Recent Juno observations have suggested that the heavy elements in Jupiter could be diluted throughout a large fraction of its gaseous envelope, providing a stabilising compositional gradient over an extended region of the planet. This could trigger layered semi-convection, which, in the context of giant planets more generally, may explain Saturn's luminosity excess and play a role in causing the abnormally large radii of some hot Jupiters. In giant planet interiors, it could take the form of density staircases, which are convective layers separated by thin stably stratified interfaces. In addition, the efficiency of tidal dissipation is known to depend strongly on the planetary internal structure. We aim to study the resulting tidal dissipation when internal waves are excited in a region of layered semi-convection by tidal gravitational forcing due to other bodies (such as moons in giant planet systems, or stars in hot Jupiter systems). We adopt a local Cartesian model with a background layered density profile subjected to an imposed tidal forcing, and we compute the viscous and thermal dissipation rates numerically. We find that the rates of tidal dissipation can be enhanced in a region of layered semi-convection compared to a uniformly convective medium, where the latter corresponds with the usual assumption adopted in giant planet interior models. In particular, a region of layered semi-convection possesses a richer set of resonances, allowing enhanced dissipation for a wider range of tidal frequencies. The details of these results significantly depend on the structural properties of the layered semi-convective regions. Layered semi-convection could contribute towards explaining the high tidal dissipation rates observed in Jupiter and Saturn, which have not yet been fully explained by theory. Further work is required to explore the efficiency of this mechanism in global models.
Layered semi-convection could operate in giant planets, potentially explaining the constraints on the heavy elements distribution in Jupiter deduced recently from Juno observations, and contributing to Saturn's luminosity excess or the abnormally large radius of some hot Jupiters. This is a state consisting of density staircases, in which convective layers are separated by thin stably stratified interfaces. The efficiency of tidal dissipation in a planet depends strongly on its internal structure. It is crucial to improve our understanding of the mechanisms driving this dissipation, since it h…
The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new i…
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…
Observations have revealed that a significant number of hot Jupiters have anomalously large radii. Layered convection induced by compositional inhomogeneity has been proposed to account for the radius anomaly of hot Jupiters. To reexamine the impact of the compositional inhomogeneity, we perform an evolutionary calculation by determining convection regime at each evolutionary time step according to the criteria from linear analyses. It is shown that the impact is limited in the case of the monotonic gradient of heavy element abundance. The layered convection is absent for the first 1 Gyr from …
Competition between gravity waves excited by convection and tides in stars that host a companion
KU Leuven（荷语鲁汶大学）；CEA（法国原子能和替代能源委员会）；Observatoire de Genève, Université de Genève（日内瓦大学天文台）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理信息与测量实验室）；Instituut voor Sterrenkunde, KU Leuven（荷语鲁汶大学天文研究所）
Layered semi-convection is a possible candidate to explain Saturn's luminosity excess and the abnormally large radius of some hot Jupiters. In giant planet interiors, it could lead to the creation of density staircases, which are convective layers separated by thin stably stratified interfaces. We study the propagation of internal waves in a region of layered semi-convection, with the aim to predict energy transport by internal waves incident upon a density staircase. The goal is then to understand the resulting tidal dissipation when these waves are excited by other bodies such as moons in gi…
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 study low frequency waves that propagate in a region of layered semi-convection. Layered semi-convection is predicted to be present in stellar and planetary interiors and can significantly modify the rate of thermal and compositional mixing. We derive a series of analytical dispersion relations for plane-parallel layered semi-convection in the Boussinesq approximation using a matrix transfer formalism. We find that like a continuously stratified medium, a semi-convective staircase -- in which small convective regions are separated by sharp density jumps -- supports internal gravity waves (g…
Oscillatory double-diffusive convection (ODDC) (also known as semi- convection) refers to a type of double diffusive instability that occurs in regions of planetary and stellar interiors which have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. (2011) first showed that ODDC can either spontaneously form layers, which significantly enhance the transport of heat and chem…
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…
Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called "semi-convection". In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and composition by ODD convection, and ultimately propose a new 1D prescription that can be used in stellar and planetary structure and evolution models. The first paper in this series demonstrated that under certa…
This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coup…
We calculate the dynamical tides raised by a close planetary companion on non-rotating stars of $1$ $\text{M}_{\odot}$ and $1.4$ $\text{M}_{\odot}$. Using the Henyey method, we solve the fully non-adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non--adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent wi…
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…
Turbulent convection is thought to act as an effective viscosity ($ν_E$) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency ($ω$) exceeds the turnover frequency of the dominant convective eddies ($ω_c$). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, …
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…
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 …
Tidal interactions are important in driving spin and orbital evolution in planetary and stellar binary systems, but the fluid dynamical mechanisms responsible remain incompletely understood. One key mechanism is the interaction between tidal flows and convection. Turbulent convection is thought to act as an effective viscosity in damping large-scale tidal flows, but there is a long-standing controversy over the efficiency of this mechanism when the tidal frequency exceeds the turnover frequency of the dominant convective eddies. This high frequency regime is relevant for many applications, suc…
Jupiter's atmosphere has been observed to be depleted in helium (Yatm~0.24), suggesting active helium sedimentation in the interior. This is accounted for in standard Jupiter structure and evolution models through the assumption of an outer, He-depleted envelope that is separated from the He-enriched deep interior by a sharp boundary. Here we aim to develop a model for Jupiter's inhomogeneous thermal evolution that relies on a more self-consistent description of the internal profiles of He abundance, temperature, and heat flux. We make use of recent numerical simulations on H/He demixing, and …
We study the properties of oscillatory double-diffusive convection (ODDC) in the presence of a uniform vertical background magnetic field. ODDC takes place in stellar regions that are unstable according to the Schwarzschild criterion and stable according to the Ledoux criterion (sometimes called semiconvective regions), which are often predicted to reside just outside the core of intermediate-mass main sequence stars. Previous hydrodynamic studies of ODDC have shown that the basic instability saturates into a state of weak wave-like convection, but that a secondary instability can sometimes tr…
Since twenty years, a large population of close-in planets orbiting various classes of low-mass stars (from M to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, the stellar rotation evolution strongly impacts angular momentum exchan…
Aims: The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk composition on the interior--atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres. Methods: We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO2) following the crystallization of a magma ocean after planet formation, predicting a compositional profile …
Since 1995, numerous close-in planets have been discovered around low-mass stars (M to A-type stars). These systems are susceptible to be tidally evolving, in particular the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and also shape the orbital architecture of the surrounding planetary system. Recent theoretical studies have shown that the amplitude of the stellar dissipation can vary over several orders of magnitude as the star evolves, and that it also depends on the stellar mass and rotation. We present here one of the first studies …
Observations of Jupiter's gravity field by Juno have revealed surprisingly small values for the high order gravitational moments, considering the abundances of heavy elements measured by Galileo 20 years ago. The derivation of recent equations of state for hydrogen and helium, much denser in the Mbar region, worsen the conflict between these two observations. In order to circumvent this puzzle, current Jupiter model studies either ignore the constraint from Galileo or invoke an ad hoc modification of the equations of state. In this paper, we derive Jupiter models which satisfy both Juno and Ga…
Mini-Neptunes and volatile-poor super-Earths coexist on adjacent orbits in proximity to host stars such as Kepler-36 and Kepler-11. Several post-formation processes have been proposed for explaining the origin of the compositional diversity: the mass loss via stellar XUV irradiation, degassing of accreted material, and in-situ accumulation of the disk gas. Close-in planets are also likely to experience giant impacts during the advanced stage of planet formation. This study examines the possibility of transforming volatile-rich super-Earths / mini-Neptunes into volatile-depleted super-Earths th…
