We study the fate of internal gravity waves approaching the centre of a non-rotating solar-type star, by performing 3D numerical simulations using a Boussinesq-type model. These waves are excited at the top of the radiation zone by the tidal forcing of a short-period planet on a circular, coplanar orbit. This extends previous work done in 2D by Barker & Ogilvie. We first derive a linear wave solution, which is not exact in 3D; however, the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves. Waves with sufficient amplitude to cause isentropic overturning break, and deposit their angular momentum near the centre. This forms a critical layer, at which the angular velocity of the flow matches the orbital angular frequency of the planet. This efficiently absorbs ingoing waves, and spins up the star from the inside out, while the planet spirals into the star. We also perform numerical integrations to determine the linearised adiabatic tidal response throughout the star, for solar-type stellar models with masses in the range 0.5 < m_star/M_sun < 1.1, throughout their main sequence lifetimes. The aim is to study the launching region for these waves at the top of the radiation zone in more detail, and to determine the accuracy of a semi-analytic approximation for the tidal torque on the star, that was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer. The main conclusions are that this nonlinear mechanism of tidal dissipation could provide an explanation for the survival of all short-period extrasolar planets observed around FGK stars, while it predicts the destruction of more massive planets. This work provides further support for the model outlined in a previous paper by Barker & Ogilvie, and makes predictions that will be tested by ongoing observational studies, such as WASP and Kepler.
Internal gravity waves are excited at the interface of convection and radiation zones of a solar-type star by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star, and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an importa…
Planets in close-in orbits interact magnetically and tidally with their host stars. These interactions lead to a net torque that makes close-in planets migrate inward or outward depending on their orbital distance. We compare systematically the strength of magnetic and tidal torques for typical observed star-planet systems (T-Tauri & hot Jupiter, M dwarf & Earth-like planet, K star & hot Jupiter) based on state-of-the-art scaling-laws. We find that depending on the characteristics of the system, tidal or magnetic effects can dominate. For very close-in planets, we find that both torques can ma…
Validated planet candidates need not lie on long-term stable orbits, and instability triggered by post-main-sequence stellar evolution can generate architectures which transport rocky material to white dwarfs, polluting them. The giant planet HD 131399Ab orbits its parent A star at a projected separation of about 50-100 au. The host star, HD 131399A, is part of a hierarchical triple with HD 131399BC being a close binary separated by a few hundred au from the A star. Here, we determine the fate of this system, and find that (i) stability along the main sequence is achieved only for a favourable…
As a star evolves off the Main Sequence, it endures major structural changes that are capable of determining the fate of the planets orbiting it. Throughout its evolution along the Red Giant Branch, the star increases its radius by two orders of magnitude. Later, during the Asymptotic Giant Branch, it loses most of its initial mass. Finally, during the Planetary Nebulae phase, it emits intense radiation before ultimately beginning its fade as a white dwarf. We show how the several competing processes (stellar mass-loss, gravitational and frictional drag, tidal forces, planet accretion and evap…
As gas giant planets evolve, they may scatter other planets far from their original orbits to produce hot Jupiters or rogue planets that are not gravitationally bound to any star. Here, we consider planets cast out to large orbital distances on eccentric, bound orbits through a gaseous disk. With simple numerical models, we show that super-Earths can interact with the gas through dynamical friction to settle in the remote outer regions of a planetary system. Outcomes depend on planet mass, the initial scattered orbit, and the evolution of the time-dependent disk. Efficient orbital damping by d…
Roughly 1000 white dwarfs are known to be polluted with planetary material, and the progenitors of this material are typically assumed to be asteroids. The dynamical architectures which perturb asteroids into white dwarfs are still unknown, but may be crucially dependent on moons liberated from parent planets during post-main-sequence gravitational scattering. Here, we trace the fate of these exomoons, and show that they more easily achieve deep radial incursions towards the white dwarf than do scattered planets. Consequently, moons are likely to play a significant role in white dwarf pollutio…
We have computed the fate of exoplanet companions around main sequence stars to explore the frequency of planet ingestion by their host stars during the red giant branch evolution. Using published properties of exoplanetary systems combined with stellar evolution models and Zahn's theory of tidal friction, we modeled the tidal decay of the planets' orbits as their host stars evolve. Most planets currently orbiting within 2 AU of their star are expected to be ingested by the end of their stars' red giant branch ascent. Our models confirm that many transiting planets are sufficiently close to th…
The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski and Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and …
The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that wou…
In about 6 Giga years our Sun will evolve into a red giant and finally end its life as a white dwarf. This stellar metamorphosis will occur to virtually all known host stars of exo-planetary systems and is therefore crucial for their final fate. It is clear that the innermost planets will be engulfed and evaporated during the giant phase and that planets located farther out will survive. However, the destiny of planets in-between, at ~ 1 - 10 au, has not yet been investigated with a multi-planet tidal treatment. We here combine for the first time multi-planet interactions, stellar evolution, a…
We show that the fate of moons of a close-in giant planet is mainly determined by the migration history of the planet in the protoplanetary disk. As the planet migrates in the disk from beyond the snow line towards a multi-day period orbit, the formed and forming moons become unstable as the planet's sphere of influence shrinks. Disk-driven migration is faster than the moons' tidal orbital evolution. Moons are eventually ejected from around close-in exoplanets or forced into collision with them before tides from the star affect their orbits. If moons are detected around close-in exoplanets, th…
Circumbinary planets whose orbits become unstable may be ejected, accreted, or even captured by one of the stars. We quantify the relative rates of these channels, for a binary of secondary star's mass fraction 0.1 with an orbit of 1AU. The most common outcome is ejection, which happens ~80% of the time. If binary systems form circumbinary planets readily and sloppily, this process may fill the Milky Way with free-floating planets. A significant fraction of the time, ~20%, the unstable planet strikes the primary or secondary. We tracked whether a Jupiter-like planet would undergo tidal strippi…
We carry out N-body simulations to examine the effects of dynamical interactions on planetary systems in young open star clusters. We explore how the planetary populations in these star clusters evolve, and how this evolution depends on the initial amount of substructure, the virial ratio, the cluster mass and density, and the initial semi-major axis of the planetary systems. The fraction of planetary systems that remains intact as a cluster member, fbps, is generally well-described by the functional form fbps=f0(1+[a/a0]^c)^-1, where (1-f0) is the fraction of stars that escapes from the clust…
In similar-sized planetary collisions, a significant part of the impactor often misses the target and continues downrange. We follow the dynamical evolution of "runners" from giant impacts to determine their ultimate fate. Surprisingly, runners re-impact their target planets only about half of the time, for realistic collisional and dynamical scenarios. Otherwise they remain in orbit for tens of millions of years (the limit of our N-body calculations) and longer, or sometimes collide with a different planet than the first one. When the runner does return to collide again with the same arget pl…
The majority of binary star systems that host exoplanets will spend the first portion of their lives within a star-forming cluster that may drive dynamical evolution of the binary-planet system. We perform numerical simulations of S-type planets, with masses and orbital architecture analogous to the solar system's 4 gas giants, orbiting within the influence of a 0.5 solar-mass binary companion. The binary-planet system is integrated simultaneously with an embedded stellar cluster environment. ~10% of our planetary systems are destabilized when perturbations from our cluster environment drive t…
Turbulence in protoplanetary disks affects planet formation in many ways. While small dust particles are mainly affected by the aerodynamical coupling with turbulent gas velocity fields, planetesimals and larger bodies are more affected by gravitational interaction with gas density fluctuations. For the latter process, a number of numerical simulations have been performed in recent years, but a fully parameter-independent understanding has not been yet established. In this study, we present simple scaling relations for the planetesimal stirring rate in turbulence driven by magnetorotational in…
Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar clus…
The orbital architecture of the Solar System is thought to have been sculpted by a dynamical instability among the giant planets. During the instability a primordial outer disk of planetesimals was destabilized and ended up on planet-crossing orbits. Most planetesimals were ejected into interstellar space but a fraction were trapped on stable orbits in the Kuiper belt and Oort cloud. We use a suite of N-body simulations to map out the diversity of planetesimals' dynamical pathways. We focus on two processes: tidal disruption from very close encounters with a giant planet, and loss of surface v…
We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Satu…
We perform $N$-body simulations of the early phases of open cluster evolution including a large population of planetesimals, initially arranged in Kuiper-belt like discs around each star. Using a new, 4th-order and time-reversible $N$-body code on Graphics Processing Units (GPUs), we evolve the whole system under the stellar gravity, i.e. treating planetesimals as test particles, and consider two types of initial cluster models, similar to IC348 and the Hyades, respectively. In both cases, planetesimals can be dynamically excited, transferred between stars or liberated to become free-floating …
We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector Machine algorithm to search for an empirical boundary that best separates stable systems from systems experiencing either ejections or collisions with the star. We propose the following new criterion for dynamical stability: $a_{\rm out}(1-e_{\rm out})/[a_{\rm in}(1+e_{\rm in})]>2.4\left[\max(μ_{\rm in},μ_{\rm out})\right]^{1/3}(a_{\rm out}/a_{\rm in})^{1/2}+…
We used {\sl \textup{ab initio}} molecular dynamics simulations to calculate the high-pressure melting temperatures of the three potential core components. The planetary adiabats were obtained by solving the hydrostatic equations in a three-layer model adjusted to reproduce the measured gravitational moments. Recently developed {\sl \textup{ab initio}} equations of state were used for the envelope and the core. We find that the cores of the giant and ice-giant planets of the solar system differ because the pressure-temperature conditions encountered in each object correspond to different regio…
A critical phase in the standard model for planet formation is the runaway growth phase. During runaway growth bodies in the 0.1--100 km size range (planetesimals) quickly produce a number of much larger seeds. The runaway growth phase is essential for planet formation as the emergent planetary embryos can accrete the leftover planetesimals at large gravitational focusing factors. However, torques resulting from turbulence-induced density fluctuations may violate the criterion for the onset of runaway growth, which is that the magnitude of the planetesimals' random (eccentric) motions are less…
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…
TRAPPIST-1 planets are invaluable for the study of comparative planetary science outside our Solar System and possibly habitability. First, we derive from N-body simulations possible planetary evolution scenarios, and show that each of the planets are likely to be in synchronous rotation. We then use a 3-D Global Climate Model to explore the possible climates of cool planets of the TRAPPIST-1 system. In particular, we look at the conditions required for cool planets to prevent possible volatile species to be lost by permanent condensation, irreversible burying or photochemical destruction. We …
The fates of planetary systems provide unassailable insights into their formation and represent rich cross-disciplinary dynamical laboratories. Mounting observations of post-main-sequence planetary systems necessitate a complementary level of theoretical scrutiny. Here, I review the diverse dynamical processes which affect planets, asteroids, comets and pebbles as their parent stars evolve into giant branch, white dwarf and neutron stars. This reference provides a foundation for the interpretation and modelling of currently known systems and upcoming discoveries.
The gravitational instability model of planet/brown dwarf formation proposes that protostellar discs can fragment into objects with masses above a few Jupiter masses at large semimajor axis. Tidal downsizing may reduce both the object mass and semimajor axis. However, most studies of tidal downsizing end when the protostellar disc disperses, while the system is embedded in its parent star-forming region. To compare disc fragment descendants with exoplanet and brown dwarf observations, the subsequent dynamical evolution must be explored. We carry out N-Body integrations of fragment-fragment sca…
All the giant planets in the solar system host a large number of natural satellites. Moons in extrasolar systems are difficult to detect, but a Neptune-sized exomoon candidate has been recently found around a Jupiter-sized planet in the Kepler-1625bsystem. Due to their relative ease of detection, hot Jupiters (HJs), which reside in close orbits around their host stars with a period of a few days, may be very good candidates to search for exomoons. It is still unknown whether the HJ population can host (or may have hosted) exomoons. One suggested formation channel for HJs is high-eccentricity m…
The discovery of CoRoT-7b, a planet of radius 1.68 +/- 0.09 R_E, mass 4.8 +/- 0.8 M_E and orbital period of 0.854 days demonstrates that small planets can orbit extremely close to their star. We use knowledge of hot Jupiters, mass loss estimates and models for the interior structure and evolution of planets to understand its composition, structure and evolution. The inferred mass and radius of CoRoT-7b are consistent with a rocky planet that would be depleted in iron relative to Earth. However, a one sigma increase in mass (5.6 M_E) and decrease in size (1.59 R_E) are compatible with an Earth-…
Nearly every star known to host planets will become a white dwarf, and nearly 100 planet-hosts are now known to be accompanied by binary stellar companions. Here, we determine how a binary companion triggers instability in otherwise unconditionally stable single-star two-planet systems during the giant branch and white dwarf phases of the planet host. We perform about 700 full-lifetime (14 Gyr) simulations with A0 and F0 primary stars and secondary K2 companions, and identify the critical binary distance within which instability is triggered at any point during stellar evolution. We estimate t…
In this chapter we summarize current knowledge of the internal structure of giant planets. We concentrate on the importance of heavy elements and their role in determining the planetary composition and internal structure, in planet formation, and during the planetary long-term evolution. We briefly discuss how internal structure models are derived, present the possible structures of the outer planets in the Solar System, and summarise giant planet formation and evolution. Finally, we introduce giant exoplanets and discuss how they can be used to better understand giant planets as a class of pl…
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education（现代天文学和天体物理学教育部重点实验室）；MEAYIN Science Center（MEAYIN科学中心）
Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilise ordinary convection and produce a stably-stratified layer near the core of these planets. This region could consist of semi-convective layers with a staircase-like density profile, which have multiple convective zones separated by thin stably-stratified interfaces, as a result of double-diffusive convection. These layers could have important effects on wave propagation and tidal dissipation that have not been fully explored. We an…
We study the radial and vertical stability of dust grains launched with all charge-to-mass ratios at arbitrary distances from rotating planets with complex magnetic fields. We show that the aligned dipole magnetic field model analyzed by Jontof-Hutter and Hamilton (2012) is an excellent approximation in most cases, but that fundamentally new physics arises with the inclusion of non-axisymmetric magnetic field terms. In particular, large numbers of distant negatively-charged dust grains, stable in a magnetic dipole, can be driven to escape by a more complex field. We trace the origin of the ins…
Planetary materials orbiting white dwarf stars reveal the ultimate fate of the planets of the Solar System and all known transiting exoplanets. Observed metal pollution and infrared excesses from debris disks support that planetary systems or their remnants are common around white dwarf stars; however, these planets are difficult to detect since a very high orbital inclination angle is required for a small white dwarf to be transited, and these transits have very short (minute) durations. The low odds of catching individual transits could be overcome by a sufficiently wide and fast photometric…
A new mechanism for the internal heating of ultra-short-period planets is proposed based on the gravitational perturbation by a non-axisymmetric quadrupole moment of their host stars. Such a quadrupole is due to the magnetic flux tubes in the stellar convection zone, unevenly distributed in longitude and persisting for many stellar rotations as observed in young late-type stars. The rotation period of the host star evolves from its shortest value on the zero-age main sequence to longer periods due to the loss of angular momentum through a magnetized wind. If the stellar rotation period comes c…
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…
Close-in giant planets with strong stellar irradiation show atmospheric circulation patterns with strong equatorial jets and global-scale stationary waves. So far, almost all modeling works on atmospheric circulations of such giant planets have mainly considered external radiation alone, without taking into account the role of internal heat fluxes or just treating it in very simplified ways. Here, we study atmospheric circulations of strongly irradiated giant planets by considering the effect of internal forcing, which is characterized by small-scale stochastic interior thermal perturbations, …
Many giant exoplanets are found near their Roche limit and in mildly eccentric orbits. In this study we examine the fate of such planets through Roche-lobe overflow as a function of the physical properties of the binary components, including the eccentricity and the asynchronicity of the rotating planet. We use a direct three-body integrator to compute the trajectories of the lost mass in the ballistic limit and investigate the possible outcomes. We find three different outcomes for the mass transferred through the Lagrangian point $L_{1}$: (i) self-accretion by the planet, (ii) direct impact …
The Pluto-Charon system has come into sharper focus following the fly by of New Horizons. We use N-body simulations to probe the unique dynamical history of this binary dwarf planet system. We follow the evolution of the debris disc that might have formed during the Charon-forming giant impact. First, we note that in-situ formation of the four circumbinary moons is extremely difficult if Charon undergoes eccentric tidal evolution. We track collisions of disc debris with Charon, estimating that hundreds to hundreds of thousands of visible craters might arise from 0.3--5 km radius bodies. New Ho…
The large number of detected giant exoplanets offers the opportunity to improve our understanding of the formation mechanism, evolution, and interior structure of gas giant planets. The two main models for giant planet formation are core accretion and disk instability. There are substantial differences between these formation models, including formation timescale, favorable formation location, ideal disk properties for planetary formation, early evolution, planetary composition, etc. First, we summarize the two models including their substantial differences, advantages, and disadvantages, and …
We perform a stability analysis of a tidally excited nonlinear internal gravity wave near the centre of a solar-type star in two-dimensions. The motivation is to understand the tidal interaction between short-period planets and their solar-type host stars, which involves the launching of gravity waves at the top of the radiation zone that propagate towards the stellar centre. Studying the instabilities of these waves near the centre, where nonlinearities are most important, is essential, since it may have implications for the survival of these planets. When the waves have sufficient amplitude …
Many extrasolar (bound) terrestrial planets and free-floating (unbound) planets have been discovered. The existence of bound and unbound terrestrial planets with liquid water is an important question, and of particular importance is the question of their habitability. Even for a globally ice-covered planet, geothermal heat from the planetary interior may melt the interior ice, creating an internal ocean covered by an ice shell. In this paper, we discuss the conditions that terrestrial planets must satisfy for such an internal ocean to exist on the timescale of planetary evolution. The question…
The growing body of observational data on extrasolar planets and protoplanetary disks has stimulated intense research on planet formation and evolution in the past few years. The extremely diverse, sometimes unexpected physical and orbital characteristics of exoplanets lead to frequent updates on the mainstream scenarios for planet formation and evolution, but also to the exploration of alternative avenues. The aim of this review is to bring together classical pictures and new ideas on the formation, orbital and internal evolutions of planets, highlighting the key role of the protoplanetary di…
Hydrodynamical simulations of two giant planets embedded in a gaseous disk have shown that in case of a smooth convergent migration they end up trapped into a mean motion resonance. These findings have led to the conviction that the onset of dynamical instability causing close encounters between the planets can occur only after the dissipation of the gas when the eccentricity damping is over. We show that a system of three giant planets may undergo planet-planet scattering when the gaseous disk, with density values comparable to that of the Minimum Mass Solar Nebula, is still interacting with …
As it has already done for Earth, the sun, and the stars, seismology has the potential to radically change the way the interiors of giant planets are studied. In a sequence of events foreseen by only a few, observations of Saturn's rings by the Cassini spacecraft have rapidly broken ground on giant planet seismology. Gravity directly couples the planet's normal mode oscillations to the orbits of ring particles, generating spiral waves whose frequencies encode Saturn's internal structure and rotation. These modes have revealed a stably stratified region near Saturn's center, and provided a new …
This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we will discuss the various types of planets appearing in this diagram and describe internal structures for each type. The review will summarize the status of theoretical and experimental works performed in the field of equation of states (EOS) for materials relevant to planetary interiors and will address the main theoretical and experimental uncertainties and ch…
Pressure is a key parameter in the physics and chemistry of planet formation and evolution. Previous studies have erroneously assumed that internal pressures monotonically increase with the mass of a body. Using smoothed particle hydrodynamics and potential field method calculations, we demonstrate that the hot, rapidly-rotating bodies produced by giant impacts can have much lower internal pressures than cool, slowly-rotating planets of the same mass. Pressures subsequently increase due to thermal and rotational evolution of the body. Using the Moon-forming impact as an example, we show that t…
Water content and the internal evolution of terrestrial planets and icy bodies are closely linked. The distribution of water in planetary systems is controlled by the temperature structure in the protoplanetary disk and dynamics and migration of planetesimals and planetary embryos. This results in the formation of planetesimals and planetary embryos with a great variety of compositions, water contents and degrees of oxidation. The internal evolution and especially the formation time of planetesimals relative to the timescale of radiogenic heating by short-lived 26Al decay may govern the amount…
For a planet to be considered habitable on its surface, it is an important advantage for it to have a magnetic field that protects its atmosphere from stellar winds as well as cosmic rays. Magnetic protection of potentially habitable planets plays a key role in determining the chances of detecting atmospheric biosignatures. This paper proposes to use the Preliminary Reference Earth Model (PREM) internal structure as the base of a numerical model. With this model, we estimate the magnetic properties of dry and water-rich Earth-like and Super-Earth-like planets. We apply it to those of this kind…
We explore the possible Proxima Centauri b's interiors assuming the planet belongs to the class of dense solid planets (rocky with possible addition of water) and derive the corresponding radii. To do so, we use an internal structure model that computes the radius of the planet along with the locations of the different layers of materials, assuming that its mass and bulk composition are known. Lacking detailed elementary abundances of the host star to constrain the planet's composition, we base our model on solar system values. We restrained the simulations to the case of solid planets without…
