study the propagation of internal waves in a region of layered semi-convection, with the aim to predict energy transport by internal waves incident upon a density staircase. The goal is then to understand the resulting tidal dissipation when these waves are excited by other bodies such as moons in gi…
The observed distribution of radii for exoplanets shows a bimodal form that can be explained by mass-loss from planetary atmospheres due to high energy radiation emitted by their host stars. The location of the minimum of this radius distribution depends on the mass-radius relation, which in turn depends on the composition of planetary cores. Current studies suggest that super-Earth and mini-Neptune planets have iron-rich and hence largely Earth-like composition cores. This paper explores how non-zero planetary magnetic fields can decrease the expected mass-loss rates from these planets. These…
We perform direct numerical simulations of the tidal encounter of a rotating planet on a highly eccentric or parabolic orbit about a central star formulated as an initial value problem. This approach enables us to extend previous work of Ivanov & Papaloizou to consider planet models with solid cores and to avoid making an anelastic approximation. We obtain a power spectrum of the tidal response of coreless models which enables global inertial modes to be identified. Their frequencies are found to be in good agreement with those obtained using either a WKBJ approach or the anelastic spectral ap…
We apply hydrodynamic evaporation models to different synthetic planet populations that were obtained from a planet formation code based on a core-accretion paradigm. We investigated the evolution of the planet populations using several evaporation models, which are distinguished by the driving force of the escape flow (X-ray or EUV), the heating efficiency in energy-limited evaporation regimes, or both. Although the mass distribution of the planet populations is barely affected by evaporation, the radius distribution clearly shows a break at approximately 2 $R_{\oplus}$. We find that evaporat…
We consider the evaporation of close in planets by the star's intrinsic EUV and X-ray radiation. We calculate evaporation rates by solving the hydrodynamical problem for planetary evaporation including heating from both X-ray and EUV radiation. We show that most close-in planets (a<0.1 AU) are evaporating hydrodynamically, with the evaporation occurring in two distinct regimes: X-ray driven, in which the X-ray heated flow contains a sonic point, and EUV driven, in which the X-ray region is entirely sub-sonic. The mass-loss rates scale as L_X/a^2 for X-ray driven evaporation, and as Phi_*^{1/2}…
