The spin-orbit angle, or obliquity, is a powerful observational marker that allows us to access the dynamical history of exoplanetary systems. Here, we have examined the distribution of spin-orbit angles for close-in exoplanets and put it in a statistical context of tidal interactions between planets and their stars. We confirm the observed trends between the obliquity and physical quantities directly connected to tides, namely the stellar effective temperature, the planet-to-star mass ratio, and the scaled orbital distance. We further devised a tidal efficiency factor combining critical parameters that control the strength of tidal effects and used it to corroborate the strong link between the spin-orbit angle distribution and tidal interactions. In particular, we developed a readily usable formula to estimate the probability that a system is misaligned, which will prove useful in global population studies. By building a robust statistical framework, we reconstructed the distribution of the three-dimensional spin-orbit angles, allowing for a sample of nearly 200 true obliquities to be analyzed for the first time. This realistic distribution maintains the sky-projected trends, and additionally hints toward a striking pileup of truly aligned systems. The comparison between the full population and a pristine subsample unaffected by tidal interactions suggests that perpendicular architectures are resilient toward tidal realignment, providing evidence that orbital misalignments are sculpted by disruptive dynamical processes that preferentially lead to polar orbits. On the other hand, star-planet interactions seem to efficiently realign or quench the formation of any tilted configuration other than for polar orbits, and in particular for antialigned orbits.
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…
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 …
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 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…
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…
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）
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-…
The distribution of close-in exoplanets is shaped by a complex interplay between atmospheric and dynamical processes. The Desert-Rim Exoplanets Atmosphere and Migration (DREAM) program aims at disentangling those processes through the study of the hot Neptune desert, whose rim hosts planets that are undergoing, or survived, atmospheric evaporation and orbital migration. In this first paper, we use the Rossiter-McLaughlin Revolutions (RMR) technique to investigate the orbital architecture of 14 close-in planets ranging from mini-Neptune to Jupiter-size and covering a broad range of orbital dist…
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…
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…
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…
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…
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…
The solar tide in an ancient Venusian ocean is simulated using a dedicated numerical tidal model. Simulations with varying ocean depth and rotational periods ranging from -243 to 64 sidereal Earth days are used to calculate the tidal dissipation rates and associated tidal torque. The results show that the tidal dissipation could have varied by more than 5 orders of magnitude, from 0.001--780 Gigawatts, depending on rotational period and ocean depth. The associated tidal torque is about 2 orders of magnitude below the present day Venusian atmospheric torque, and could change the Venusian day le…
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…
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…
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…
