Time-dependent insolation in a planetary atmosphere induces a mass quadrupole upon which the stellar tidal acceleration can exert a force. This "thermal tide" force can give rise to secular torques on the planet and orbit as well as radial forces causing eccentricity evolution. We apply this idea to the close-in gas giant exoplanets ("hot Jupiters"). The response of radiative atmospheres is computed in a hydrostatic model which treats the insolation as a time-dependent heat source, and solves for thermal radiation using flux-limited diffusion. Fully nonlinear numerical simulations are compared to solutions of the linearized equations, as well as analytic approximations, all of which are in good agreement. We find generically that thermal tide density perturbations {\it lead} the semi-diurnal forcing. As a result thermal tides can generate asynchronous spin and eccentricity. Our results are as follows: (1) Departure from synchronous spin is significant for hot Jupiters, and increases with orbital period. (2) Ongoing gravitational tidal dissipation in spin equilibrium leads to steady-state internal heating rates up to $\sim 10^{28} {\rm erg\ s^{-1}}$. If deposited sufficiently deep, these heating rates may explain the anomalously large radii of many hot Jupiters in terms of a "tidal main sequence" where cooling balances tidal heating. At fixed stellar type, planet mass and tidal $Q$, planetary radius increases strongly toward the star inside orbital periods $\la 2$ weeks. (3) There exists a narrow window in orbital period where small eccentricities, $e$, grow exponentially with a large rate. This window may explain the $\sim 1/4$ of hot Jupiters which should have been circularized by the gravitational tide long ago, but are observed to have significant nonzero $e$.(Abridged)
As evident from the nearby examples of Proxima Centauri and TRAPPIST-1, Earth-sized planets in the habitable zone of low-mass stars are common. Here, we focus on such planetary systems and argue that their (oceanic) tides could be more prominent due to stronger tidal forces. We identify the conditions under which tides may exert a significant positive influence on biotic processes including abiogenesis, biological rhythms, nutrient upwelling and stimulating photosynthesis. We conclude our analysis with the identification of large-scale algal blooms as potential temporal biosignatures in reflec…
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…
This paper reviews the basic equations used in the study of the tidal variations of the rotational and orbital elements of a system formed by one star and one close-in planet as given by the creep tide theory and Darwin's constant time lag (CTL) theory. At the end, it reviews and discusses the determinations of the relaxation factors (and time lags) in the case of host stars and hot Jupiters based on actual observations of orbital decay, stellar rotation and age, etc. It also includes a recollection of the basic facts concerning the variations of the rotation of host stars due to the leakage o…
In recent years, there has been interest in Earth-like exoplanets in the habitable zones of low mass stars ($\sim0.1-0.6\,M_\odot$). Furthermore, it has been argued that a large moon may be important for stabilizing conditions on a planet for life. If these two features are combined, then an exoplanet can feel a similar tidal influence from both its moon and parent star, leading to potentially interesting dynamics. The moon's orbital evolution depends on the exoplanet's initial spin period $P_0$. When $P_0$ is small, transfer of the exoplanet's angular momentum to the moon's orbit can cause th…
One outstanding problem in extrasolar planet studies is why no co-orbital exoplanets have been found, despite numerous searches among the many known planetary systems, many of them in other mean-motion resonances. Here we examine the hypothesis that dissipation of energy by tides in Trojan planets is preventing their survival. The Appendix of this paper generalizes the conventional theory of tides to include tidal forces independent of dissipation, as well as the effects of one body on tides raised by another. The main text applies this theory to a model system consisting of a primary of stell…
Exomoons may play an important role in determining the habitability of worlds outside of our solar system. They can stabilize conditions, alter the climate by breaking tidal locking with the parent star, drive tidal heating, and perhaps even host life themselves. However, the ability of an exoplanet to sustain an exomoon depends on complex tidal interactions. Motivated by this, we make use of simplified tidal lag models to follow the evolution of the separations and orbital and rotational periods in planet, star, and moon systems. We apply these models to known exoplanet systems to assess the …
Tides may be crucial to the habitability of exoplanets. If such planets form around low-mass stars, then those in the circumstellar habitable zone will be close enough to their host stars to experience strong tidal forces. Tides may result in orbital decay and circularization, evolution toward zero obliquity, a fixed rotation rate (not necessarily synchronous), and substantial internal heating. Due to tidal effects, the range of habitable orbital locations may be quite different from that defined by the traditional concept of a habitable zone (HZ) based on stellar insolation, atmospheric effec…
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…
The distribution of the orbits of close-in exoplanets shows evidence for on-going removal and destruction by tides. Tides raised on a planet's host star cause the planet's orbit to decay, even after the orbital eccentricity has dropped to zero. Comparison of the observed orbital distribution and predictions of tidal theory show good qualitative agreement, suggesting tidal destruction of close-in exoplanets is common. The process can explain the observed cut-off in small a-values, the clustering of orbital periods near three days, and the relative youth of transiting planets. Contrary to previo…
This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly from the solution of a non-homogeneous ordinary differential equation. Lags appear in the solution but as quantities determined from the solution of the equation and are not arbitrary external quantities plugged in an elastic model. The resulting lags of the tide components are increasing functions of their frequencies (as in Darwin's theory), but not small qua…
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…
Close-in, massive exoplanets raise significant tides in their stellar hosts. We compute the radial velocity (RV) signal due to this fluid motion in the equilibrium tide approximation. The predicted radial velocities in the observed sample of exoplanets exceed 1 m/s for 17 systems, with the largest predicted signal being ~30 m/s for WASP-18 b. Tidally-induced RV's are thus detectable with present methods. Both tidal fluid flow and the epicyclic motion of a slightly eccentric orbit produce an RV signal at twice the orbital frequency. If care is not taken, the tidally induced RV may, in some case…
By analogy with a mechanism proposed by Gold and Soter to explain the retrograde rotation of Venus, Arras and Socrates suggest that thermal tides may excite hot jovian exoplanets into nonsynchronous rotation, and perhaps also noncircular orbits. It is shown here that because of the absence of a solid surface above the convective core of a jovian planet, the coupling of the gravitational and thermal tides vanishes to zeroth order in the ratio of the atmospheric scale height to the planetary radius. At the next order, the effect probably has the sign opposite to that claimed by the latter author…
We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rat…
The lower limit to the distribution of orbital periods P for the current population of close-in exoplanets shows a distinctive discontinuity located at approximately one Jovian mass. Most smaller planets have orbital periods longer than P~2.5 days, while higher masses are found down to P~1 day. We analyze whether this observed mass-period distribution could be explained in terms of the combined effects of stellar tides and the interactions of planets with an inner cavity in the gaseous disk. We performed a series of hydrodynamical simulations of the evolution of single-planet systems in a gase…
The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin-orbit alignment is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique -- based on the amplitude of starspot-induced photometric variability -- to conclude that spin-orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically s…
NASA's Kepler mission revealed that $\sim 30\%$ of Solar-type stars harbor planets with sizes between that of Earth and Neptune on nearly circular and co-planar orbits with periods less than 100 days. Such short-period compact systems are rarely found with planet pairs in mean-motion resonances (MMRs) -- configurations in which the planetary orbital periods exhibit a simple integer ratio -- but there is a significant overabundance of planet pairs lying just wide of the first-order resonances. Previous work suggests that tides raised on the planets by the host star may be responsible for forcin…
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）
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…
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.
Equation of motion for the galactic tide is treated for the case of a comet situated in the Oort cloud of comets. We take into account that galactic potential and mass density depend on a distance from the galactic equator and on a distance from the rotational axis of the Galaxy. Secular evolution of orbital elements is presented. New terms generated by the Sun's oscillation about the galactic plane are considered. The inclusion of the new terms into the equation of motion of the comet leads to orbital evolution which may be significantly different from the conventional approach. The usage of …
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…
Tracing the Influence of Distant companions on Exoplanetary Systems (TIDES) I. Highly Eccentric and Misaligned Binary Companions to Hot Jupiters
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；Institute for Astronomy, University of Hawai‘i（夏威夷大学天文研究所）；California Institute of Technology（加州理工学院）
The majority of Milky Way extrasolar planets likely reside within a few kpc of the Galactic centre. The Galactic tidal forces acting on planets scale inversely with radius in the Galaxy and so are much greater in the inner Galaxy than in the Solar neighbourhood. Within a range of 3.5 to 10 kpc, the vertical tide from the Galactic disc is predominant. Interior to 3.5 kpc, the effects of the Galactic bulge cannot be neglected and the in-plane tidal components are as important as the vertical ones. Here, we quantify the orbital changes induced by these tides. We find that the greatest perturbatio…
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…
We calculate tidal torque due to semi-diurnal thermal tides in rotating hot Jupiters, taking account of the effects of radiative cooling in the envelope and of the planets rotation on the tidal responses. We use a simple Jovian model composed of a nearly isentropic convective core and a thin radiative envelope. To represent the tidal responses of rotating planets, we employ series expansions in terms of spherical harmonic functions $Y_l^m$ with different $l$s for a given $m$. For low forcing frequency, there occurs frequency resonance between the forcing and the $g$- and $r$-modes in the envel…
Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate to determine the possible climates and general circulations of the atmospheres of these planets. In this work, we write the equations governing the dynamics of thermal tides in a local vertically-stratified section of a rotating planetary atmosphere by taking into account the effects of the complete Coriolis acceleration on tidal waves. This allows us to derive analytically the tidal torque and the tidally dissipated energy, which we use to di…
The paper deals with several properties of the Oort cloud of comets. Sun, Galaxy (and Jupiter) gravitationally act on the comets. New physical model of galactic tide is considered. The main results can be summarized as follows: 1. Mass of the Oort cloud of comets is less than 1 mass of the Earth ($M_{E}$), probably not greater than 1/2 $M_{E}$. 2. Theoretical number of long-period comets with perihelion distance $q$ $<$ 5 AU is about 50-times greater than the conventional approach yields. Gravity of Jupiter was taken into account in finding this result. 3. Semi-major axis $a$ and period of osc…
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…
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…
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…
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…
There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing heating and deformation that, if measured, can probe their interior structures. In addition to Jupiter-raised tides, each moon also raises tides on the others. We investigate moon-moon tides for the first time in the Galilean moons, and show that they can cause significant heating through the excitation of high-frequency resonant tidal waves in their subsurface …
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…
A unique short-period Mercury-size Kepler exoplanet candidate KIC012557548b has been discovered recently by Rappaport et al. (2012). This object is a transiting disintegrating exoplanet with a circum-planetary material - comet-like tail. Close-in exoplanets, like KIC012557548b, are subjected to the greatest planet-star interactions. This interaction may have various forms. In certain cases it may cause formation of the comet-like tail. Strong interaction with the host star, and/or presence of an additional planet may lead to variations in the orbital period of the planet. Our main aim is to se…
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…
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…
The solar system's Oort cloud can be perturbed by the Galactic tide and by individual passing stars. These perturbations can inject Oort cloud objects into the inner parts of the solar system, where they may be observed as the long-period comets (periods longer than 200 years). Using dynamical simulations of the Oort cloud under the perturbing effects of the tide and 61 known stellar encounters, we investigate the link between long-period comets and encounters. We find that past encounters were responsible for injecting at least 5% of the currently known long-period comets. This is a lower lim…
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 study the role of nonlinear effects on tidally-excited internal gravity waves in stellar radiation zones in exoplanetary or binary systems. We are partly motivated to study tides due to massive short-period hot Jupiters, which preferentially orbit stars with convective cores, for which wave breaking near the stellar centre cannot operate. We develop a theory (and test it with numerical calculations) for the nonlinear excitation of super-harmonic "secondary" waves (with frequencies $2ω_p$) by a "primary" tidal wave (with frequency $ω_p$) near the interface between the radiation zone and conv…
The number of exoplanet detections continues to grow following the development of better instruments and missions. Key steps for the understanding of these worlds comes from their characterization and its statistical studies. We explore the metallicity-period-mass diagram for known exoplanets by using an updated version of The Stellar parameters for stars With ExoplanETs CATalog (SWEET-Cat), a unique compilation of precise stellar parameters for planet-host stars provided for the exoplanet community. Here we focus on the planets with minimum mass below 30 M$_{\oplus}$ which seems to present a …
The angle between the stellar spin and the planetary orbit axes (spin-orbit angle) is supposed to carry valuable information on the initial condition of the planet formation and the subsequent migration history. Indeed current observations of the Rossiter- McLaughlin effect have revealed a wide range of spin-orbit misalignments for transiting exoplanets. We examine in detail the tidal evolution of a simple system comprising a Sun-like star and a hot Jupiter adopting the equilibrium tide and the inertial wave dissipation effects simultaneously. We find that the combined tidal model works as a v…
We perform a linear analysis to investigate the dynamical response of a non-synchronized hot Jupiter to stellar irradiation. In this work, we consider the diurnal Fourier harmonic of the stellar irradiation acting at the top of a radiative layer of a hot Jupiter with no clouds and winds. In the absence of the Coriolis force, the diurnal thermal forcing can excite internal waves propagating into the planet's interior when the thermal forcing period is longer than the sound crossing time of the planet's surface. When the Coriolis effect is taken into consideration, the latitude-dependent stellar…
