In this paper, we study the behavior of a pair of co-orbital planets, both orbiting a central star on the same plane and undergoing tidal interactions. Our goal is to investigate final orbital configurations of the planets, initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting tidal evolution. The study is done in the form of purely numerical simulations of the exact equations of motions accounting for gravitational and tidal forces. The results obtained show that, at least for equal mass planets, the combined effects of the resonant and tidal interactions provoke the orbital instability of the system, often resulting in collision between the planets. We first discuss the case of two hot-super-Earth planets, whose orbital dynamics can be easily understood in the frame of our semi-analytical model of the 1/1 MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.
Aims. On Earth, plate tectonics play an integral role in driving the long-term carbon cycle; however, on tidally locked rocky exoplanets alternative tectonic mechanisms driven by tidal stress and tidal heating could serve in an analogous way. Methods. We calculate tidal stress and tidal heating rates to model the likelihood of tectonic activity maintaining stable climates suitable for surface liquid water on tidally locked rocky exoplanets with radii ${R}_{p}$ $\le$ 1.23R$_\oplus$. Results. Applying the tidal models to our sample of 767 tidally locked rocky exoplanets reveals that $\sim$10% of…
Planets close to their host stars are believed to undergo significant tidal interactions, leading to a progressive damping of the orbital eccentricity. Here we show that, when the orbit of the planet is excited by an outer companion, tidal effects combined with gravitational interactions may give rise to a secular increasing drift on the eccentricity. As long as this secular drift counterbalances the damping effect, the eccentricity can increase to high values. This mechanism may explain why some of the moderate close-in exoplanets are observed with substantial eccentricity values.
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…
Our work examines the detectability of tidally distorted solid exoplanets in synchronous rotation. Previous work has shown that tidally distorted shapes of close-in gas giants can give rise to radius underestimates and subsequently density overestimates for those planets. We examine the assumption that such an effect is too minimal for rocky exoplanets and find that for smaller M Class stars there may be an observationally significant tidal distortion effect at very close-in orbits. We quantify the effect for different stellar types and planetary properties using some basic assumptions. Finall…
The determination of an exoplanet as rocky is critical for the assessment of planetary habitability. Observationally, the number of small-radius, transiting planets with accompanying mass measurements is insufficient for a robust determination of the transitional mass or radius. Theoretically, models predict that rocky planets can grow large enough to become gas giants when they reach ~10 Earth-masses, but the transitional mass remains unknown. Here I show how transit data, interpreted in the context of tidal theory, can reveal the critical radius that separates rocky and gaseous exoplanets. S…
Using an idealised general circulation model, we investigate the atmospheric circulation of Earth-like terrestrial planets in a variety of orbital configurations. We relax the common assumption of the planet being tidally-locked, and look at the role atmospheric dynamics can have in the observed thermal phase curve when the substellar point is non-stationary. In slowly rotating planets, a moving forcing can induce strong jets in the upper troposphere, both prograde and retrograde, sensitive to the speed and direction of the diurnal forcing. We find that, consistent with previous shallow water …
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…
We present a model to study secularly and tidally evolving three-body systems composed by two low-mass planets orbiting a star, in the case where the bodies rotation axes are always perpendicular to the orbital plane. The tidal theory allows us to study the spin and orbit evolution of both stiff Earth-like planets and predominantly gaseous Neptune-like planets. The model is applied to study two recently-discovered exoplanetary systems containing potentially habitable exoplanets (PHE): LHS-1140 b-c and K2-18 b-c. For the former system, we show that both LHS-1140 b and c must be in nearly-circul…
In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal mo…
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…
The Coupled Tidal Evolution of the Moons and Spins of Warm Exoplanets
Princeton University（普林斯顿大学）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；Observatoire de Paris, Université PSL, Sorbonne Université, Université de Lille, LNE, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，里尔大学，LNE，法国国家科学研究中心）
Tidal friction in exoplanet systems, driven by orbits that allow for durable nonzero eccentricities at short heliocentric periods, can generate internal heating far in excess of the conditions observed in our own solar system. Secular perturbations or a notional 2:1 resonance between a Hot Earth and Hot Jupiter can be used as a baseline to consider the thermal evolution of convecting bodies subject to strong viscoelastic tidal heating. We compare results first from simple models using a fixed Quality factor and Love number, and then for three different viscoelastic rheologies: the Maxwell body…
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 …
Thermal, orbital, and rotational dynamics of tidally loaded exoplanets are interconnected by intricate feedback. The rheological structure of the planet determines its susceptibility to tidal deformation and, as a consequence, participates in shaping its orbit. The orbital parameters and the spin state, conversely, control the rate of tidal dissipation and may lead to substantial changes of the interior. We investigate the coupled thermal-orbital evolution of differentiated rocky exoplanets governed by the Andrade viscoelastic rheology. The coupled evolution is treated by a semi-analytical mod…
The discovery and characterization of Earth-sized planets that are in, or near, a tidally-locked state are of crucial importance to understanding terrestrial planet evolution, and for which Venus is a clear analog. Exoplanetary science lies at the threshold of characterizing hundreds of terrestrial planetary atmospheres, thereby providing a statistical sample far greater than the limited inventory of terrestrial planetary atmospheres within the Solar System. However, the model-based approach for characterizing exoplanet atmospheres relies on Solar System data, resulting in our limited inventor…
The transiting planet candidate KOI 1843.03 ($0.6 R_\oplus$ radius, 4.245 hour orbital period, $0.46 M_\odot$ host star) has the shortest orbital period of any planet yet discovered. Here we show, using the first three-dimensional interior structure simulations of ultra-short-period tidally distorted rocky exoplanets, that KOI 1843.03 may be shaped like an American football, elongated along the planet-star axis with an aspect ratio of up to 1.79. Furthermore, for KOI 1843.03 to have avoided tidal disruption (wherein the planet is pulled apart by the tidal gravity of its host star) on such a cl…
Using a shallow water model with time-dependent forcing we show that the peak of an exoplanet thermal phase curve is, in general, offset from secondary eclipse when the planet is rotating. That is, the planetary hot-spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset is a function of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady-state in the reference frame of the moving forcing. The model is an extension of the well studied Matsuno-Gill model into a f…
Since the launch of Kepler and Hubble more than a decade ago, we have come a long way in the quest to find a potentially habitable exoplanet. To date, we have already discovered more than 4000 exoplanets most of which are not suitable for sustaining life. Of all those that can potentially sustain life, A large number has been found rotating synchronously around their parent star, mostly Red dwarf star. Due to their synchronous rotation, these planets receive very uneven stellar heating. Synchronous rotation of these planets causes one side of the planet to permanently face the parent star whil…
Improvements in the number of confirmed planets and the precision of observations imply a need to better understand subtle effects that may bias interpretations of exoplanet observations. One such effect is the distortion of a short period planet by its host star, affecting its derived density. We extend the work of Burton et al., Correia, and others, using a gravitational potential formulation to a sample of nearly 200 planets with periods less than 3 days. We find five planets exhibiting density variations of >10% and as many as 20 planets with deviations >5%. We derive an analytic approxima…
Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. I calculate how habitable planets evolve under two commonly-used models and find, for example, that one model predicts that the Earth's rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no s…
Context. New estimates of the masses and radii of the seven planets orbiting the ultracool M-dwarf TRAPPIST-1 star permit improved modelling of their compositions, heating by tidal dissipation, and removal of tidal heat by solid-state convection. Aims. Here, we compute the heat flux due to insolation and tidal heating for the inner four planets. Methods. We apply a Maxwell viscoelastic rheology to compute the tidal response of the planets using the volume-weighted average of the viscosities and rigidities of the metal, rock, high-pressure ice and liquid water/ice I layers. Results. We show tha…
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…
A large fraction of known terrestrial-size exoplanets located in the Habitable Zone of M-dwarfs are expected to be tidally-locked. Numerous efforts have been conducted to study the climate of such planets, using in particular 3-D Global Climate Models (GCM). One of the biggest challenges in simulating such an extreme environment is to properly represent the effects of sub-grid convection. Most GCMs use either a simplistic convective-adjustment parametrization or sophisticated (e.g., mass flux scheme) Earth-tuned parametrizations. One way to improve the representation of convection is to study …
The internal thermal and magnetic evolution of rocky exoplanets is critical to their habitability. We focus on the thermal-orbital evolution of Earth-mass planets around low mass M stars whose radiative habitable zone overlaps with the "tidal zone". We develop a thermal-orbital evolution model calibrated to Earth that couples tidal dissipation, with a temperature-dependent Maxwell rheology, to orbital circularization and migration. We illustrate thermal-orbital steady states where surface heat flow is balanced by tidal dissipation and cooling can be stalled for billions of years until circular…
We study orbital evolution of multi-planet systems that form a resonant chain, with nearest neighbours close to first order commensurabilities, incorporating orbital circularisation produced by tidal interaction with the central star. We develop a semi-analytic model applicable when the relative proximities to commensurability, though small, are large compared to epsilon^(2/3) , with epsilon being a measure of the characteristic planet to central star mass ratio. This enables determination of forced eccentricities as well as which resonant angles enter libration. When there are no active linke…
We study the orbits, tidal heating and mass loss from satellites around close-in gas giant exoplanets. The focus is on large satellites which are potentially observable by their transit signature. We argue that even Earth-size satellites around hot Jupiters may be immune to destruction by orbital decay; detection of such a massive satellite would strongly constrain theories of tidal dissipation in gas giants, in a manner complementary to orbital circularization. The star's gravity induces significant periodic eccentricity in the satellite's orbit. The resulting tidal heating rates, per unit ma…
Co-orbital planets (in a $1:1$ mean motion resonance) can be formed within a Laplace resonance chain. Here, we develop a secular model to study the dynamics of the resonance chain $p:p:p+1$, where the co-orbital pair is in a first-order mean motion resonance with the outermost third planet. Our model takes into account tidal dissipation through the use of a Hamiltonian version of the constant time-lag model, which extends the Hamiltonian formalism of the point-mass case. We show the existence of several families of equilibria, and how these equilibria extend to the complete system. In one fami…
The architecture of many exoplanetary systems is different from the solar system, with exoplanets being in close orbits around their host stars and having orbital periods of only a few days. We can expect interactions between the star and the exoplanet for such systems that are similar to the tidal interactions observed in close stellar binary systems. For the exoplanet, tidal interaction can lead to circularization of its orbit and the synchronization of its rotational and orbital period. For the host star, it has long been speculated if significant angular momentum transfer can take place be…
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…
This paper deals with a new formulation of the creep tide theory (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 116}, 109, 2013 $-$ Paper I) and with the tidal dissipation predicted by the theory in the case of stiff bodies whose rotation is not synchronous but is oscillating around the synchronous state with a period equal to the orbital period. We show that the tidally forced libration influences the amount of energy dissipated in the body and the average perturbation of the orbital elements. This influence depends on the libration amplitude and is generally neglected in the study of planetary …
We investigate the obliquity and spin period of Earth-Moon like systems after 4.5 Gyr of tidal evolution with various satellite masses and initial planetary obliquity and discuss their relations to the habitability of the planet. We find three possible outcomes: either i) the system is still evolving, ii) the system is double synchronous or iii) the satellite has collided with the planet. The transition between case i) and ii) is abrupt and occurs at slightly larger satellite mass ($m_s \sim 0.02m_p$) than the lunar mass. We suggest that cases ii) and iii) are less habitable than case i). Usin…
Atmospheric Collapse and Habitability on Tidally-Locked Exoplanets
Earth-Life Science Institute, Institute of Science Tokyo（地球生命研究所，东京科学大学）；Department of Earth and Planetary Sciences, Institute of Science Tokyo（地球行星科学系，东京科学大学）；Laboratoire de Météorologie Dynamique/IPSL, CNRS, Sorbonne Université, Ecole Normale Supérieure, PSL Research University, Ecole Polytechnique（气象动力学实验室/IPSL，法国国家科学研究中心，索邦大学，巴黎高等师范学院，PSL研究大学，巴黎综合理工学院）；Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS（波尔多天体物理实验室，波尔多大学，法国国家科学研究中心）；Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，地球与行星物理学研究所）；Institute of Science Tokyo（东京科学大学）
The atmospheres of synchronously rotating exoplanets are intrinsically three-dimensional, and fast vertical and horizontal winds are expected to mix the atmosphere, driving the chemical composition out of equilibrium. Due to the longer computation times associated with multi-dimensional forward models, horizontal mixing has only been investigated for a few case studies. In this paper, we aim to generalize the impact of horizontal and vertical mixing on the chemistry of exoplanet atmospheres over a large parameter space. We do this by applying a sequence of post-processed forward models for a l…
Stars with hot Jupiters tend to be rotating faster than other stars of the same age and mass. This trend has been attributed to tidal interactions between the star and planet. A constraint on the dissipation parameter $Q_\star'$ follows from the assumption that tides have managed to spin up the star to the observed rate within the age of the system. This technique was applied previously to HATS-18 and WASP-19. Here we analyze the sample of all 188 known hot Jupiters with an orbital period $< 3.5$ days and a "cool" host star ($T_{eff} < 6100$ K). We find evidence that the tidal dissipation para…
The advanced rheological models of Andrade (1910) and Sundberg & Cooper (2010) are compared to the traditional Maxwell model to understand how each affects the tidal dissipation of heat within rocky bodies. We find both the Andrade and Sundberg-Cooper rheologies can produce at least 10$\times$ the tidal heating compared to a traditional Maxwell model for a warm (1400-1600 K) Io-like satellite. Sundberg-Cooper can cause even larger dissipation around a critical temperature and frequency. These models allow cooler planets to stay tidally active in the face of orbital perturbations-a condition we…
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…
Previous studies have demonstrated that continental carbon-silicate weathering is important to the continued habitability of a terrestrial planet. Despite this, few studies have considered the influence of land on the climate of a tidally-locked planet. In this work we use the Met Office Unified Model, coupled to a land surface model, to investigate the climate effects of a continent located at the sub-stellar point. We choose to use the orbital and planetary parameters of Proxima Centauri B as a template, to allow comparison with the work of others. A region of the surface where $T_{\text{s}}…
Using the Andrade-derived Sundberg-Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto-Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including $e^{20}$), we find divergences from the traditionally used $e^{2}$ truncation starting around $e=0.1$. Order-of-magnitude differences begin to occur for $e>0.6$. Critically, higher-order eccentricity terms activate additional spin-orbit resonances. Worlds experiencing non-synchronous rotation can fall into and …
This paper deals with the application of the creep tide theory (Ferraz-Mello, CeMDA 116, 109, 2013) to the rotation of close-in satellites, Mercury, close-in exoplanets and their host stars. The solutions show two extreme cases: close-in giant gaseous planets, with fast relaxation (low viscosity) and satellites and Earth-like planets, with slow relaxation (high viscosity). The rotation of close-in gaseous planets follows the classical Darwinian pattern: it is tidally driven towards a stationary solution which is synchronized, but, if the orbit is elliptical, with a frequency larger than the or…
Next-generation space telescopes will observe the atmospheres of rocky planets orbiting nearby M-dwarfs. Understanding these observations will require well-developed theory in addition to numerical simulations. Here we present theoretical models for the temperature structure and atmospheric circulation of dry, tidally locked rocky exoplanets with grey radiative transfer and test them using a general circulation model (GCM). First, we develop a radiative-convective model that captures surface temperatures of slowly rotating and cool atmospheres. Second, we show that the atmospheric circulation …
We develop a method to infer or rule out the presence of an atmosphere on a tidally-locked hot super Earth. The question of atmosphere retention is a fundamental one, especially for planets orbiting M stars due to the star's long-duration active phase and corresponding potential for stellar-induced planetary atmospheric escape and erosion. Tidally-locked planets with no atmosphere are expected to show a Lambertian-like thermal phase curve, causing the combined light of the planet-star system to vary with planet orbital phase. We report Spitzer 8 micron IRAC observations of GJ 876 taken over 32…
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…
WASP-19b has the shortest orbital period of any known exoplanet, orbiting at only 1.2 times the Roche tidal radius. By observing the Rossiter-McLaughlin effect we show that WASP-19b's orbit is aligned, with lambda = 4.6 +/- 5.2 degrees. Using, in addition, a spectroscopic vsini and the observed rotation period we conclude that the obliquity, psi, is less than 20 degrees. Further, the eccentricity of the orbit is less than 0.02. We argue that hot Jupiters with orbital periods as short as that of WASP-19b are two orders of magnitude less common than hot Jupiters at the 3-4-d `pileup'. We discuss…
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 in M dwarf stars' habitable zones are likely to be tidally locked with orbital periods of order tens of days. This means that the effects of rotation on atmospheric dynamics will be relatively weak, which requires small horizontal temperature gradients above the boundary layer of terrestrial atmospheres. An analytically solvable and dynamically consistent model for planetary climate with only three free parameters can be constructed by making the weak temperature gradient (WTG) approximation, which assumes temperatures are horizontally uniform aloft. The extreme numerical efficiency of…
We use the distribution of extrasolar planets in circular orbits around stars with surface convective zones detected by ground based transit searches to constrain how efficiently tides raised by the planet are dissipated on the parent star. We parameterize this efficiency as a tidal quality factor (Q*). We conclude that the population of currently known planets is inconsistent with Q*<10^7 at the 99% level. Previous studies show that values of Q* between 10^5 and 10^7 are required in order to explain the orbital circularization of main sequence low mass binary stars in clusters, suggesting tha…
The increasing richness of exoplanet observations has motivated a variety of three-dimensional atmospheric circulation models of these planets. Under strongly irradiated conditions, models of tidally locked, short-period planets (both hot Jupiters and terrestrial planets) tend to exhibit a circulation dominated by a fast eastward, or "superrotating," jet stream at the equator. Under appropriate conditions, this phenomenon can cause the hottest regions to be displaced eastward from the substellar point by tens of degrees longitude. Such an offset has been observed on HD 189733b, supporting the …
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…
