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.     

Internal structure of massive terrestrial planets

Planetary formation models predict the existence of massive terrestrial planets and experiments are now being designed that should succeed in discovering them and measuring their masses and radii. We calculate internal structures of planets with one to ten times the mass of the Earth (Super-Earths) to obtain scaling laws for total radius, mantle thickness, core size and average density as a function of mass. We explore different compositions and obtain a scaling law of R∝M0.267-0.272 for Super-Earths. We also study a second family of planets, Super-Mercuries with masses ranging from one mercury-mass to ten mercury-masses with similar composition to the Earth's but with a larger core mass fraction. We explore the effect of surface temperature and core mass fraction on the scaling laws for these planets. The scaling law obtained for the Super-Mercuries is R∝M∼0.3.     

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_⊕.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Planet mass stability margin of two-planetary systems

The Lagrange stability of the Sun-Jupiter-Saturn and 47 UMa two-planetary systems at a time scale of 10⁶ yr was studied using the method of averaging. When the masses of Jupiter and Saturn increase by 19 times, these planets can closely converge. The study of Lagrange stability in the case of successive mass increase allows for the obtainment of upper estimates of possible masses of extrasolar planets. Close approachs in the 47 UMa system are possible when minimal masses increase by 38 times. approachs are revealed when analyzing osculating elements; in averaged elements, approachs are absent. Resonant properties of six extrasolar two-planetary systems where the outer planet is less massive than the inner one are studied. The values of semi-major axes of planet orbits in HD 82943 and HD 73526 systems lie in a narrow resonant zone; in 47 UMa, μ Ara and HD 108874 systems lie in a wide resonant zone. In the HD 12661, the system resonances of a lower order were not revealed.     

On the stability of a planet between Mars and the asteroid belt: Implications for the Planet V hypothesis

The stability of an additional planet between the orbit of Mars and the asteroid belt is examined in the context of the Planet V hypothesis. In this model, the Solar System initially contained a fifth terrestrial planet, “Planet V,” which was removed after ∼700 Myr, a possible trigger for the late heavy bombardment on the inner planets. The model is investigated using 96 N-body integrations of the 8 major planets with an additional body between Mars and the asteroid belt. In more than 1/4 of simulations, Planet V survives for 1000 Myr. In most other cases, Planet V collides with the Sun or hits another planet after several hundred Myr, leaving 4 surviving terrestrial planets. In 24/96 simulations, Planet V is lost by ejection or collision with the Sun while the other four terrestrial planets survive without undergoing a collision. In 18 cases, Planet V is removed at least 200 Myr after the beginning of the simulation. The endstate depends sensitively on the mass of Planet V. Collision with the Sun is likely when Planet V's mass is 0.25 Mars masses or less. When Planet V is more massive than this, collisions involving it and/or other terrestrial planets become commonplace. In unstable systems, the times of first encounter and first collision/ejection depend on the initial aphelion distance of Mars. Reducing Mars's aphelion distance increases these times and also increases the fraction of systems surviving for 1000 Myr. When Mars's current orbit is used, the stability of Planet V increases when these two planets are widely separated initially. Planet V's aphelion distance Q typically begins to cross the asteroid belt within a few tens to a few hundred Myr, and its orbit last leaves the belt several hundred Myr later in most cases. The total time spent with Q>2.1 AU is typically less than 200 Myr.     

Predictions for the frequency and orbital radii of massive extrasolar planets

We investigate the migration of massive extrasolar planets caused by gravitational interaction with a viscous protoplanetary disc. We show that a model in which planets form at 5 au at a constant rate, before migrating, leads to a predicted distribution of planets that is a steeply rising function of log( a ), where a is the orbital radius. Between 1 and 3 au, the expected number of planets per logarithmic interval in a roughly doubles. We demonstrate that, once selection effects are accounted for, this is consistent with current data, and then extrapolate the observed planet fraction to masses and radii that are inaccessible to current observations. In total, approximately 15 per cent of stars targeted by existing radial velocity searches are predicted to possess planets with masses  0.3< M _p sin( i )<10 M _J  and radii  0.1< a <5 au  . A third of these planets (around 5 per cent of the target stars) lie at the radii most amenable to detection via microlensing. A further  5–10  per cent of stars could have planets at radii of  5< a <8 au  that have migrated outwards. We discuss the probability of forming a system (akin to the Solar system) in which significant radial migration of the most massive planet does not occur. Approximately  10–15  per cent of systems with a surviving massive planet are estimated to fall into this class. Finally, we note that a smaller fraction of low-mass planets than high-mass planets is expected to survive without being consumed by the star. The initial mass function for planets is thus predicted to rise more steeply towards small masses than the observed mass function.     

Thermal history and evolution of Mars

A theoretical thermal evolution model of Mars is constructed, utilizing as constraints the available geophysical and geological data, including those provided by the Viking missions. The calculation includes conduction and subsolidus mantle convection. Calculated models indicate that Martian evolution can be roughly characterized by four different stages. (1) Core formation and crust differentiation: this stage starts from the planet formation to about 1 by thereafter. During this period, Martian core is separated and the initial crust is differentiated. (2) Heating, expansion, and mantle differentiation: this stage begins after the core separation and extends to about 3 by. First, mantle temperatures rise and reach partial melting. Between 2 and 3 by, extensive melting, differentiation, and outgassing occur. Planetary radius increases and extensional features observed at the surface are most likely generated at this stage. (3) Mature phase: after 3 by, the planet reaches maturity. Between 3 and 4 by slow and sustained evolution continues. Lithosphere thickens and partial melt zone deepens. (4) Cooling period: this stage represents the last phase of Martian history. The planet is cooling slowly. The partial melting zone shrinks and volcanic activity tapers off. At present, Martian lithosphere is about 200 km thick and the mantle is convecting slowly. The models suggest that the core is molten, and the calculated surface heat flux is 35 erg cm^?2 sec^?1.     

The effects of metallicity and grain growth and settling on the early evolution of gaseous protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large (∼1 AU) and internal temperatures are low (<2000 K). The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of isolated, non-accreting planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.     

Atmospheric circulations of terrestrial planets orbiting low-mass stars

Circulations and habitable zones of planets orbiting low-mass stars are investigated. Many of these planets are expected to rotate synchronously relative to their parent stars, thereby raising questions about their surface temperature distributions and habitability. We use a global circulation model to study idealized, synchronously rotating (tidally locked) planets of various rotation periods, with surfaces of all land or all water, but with an Earth-like atmosphere and solar insolation. The dry planets exhibit wide variations in surface temperature: >80 °C on the dayside to <−110 °C on the nightside for the 240-h rotator, for example. The water-covered aquaplanets are warmer and exhibit narrower ranges of surface temperatures, e.g., ∼40 °C to >−60 °C for the 240-h orbiter. They also have a larger habitable area, defined here as the region where average surface temperatures are between 0 °C and 50 °C. This concept has little relevance for either dry or aquaplanets, but might become relevant on a planet with both land area and oceans.The circulations on these tidally locked planets exhibit systematic changes as the rotation period is varied. However, they also reveal abrupt transitions between two different circulation regimes and multiple equilibria. For the dry planet, the transition occurs between a 4-day and a 5-day period, while for the aquaplanet, it occurs between a 3-day and a 4-day period. For both dry and aqua planets, this transition occurs when the Rossby deformation radius exceeds half the planetary radius. Further investigation on the dry planet reveals that multiple equilibria exist between 100- and 221-h periods. These multiple equilibria may be relevant for real planets within the habitable zones of late K and M stars, because these planets are expected to have rotation periods between 8 and 100 Earth days.     

Giant planet migration through the action of disk torques and planet-planet scattering

This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Mass-radius curve for extrasolar Earth-like planets and ocean planets

By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H₂O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H₂O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H₂O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for ¹⁰⁻²MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H₂O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for ¹⁰⁻²MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.     

The partial volatilization of Mercury

During recent years my research on the primitive solar nebular has followed two main themes: (1) Very early in the development of the nebula conditions probably favored the occurence of major gaseous instabilities leading to the formation of giant gaseous protoplanets, but the rapid rise of the external temperature soon evaporated the envelopes of these protoplanets, possibly leaving behind precipitated solids which formed the cores and mantles of the terrestrial planets. (2) Models of the nebula indicate a later stage when conditions in the inner Solar System became very hot; at the position of Mercury the temperature was probably in the range 2500–3500°K. This leads to the hypothesis that the original protomercury was a body substantially more massive than the present planet and of normal composition, but that when it was immersed in the high-temperature field of the dissipating solar nebula, most of the rocky mantle was vaporized and mixed into the solar nebula gases and carried away by them. This hypothesis is investigated in the present paper. For simplicity the vaporization of a mantle composed of enstatite, MgSiO₃, was computed for a planet with 2.25 the mass of Mercury at a temperature of 3000°K. It is argued that the mantle could probably be largely removed in the available time of 3 × 10⁴ years. Subsequent accretion would restore some magnesium silicates to the mantle of the planet.     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.     

Terrestrial planet formation surrounding close binary stars

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around both components of some young close binary star systems. Additionally, it has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around ‘close’ binary star systems with stellar separations 0.05 AU?aB?0.4 AU and binary eccentricities 0?eB?0.8. In each simulation, the sum of the masses of the two stars is 1 M_⊙, and giant planets are included. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet formation within our Solar System by Chambers [Chambers, J.E., 2001. Icarus 152, 205-224], and around each individual component of the α Centauri AB binary star system by Quintana et al. [Quintana, E.V., Lissauer, J.J., Chambers, J.E., Duncan, M.J., 2002. Astrophys. J. 576, 982-996]. Multiple simulations are performed for each binary star system under study, and our results are statistically compared to a set of planet formation simulations in the Sun-Jupiter-Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances QB≡aB(1+eB)?0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities.     

Why are there so few hot Jupiters?

We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of 'hot Jupiters' (extrasolar planets with semimajor axes   a < 0.1  au). For planet masses   M _pl sin  i > 0.5 M _J  , the evidence for any 'pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high-mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth time-scales of a few ×10⁵ yr, suggesting that these planets may often be rapidly destroyed. Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.     

The motion of major planets from observations 1769–1988 and some astronomical constants

Modern planetary theories may be considered as a realisation of a four-dimensional dynamical reference frame. The existence of secular trends between the dynamical system and the adopted system of the Fundamental Catalogue (as well as between time scales involved) has been studied by discussing planetary observations of different types and by comparison with a numerical theory constructed for the time span 1769–1988. Parameters of the theory were fitted to radar ranging data for 1961–1988 for inner planets and to meridian observations of 18^th–20^th centuries for outer planets. Then a set of the inner planet optical observations, which includes USNO meridian observations, transits through the solar disk and occultations of fundamental stars are discussed. The main results are the following:

1. Radar data were used to estimate the time derivative? of the gravitational constantG (in another interpretation, the secular trend between the atomic and dynamic time scales): $$\dot G/G = (0.37 \pm 0.45) \times 10^{ - 11} /y.$$ This estimation, being statistically insignificant, gives some physically meaningful restriction to?.
2. From the same data a new estimation of relativistic effects in the motion of Mercury was obtained, which has confirmed the Einstein value of the perihelion advance with the error 0″.06/cy. So in the frame of Einstein's theory the value of solar dynamic oblateness cannot be larger than 2×10^?6.
3. The analysis of time behavior of residuals in the inner planet longitudes shows secular trends. It is demonstrated that these trends may be explained by combined action of a linear trenddT of Brouwer's time scale (which is adopted as a standard for reduction of observations before 1959) and the error in Newcomb's value of the constant of precession. From USNO meridian observations fordT the following estimate was obtained:dT=?14.5±2.1 sec/cy with the corresponding correction,dp, to Newcomb's precessiondp=0″.46±0″.13/cy. The estimate ofdT is in good agreement with the value ofdT determined from transits of Mercury and Venus through the solar diskdT=?12.9±1.3 sec/cy which does not depend on any precession error.
4. As a by-product, new accurate ephemerides of the outer planets are obtained over the time interval 1769–1988, the average residuals being presented.

     

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.     

Atmospheric Chemistry in Giant Planets, Brown Dwarfs, and Low-Mass Dwarf Stars: I. Carbon, Nitrogen, and Oxygen

The chemical species containing carbon, nitrogen, and oxygen in atmospheres of giant planets, brown dwarfs (T and L dwarfs), and low-mass stars (M dwarfs) are identified as part of a comprehensive set of thermochemical equilibrium and kinetic calculations for all elements. The calculations cover a wide temperature and pressure range in the upper portions of giant planetary and T-, L-, and M-dwarf atmospheres. Emphasis is placed on the major gases CH₄, CO, NH₃, N₂, and H₂O but other less abundant gases are included. The results presented are independent of particular model atmospheres, and can be used to constrain model atmosphere temperatures and pressures from observations of different gases. The influence of metallicity on the speciation of these key elements under pressure-temperature (P-T) conditions relevant to low-mass object atmospheres is discussed. The results of the thermochemical equilibrium computations indicate that several compounds may be useful to establish temperature or pressure scales for giant planet, brown dwarf, or dwarf star atmospheres. We find that ethane and methanol abundance are useful temperature probes in giant planets and methane dwarfs such as Gl 229B, and that CO₂ can serve as a temperature probe in more massive objects. Imidogen (NH) abundances are a unique pressure-independent temperature probe for all objects. Total pressure probes for warmer brown dwarfs and M dwarfs are HCN, HCNO, and CH₂O. No temperature-independent probes for the total pressure in giant planets or T-dwarf atmospheres are identified among the more abundant C, N, and O bearing gases investigated here.