Unveiling the fate of ultra-short period (USP) planets may help us understand the qualitative agreement between tidal theory and the observed exoplanet distribution. Nevertheless, due to the time-varying interchange of spin-orbit angular momentum in star-planet systems, the expected amount of tidal friction is unknown and depends on the dissipative properties of stellar and planetary interiors. In this work, we couple structural changes in the star and the planet resulting from the energy released per tidal cycle and simulate the orbital evolution of USP planets and the spin-up produced on their host star. For the first time, we allow the strength of magnetic braking to vary within a model that includes photo-evaporation, drag caused by the stellar wind, stellar mass loss, and stellar wind enhancement due to the in-falling USP planet. We apply our model to the two exoplanets with the shortest periods known to date, NGTS-10b and WASP-19b. We predict they will undergo orbital decay in time-scales that depend on the evolution of the tidal dissipation reservoir inside the star, as well as the contribution of the stellar convective envelope to the transfer of angular momentum. Contrary to previous work, which predicted mid-transit time shifts of $\sim30-190$ s over 10 years, we found that such changes would be smaller than 10 s. We note this is sensitive to the assumptions about the dissipative properties of the system. Our results have important implications for the search for observational evidence of orbital decay in USP planets, using present and future observational campaigns.
Turbulent friction in convective regions in stars and planets is one of the key physical mechanisms that drive the dissipation of the kinetic energy of tidal flows in their interiors and the evolution of their systems. This friction acts both on the equilibrium/non-wave like tide and on tidal inertial waves in these layers. It is thus necessary to obtain a robust prescription for this friction. In the current state-of-the-art, it is modeled by a turbulent eddy-viscosity coefficient, based on mixing-length theory, applied on velocities of tides. However, none of the current prescriptions take i…
White dwarf-white dwarf (WD-WD) mergers may lead to type Ia supernovae events. Thompson (2011) suggested that many such binaries are produced in hierarchical triple systems. The tertiary induces eccentricity oscillations in the inner binary via the Kozai-Lidov mechanism, driving the binary to high eccentricities, and significantly reducing the gravitational wave merger timescale (T_GW) over a broad range of parameter space. Here, we investigate the role of tidal forces in these systems. We show that tidal effects are important in the regime of moderately high initial relative inclination betwe…
Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction Eggleton, Kiseleva & Hut (1998), we analyse the effects of the inclusion of stellar magnetic braking on the evolution of such systems. A phase-plane analysis of a simplified system of equations, including only the stellar tide together with a model of the braking torque proposed by Verbunt & Zwaan (1981), is presented. The inclusion of stellar magnetic braking is found to be extremely impor…
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…
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directly relevant to the studies of habitability of planets and their moons. Our work begins with an explanation of how friction and lagging should be built into the theory of bodily tides. Although much of this material can be found in various publications, a short but self-consistent summary on the topic has been lacking in the hitherto literature, and…
The occurrence distribution of the shortest period giant exoplanets as found by Kepler show a drop-off that is a remarkable match to the drop-off expected by taking migration due to tides in the star. We present a comparison that can show the level of tidal dissipation (friction) as a function of the distribution of the ages of the star and planet system, with known dependencies on basic star and planet parameters. Use of this relation enables constraints to be put on the value of the tidal dissipation, constraints that will be improved as the distribution of the ages are determined. For the g…
We investigate how night side cooling and surface friction impact surface temperatures and large scale circulation for tidally locked Earth-like planets. For each scenario, we vary the orbital period between $P_{rot}=1-100$~days and capture changes in climate states. We find drastic changes in climate states for different surface friction scenarios. For very efficient surface friction ($t_{s,fric}=$ 0.1 days), the simulations for short rotation periods ($P_{rot} \leq$ 10 days) show predominantly standing extra tropical Rossby waves. These waves lead to climate states with two high latitude wes…
Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with tidal friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov…
We present a self-consistent model for the tidal evolution of circumbinary planets. Based on the weak-friction model, we derive expressions of the resulting forces and torques considering complete tidal interactions between all the bodies of the system. Although the tidal deformation suffered by each extended mass must take into account the combined gravitational effects of the other two bodies, the only tidal forces that have a net effect on the dynamic are those that are applied on the same body that exerts the deformation, as long as no mean-motion resonance exists between the masses. We ap…
With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, the correct treatment of tidal interactions is becoming necessary. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeed the result of tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets, which can then be responsible for volcanism and/or surface deformation. In the majority of studies to estimate the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology…
Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency $ω_{\rm tide}$; when $ω_{\rm tide}$ is larger than the turnover frequency of convective …
Tidal dissipation is known as one of the main drivers of the secular evolution of planetary systems. It directly results from dissipative mechanisms that occur in planets and stars' interiors and strongly depends on the structure and dynamics of the bodies. This work focuses on the mechanism of viscous friction in stars and planetary layers. A local model is used to study tidal dissipation. It provides general scaling laws that give a qualitative overview of the different possible behaviors of fluid tidal waves. Furthermore, it highlights the sensitivity of dissipation to the tidal frequency a…
By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $ε=Ω^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth the asymptotic result was derived. When it is not so small, e.g. a rapidly rotating star or planet, we perform numerical calculations. It is found that when rotation is sufficiently fast ($ε$ reaches $0.1$) a great amount of tidal resonances appear. To generate the same level of tide, a faster rotation corresponds to a lower tidal frequency. Friction suppresses tidal r…
Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction, we study the evolution of close-in planets on inclined orbits, due to tides. We analyse the effects of the inclusion of stellar magnetic braking by performing a phase-plane analysis of a simplified system of equations, including the braking torque. The inclusion of magnetic braking is found to be important, and its neglect can result in a very different system history. We then present the …
We develop a description of tidal effects in astrophysical systems using effective field theory techniques. While our approach is equally capable of describing objects in the Newtonian regime (e.g. moons, rocky planets, main sequence stars, etc.) as well as relativistic objects (e.g. neutron stars and black holes), in this paper we focus special attention on the Newtonian regime. In this limit, we recover the dynamical equations for the "weak friction model" with additional corrections due to tidal and rotational deformations.
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Tidal dissipation inside the fluid layers of celestial bodies are intrinsically linked to the dynamics and the physical properties of the latter. This complex dependence must be characterized. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Car…
More than 1500 exoplanets have been discovered around a large diversity of host stars (from M- to A-type stars). Tidal dissipation in their convective envelope is a key actor that shapes the orbital architecture of short-period systems and that still remains unknown. Using a simplified two-layer assumption and grids of stellar models, we compute analytically an equivalent modified tidal quality factor, which is proportional to the inverse of the frequency-averaged dissipation due to the viscous friction applied by turbulent convection on tidal waves. It leads the conversion of their kinetic en…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints are now obtained both in the Solar and exoplanetary systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this letter, we compute separately the contributions of the potential dense rocky/icy core and the convective fluid envelope of gaseous giant p…
Sub-Neptunes around FGKM dwarfs are evenly distributed in log orbital period down to $\sim$10 days, but dwindle in number at shorter periods. Both the break at $\sim$10 days and the slope of the occurrence rate down to $\sim$1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at co-rotation. We demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks---as might be expected if planet…
It has been unambiguously shown in both individual systems and at the population level that hot Jupiters experience tidal inspiral before the end of their host stars' main sequence lifetimes. Ultra-short-period (USP) planets have orbital periods $P < 1$ day, rocky compositions, and are expected to experience tidal decay on similar timescales to hot Jupiters if the efficiency of tidal dissipation inside their host stars parameterized as $Q_\ast'$ is independent of $P$ and/or secondary mass $M_{\mathrm{p}}$. Any difference between the two classes of systems would reveal that a constant $Q_\ast'$…
Planetary systems evolve over secular time scales. One of the key mechanisms that drive this evolution is tidal dissipation. Submitted to tides, stellar and planetary fluid layers do not behave like rocky ones. Indeed, they are the place of resonant gravito-inertial waves. Therefore, tidal dissipation in fluid bodies strongly depends on the excitation frequency while this dependence is smooth in solid ones. Thus, the impact of the internal structure of celestial bodies must be taken into account when studying tidal dynamics. The purpose of this work is to present a local model of tidal gravito…
Oceanic tides are a major source of tidal dissipation. They are a key actor for the orbital and rotational evolution of planetary systems, and contribute to the heating of icy satellites hosting a subsurface ocean. Oceanic tides are characterized by a highly frequency-resonant behavior, which is mainly due to the propagation of surface gravity waves in the case of thin oceans, and internal waves when they are deeper. In this work, we derive self-consistent ab initio expressions of the oceanic tidal torque as a function of the key physical parameters of the system (the ocean depth, the Brunt-Vä…
Small, rocky planets have been found orbiting in extreme proximity to their host stars, sometimes down to only $\sim 2$ stellar radii. These ultra-short-period planets (USPs) likely did not form in their present-day orbits, but rather migrated from larger initial separations. While tides are the probable cause of this migration, the tidal source has remained uncertain. Here we introduce planetary obliquity tides as a natural pathway for the production of USPs within close-in multi-planet systems. The crucial idea is that tidal dissipation generally forces planetary spin vectors to equilibrium …
Giant planets are believed to host central dense rocky/icy cores that are key actors in the core-accretion scenario for their formation. In the same time, some of their components are unstable in the temperature and pressure regimes of central regions of giant planets and only ab-initio EOS computations can address the question of the state of matter. In this framework, several works demonstrated that erosion and redistribution of core materials in the envelope must be taken into account. These complex mechanisms thus may deeply modify giant planet interiors for which signatures of strong tida…
We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a "spin + companion" system (called Colombo's top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria ("Tidal Cassini Equilibria", tCE) that are stable and attracting: the "simple" tC…
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…
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…
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…
The rate of tidal evolution of asteroidal binaries is defined by the dynamical Love numbers divided by quality factors. Common is the (often illegitimate) approximation of the dynamical Love numbers with their static counterparts. As the static Love numbers are, approximately, proportional to the inverse rigidity, this renders a popular fallacy that the tidal evolution rate is determined by the product of the rigidity by the quality factor: $\,k_l/Q\propto 1/(μQ)\,$. In reality, the dynamical Love numbers depend on the tidal frequency and all rheological parameters of the tidally perturbed bod…
