Abstract
We construct models for Jupiter’s interior that match the gravity data obtained by the Juno and Galileo spacecraft. To generate ensembles of models, we introduce a novel
quadratic
Monte ...Carlo technique, which is more efficient in confining fitness landscapes than the affine invariant method that relies on linear stretch moves. We compare how long it takes the ensembles of walkers in both methods to travel to the most relevant parameter region. Once there, we compare the autocorrelation time and error bars of the two methods. For a ring potential and the 2d Rosenbrock function, we find that our quadratic Monte Carlo technique is significantly more efficient. Furthermore, we modified the
walk
moves by adding a scaling factor. We provide the source code and examples so that this method can be applied elsewhere. Here we employ our method to generate five-layer models for Jupiter’s interior that include winds and a prominent dilute core, which allows us to match the planet’s even and odd gravity harmonics. We compare predictions from the different model ensembles and analyze how much an increase in the temperature at 1 bar and ad hoc change to the equation of state affect the inferred amount of heavy elements in the atmosphere and in the planet overall.
Super-Earths are extremely common among the numerous exoplanets that have been discovered. The high pressures and temperatures in their interiors are likely to lead to long-lived magma oceans. If ...their electrical conductivity is sufficiently high, the mantles of Super-Earth would generate their own magnetic fields. With ab initio simulations, we show that upon melting, the behavior of typical mantle silicates changes from semi-conducting to semi-metallic. The electrical conductivity increases and the optical properties are substantially modified. Melting could thus be detected with high-precision reflectivity measurements during the short time scales of shock experiments. We estimate the electrical conductivity of mantle silicates to be of the order of 100 Ω
cm
, which implies that a magnetic dynamo process would develop in the magma oceans of Super-Earths if their convective velocities have typical values of 1 mm/s or higher. We predict exoplanets with rotation periods longer than 2 days to have multipolar magnetic fields.
Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He ...layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10,000 K, implying the potential for significant redistribution of rocky core material in Jupiter and larger exoplanets.
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Abstract
The elements hydrogen, carbon, nitrogen and oxygen are assumed to comprise the bulk of the interiors of the ice giant planets Uranus, Neptune, and sub-Neptune exoplanets. The details of ...their interior structures have remained largely unknown because it is not understood how the compounds H
2
O, NH
3
and CH
4
behave and react once they have been accreted and exposed to high pressures and temperatures. Here we study thirteen H-C-N-O compounds with ab initio computer simulations and demonstrate that they assume a superionic state at elevated temperatures, in which the hydrogen ions diffuse through a stable sublattice that is provided by the larger nuclei. At yet higher temperatures, four of the thirteen compounds undergo a second transition to a novel doubly superionic state, in which the smallest of the heavy nuclei diffuse simultaneously with hydrogen ions through the remaining sublattice. Since this transition and the melting transition at yet higher temperatures are both of first order, this may introduce additional layers in the mantle of ice giant planets and alter their convective patterns.
Abstract
We study the relationship of zonal gravity coefficients,
J
2
n
, zonal winds, and axial moment of inertia (MoI) by constructing models for the interiors of giant planets. We employ the ...nonperturbative concentric Maclaurin spheroid method to construct both physical (realistic equation of state and barotropes) and abstract (small number of constant-density spheroids) interior models. We find that accurate gravity measurements of Jupiter’s and Saturn’s
J
2
,
J
4
, and
J
6
by the Juno and Cassini spacecraft do not uniquely determine the MoI of either planet but do constrain it to better than 1%. Zonal winds (or differential rotation (DR)) then emerge as the leading source of uncertainty. For Saturn they are predicted to decrease the MoI by 0.4% because they reach a depth of ∼9000 km, while on Jupiter they appear to reach only ∼3000 km. We thus predict DR to affect Jupiter’s MoI by only 0.01%, too small by one order of magnitude to be detectable by the Juno spacecraft. We find that winds primarily affect the MoI indirectly via the gravity harmonic
J
6
, while direct contributions are much smaller because the effects of pro- and retrograde winds cancel. DR contributes +6% and −0.8% to Saturn’s and Jupiter’s
J
6
value, respectively. This changes the
J
6
contribution that comes from the uniformly rotating bulk of the planet that correlates most strongly with the predicted MoI. With our physical models, we predict Jupiter’s MoI to be 0.26393 ± 0.00001. For Saturn, we predict 0.2181 ± 0.0002, assuming a rotation period of 10:33:34 hr that matches the observed polar radius.
We present a 5-phase equation of state for elemental carbon which addresses a wide range of density and temperature conditions: 3g/cc < rho < 20g/ cc, 0 K < T < infinity. The phases considered are ...diamond, BC8, simple cubic, simple hexagonal, and the liquid/plasma state. The solid phase free energies are constrained by density functional theory (DFT) calculations. Vibrational contributions to the free energy of each solid phase are treated within the quasiharmonic framework. The liquid free energy model is constrained by fitting to a combination of DFT molecular dynamics performed over the range 10 000K < T < 100 000K, and path integral quantum Monte Carlo calculations for T > 100 000K (both for rho between 3 and 12 g/cc, with select higher-rho DFT calculations as well). The liquid free energy model includes an atom-in-jellium approach to account for the effects of ionization due to temperature and pressure in the plasma state, and an ion-thermal model which includes the approach to the ideal gas limit. The precise manner in which the ideal gas limit is reached is greatly constrained by both the highest-temperature DFT data and the path integral data, forcing us to discard an ionthermal model we had used previously in favor of a new one. Predictions are made for the principal Hugoniot and the room-temperature isotherm, and comparisons are made to recent experimental results.
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Using density functional molecular dynamics free energy calculations, we show that the body centered cubic (bcc) phase of superionic ice previously believed to be the only phase is, in fact, ...thermodynamically unstable compared to a novel phase with oxygen positions in face centered cubic lattice sites. The novel phase has a lower proton mobility than the bcc phase and may exhibit a higher melting temperature. We predict a transition between the two phases at a pressure of 1±0.5 Mbar, with potential consequences for the interiors of ice giants such as Uranus and Neptune.
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Based on density functional calculations we predict water ice to attain two new crystal structures with Pbca and Cmcm symmetry at 7.6 and 15.5 Mbar, respectively. The known high-pressure ice phases ...VII, VIII, X, and Pbcm as well as the Pbca phase are all insulating and composed of two interpenetrating hydrogen bonded networks, but the Cmcm structure is metallic and consists of corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral positions between next-nearest O atoms while they occupy tetrahedral positions between nearest O atoms in the ice X, Pbcm, and Pbca phases.
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Abstract
Super-Earths and sub-Neptunes are the most common planet types in our galaxy. A subset of these planets is predicted to be water worlds, bodies that are rich in water and poor in hydrogen ...gas. The interior structures of water worlds have been assumed to consist of water surrounding a rocky mantle and iron core. In small planets, water and rock form distinct layers with limited incorporation of water into silicate phases, but these materials may interact differently during the growth and evolution of water worlds due to greater interior pressures and temperatures. Here, we use density functional molecular dynamics (DFT-MD) simulations to study the miscibility and interactions of enstatite (MgSiO
3
), a major end-member silicate phase, and water (H
2
O) at extreme conditions in water world interiors. We explore pressures ranging from 30 to 120 GPa and temperatures from 500 to 8000 K. Our results demonstrate that enstatite and water are miscible in all proportions if the temperature exceeds the melting point of MgSiO
3
. Furthermore, we performed smoothed particle hydrodynamics simulations to demonstrate that the conditions necessary for rock-water miscibility are reached during giant impacts between water-rich bodies of 0.7–4.7 Earth masses. Our simulations lead to water worlds that include a mixed layer of rock and water.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
The accretion of a terrestrial body and differentiation of its silicate/oxide mantle from iron core provide abundant energy for heating its interior to temperatures much higher than the present day ...Earth. The consequences of differentiation on the structure and composition of planets are typically addressed considering only the interaction of molten iron with an immiscible ‘rocky’ phase. We demonstrate that mixing in a representative system of liquid or solid MgO and liquid iron to a single homogeneous liquid occurs at sufficiently low temperature to be present in the aftermath of a giant impact. Applying the thermodynamic integration technique to density functional theory molecular dynamics simulations, we determine the solvus closure temperature for the Fe–MgO system for pressures up to 400 GPa. Solvus closure occurs at ∼4000 K at low pressure, and has a weak positive pressure dependence, such that its gradient with respect to depth is less steep than an adiabatic temperature profile. This predicts a new mode of core–mantle differentiation following the most energetic giant impacts, with exsolution of iron from the mixture beginning in the outer layers of the planet. We demonstrate that high-temperature equilibration results in delivery of nominally insoluble Mg-rich material to the early core. Since MgO is the least soluble major mantle component in iron at low temperatures, these results may represent an upper bound on temperature for mixing in terrestrial planets.
•First principles simulations were performed on mixtures of Fe and MgO.•The Fe–MgO solvus closure temperature was determined at pressures up to 400 GPa.•The pressure dependence of solvus closure is less steep than an adiabatic profile.•Mixing of Fe and MgO occurs at temperatures readily achieved during giant impacts.•The results are consistent with negligible mixing in experiments at 3000 K.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
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