Hydrogen Eos at Megabar Pressures and the Search for Jupiter’s Core

The interior structure of Jupiter serves as a benchmark for an entire astrophysical class of liquid–metallic hydrogen-rich objects with masses ranging from ~0.1M _J to ~80M _J (1M _J = Jupiter mass = 1.9e30 g), comprising hydrogen-rich giant planets (mass < 13M _J) and brown dwarfs (mass > 13M _J but ~ < 80M _J), the so-called substellar objects (SSOs). Formation of giant planets may involve nucleated collapse of nebular gas onto a solid, dense core of mass ~0.04M _J rather than a stellar-like gravitational instability. Thus, detection of a primordial core in Jupiter is a prime objective for understanding the mode of origin of extrasolar giant planets and other SSOs. A basic method for core detection makes use of direct modeling of Jupiter’s external gravitational potential terms in response to rotational and tidal perturbations, and is highly sensitive to the thermodynamics of hydrogen at multi-megabar pressures. The present-day core masses of Jupiter and Saturn may be larger than their primordial core masses due to sedimentation of elements heavier than hydrogen. We show that there is a significant contribution of such sedimented mass to Saturn’s core mass. The sedimentation contribution to Jupiter’s core mass will be smaller and could be zero.     

Mercury: Internal structure and thermal evolution

Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR² is 0.325 (J₂=0.302×10^?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR²=0.394 (J₂=0.487×10^?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.     

Core formation in giant gaseous protoplanets

Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M_⊕ and ∼0.5 M_⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M_⊕. Saturn's core mass is found to be ∼8 M_⊕.     

M dwarfs: planet formation and long term evolution

The first part of this paper discusses how planet formation proceeds in the disks orbiting M dwarf stars. These environments are different from those associated with solar‐type stars in several ways: The planet forming clock (set by orbits) runs slower, the disks are more prone to evaporation, the supply of raw material is lower, the snowline is closer in, and planetary systems are more easily disrupted. Because of these considerations, red dwarfs are less likely to harbor giant planets, but can readily produce smaller planets. The second part of this paper describes stellar evolution calculations for M dwarfs, which live far longer than the current age of the universe. These diminutive stellar objects remain convective over most of their lives, continue to burn hydrogen for trillions of years, and do not experience red giant phases in their old age. Instead, red dwarfs turn into blue dwarfs and finally white dwarfs. This work also shows (in part) why larger stars become red giants. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gravitational interaction between a planet and an optically thin disc

We investigate the gravitational interaction between a planet and an optically thin protoplanetary disc, performing local three-dimensional hydrodynamical simulations. In the present study, we take account of radiative energy transfer in optically thin discs. Before the stage of planetary accretion, dust opacity is expected to decrease significantly because of grain growth and planetesimal formation. Thus, it would be reasonable to consider optically thin discs in the disc–planet interaction. Furthermore, we focus on small planets that can neither capture disc gas nor open a disc gap. The one-sided torque exerted on a planet by an optically thin disc is examined for various values of the disc optical thickness (<1). In optically thin discs, the temperature behind the density waves is lower than the unperturbed value because of radiative cooling. Heating due to shock dissipation is less effective than radiative cooling. Because of radiative cooling, the density distribution around the planet is not axisymmetric, which exerts an additional torque on the planet. The torque enhancement becomes maximum when the cooling time is comparable with the Keplerian period. The enhancement is significant for low-mass planets. For planets with  3 M_⊕  , the additional one-sided torque can be 40 per cent of the torque in the isothermal case. The radiative cooling is expected to change the differential torque and the migration speed of planets, too.     

The formation and habitability of terrestrial planets in the presence of close-in giant planets

‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.     

Observable consequences of planet formation models in systems with close-in terrestrial planets

To date, two planetary systems have been discovered with close-in, terrestrial-mass planets     . Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form 'hot Earths' and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward 'type 1' migration; (3) formation from material being 'shepherded' inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets     with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than     , photoevaporation can remove the planet's envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet's radius).     

Models and theoretical spectrum for the free oscillations of Saturn

We constructed new models of Saturn with an allowance made for a helium mass fraction of ～0.18–0.25 in its atmosphere. Our modeling shows that the composition of Saturn differs markedly from the solar composition; more specifically, during its formation, the planet was ～11–15 planetary masses short of the hydrogen-helium component. Saturn, as well as the other giant planets, must have been formed according to Schmidt’s scenario, through the formation of embryonic nuclei, rather than according to Laplace’s scenario. The masses of the embryonic nuclei themselves lie within the range (3.5–8) M_⊕. We calculated a theoretical free-oscillation spectrum for our models of Saturn, each of which fits all of the available observational data. The results of our calculations are presented graphically and in tables. Of particular interest are the diagnostic potentialities of the discontinuity gravitational modes related to density jumps in the molecular envelope of Saturn and at the interface between its molecular and metallic envelopes. When observational data appear, our results can be used both to identify the observed modes and to improve the models themselves. We discuss some of the cosmogonical aspects associated with the formation of the giant planets.     

Formation of the giant planets

Observational constraints on interior models of the giant planets indicate that these planets were all much hotter when they formed and they all have rock and/or ice cores of ten to thirty earth masses. These cores are probably soluble in the envelopes above, especially in Jupiter and Saturn, and are therefore likely to be primordial. They persist despite the continual upward mixing by thermally driven convection throughout the age of the solar system, because of the inefficiency of double-diffusive convection. Thus, these planets most probably formed by the hydrodynamic collapse of a gaseous envelope onto a core rather than by direct instability of the gaseous solar nebula. Recent calculations by Mizuno (1980, Prog. Theor. Phys.64, 544) show that this formation mechanism may explain the similarity of giant planet core masses. Problems remain however, and no current model is entirely satisfactory in explaining the properties of the giant planets and simultaneously satisfying the terrestrial planet constraints. Satellite systematics and protoplanetary disk nebulae are also discussed and related to formation conditions.     

Stability of a planet in the HD 41004 binary system

The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M_⊙ and 0.4 M_⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 M_J) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 M_J planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oligarchic growth of giant planets

Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M_⊕) within the lifetime of the nebular gas (?10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.     

Water in star‐forming regions with Herschel

The Herschel Space Observatory is well suited to address several important questions in star‐ and planet formation, as is evident from its first year of operation. This paper focuses on observations of water, a key molecule in the physics and chemistry of star‐formation. In the WISH Key Program, a comprehensive set of water lines is being obtained with the HIFI and PACS instruments toward a large sample of well‐characterized protostars, covering a wide range of luminosities and evolutionary stages. Lines of H₂O, CO and their isotopologues, as well as chemically related hydrides, [O I] and [C II] are observed. Together, the data determine the abundance of water in cold and warm gas, reveal the entire CO ladder up to 4000 K above ground, elucidate the physical processes responsible for the warm gas (passive heating, UV or X‐ray‐heating, shocks), quantify the main cooling agents, and probe dynamical processes associated with forming stars and planets (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of inclined orbits of terrestrial planets in habitable zones

In long-term stability studies of terrestrial planets moving in the habitable zone (HZ) of a sun-like star, we distinguish four different configurations: (i) planets moving in binary star systems, (ii) the inner type (where the gas giant moves outside the HZ), (iii) the outer type (where the gas giant is closer to the star, than the HZ) and (iv) the Trojan type (where the gas giant moves in the HZ). Since earlier calculations indicated, that the stability of the motion in the HZ also depends on the inclination of the terrestrial planet orbits, we present a detailed numerical investigation to show correlations between the eccentricity, the mass and the distance of the giant planet for various inclinations of the terrestrial planets. The orbital stability of the HZ was examined for all four configurations stated above. While we could find hardly any stable orbits for the first three types for inclinations higher than 40^°, the Trojan planets can be stable up to an inclination of 60^°. Additionally, we could also find some stabilizing effects of the inclination for the first three types. As dynamical model we used the elliptic restricted three-body problem, which consists of two massive and one mass-less body. This allows an application to all detected and future extrasolar single planet systems.     

Planetesimal dissolution in the envelopes of the forming,giant planets

We have assessed the ability of planetesimals to penetrate through the envelopes of growing giant planets that form by a “core-instability” mechanism. According to this mechanism, a core grows by the accretion of solid bodies in the solar nebula and the growing core becomes progressively more effective in gravitationally concentrating gas from the surrounding solar nebula in an envelope until a “runaway” accretion of gas occurs. In performing this assessment, we have considered the ability of gas drag to slow down a planetesimal; the effectiveness of gas dynamical pressure in fracturing and ultimately finely fragmenting it; the ability of its strength and self-gravity to resist such fracturing; and the degree to which it is evaporated due to heating by the surrounding envelope, including shock heating that develops during the supersonic portion of its trajectory. We also consider what happens if the planetesimal is able to reach the core at free-fall velocity and the ability of the envelope to convectively mix dissolved materials to different radial distances. These calculations were performed for various epochs in the growth of a giant planet with the model envelopes derived by Bodenheimer and Pollack (1986,67, 391–408). As might have been anticipated, our results vary significantly with the size of the planetesimal, its composition, and the stage of growth of the giant planet and hence the mass of its envelope. Over much of the growth phase of the core, prior to its reaching its critical mass for runaway gas accretion, icy planetesimals less than about 1 m in size dissolve in the outer region of the envelope, ones larger than about 1 m and smaller than about 1 km dissolve in the middle region of the envelope, ones larger than 1 km either reach the core interface or dissolve in the deeper regions of the envelope. Similarly rocky planetesimals smaller than about a kilometer dissolve in the middle portion of the envelope, while larger ones can penetrate more deeply. Furthermore, the convection zones of the envelopes during this stage are confined to localized regions and hence dissolved materials experience little radial mixing then. Thus, if much of the accreted mass is contained in planetesimals larger than about a kilometer, the critical core mass for runaway accretion is not expected to change significantly when planetesimal dissolution is taken into account. After accretion is terminated and the planet contracts toward its present size, the convection zone grows until it encompasses the entire envelope. Therefore, dissolved material should eventually become well mixed through the envelope. We proposed that the envelopes of the giant planets should contain significant enhancements above solar proportions in the abundances of virtually all elements relative to that of hydrogen, with the magnitude of the enhancement increasing approximately linearly with the ratio of the high Z mass to the (H, He) mass for the bulk of the planet. This prediction is in accord both qualitatively and quantitatively with the systematic increase in the atmospheric C/H ratio from Jupiter to Saturn to Uranus and Neptune and semiquantitatively with the results of recent interior models of the giant planets. It is not clear whether it is consistent with the abundances of H₂O and NH₃ in the atmospheres of some of the outer planets. Finally, the complete reduction of some dissolved materials, especially C containing compounds, is expected to consume some of the H₂ in the envelopes. Consequently, the He/H₂ ratios in the atmospheres of Uranus and Neptune may be slightly enhanced over the solar ratio. We estimate that the He/H₂ ratios for Uranus' and Neptune's atmospheres should be about 6 and 15% larger, respectively, than the solar ratio.     

Model bond albedos of extrasolar giant planets

The atmospheres of extrasolar giant planets are modeled with various effective temperatures and gravities, with and without clouds. Bond albedos are computed by calculating the ratio of the flux reflected by a planet (integrated over wavelength) to the total stellar flux incident on the planet. This quantity is useful for estimating the effective temperature and evolution of a planet. We find it is sensitive to the stellar type of the primary. For a 5 M_Jup planet the Bond albedo varies from 0.4 to 0.3 to 0.6 as the primary star varies from A5V to G2V to M2V in spectral type. It is relatively insensitive to the effective temperature and gravity for cloud-free planets. Water clouds increase the reflectivity of the planet in the red, which increases the Bond albedo. The Bond albedo increases by an order of magnitude for a 13 M_Jup planet with an M2V primary when water clouds are present. Silicate clouds, on the other hand, can either increase or decrease the Bond albedo, depending on whether there are many small grains (the former) or few large grains (the latter).     

The road to Earth twins – Karl Schwarzschild Award Lecture 2010

A rich population of low‐mass planets orbiting solar‐type stars on tight orbits has been detected by Doppler spectroscopy. These planets have masses in the domain of super‐Earths and Neptune‐type objects, and periods less than 100 days. In numerous cases these planets are part of very compact multiplanetary systems. Up to seven planets have been discovered orbiting one single star. These low‐mass planets have been detected by the HARPS spectrograph around 30 % of solar‐type stars. This very high occurrence rate has been recently confirmed by the results of the Kepler planetary transit space mission. The large number of planets of this kind allows us to attempt a first characterization of their statistical properties, which in turn represent constraints to understand the formation process of these systems. The achieved progress in the sensitivity and stability of spectrographs have already led to the discovery of planets with masses as small as 1.5 M_⊕ (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metallicity, debris discs and planets

We investigate the populations of main-sequence stars within 25 pc that have debris discs and/or giant planets detected by Doppler shift. The metallicity distribution of the debris sample is a very close match to that of stars in general, but differs with >99 per cent confidence from the giant planet sample, which favours stars of above average metallicity. This result is not due to differences in age of the two samples. The formation of debris-generating planetesimals at tens of au thus appears independent of the metal fraction of the primordial disc, in contrast to the growth and migration history of giant planets within a few au. The data generally fit a core accumulation model, with outer planetesimals forming eventually even from a disc low in solids, while inner planets require fast core growth for gas to still be present to make an atmosphere.     

GJ 581 update: Additional evidence for a Super‐Earth in the habitable zone

We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super‐Earth‐mass planet in the star's Habitable Zone. We were able to reproduce their reported χ²_ν and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N‐body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6σ detection of e = 0.32 for the eccentricity of GJ 581e is manifestly incompatible with the system's dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the χ²_ν and demonstrates the need for including non‐Keplerian orbital precession when modeling this system. We find that a four‐planet model with all of the planets on circular or nearly circular orbits provides both an excellent self‐consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4‐planet all‐circular‐orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240‐point HARPS data set, when analyzed in its entirety, and modeled with fully self‐consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a false alarm probability of <4% and is consistent with a planet of minimum mass 2.2 M_⊕, orbiting squarely in the star's habitable zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jupiter and Super-Earth embedded in a gaseous disc

In this paper we investigate the evolution of a pair of interacting planets – a Jupiter-mass planet and a Super-Earth with a mass of  5.5 M _⊕  – orbiting a Solar-type star and embedded in a gaseous protoplanetary disc. We focus on the effects of type I and II orbital migrations, caused by the planet–disc interaction, leading to the capture of the Super-Earth in first-order mean-motion resonances by the Jupiter. The stability of the resulting resonant system in which the Super-Earth is on the internal orbit relative to the Jupiter is studied numerically by means of full 2D hydrodynamical simulations. Our main aim is to determine the Super-Earth behaviour in the presence of the gas giant in the system. It is found that the Jupiter captures the Super-Earth into the interior 3:2 or 4:3 mean-motion resonance, and that the stability of such configurations depends on the initial positions of the planets and on the evolution of the eccentricity. If the initial separation of the orbits of the planets is larger than or close to that required for the exact resonance, the final outcome is the migration of the pair of planets at a rate similar to that of the gas giant, at least for the time of our simulations. Otherwise, we observe a scattering of the Super-Earth from the disc. The evolution of planets immersed in a gaseous disc is compared with their behaviour in the case of the classical three-body problem when the disc is absent.