The orbits of short-period exoplanets are sculpted by tidal dissipation. However, the mechanisms and associated efficiencies of these tidal interactions are poorly constrained. We present robust constraints on the tidal quality factors of short-period exoplanetary host stars through the usage of a novel empirical technique. The method is based on analyzing structures in the population-level distribution of tidal decay times, defined as the time remaining before a planet spirals into its host star due to stellar tides. Using simple synthetic planet population simulations and analytic theory, we show that there exists a steady-state portion of the decay time distribution with an approximately power-law form. This steady-state feature is clearly evident in the decay time distribution of the observed short-period planet population. We use this to constrain both the magnitude and frequency dependence of the stellar tidal quality factor and show that it must decrease sharply with planetary orbital period. Specifically, with $Q_{\star}' = Q_0 (P/2 \ \mathrm{days})^α$, we find $10^{5.5} \lesssim Q_0 \lesssim 10^7$ and $-4.33 \lesssim α\lesssim -2$. Our results are most consistent with predictions from tidal resonance locking, in which the planets are locked into resonance with a tidally excited gravity mode in their host stars.
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…
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$10% of…
A large fraction of known exoplanets have short orbital periods where tidal excitation of gravity waves within the host star causes the planets' orbits to decay. We study the effects of tidal resonance locking, in which the planet locks into resonance with a tidally excited stellar gravity mode. Because a star's gravity mode frequencies typically increase as the star evolves, the planet's orbital frequency increases in lockstep, potentially causing much faster orbital decay than predicted by other tidal theories. Due to nonlinear mode damping, resonance locking in Sun-like stars likely only op…
Tidal dissipation is responsible for circularizing the orbits and synchronizing the spins of solar-type close binary stars, but the mechanisms responsible are not fully understood. Previous work has indicated that significant enhancements to the theoretically-predicted tidal dissipation rates are required to explain the observed circularization periods ($P_\mathrm{circ}$) in various stellar populations, and their evolution with age. This was based partly on the common belief that the dominant mechanism of tidal dissipation in solar-type stars is turbulent viscosity acting on equilibrium tides …
WASP-33 is one of the few $δ$ Sct stars with a known planetary companion. By analyzing the stellar oscillations, we search for possible star-planet interactions in the pattern of the pulsation. We made use of the Transit and Light Curve Modeller (TLCM) to solve the light curve from the Transiting Exoplanet Survey Satellite (TESS). We include gravity darkening into our analysis. The stellar oscillation pattern of WASP-33 clearly shows signs of several tidally perturbed modes. We find that there are peaks in the frequency spectrum that are at or near the $3$rd, $12$th and $25$th orbital harmonic…
Gravitational perturbations on an exoplanet from a massive outer body, such as the Kozai-Lidov mechanism, can pump the exoplanet's eccentricity up to values that will destroy it via a collision or strong interaction with its parent star. During the final stages of this process, any exomoons orbiting the exoplanet will be detached by the star's tidal force and placed into orbit around the star. Using ensembles of three and four-body simulations, we demonstrate that while most of these detached bodies either collide with their star or are ejected from the system, a substantial fraction, ~10%, of…
Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in XUV irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system, and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on a UV continuum flux measurement (centered around $\sim1900$ Angstroms) for the star TRAPPIST-1, based on…
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typi…
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…
Tidal dissipation in rotating low-mass stars and implications for the orbital evolution of close-in planets I. From the PMS to the RGB at solar metallicity
在恒星模型中必须考虑恒星与行星的相互作用，以理解近距离行星的动力学演化。潮汐相互作用对恒星结构和自转演化的依赖性具有特殊的重要性，应正确对待。我们量化的潮汐耗散的对流信封旋转的低质量恒星的演变，从主序前的红巨星分支取决于初始恒星质量。我们调查的后果，这种演变对行星轨道的演变。我们将Mathis（2015）中描述的潮汐耗散形式与恒星演化代码STAREVOL相结合，并将其应用于质量在0.3和1.4 M $_\odot$之间的旋转恒星。此外，我们通过使用恒星演化高级阶段的新潮汐耗散预测来跟踪近距离行星的轨道演化，从而推广了Bolmont & Mathis（2016）的工作。在PMS上，潮汐耗散的演化受控于收缩星内部结构的演化。在MS上，它受到表面旋转变化的强烈驱动，而表面旋转变化受到磁化恒星风制动的影响。考虑到恒星的旋转演化的主要影响是降低潮汐耗散强度约四个数量级的主序列，相比之下，归一化的耗散率，只考虑到结构的变化。耗散的演化强烈依赖于恒星内部结构和自转的演化。从前主序星到红巨星分支的顶端，它的变化有几个数量级，对近距离大质量行星的轨道演化有很大的影响。这些效应在主序前最强，意味着行星主要对恒星的早期历史敏感。
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…
This is an erratum for the publication Bolmont & Mathis 2016 (Celestial Mechanics and Dynamical Astronomy, 126, 275-296, https://doi.org/10.1007/s10569-016-9690-3). There was a small mistake for the spin integration of our code which we corrected and we take advantage of this erratum to investigate a bit further the influence of a planet on the spin of its host star.
In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. Tidally-forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tida…
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…
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）
[Abridged] Most exoplanets detected so far are close-in planets, which are likely to be affected by tidal dissipation in their host star. To get a complete picture of the evolution of star-planet systems one needs to consider the impact of tides within both stellar radiative and convective zones. We aim to provide a general formalism to assess tidal dissipation in stellar radiative zones for all spectral types, allowing for the study of the dynamics of a given system throughout stellar evolution. We investigate the influence of stellar structure and evolution on tidal dissipation in the radiat…
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 …
We investigate effects of the presence of a magnetic field on tidal dissipation in rotating fluid bodies. We consider a simplified model consisting of a rigid core and a fluid envelope, permeated by a background magnetic field (either a dipolar field or a uniform axial field). The wavelike tidal responses in the fluid layer are in the form of magnetic-Coriolis waves, which are restored by both the Coriolis force and the Lorentz force. Energy dissipation occurs through viscous damping and Ohmic damping of these waves. Our numerical results show that the tidal dissipation can be dominated by Ohm…
The energy dissipation of wave-like tidal flows in the convective envelope of low-mass stars is one of the key physical mechanisms that shape the orbital and rotational dynamics of short-period planetary systems. Tidal flows, and the excitation, propagation, and dissipation of tidally-induced inertial waves can be modified by stellar magnetic fields (e.g., Wei 2016, 2018, Lin and Ogilvie 2018). It is thus important to assess for which stars, at which location of their internal structure, and at which phase of their evolution, one needs to take into account the effects of magnetic fields on tid…
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…
In rotating stars and planets, excitation of inertial waves in convective envelopes provides an important channel for tidal dissipation, but the dissipation rate due to inertial waves depends erratically on the tidal frequency. Tidal dissipation is significantly enhanced at some frequencies, suggesting possible resonances between the tidal forcing and some eigenmodes. However, the nature of these resonances remains enigmatic owing to the singularity of the eigenvalue problem of inertial waves, and the resonances are often mistakenly attributed to wave attractors in the literature. In this lett…
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…
