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 analyse the effects of these layers on the propagation and transmission of internal waves within giant planets, extending prior work in a local Cartesian model. We adopt a simplified global Boussinesq planetary model in which we explore the internal waves in a non-rotating spherical body. We begin by studying the free modes of a region containing semi-convective layers. We then analyse the transmission of internal waves through such a region. The free modes depend strongly on the staircase properties, and consist of modes with both internal and interfacial gravity wave-like behaviour. We determine the frequency shifts of these waves as a function of the number of steps to explore their potential to probe planetary internal structures. We also find that wave transmission is strongly affected by the presence of a staircase. Very large-wavelength waves are transmitted efficiently, but small-scale waves are only transmitted if they are resonant with one of the free modes. The effective size of the core is therefore larger for non-resonant modes.
A monomodal model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of rotation rate as well as with thermal and viscous diffusivities. The convection model is used as a boundary condition for a linearization of the equations of motion in the transition region between convectively unstable and stably-stratified regions, yielding the depth to which convection penetrates into the stable region and establishing a relationship between that depth and the local convective Rossby number, di…
We use a simplified model to study wave reflection and transmission at interface of convective region and stably stratified region (e.g. radiative zone in star or stratification layer in gaseous planet). Inertial wave in convective region and gravito-inertial wave in stably stratified region are considered. We begin with polar area and then extend to any latitude. Six cases are discussed (see Table 1), and in Case 2 both waves co-exist in both regions. Four configurations are further discussed for Case 2. The angles and energy ratios of wave reflection and transmission are calculated. It is fo…
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…
Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter …
We derive the scaling of differential rotation in both slowly- and rapidly-rotating convection zones using order of magnitude methods. Our calculations apply across stars and fluid planets and all rotation rates, as well as to both magnetized and purely hydrodynamic systems. We find shear $|R\nablaΩ|$ of order the angular frequency $Ω$ for slowly-rotating systems with $Ω\ll |N|$, where $N$ is the \brvs\ frequency, and find that it declines as a power-law in $Ω$ for rapidly-rotating systems with $Ω\gg |N|$. We further calculate the meridional circulation rate and baroclinicity and examine the m…
Differential rotation is central to a great many mysteries in stars and planets. In Part I we predicted the order of magnitude and scaling of the differential rotation in both hydrodynamic and magnetohydrodynamic convection zones. Our results apply to both slowly- and rapidly-rotating systems, and provide a general picture of differential rotation in stars and fluid planets. We further calculated the scalings of the meridional circulation, entropy gradient and baroclinicity. In this companion paper we compare these predictions with a variety of observations and numerical simulations. With a fe…
We present a radiative-convective equilibrium model for young giant exoplanets. Model predictions are compared with the existing photometric measurements of planet beta Pictoris b in the J, H, Ks, L', NB 4.05, M' bands . This model will be used to interpret future photometric and spectroscopic observations of exoplanets with SPHERE, mounted at the VLT with a first light expected mid-2014.
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…
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 in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency $|ω_t|$ exceeds the turnover frequency $ω_{cν}$ of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equ…
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…
Terrestrial planets are believed to be formed via giant impacts of Mars-sized protoplanets. Planets formed via giant impacts have highly eccentric orbits. A swarm of planetesimals around the planets may lead to eccentricity damping for the planets via the equipartition of random energies (dynamical friction). However, dynamical friction increases eccentricities of planetesimals, resulting in high velocity collisions between planetesimals. The collisional cascade grinds planetesimals to dust until dust grains are blown out due to radiation pressure. Therefore, the total mass of planetesimals de…
White-light flares are magnetically driven localized brightenings on the surfaces of stars. Their temporal, spectral, and statistical properties present a treasury of physical information about stellar magnetic fields. The spatial distributions of magnetic spots and associated flaring regions help constrain dynamo theories. Moreover, flares are thought to crucially affect the habitability of exoplanets that orbit these stars. Measuring the location of flares on stars other than the Sun is challenging due to the lack of spatial resolution. Here we present four fully convective stars observed wi…
When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium ti…
A scatter plot of exoplanet mass against red giant host star radius demonstrates an interesting positive trend: larger stars have more massive planets. This implies that the evolution of a star towards a red giant affects the masses of planets in the system.
We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these …
Recent surveys have revealed a lack of close-in planets around evolved stars more massive than 1.2 Msun. Such planets are common around solar-mass stars. We have calculated the orbital evolution of planets around stars with a range of initial masses, and have shown how planetary orbits are affected by the evolution of the stars all the way to the tip of the Red Giant Branch (RGB). We find that tidal interaction can lead to the engulfment of close-in planets by evolved stars. The engulfment is more efficient for more-massive planets and less-massive stars. These results may explain the observed…
We use a high-precision radial velocity survey of FGKM stars to study the conditional occurrence of two classes of planets: close-in small planets (0.023--1 au, 2--30 Earth masses) and distant giant planets (0.23--10 au, 30--6000 Earth masses). We find that $41^{+15}_{-13}\%$ of systems with a close-in, small planet also host an outer giant, compared to $17.6^{+2.4}_{-1.9}\%$ for stars irrespective of small planet presence. This implies that small planet hosts may be enhanced in outer giant occurrence compared to all stars with $1.7σ$ significance. Conversely, we estimate that $42^{+17}_{-13}\…
Observations from the Juno and Cassini missions provide essential constraints on the internal structures and compositions of Jupiter and Saturn, resulting in profound revisions of our understanding of the interior and atmospheres of Gas Giant planets. The next step to understand planetary origins in our Solar System requires a mission to their Ice Giant siblings, Uranus and Neptune.
We present here a small anomalous radial velocity (RV) signal expected to be present in RV curves measured during planetary transits. This signal is induced by the convective blueshift (CB) effect --- a net blueshift emanating from the stellar surface, resulting from a larger contribution of rising hot and bright gas relative to the colder and darker sinking gas. Since the CB radial component varies across the stellar surface, the light blocked by the planet during a transit will have a varying RV component, resulting in a small shift of the measured RVs. The CB-induced anomalous RV curve is d…
Based on a suite of Monte Carlo simulations, I show that a stellar-mass dependent lifetime of the gas disks from which planets form can explain the lack of hot Jupiters/close-in giant planets around high-mass stars and other key features of the observed semimajor axis distribution of radial velocity-detected giant planets. Using reasonable parameters for the Type II migration rate, regions of planet formation, and timescales for gas giant core formation, I construct synthetic distributions of jovian planets. A planet formation/migration model assuming a stellar mass-dependent gas disk lifetime…
Every Sun-like star will eventually evolve into a red giant, a transition which can profoundly affect the evolution of a surrounding planetary system. The timescale of dynamical planet evolution and orbital decay has important implications for planetary habitability, as well as post-main sequence star and planet interaction, evolution and internal structure. Here, we investigate these effects by estimating planet occurrence around 2476 low-luminosity red giant branch (LLRGB) stars observed by the NASA K2 mission. We measure stellar masses and radii using asteroseismology, with median random un…
Studying the atmospheric Planetary Boundary Layer (PBL) is crucial to understand the climate of a planet. The meteorological measurements by the instruments onboard InSight at a latitude of 4.5$^{\circ}$N make a uniquely rich dataset to study the active turbulent dynamics of the daytime PBL on Mars. Here we use the high-sensitivity continuous pressure, wind, temperature measurements in the first 400 sols of InSight operations (from northern late winter to midsummer) to analyze wind gusts, convective cells and vortices in Mars' daytime PBL. We compare InSight measurements to turbulence-resolvin…
Celestial bodies with a mass of M ~ 10 M_Jup have been found orbiting nearby stars. It is unknown whether these objects formed like gas-giant planets through core accretion or like stars through gravitational instability. I show that objects with M <~ 4 M_Jup orbit metal-rich solar-type dwarf stars, a property associated with core accretion. Objects with M >~ 10 M_Jup do not share this property. This transition is coincident with a minimum in the occurrence rate of such objects, suggesting that the maximum mass of a celestial body formed through core accretion like a planet is less than 10 M_J…
Context: More than 40 planets have been found around giant stars, revealing a lack of systems orbiting interior to $\sim$ 0.6 AU. This observational fact contrasts with the planetary population around solar-type stars and has been interpreted as the result of the orbital evolution of planets due to the interaction with the host star and/or because of a different formation/migration scenario of planets around more massive stars. Aims: We are conducting a radial velocity study of a sample of 166 giant stars aimed at studying the population of close-in planets orbiting post-main sequence stars. M…
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…
Clouds are ubiquitous\, -- \,they arise for every solar system planet that possesses an atmosphere and have also been suggested as a leading mechanism for obscuring spectral features in exoplanet observations. As exoplanet observations continue to improve, there is a need for efficient and general planetary climate models that appropriately handle the possible cloudy atmospheric environments that arise on these worlds. We generate a new 1D radiative-convective terrestrial planet climate model that self-consistently handles patchy clouds through a parameterized microphysical treatment of conden…
It is still being debated whether the well-known metallicity - giant planet correlation for dwarf stars is also valid for giant stars. For this reason, having precise metallicities is very important. Different methods can provide different results that lead to discrepancies in the analysis of planet hosts. To study the impact of different analyses on the metallicity scale for evolved stars, we compare different iron line lists to use in the atmospheric parameter derivation of evolved stars. Therefore, we use a sample of 71 evolved stars with planets. With these new homogeneous parameters, we r…
We present the discovery of three new giant planets around three metal-deficient stars: HD5388b (1.96M_Jup), HD181720b (0.37M_Jup), and HD190984b (3.1M_Jup). All the planets have moderately eccentric orbits (ranging from 0.26 to 0.57) and long orbital periods (from 777 to 4885 days). Two of the stars (HD181720 and HD190984) were part of a program searching for giant planets around a sample of ~100 moderately metal-poor stars, while HD5388 was part of the volume-limited sample of the HARPS GTO program. Our discoveries suggest that giant planets in long period orbits are not uncommon around mode…
The relationship between the compositions of giant planets and their host stars is of fundamental interest in understanding planet formation. The solar system giant planets are enhanced above solar composition in metals, both in their visible atmospheres and bulk compositions. A key question is whether the metal enrichment of giant exoplanets is correlated with that of their host stars. Thorngren et al. (2016) showed that in cool (Teq < 1000 K) giant exoplanets, the total heavy-element mass increases with total Mp and the heavy element enrichment relative to the parent star decreases with tota…
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…
We calculate overstable convective modes of uniformly rotating hot Jupiters, which have a convective core and a thin radiative envelope. Convective modes in rotating planets have complex frequency $ω$ and are stabilized by rapid rotation so that their growth rates $\proptoω_{\rm I}={\rm Im}(ω)$ are much smaller than those for the non-rotating planets. The stabilized convective modes excite low frequency gravity waves in the radiative envelope by frequency resonance between them. We find that the convective modes that excite envelope gravity waves remain unstable even in the presence of non-adi…
In this paper, we have studied the convectively coupled equatorially trapped waves in rotating stars, with and without magnetic field. The equatorial trapped HD and MHD Poincaré, Rossby, mixed Rossby-Poincaré, and Kelvin waves were identified. The effects of stratification and non-traditional Coriolis force terms have been investigated. When the flow is strongly stratified, the wave frequencies of the convectively coupled model are almost the same as those of shallow water model. However, when the flow is weakly stratified, the wave frequencies are constrained by the buoyancy frequency. The no…
The Ice Giants Uranus and Neptune have hydrogen-based atmospheres with several constituents that condense in their cold upper atmospheres. A small number of bright cloud systems observed in both planets are good candidates for moist convective storms, but their observed properties (size, temporal scales and cycles of activity) differ from moist convective storms in the Gas Giants. These clouds and storms are possibly due to methane condensation and observations also suggest deeper clouds of hydrogen sulfide (H$_2$S) at depths of a few bars. Even deeper, thermochemical models predict clouds of …
Possibilities and difficulties of applying the theory of magnetic field generation by convection flows in rotating spherical fluid shells to the Giant Planets are outlined. Recent progress in the understanding of the distribution of electrical conductivity in the Giant Planets suggests that the dynamo process occurs predominantly in regions of semiconductivity. In contrast to the geodynamo the magnetic field generation in the Giant Planets is thus characterized by strong radial conductivity variations. The importance of the constraint on the Ohmic dissipation provided by the planetary luminosi…
The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early …
Exoplanetary systems host giant planets on substantially non-circular, close-in orbits. We propose that these eccentricities arise in a phase of giant impacts, analogous to the final stage of Solar System assembly that formed Earth's Moon. In this scenario, the planets scatter each other and collide, with corresponding mass growth as they merge. We numerically integrate an ensemble of systems with varying total planet mass, allowing for collisional growth, to show that (1) the high-eccentricity giants observed today may have formed preferentially in systems of higher initial total planet mass,…
The detection of many extrasolar gas giants with high eccentricities indicates that dynamical instabilities in planetary systems are common. These instabilities can alter the orbits of gas giants as well as the orbits of terrestrial planets and therefore eject or move a habitable planet out of the habitable zone. In this work 423 simulations with 153 different hypothetical planetary systems with gas giants and terrestrial planets have been modelled to explore the orbital stability of habitable planets. The initial parameter variations include the number, distances and masses of the giant plane…
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…
Planet-Disk Interactions and the Convective Overstability. I. Low Mass Planets
Iowa State University（爱荷华州立大学）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；National Center for Theoretical Sciences（国家理论科学中心）
The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these "stable" orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that t…
