Dynamical stability of giant planets: the critical adiabatic index in the presence of a solid core

ABSTRACT The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduce the effective adiabatic index γ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at γ = 4/3, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all γ > 1). When instability is possible, unstable planetary configurations occupy a strip of γ values whose upper boundary falls below γ = 4/3. Fiducial evolutionary tracks of giant planets forming through core accretion appear unlikely to cross the dynamical instability strip that we define.

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The fate of planetary cores in giant and ice-giant planets

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936288 ◽

2019 ◽

Vol 631 ◽

pp. L4 ◽

Cited By ~ 1

Author(s):

S. Mazevet ◽

R. Musella ◽

F. Guyot

Keyword(s):

High Pressure ◽

Ab Initio ◽

Inner Core ◽

Giant Planets ◽

Ab Initio Molecular Dynamics ◽

Solid Core ◽

Potential Core ◽

Melting Temperatures ◽

The Core ◽

Pressure Melting

Context. The Juno probe that currently orbits Jupiter measures its gravitational moments with great accuracy. Preliminary results suggest that the core of the planet may be eroded. While great attention has been paid to the material properties of elements constituting the envelope, little is known about those that constitute the core. This situation clutters our interpretation the Juno data and modeling of giant planets and exoplanets in general. Aims. We calculate the high-pressure melting temperatures of three potential components of the cores of giant planets, water, iron, and a simple silicate, MgSiO3, to investigate the state of the deep inner core. Methods. We used ab initio molecular dynamics simulations to calculate the high-pressure melting temperatures of the three potential core components. The planetary adiabats were obtained by solving the hydrostatic equations in a three-layer model adjusted to reproduce the measured gravitational moments. Recently developed ab initio equations of state were used for the envelope and the core. Results. We find that the cores of the giant and ice-giant planets of the solar system differ because the pressure–temperature conditions encountered in each object correspond to different regions of the phase diagrams. For Jupiter and Saturn, the results are compatible with a diffuse core and mixing of a significant fraction of metallic elements in the envelope, leading to a convective and/or a double-diffusion regime. We also find that their solid cores vary in nature and size throughout the lifetimes of these planets. The solid cores of the two giant planets are not primordial and nucleate and grow as the planets cool. We estimate that the solid core of Jupiter is 3 Gyr old and that of Saturn is 1.5 Gyr old. The situation is less extreme for Uranus and Neptune, whose cores are only partially melted. Conclusions. To model Jupiter, the time evolution of the interior structure of the giant planets and exoplanets in general, their luminosity, and the evolution of the tidal effects over their lifetimes, the core should be considered as crystallizing and growing rather than gradually mixing into the envelope due to the solubility of its components.

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Planetesimal Capture by an Evolving Giant Gaseous Protoplanet

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313012957 ◽

2012 ◽

Vol 8 (S293) ◽

pp. 263-269

Author(s):

Morris Podolak ◽

Nader Haghighipour

Keyword(s):

Mass Distribution ◽

Total Mass ◽

Size Composition ◽

Giant Planets ◽

The Core ◽

Last Stage ◽

Core Accretion ◽

Gaseous Envelope ◽

Gas Drag ◽

Probability Of Capture

AbstractBoth the core-accretion and disk-instability models suggest that at the last stage of the formation of a gas-giant, the core of this object is surrounded by an extended gaseous envelope. At this stage, while the envelope is contracting, planetesimals from the protoplanetary disk may be scattered into the protoplanets atmosphere and deposit some or all of their materials as they interact with the gas. We have carried out extensive simulations of approximately 104 planetesimals interacting with a envelope of a Jupiter-mass protoplanet including effects of gas drag, heating, and the effect of the protoplanets extended mass distribution. Simulations have been carried out for different radii and compositions of planetesimals so that all three processes occur to different degrees. We present the results of our simulations and discuss their implications for the enrichment of ices in giant planets. We also present statistics for the probability of capture (i.e. total mass-deposition) of planetesimals as a function of their size, composition, and closest approach to the center of the protoplanetary body.

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Evolutionary models of cold and low-mass planets: cooling curves, magnitudes, and detectability

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833873 ◽

2019 ◽

Vol 623 ◽

pp. A85 ◽

Cited By ~ 19

Author(s):

Esther F. Linder ◽

Christoph Mordasini ◽

Paul Mollière ◽

Gabriel-Dominique Marleau ◽

Matej Malik ◽

...

Keyword(s):

Effective Temperature ◽

Initial Conditions ◽

Giant Planets ◽

Evolutionary Models ◽

Cooling Curves ◽

Mid Infrared ◽

The Core ◽

Low Mass ◽

Core Accretion ◽

The Impact

Context. Future instruments like the Near Infrared Camera (NIRCam) and the Mid Infrared Instrument (MIRI) on the James Webb Space Telescope (JWST) or the Mid-Infrared E-ELT Imager and Spectrograph (METIS) at the European Extremely Large Telescope (E-ELT) will be able to image exoplanets that are too faint (because they have a low mass, and hence a small size or low effective temperature) for current direct imaging instruments. On the theoretical side, core accretion formation models predict a significant population of low-mass and/or cool planets at orbital distances of ~10–100 au. Aims. Evolutionary models predicting the planetary intrinsic luminosity as a function of time have traditionally concentrated on gas-dominated giant planets. We extend these cooling curves to Saturnian and Neptunian planets. Methods. We simulated the cooling of isolated core-dominated and gas giant planets with masses of 5 M⊕–2 M♃. The planets consist of a core made of iron, silicates, and ices surrounded by a H/He envelope, similar to the ice giants in the solar system. The luminosity includes the contribution from the cooling and contraction of the core and of the H/He envelope, as well as radiogenic decay. For the atmosphere we used grey, AMES-Cond, petitCODE, and HELIOS models. We considered solar and non-solar metallicities as well as cloud-free and cloudy atmospheres. The most important initial conditions, namely the core-to-envelope-mass ratio and the initial (i.e. post formation) luminosity are taken from planet formation simulations based on the core accretion paradigm. Results. We first compare our cooling curves for Uranus, Neptune, Jupiter, Saturn, GJ 436b, and a 5 M⊕ planet with a 1% H/He envelope with other evolutionary models. We then present the temporal evolution of planets with masses between 5 M⊕ and 2 M♃ in terms of their luminosity, effective temperature, radius, and entropy. We discuss the impact of different post formation entropies. For the different atmosphere types and initial conditions, magnitudes in various filter bands between 0.9 and 30 micrometer wavelength are provided. Conclusions. Using blackbody fluxes and non-grey spectra, we estimate the detectability of such planets with JWST. We found that a 20 (100) M⊕ planet can be detected with JWST in the background limit up to an age of about 10 (100) Myr with NIRCam and MIRI, respectively.

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Composition of massive giant planets

Proceedings of the International Astronomical Union ◽

10.1017/s174392131102000x ◽

2010 ◽

Vol 6 (S276) ◽

pp. 95-100

Author(s):

Ravit Helled ◽

Peter Bodenheimer ◽

Jack J. Lissauer

Keyword(s):

Large Range ◽

Giant Planet ◽

Giant Planets ◽

Heavy Elements ◽

Formation Model ◽

The Core ◽

Accretion Model ◽

Low Mass ◽

Core Accretion ◽

Host Stars

AbstractThe two current models for giant planet formation are core accretion and disk instability. We discuss the core masses and overall planetary enrichment in heavy elements predicted by the two formation models, and show that both models could lead to a large range of final compositions. For example, both can form giant planets with nearly stellar compositions. However, low-mass giant planets, enriched in heavy elements compared to their host stars, are more easily explained by the core accretion model. The final structure of the planets, i.e., the distribution of heavy elements, is not firmly constrained in either formation model.

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Heavy-metal Jupiters by major mergers: metallicity versus mass for giant planets

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2500 ◽

2020 ◽

Vol 498 (1) ◽

pp. 680-688 ◽

Cited By ~ 2

Author(s):

Sivan Ginzburg ◽

Eugene Chiang

Keyword(s):

Heavy Metal ◽

Accretion Rate ◽

Giant Planet ◽

Giant Planets ◽

Solid Core ◽

Core Mass ◽

The Core ◽

Multiple Cores ◽

Merger Rate ◽

Gas Accretion

ABSTRACT Some Jupiter-mass exoplanets contain ${\sim}100\, {\rm M}_{\hbox{$\oplus $}}$ of metals, well above the ${\sim}10\, {\rm M}_{\hbox{$\oplus $}}$ typically needed in a solid core to trigger giant planet formation by runaway gas accretion. We demonstrate that such ‘heavy-metal Jupiters’ can result from planetary mergers near ∼10 au. Multiple cores accreting gas at runaway rates gravitationally perturb one another on to crossing orbits such that the average merger rate equals the gas accretion rate. Concurrent mergers and gas accretion implies the core mass scales with the total planet mass as Mcore ∝ M1/5 – heavier planets harbour heavier cores, in agreement with the observed relation between total mass and metal mass. While the average gas giant merges about once to double its core, others may merge multiple times, as merger trees grow chaotically. We show that the dispersion of outcomes inherent in mergers can reproduce the large scatter in observed planet metallicities, assuming $3{-}30\, {\rm M}_{\hbox{$\oplus $}}$ pre-runaway cores. Mergers potentially correlate metallicity, eccentricity, and spin.

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Quasi-static contraction during runaway gas accretion onto giant planets

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834413 ◽

2019 ◽

Vol 630 ◽

pp. A82 ◽

Cited By ~ 9

Author(s):

M. Lambrechts ◽

E. Lega ◽

R. P. Nelson ◽

A. Crida ◽

A. Morbidelli

Keyword(s):

Outer Part ◽

Giant Planets ◽

Gas Flows ◽

Solid Core ◽

Static Contraction ◽

Accretion Rates ◽

Outer Atmosphere ◽

Hydrodynamical Simulations ◽

Gas Accretion ◽

Core Accretion

Gas-giant planets, like Jupiter and Saturn, acquire massive gaseous envelopes during the approximately 3 Myr-long lifetimes of protoplanetary discs. In the core accretion scenario, the formation of a solid core of around ten Earth masses triggers a phase of rapid gas accretion. Previous 3D grid-based hydrodynamical simulations found that runaway gas accretion rates correspond to approximately 10 to 100 Jupiter masses per Myr. Such high accretion rates would result in all planets with larger than ten Earth-mass cores to form Jupiter-like planets, which is in clear contrast to the ice giants in the Solar System and the observed exoplanet population. In this work, we used 3D hydrodynamical simulations, that include radiative transfer, to model the growth of the envelope on planets with different masses. We find that gas flows rapidly through the outer part of the envelope, but this flow does not drive accretion. Instead, gas accretion is the result of quasi-static contraction of the inner envelope, which can be orders of magnitude smaller than the mass flow through the outer atmosphere. For planets smaller than Saturn, we measured moderate gas accretion rates that are below one Jupiter mass per Myr. Higher mass planets, however, accrete up to ten times faster and do not reveal a self-driven mechanism that can halt gas accretion. Therefore, the reason for the final masses of Saturn and Jupiter remains difficult to understand, unless their completion coincided with the dissipation of the solar nebula.

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