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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Protoplanetary disks including radiative feedback from accreting planets

While recent observational progress is converging on the detection of compact regions of thermal emission due to embedded protoplanets, further theoretical predictions are needed to understand the response of a protoplanetary disk to the radiative feedback from planet formation. This is particularly important to make predictions for the observability of circumplanetary regions. In this work we use 2D hydrodynamical simulations to examine the evolution of a viscous protoplanetary disk in which a luminous Jupiter-mass planet is embedded. We use an energy equation that includes the radiative heating of the planet as an additional mechanism for planet formation feedback. Several models are computed for planet luminosities ranging from 10{sup −5} to 10{sup −3} solar luminosities. We find that the planet radiative feedback enhances the disk’s accretion rate at the planet’s orbital radius, producing a hotter and more luminous environement around the planet, independently of the prescription used to model the disk’s turbulent viscosity. We also estimate the thermal signature of the planet feedback for our range of planet luminosities, finding that the emitted spectrum of a purely active disk, without passive heating, is appreciably modified in the infrared. We simulate the protoplanetary disk around HD 100546 where a planet companion is located at about 68 AU from the star. Assuming the planet mass is five Jupiter masses and its luminosity is ∼2.5×10{sup −4} L{sub ⊙}, we find that the radiative feedback of the planet increases the luminosity of its ∼5 AU circumplanetary disk from 10{sup −5} L{sub ⊙} (without feedback) to 10{sup −3} L{sub ⊙}, corresponding to an emission of ∼1 mJy in the L{sup ′} band after radiative transfer calculations, a value that is in good agreement with HD 100546b observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2017

The Demographics of Rocky Free-Floating Planets and Their Detectability by WFIRST

Planets are thought to form via accretion from a remnant disk of gas and solids around a newly formed star. During this process, material in the disk either remains bound to the star as part of either a planet, a smaller celestial body, or makes up part of the the interplanetary medium; falls into the star; or is ejected from the system. Herein we use dynamical models to probe the abundance and properties of ejected material during late-stage planet formation and estimate their contribution to the free-floating planet population. We present 300 N-body simulations of terrestrial planet formation around a solar-type star, with and without giant planets present, using a model that accounts for collisional fragmentation. In simulations with Jupiter and Saturn analogs, about one-third of the initial (approx. 5 solar mass) disk mass is ejected, about half in planets more massive than Mercury but with a mass lower than 0.3 solar mass, and the remainder in smaller bodies. Most ejections occur within 25 Myr, which is shorter than the timescale typically required for Earth-mass planets to grow (30-100 Myr). When giant planets are omitted from our simulations, almost no material is ejected within 200 Myr and only about 1% of the initial disk is ejected by 2 Gyr. We show that about 2.5 terrestrial-mass planets are ejected per star in the Galaxy. We predict that the space-borne microlensing search for free-floating planets from the Wide-Field Infra-Red Space Telescope will discover up to 15 Mars-mass planets, but few free-floating Earth-mass planets.

Barclay, Thomas S.↗
NASA NTRS2019

Architecture and Dynamics of Kepler's Multi-Transiting Planet Systems.III. Comprehensive Investigation Using All Four Years of Kepler Mission Data

We study the orbital architectures of planetary systems orbiting within ∼1 AU of their stars by analyzing the ensemble of Kepler systems having two or more planet candidates. We use data from the entire Kepler mission, and in many cases we apply improved analysis techniques (e.g., replacing histograms by top-hat Kernel Density Estimators that avoid the loss of information resulting from choosing a particular phase for the bin boundaries) to extend and enhance the studies of Lissauer et al. (2011, ApJS 197, 8) and Fabrycky et al. (2014, ApJ 790, 146).These data show ~ 1700 transiting planet candidates in > 600 multiple-planet systems, far more than were available for our previous two studies. The increased numbers and better information about planetary radii and the properties of stellar hosts made possible by Gaia DR2 allow more statistically-robust analyses of the entire ensemble of Kepler multis as well as independent analyses of subsets of the population. We are thus able to contrast the dynamical configurations of small and large planets, short-period and longer-period planets, and planets orbiting various types of host stars. We reinforce our previous findings that most pairs of planets within the same system are neither in nor near low-order mean motion resonances and that there is a substantial excess of planets having period ratios slightly larger than those of first-order mean-motion resonances. However, neglecting three systems whose planets are locked in 3- body resonances and summing over all first-order mean motion resonances, the deficit of planet pairs with period ratios just narrow of resonance is as large as the excess of planets wide of resonance (within statistical uncertainties), suggesting that overall there is no overall excess of planet pairs in the vicinity of resonance. Other aspects of our study, including estimates of the typical relative inclinations of planetary orbits and their variations as functions of orbital period, planet sizes and stellar properties, are in progress, with results expected to be available for presentation by the time of the conference.

Lissauer, Jack↗
NASA NTRS2016

Migration of Accreting Planets in Radiative Discs From Dynamical Torques

We present the results of hydrodynamical simulations of the orbital evolution of planets undergoing runaway gas accretion in radiative discs. We consider accreting disc models with constant mass flux through the disc, and where radiative cooling balances the effect of viscous heating and stellar irradiation. We assume that 20–30 M(sub ⨁) giant planet cores are formed in the region where viscous heating dominates and migrate outward under the action of a strong entropy-related corotation torque. In the case where gas accretion is neglected and for an α viscous stress parameter α = 2 × 10(exp -3), we find evidence for strong dynamical torques in accreting discs with accretion rates M ̇ ≳ 7 × 10(exsp -8)M(sub ⨀) yr(exp -1). Their main effect is to increase outward migration rates by a factor of ∼2 typically. In the presence of gas accretion, however, runaway outward migration is observed with the planet passing through the zero-torque radius and the transition between the viscous heating and stellar heating dominated regimes. The ability for an accreting planet to enter a fast migration regime is found to depend strongly on the planet growth rate but can occur for values of the mass flux through the disc of M ̇ ≳ 5 × 10(exp -8)M(sub ⨀) yr(exp -1).We find that an episode of runaway outward migration can cause an accreting planet formed in the 5–10 au region to temporarily orbit at star–planet separations as large as∼60–70 au. However, increase in the amplitude of the Lindblad torque associated with planet growth plus change in the streamline topology near the planet systematically cause the direction of migration to be reversed. Subsequent evolution corresponds to the planet migrating inward rapidly until it becomes massive enough to open a gap in the disc and migrate in the type II regime. Our results indicate that a planet can reach large orbital distances under the combined effect of dynamical torques and gas accretion, but an alternative mechanism is required to explain the presence of massive planets on wide orbits.

Accretion↗
DOE OSTI2012

THE COMPOSITIONAL DIVERSITY OF EXTRASOLAR TERRESTRIAL PLANETS. II. MIGRATION SIMULATIONS

Prior work has found that a variety of terrestrial planetary compositions are expected to occur within known extrasolar planetary systems. However, such studies ignored the effects of giant planet migration, which is thought to be very common in extrasolar systems. Here we present calculations of the compositions of terrestrial planets that formed in dynamical simulations incorporating varying degrees of giant planet migration. We used chemical equilibrium models of the solid material present in the disks of five known planetary host stars: the Sun, GJ 777, HD4203, HD19994, and HD213240. Giant planet migration has a strong effect on the compositions of simulated terrestrial planets as the migration results in large-scale mixing between terrestrial planet building blocks that condensed at a range of temperatures. This mixing acts to (1) increase the typical abundance of Mg-rich silicates in the terrestrial planets' feeding zones and thus increase the frequency of planets with Earth-like compositions compared with simulations with static giant planet orbits, and (2) drastically increase the efficiency of the delivery of hydrous phases (water and serpentine) to terrestrial planets and thus produce waterworlds and/or wet Earths. Our results demonstrate that although a wide variety of terrestrial planet compositions can still be produced, planets with Earth-like compositions should be common within extrasolar planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CONSTRAINTS ON PLANET OCCURRENCE AROUND NEARBY MID-TO-LATE M DWARFS FROM THE MEARTH PROJECT

The MEarth Project is a ground-based photometric survey intended to find planets transiting the closest and smallest main-sequence stars. In its first four years, MEarth discovered one transiting exoplanet, the 2.7 R{sub ⊕} planet GJ1214b. Here, we answer an outstanding question: in light of the bounty of small planets transiting small stars uncovered by the Kepler mission, should MEarth have found more than just one planet so far? We estimate MEarth's ensemble sensitivity to exoplanets by performing end-to-end simulations of 1.25 × 10{sup 6} observations of 988 nearby mid-to-late M dwarfs, gathered by MEarth between 2008 October and 2012 June. For 2-4 R{sub ⊕} planets, we compare this sensitivity to results from Kepler and find that MEarth should have found planets at a rate of 0.05-0.36 planets yr{sup –1} in its first four years. As part of this analysis, we provide new analytic fits to the Kepler early M dwarf planet occurrence distribution. When extrapolating between Kepler's early M dwarfs and MEarth's mid-to-late M dwarfs, we find that assuming the planet occurrence distribution stays fixed with respect to planetary equilibrium temperature provides a good match to our detection of a planet with GJ1214b's observed properties. For larger planets, we find that the warm (600-700 K), Neptune-sized (4 R{sub ⊕}) exoplanets that transit early M dwarfs like Gl436 and GJ3470 occur at a rate of <0.15 star{sup –1} (at 95% confidence) around MEarth's later M dwarf targets. We describe a strategy with which MEarth can increase its expected planet yield by 2.5 × without new telescopes by shifting its sensitivity toward the smaller and cooler exoplanets that Kepler has demonstrated to be abundant.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

DISK-PLANETS INTERACTIONS AND THE DIVERSITY OF PERIOD RATIOS IN KEPLER'S MULTI-PLANETARY SYSTEMS

The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order mean-motion resonances. This feature has been shown to be a natural outcome of orbital circularization of resonant planetary pairs due to star-planet tidal interactions. However, this feature holds in multi-planetary systems with periods longer than 10 days, in which tidal circularization is unlikely to provide efficient divergent evolution of the planets' orbits to explain these orbital period ratios. Gravitational interactions between planets and their parent protoplanetary disk may instead provide efficient divergent evolution. For a planet pair embedded in a disk, we show that interactions between a planet and the wake of its companion can reverse convergent migration and significantly increase the period ratio from a near-resonant value. Divergent evolution due to wake-planet interactions is particularly efficient when at least one of the planets opens a partial gap around its orbit. This mechanism could help account for the diversity of period ratios in Kepler's multiple systems from super-Earth to sub-Jovian planets with periods greater than about 10 days. Diversity is also expected for pairs of planets massive enough to merge their gap. The efficiency of wake-planet interactions is then much reduced, but convergent migration may stall with a variety of period ratios depending on the density structure in the common gap. This is illustrated for the Kepler-46 system, for which we reproduce the period ratio of Kepler-46b and c.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

M dwarf metallicities and giant planet occurrence: Ironing out uncertainties and systematics

Comparisons between the planet populations around solar-type stars and those orbiting M dwarfs shed light on the possible dependence of planet formation and evolution on stellar mass. However, such analyses must control for other factors, i.e., metallicity, a stellar parameter that strongly influences the occurrence of gas giant planets. We obtained infrared spectra of 121 M dwarfs stars monitored by the California Planet Search and determined metallicities with an accuracy of 0.08 dex. The mean and standard deviation of the sample are –0.05 and 0.20 dex, respectively. We parameterized the metallicity dependence of the occurrence of giant planets on orbits with a period less than two years around solar-type stars and applied this to our M dwarf sample to estimate the expected number of giant planets. The number of detected planets (3) is lower than the predicted number (6.4), but the difference is not very significant (12% probability of finding as many or fewer planets). The three M dwarf planet hosts are not especially metal rich and the most likely value of the power-law index relating planet occurrence to metallicity is 1.06 dex per dex for M dwarfs compared to 1.80 for solar-type stars; this difference, however, is comparable to uncertainties. Giant planet occurrence around both types of stars allows, but does not necessarily require, a mass dependence of ∼1 dex per dex. The actual planet-mass-metallicity relation may be complex, and elucidating it will require larger surveys like those to be conducted by ground-based infrared spectrographs and the Gaia space astrometry mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A STELLAR-MASS-DEPENDENT DROP IN PLANET OCCURRENCE RATES

The Kepler spacecraft has discovered a large number of planets with up to one-year periods and down to terrestrial sizes. While the majority of the target stars are main-sequence dwarfs of spectral type F, G, and K, Kepler covers stars with effective temperatures as low as 2500 K, which corresponds to M stars. These cooler stars allow characterization of small planets near the habitable zone, yet it is not clear if this population is representative of that around FGK stars. In this paper, we calculate the occurrence of planets around stars of different spectral types as a function of planet radius and distance from the star and show that they are significantly different from each other. We further identify two trends. First, the occurrence of Earth- to Neptune-sized planets (1-4 R {sub ⊕}) is successively higher toward later spectral types at all orbital periods probed by Kepler; planets around M stars occur twice as frequently as around G stars, and thrice as frequently as around F stars. Second, a drop in planet occurrence is evident at all spectral types inward of a ∼10 day orbital period, with a plateau further out. By assigning to each spectral type a median stellar mass, we show that the distance from the star where this drop occurs is stellar mass dependent, and scales with semi-major axis as the cube root of stellar mass. By comparing different mechanisms of planet formation, trapping, and destruction, we find that this scaling best matches the location of the pre-main-sequence co-rotation radius, indicating efficient trapping of migrating planets or planetary building blocks close to the star. These results demonstrate the stellar-mass dependence of the planet population, both in terms of occurrence rate and of orbital distribution. The prominent stellar-mass dependence of the inner boundary of the planet population shows that the formation or migration of planets is sensitive to the stellar parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Two transiting earth-size planets near resonance orbiting a nearby cool star

Discoveries from the prime Kepler mission demonstrated that small planets (<3 R{sub ⊕}) are common outcomes of planet formation. While Kepler detected many such planets, all but a handful orbit faint, distant stars and are not amenable to precise follow up measurements. Here, we report the discovery of two small planets transiting K2-21, a bright (K = 9.4) M0 dwarf located 65±6 pc from Earth. We detected the transiting planets in photometry collected during Campaign 3 of NASA’s K2 mission. Analysis of transit light curves reveals that the planets have small radii compared to their host star, R{sub P}/R{sub ⋆} = 2.60±0.14% and 3.15±0.20%, respectively. We obtained follow up NIR spectroscopy of K2-21 to constrain host star properties, which imply planet sizes of 1.59 ± 0.43 R{sub ⊕} and 1.92 ± 0.53 R{sub ⊕}, respectively, straddling the boundary between high-density, rocky planets and low-density planets with thick gaseous envelopes. The planets have orbital periods of 9.32414 days and 15.50120 days, respectively, and a period ratio P{sub c}/P{sub b} = 1.6624, very near to the 5:3 mean motion resonance, which may be a record of the system’s formation history. Transit timing variations due to gravitational interactions between the planets may be detectable using ground-based telescopes. Finally, this system offers a convenient laboratory for studying the bulk composition and atmospheric properties of small planets with low equilibrium temperatures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

ON THE MISALIGNMENT OF THE DIRECTLY IMAGED PLANET {beta} PICTORIS b WITH THE SYSTEM'S WARPED INNER DISK

The vertical warp in the debris disk {beta} Pictoris-an inclined inner disk extending into a flat outer disk-has long been interpreted as the signpost of a planet on an inclined orbit. Direct images spanning 2004-2010 have revealed {beta} Pictoris b, a planet with a mass and orbital distance consistent with this picture. However, it was recently reported that the orbit of planet b is aligned with the flat outer disk, not the inclined inner disk, and thus lacks the inclination to warp the disk. We explore three scenarios for reconciling the apparent misalignment of the directly imaged planet {beta} Pictoris b with the warped inner disk of {beta} Pictoris: observational uncertainty, an additional planet, and damping of planet b's inclination. We find that, at the extremes of the uncertainties, the orbit of {beta} Pictoris b has the inclination necessary to produce the observed warp. We also find that if planet b were aligned with the flat outer disk, it would prevent another planet from creating a warp with the observed properties; therefore planet b itself must be responsible for the warp. Finally, planet b's inclination could have been damped by dynamical friction and still produce the observed disk morphology, but the feasibility of damping depends on disk properties and the presence of other planets. More precise observations of the orbit of planet b and the position angle of the outer disk will allow us to distinguish between the first and third scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Discovery of a Third Transiting Planet in the Kepler-47 Circumbinary System

Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the “inner planet”) has an orbital period of 49.5 days and a radius of about 3 R {sub ⊕}. Kepler-47 c (the “outer planet”) has an orbital period of 303.2 days and a radius of about 4.7 R {sub ⊕}. Here we report the discovery of a third planet, Kepler-47 d (the “middle planet”), which has an orbital period of 187.4 days and a radius of about 7 R {sub ⊕}. The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the 1σ ranges are less than 26 M {sub ⊕}, between 7–43 M {sub ⊕}, and between 2–5 M {sub ⊕} for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities, with ρ{sub middle}<0.68 g cm{sup −3} and ρ {sub outer} < 0.26 g cm{sup −3} at the 1σ level. The two outer planets are “tightly packed,” assuming the nominal masses, meaning no other planet could stably orbit between them. All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Dark Planets of the WASP-47 Planetary System

Exoplanet discoveries have demonstrated a vast range of planetary system architectures. The demographic of compact planetary systems are especially interesting from the perspective of planetary formation and the evolution of orbital dynamics. Another interesting demographic is that of giant planets in eccentric orbits, since these planets have likely had a dynamical history involving planet–planet scattering events. The WASP-47 system is particularly fascinating since it combines these two demographics, having both compact planetary orbits and a giant planet on an eccentric orbit within the system the habitable zone. Here we provide an analysis of the WASP-47 system from the perspective of atmospheric detection and characterization. We discuss the system architecture and the potential for additional long-period planets. We simulate expected phase variations as a function of planet orbital phase for the system due to the combined effect of the planets. We present an analysis of precision photometry of WASP-47 from the K2 mission, phased on each of the planets. The analysis rules out the detection of phase signatures for the two inner-most planets, enabling constraints upon their albedos and atmospheric properties. Our study concludes that WASP-47b is an example of a “dark” planet with a tentative geometric albedo of 0.016 and a 1σ upper limit of 0.17. The WASP-47e data are consistent with a broad range of albedos, but also show early evidence of having a relatively low albedo. The growing number of dark, short-period giant planets provide the framework of an ideal sample for studying low albedo dependence on atmospheric composition.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Perturbations, TTVs & the (Un)reliability of Ephemerides of Kepler Planets

Fractional uncertainties quoted for orbital periods of the vast majority of planet candidates listed in recent Kepler catalogs are $<10^{-5}$, with values $\sim 10^{-6}$ (corresponding to 2 minutes per 4 years) being typical. These small uncertainties suggest ephemeris predictions for most Kepler planets are robust for decades to come. Tabulated periods list formal uncertainties in the mean times between midpoints of successive transits during the time interval in which transits were observed. However, transit timing variations (TTVs) produce errors in estimates of some planets’ orbital periods that need to be accounted for in certain dynamical investigations and ephemeris predictions. Periodic TTVs with timescales short compared to the interval of Kepler observations largely average out and do not produce significant errors in estimates of orbital periods. TTVs with timescales comparable to the interval of Kepler observations have been fit for dozens of Kepler planet candidates to estimate long-term average orbital periods (Holczer et al. 2016, ApJS 225, 9), and more detailed dynamical models have been used to estimate long-term average periods of a small number of well-studied planets. Most Kepler planets that show large TTVs are near mean-motion orbital resonances with other planets. The largest effect for planets moderately close to two-body resonances are due to rotation of the forced eccentricity vector by resonant perturbations; the timescale for this precession is typically short, so the variations tend to average out. Libration of planets locked in resonances typically occurs on timescales longer than the Kepler baseline, but few Kepler planets appear to be resonantly-locked. The more general but smaller (during the era of Kepler observations) effect is caused by secular precession of the planets' free eccentricities usually has a period much longer than the baseline of the Kepler observations, so it is not accounted for in estimates of mean periods or uncertainties. This precession causes a discrepancy between Kepler era mean orbital period and long-term mean orbital period can exist even for planets having TTVs that are too small to be observable during the epoch of Kepler observations.

Kepler↗
NASA NTRS1998

The Kepler Mission: A Photometric Search for Earthlike Planets

If Earth lies in or near the orbital plane of an extrasolar planet, that planet passes in front of the disk of its star once each orbit as viewed from Earth. Precise photometry can reveal such transits, which can be distinguished from rotationally-modulated starspots and intrinsic stellar variability by their periodicity, square-well shapes and relative spectral neutrality. Transit observations would provide the size and orbital period of the detected planet. Although geometrical considerations limit the fraction of planets detectable by this technique, many stars can be surveyed within the field of view of one telescope, so transit photometry is quite efficient. Scintillation in and variability of Earth's atmosphere limit photometric precision to roughly one-thousandth of a magnitude, allowing detection of transits by Jupiter-sized planets but not by Earth-sized planets from the ground. The COROT spacecraft will be able to detect Uranus-sized planets orbiting near stars. The Kepler Mission, which is being proposed to NASA's Discovery Program this year, will have a photometer with a larger aperture (1 meter) than will COROT, so it will be able to detect transits by planets as small as Earth. Moreover, the Kepler mission will examine the same star field for four years, allowing confirmation of planets with orbital periods of a year. If the Sun's planetary system is typical for single stars, Kepler should detect approximately 480 terrestrial planets. Assuming the statistics from radial velocity surveys are typical, Kepler should also detect transits of 150 inner giant planets and reflected light variations of 1400 giant planets with orbital periods of less than one week.

Lissauer, Jack J.↗
NASA NTRS2002

Planet Formation

Modern theories of star and planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. The most detailed models of planetary growth are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. These models predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. A potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed, and the methods that are being used and planned for detecting and characterizing extrasolar planets are reviewed.

Lissauer, Jack J.↗
NASA NTRS2006

Formation of the giant planets

The observed properties of giant planets, models of their evolution and observations of protoplanetary disks provide constraints on the formation of gas giant planets. The four largest planets in our Solar System contain considerable quantities of hydrogen and helium, which could not have condensed into solid planetesimals within the protoplanetary disk. All three (transiting) extrasolar giant planets with well determined masses and radii also must contain substantial amounts of these light gases. Jupiter and Saturn are mostly hydrogen and helium, but have larger abundances of heavier elements than does the Sun. Neptune and Uranus are primarily composed of heavier elements. HD 149026 b, which is slightly more massive than is Saturn, appears to have comparable quantities of light gases and heavy elements. HD 209458 b and TrES-1 are primarily hydrogen and helium, but may contain supersolar abundances of heavy elements. Spacecraft flybys and observations of satellite orbits provide estimates of the gravitational moments of the giant planets in our Solar System, which in turn provide information on the internal distribution of matter within Jupiter, Saturn, Uranus and Neptune. Atmospheric thermal structure and heat flow measurements constrain the interior temperatures of planets. Internal processes may cause giant planets to become more compositionally differentiated or alternatively more homogeneous; high-pressure laboratory .experiments provide data useful for modeling these processes. The preponderance of evidence supports the core nucleated gas accretion model. According to this model, giant planets begin their growth by the accumulation of small solid bodies, as do terrestrial planets. However, unlike terrestrial planets, the growing giant planet cores become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. The primary questions regarding the core nucleated growth model is under what conditions planets with small cores/total heavy element abundances can accrete gaseous envelopes within the lifetimes of gaseous protoplanetary disks.

Lissauer, Jack J.↗
DOE OSTI2012

ON THE MIGRATION OF JUPITER AND SATURN: CONSTRAINTS FROM LINEAR MODELS OF SECULAR RESONANT COUPLING WITH THE TERRESTRIAL PLANETS

We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. Using a modified secular model we have identified six secular resonances between the {nu}{sub 5} frequency of Jupiter and Saturn and the four apsidal eigenfrequencies of the terrestrial planets (g{sub 1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. Because of the small amplitudes of the j = 2, 3 terrestrial eigenmodes the g{sub 2} - {nu}{sub 5} and g{sub 3} - {nu}{sub 5} resonances provide the strongest constraints on giant planet migration. If Jupiter and Saturn migrated with eccentricities comparable to their present-day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration ({tau} {approx} 5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g., {tau} {approx}< 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j = 2, 3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Results of orbital integrations show that very short migration timescales ({tau} < 0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9 {+-} 0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗