After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander in and out of the planets' Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host stars' tidal perturbation induces a barrier across the converging streamlines' interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. We carry out a series of numerical simulations to test the influence of this tidal barrier on super thermal planets. In weakly viscous disks, protoplanets' accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion time scale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets' asymptotic masses exceed several times that of Jupiter. Two dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three dimensional simulations. Based on the upper falloff in the observe mass distribution of known exoplanets, we suggest their natal disks had relatively low viscosity alpha sim 0.001, modest thickness H/R sim 0.03 to 0.05, and limited masses comparable to that of minimum mass solar nebula model.
Tidal Downsizing (TD) is a recently developed planet formation theory that supplements the classical Gravitational disc Instability (GI) model with planet migration inward and tidal disruptions of GI fragments in the inner regions of the disc. Numerical methods for a detailed population synthesis of TD planets are presented here. As an example application, the conditions under which GI fragments collapse faster than they migrate into the inner $a\sim$ few AU disc are considered. It is found that most gas fragments are tidally or thermally disrupted unless (a) their opacity is $\sim 3$ orders o…
We present analytical expressions for the tidal Love numbers of a giant planet with a solid core and a fluid envelope. We model the core as a uniform, incompressible, elastic solid, and the envelope as a non-viscous fluid satisfying the $n=1$ polytropic equation of state. We discuss how the Love numbers depend on the size, density, and shear modulus of the core. We then model the core as a viscoelastic Maxwell solid and compute the tidal dissipation rate in the planet as characterized by the imaginary part of the Love number $k_2$. Our results improve upon existing calculations based on planet…
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…
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 add…
We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, ${\rm Im}[{\tilde k}_2(ω)]$, as a function of the forcing frequency $ω$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we…
Hypothetical exomoons around close-in giant planets may migrate inwards and/or outwards in virtue of the interplay of the star, planet and moon tidal interactions. These processes could be responsible for the disruption of lunar systems, the collision of moons with planets or could provide a mechanism for the formation of exorings. Several models have been developed to determine the fate of exomoons when subject to the tidal effects of their host planet. None of them have taken into account the key role that planetary evolution could play in this process. In this paper we put together numerica…
Astrophysical fluid bodies that orbit close to one another induce tidal distortions and flows that are subject to dissipative processes. The spin and orbital motions undergo a coupled evolution over astronomical timescales, which is relevant for many types of binary star, short-period extrasolar planetary systems and the satellites of the giant planets in the solar system. I review the principal mechanisms that have been discussed for tidal dissipation in stars and giant planets in both linear and nonlinear regimes. I also compare the expectations based on theoretical models with recent observ…
In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however the current lunar orbital inclination of 5 degrees requires a subsequent dynamical process that is still debated. In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model …
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…
In order to explain the inflated radii of some transiting extrasolar giant planets, we investigate a tidal heating scenario for the inflated planets WASP-4b, WASP-6b, WASP-12b, WASP-15b, and TrES-4. To do so, we assume that they retain a nonzero eccentricity, possibly by dint of continuing interaction with a third body. We calculate the amount of extra heating in the envelope that is then required to fit the radius of each planet, and we explore how this additional power depends on the planetary atmospheric opacity and on the mass of a heavy-element central core. There is a degeneracy between …
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…
We revisit the tidal stability of extrasolar systems harboring a transiting planet and demonstrate that, independently of any tidal model, none but one (HAT-P-2b) of these planets has a tidal equilibrium state, which implies ultimately a collision of these objects with their host star. Consequently, conventional circularization and synchronization timescales cannot be defined because the corresponding states do not represent the endpoint of the tidal evolution. Using numerical simulations of the coupled tidal equations for the spin and orbital parameters of each transiting planetary system, we…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon 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 work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant planets, as a function of core size and mass. We demonstrate that in general …
Hot and Warm Jupiters (HJs&WJs) are gas-giant planets orbiting their host stars at short orbital periods, posing a challenge to their efficient in-situ formation. Therefore, most of the HJs&WJs are thought to have migrated from an initially farther-out birth locations. Current migration models, i.e disc-migration (gas-dissipation driven) and eccentric-migration (tidal evolution driven), fail to produce the occurrence rate and orbital properties of HJs&WJs. Here we study the role of the thermal evolution and its coupling to tidal evolution. We use the AMUSE, numerical environment, and MESA, pla…
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 Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院）；University of Leeds（利兹大学）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
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 work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant …
Core Accretion (CA), the de-facto accepted theory of planet formation, requires formation of massive solid cores as a prerequisite for assembly of gas giant planets. The observed metallicity correlations of exoplanets are puzzling in the context of CA. While gas giant planets are found preferentially around metal-rich host stars, planets smaller than Neptune orbit hosts with a wide range of metallicities. We propose an alternative interpretation of these observations in the framework of a recently developed planet formation hypothesis called Tidal Downsizing (TD). We perform population synthes…
We hypothesise that planets are made by tidal downsizing of migrating giant planet embryos. The proposed scheme for planet formation consists of these steps: (i) a massive young protoplanetary disc fragments at R ~ several tens to hundreds of AU on gaseous clumps with masses of a few Jupiter masses; (ii) the clumps cool and contract, and simultaneously migrate closer in to the parent star; (iii) as earlier suggested by Boss (1998), dust sediments inside the gas clumps to form terrestrial mass solid cores; (iv) if the solid core becomes more massive than ~ 10 Earth masses, a massive gas atmosph…
Quantifying the energy budget of Earth in the first few million years following the Moon-forming giant impact is vital to understanding Earth's initial thermal state and the dynamics of lunar tidal evolution. After the impact, the body was substantially vaporized and rotating rapidly, very different from the planet we know today. The subsequent evolution of Earth's energy budget, as the body cooled and angular momentum was transferred during lunar tidal recession, has not been accurately calculated with all relevant energy components included. Here, we use giant impact simulations and planetar…
Tidal effects in planetary systems are the main driver in the orbital migration of natural satellites. They result from physical processes occurring deep inside celestial bodies, whose effects are rarely observable from surface imaging. For giant planet systems, the tidal migration rate is determined by poorly understood dissipative processes in the planet, and standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance, implying little migration for outer moons such as Saturn's largest moon, Titan. Here, we use two independent measurements obtained…
It has been proposed recently that the first step in the formation of both rocky and gas giant planets is dust sedimentation into a solid core inside a gas clump (giant planet embryo). The clumps are then assumed to migrate closer to the star where their metal poor envelopes are sheared away by the tidal forces or by an irradiation-driven mass loss. We consider the implications of this hypothesis for natal rotation rates of both terrestrial and gas giant planets. It is found that both types of planets may rotate near their break up angular frequencies at birth. The direction of the spin should…
Some transiting extrasolar giant planets have measured radii larger than predicted by the standard theory. In this paper, we explore the possibility that an earlier episode of tidal heating can explain such radius anomalies and apply the formalism we develop to HD 209458b as an example. We find that for strong enough tides the planet's radius can undergo a transient phase of inflation that temporarily interrupts canonical, monotonic shrinking due to radiative losses. Importantly, an earlier episode of tidal heating can result in a planet with an inflated radius, even though its orbit has nearl…
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…
I argue that feedback is as important to formation of planets as it is to formation of stars and galaxies. Energy released by massive solid cores puffs up pre-collapse gas giant planets, making them vulnerable to tidal disruptions by their host stars. I find that feedback is the ultimate reason for some of the most robust properties of the observed exoplanet populations: the rarity of gas giants at all separations from $\sim 0.1$ to $\sim 100$~AU, the abundance of $\sim 10 M_\oplus$ cores but dearth of planets more massive than $\sim 20 M_\oplus$. Feedback effects can also explain (i) rapid as…
The discovery of many giant planets in close-in orbits and the effect of planetary and stellar tides in their subsequent orbital decay have been extensively studied in the context of planetary formation and evolution theories. Planets orbiting close to their host stars undergo close encounters, atmospheric photoevaporation, orbital evolution, and tidal interactions. In many of these theoretical studies, it is assumed that the interior properties of gas giants remain static during orbital evolution. Here we present a model that allows for changes in the planetary radius as well as variations in…
A large population of planetary candidates in short-period orbits have been found through transit searches. Radial velocity surveys have also revealed several Jupiter-mass planets with highly eccentric orbits. Measurements of the Rossiter-McLaughlin effect indicate some misaligned planetary systems. This diversity could be induced by post-formation dynamical processes such as planet-planet scattering, the Kozai effect, or secular chaos which brings planets to the vicinity of their host stars. In this work, we propose a novel mechanism to form close-in super-Earths and Neptune-like planets thro…
The origin of rings around giant planets remains elusive. Saturn's rings are massive and made of 90-95% of water ice. In contrast, the much less massive rings of Uranus and Neptune are dark and likely to have higher rock fraction. Here we investigate, for the first time, the tidal disruption of a passing object, including the subsequent formation of planetary rings. First, we perform SPH simulations of the tidal destruction of big differentiated objects ($M_{\rm body}=10^{21-23}$) that experience close encounters with Saturn or Uranus. We find that about $0.1-10$% of the mass of the passing bo…
Planets of 1-4 times Earth's size on orbits shorter than 100 days exist around 30-50% of all Sun-like stars. In fact, the Solar System is particularly outstanding in its lack of "hot super-Earths" (or "mini-Neptunes"). These planets -- or their building blocks -- may have formed on wider orbits and migrated inward due to interactions with the gaseous protoplanetary disk. Here, we use a suite of dynamical simulations to show that gas giant planets act as barriers to the inward migration of super-Earths initially placed on more distant orbits. Jupiter's early formation may have prevented Uranus …
It has been suggested that tidal interaction is important for shaping the orbital configurations of close orbiting giant planets. The excitation of propagating waves and normal modes (dynamical tide) will be important for estimating time scales for orbital evolution. We consider the tidal interaction of a Jupiter mass planet orbiting a solar type primary. Tidal and rotational frequencies are assumed comparable making the effect of rotation important. Although centrifugal distortion is neglected, Coriolis forces are fully taken into account. We focus in detail on the potentially resonant excita…
A gas giant planet which survives the giant branch stages of evolution at a distance of many au and then is subsequently perturbed sufficiently close to a white dwarf will experience orbital shrinkage and circularization due to star-planet tides. The circularization timescale, when combined with a known white dwarf cooling age, can place coupled constraints on the scattering epoch as well as the active tidal mechanisms. Here, we explore this coupling across the entire plausible parameter phase space by computing orbit shrinkage and potential self-disruption due to chaotic f-mode excitation and…
According to core-accretion formation models, the conditions under which gas giants will form around M dwarfs are very restrictive. Also, the correlation of the occurrence of these planets with the metallicity of host stars is still unknown due to the intrinsic faintness of M dwarfs in the optical and some intricacies in their spectra. Interestingly, NASA's TESS mission has started to create a growing sample of these systems, with eleven observed planets located in close-in orbits: contrary to what is expected for low stellar masses. Tidal interactions with the host star will play a key role i…
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…
We present population synthesis calculations of the Tidal Downsizing (TD) hypothesis for planet formation. Our models address the following observations: (i) most abundant planets being Super Earths; (ii) cores more massive than $\sim 5-15 M_\oplus$ are enveloped by massive atmospheres; (iii) the frequency of occurrence of close-in gas giant planets correlates strongly with metallicity of the host star; (iv) no such correlation is found for sub-Neptune planets; (v) presence of massive cores in giant planets; (vi) gas giant planets are over-abundant in metals compared to their host stars; (vii)…
Planets are known to orbit giant stars, yet there is a shortage of planets orbiting within ~0.5 AU (P<100 days). First-ascent giants have not expanded enough to engulf such planets, but tidal forces can bring planets to the surface of the star far beyond the stellar radius. So the question remains: are tidal forces strong enough in these stars to engulf all the missing planets? We describe a high-cadence observational program to obtain precise radial velocities of bright giants from Weihai Observatory of Shandong University. We present data on the planet host Beta Gem (HD 62509), confirming ou…
During the runaway phase of their formation, gas giants fill their gravitational spheres of influence out to Bondi or Hill radii. When runaway ends, planets shrink several orders of magnitude in radius until they are comparable in size to present-day Jupiter; in 1D models, the contraction occurs on the Kelvin-Helmholtz time-scale $t_{\rm KH}$, which is initially a few thousand years. However, if angular momentum is conserved, contraction cannot complete, as planets are inevitably spun up to their breakup periods $P_{\rm break}$. We consider how a circumplanetary disc (CPD) can de-spin a primor…
Transit and radial velocity observations continuously discover an increasing number of exoplanets. However, when it comes to the composition of the observed planets the data are compatible with several interior structure models. Thus, a planetary parameter sensitive to the planet's density distribution could help constrain this large number of possible models even further. We aim to investigate to what extent an exoplanet's interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k_2 into account as an additional possibly observable parameter. …
Detached circumplanetary disks are unstable to tilting as a result of the stellar tidal potential. We examine how a tilted circumplanetary disk affects the evolution of the spin axis of an oblate planet. The disk is evolved using time-dependent equations for linear wave-like warp evolution, including terms representing the effect of the tidal potential and planetary oblateness. For a disk with a sufficiently large mass, we find that the planet spin quickly aligns to the misaligned disk. The tilt of the planetary spin axis then increases on the same timescale as the disk. This can be an efficie…
Tidally locked gas giants are typically in several-day orbits, implying a modest role for rotation in the atmospheric circulation. Nevertheless, there exist a class of gas-giant, highly irradiated objects---brown dwarfs orbiting white dwarfs in extremely tight orbits---whose orbital and hence rotation periods are as short as 1-2 hours. Phase curves and other observations have already been obtained for this class of objects, raising fundamental questions about the role of increasing planetary rotation rate in controlling the circulation. So far, most modeling studies have investigated rotation …
The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution II: The effect of tides in the misaligned case
Centaurs are minor planets orbiting between Jupiter and Neptune that have or had crossing orbits with one or more giant planets. Recent observations and reinterpretation of previous observations have revealed the existence of ring systems around 10199 Chariklo and 2060 Chiron. However, the origin of the ring systems around such a minor planet is still an open question. Here, we propose that the tidal disruption of a differentiated object that experiences a close encounter with a giant planet could naturally form diverse ring-satellite systems around the Centaurs. During the close encounter, th…
The Kepler observations indicate that many exoplanets are super-Earths, which brings about a puzzle for the core-accretion scenario. Since observed super-Earths are in the range of critical mass, they would accrete gas efficiently and become gas giants. Theoretically, super-Earths are predicted to be rare in the core-accretion framework. To resolve this contradiction, we propose that the tidally-forced turbulent diffusion may affect the heat transport inside the planet. Thermal feedback induced by turbulent diffusion is investigated. We find that the tidally-forced turbulence would generate ps…
Observed Hot Jupiters exhibit a wide range of physical properties. For a given mass, many planets have inflated radii, while others are surprisingly compact and may harbor large central cores. Motivated by the observational sample, this paper considers possible effects from collisions of smaller rocky planets with gas giant planets. In this scenario, the Jovian planets migrate first and enter into (approximately) 4 day orbits, whereas rocky planets (mass = 0.1-20 that of Earth) migrate later and then encounter the gaseous giants. Previous work indicates that the collision rates are high for su…
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…
The mass-period or radius-period distribution of close-in exoplanets shows a paucity of intermediate mass/size (sub-Jovian) planets with periods ~< 3 days. We show that this sub-Jovian desert can be explained by the photoevaporation of highly irradiated sub-Neptunes and the tidal disruption barrier for gas giants undergoing high-eccentricity migration. The distinctive triangular shape of the sub-Jovain desert result from the fact that photoevaporation is more effective closer to the host star, and that in order for a gas giant to tidally circularise closer to the star without tidal disruption …
The tidal interaction of an orbiting giant planet with a star near the Kraft break: the excitation of $r$-modes and the retention of orbital and spin angular momenta misalignment
