Planetary Interiors Research Articles

DMPP-3: confirmation of short-period S-type planet(s) in a compact eccentric binary star system, and warnings about long-period RV planet detections

ABSTRACT We present additional HARPS radial velocity observations of the highly eccentric (e ∼ 0.6) binary system DMPP-3AB, which comprises a K0V primary and a low-mass companion at the hydrogen burning limit. The binary has a 507 d orbital period and a 1.2 au semimajor axis. The primary component harbours a known 2.2 M⊕ planet, DMPP-3A b, with a 6.67-d orbit. New HARPS measurements constrain periastron passage for the binary orbit and add further integrity to previously derived solutions for both companion and planet orbits. Gaia astrometry independently confirms the binary orbit and establishes the inclination of the binary is 63.89 ± 0.78°. We performed dynamical simulations that establish that the previously identified ∼800 d RV signal cannot be attributed to an orbiting body. The additional observations, a deviation from strict periodicity, and our new analyses of activity indicators suggest the ∼800 d signal is caused by stellar activity. We conclude that there may be long-period planet ‘detections’ in other systems, which are similar misinterpreted stellar activity artefacts. Without the unusual eccentric binary companion to the planet-hosting star, we could have accepted the ∼800 d signal as a probable planet. Further monitoring of DMPP-3 will reveal which signatures can be used to most efficiently identify these imposters. We also report a threshold detection (0.2 per cent FAP) of a ∼2.26 d periodicity in the RVs, potentially attributed to an Earth-mass S-type planet interior to DMPP-3A b.

Assessing the stability fields of molecular and polymeric CO2

We investigated the stability of polymeric $\mathrm{C}{\mathrm{O}}_{2}$ over a wide range of pressures, temperatures, and chemical environments. We find that the $I\overline{4}2d$ polymeric structure, consisting of a three-dimensional network of corner sharing $\mathrm{C}{\mathrm{O}}_{4}$ tetrahedra, forms at 40--140 GPa and from a $\text{CO-}{\mathrm{N}}_{2}$ mixture at 39 GPa. An exceptional stability field of 0--286 GPa and 100--2500 K is documented for this structure, making it a viable candidate for planetary interiors. The stability of the tetrahedral polymeric motif of $\mathrm{C}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{V}$ is a consequence of the rigidity of $s{p}^{3}$ hybridized orbitals of carbon in a closed-packed oxygen sublattice.

MAGUS: machine learning and graph theory assisted universal structure searcher.

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

Thermo‐electrohydrodynamic convection in a differentially heated shell with electric central force field

AbstractThermo‐electrohydrodynamic convection is investigated in a shell with central force field to investigate convective pattern formation for potential heat transfer application and small scaled laboratory experiments e.g. the modelling of convection in planetary interiors or atmospheres. To induce TEHD convection the outer and inner shells are heated at different temperatures whereas an alternating electric potential is applied between both shells. The observation of the convective pattern formation suggest that dielectric fluids have a significant response to thermal and electrical forcing. The observed patterns ranged from quasi‐stationary convective modes in azimuthal direction to shape and mode amplitude vacillations with mode merging and separation that are classified into three regimes. The heat transfer was evaluated by the Nusselt number and showed an increase in heat transfer with electric forcing. However, the results indicate a much smaller heat transfer when compared to natural convection.

Relation of Gravity, Winds, and the Moment of Inertia of Jupiter and Saturn

We study the relationship of zonal gravity coefficients, J 2n , 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.

Global Hall MHD Simulations of Mercury's Magnetopause Dynamics and FTEs Under Different Solar Wind and IMF Conditions

AbstractMercury possesses a miniature but dynamic magnetosphere driven primarily by the solar wind through magnetic reconnection. A prominent feature of the dayside magnetopause reconnection that has been frequently observed is flux transfer events (FTEs), which are thought to be an important player in driving the global convection at Mercury. Using the BATSRUS Hall magnetohydrodynamics model with coupled planetary interior, we have conducted a series of global simulations to investigate the generation and characteristics of FTEs under different solar wind Alfvénic Mach numbers (MA) and interplanetary magnetic field (IMF) orientations. An automated algorithm was also developed to consistently identify FTEs and extract their key properties from the simulations. In all simulations driven by steady upstream conditions, FTEs are formed quasi‐periodically with recurrence time ranging from 2 to 9 s, and their characteristics vary in time as they evolve and interact with the surrounding plasma and magnetic field. Our statistical analysis of the simulated FTEs reveals that the key properties of FTEs, including spatial size, traveling speed and core field strength, all exhibit notable dependence on the solar wind MA and IMF orientation, and the trends identified from the simulations are generally consistent with previous MErcury Surface Space ENvironment, GEochemistry, and Ranging observations. It is also found that FTEs formed in the simulations contribute about 3%–13% of the total open flux created at the dayside magnetopause that participates in the global circulation, suggesting that FTEs indeed play an important role in driving the Dungey cycle at Mercury.

Pioneers project: Looking inside planetary interiors

Pioneers project: Looking inside planetary interiors PIONEERS European project develops the next generation of instruments that will reveal planetary interiors, explains Professor Raphael F. Garcia from ISAE-SUPAERO. After decades of exploration of planetary surfaces, our knowledge of planetary interiors and internal structures remains very limited. However, the structure of a planetary body tells us a lot about how it formed and evolved during the last 4.5 billion years. It is critical to understand our solar system to know better the thousands of planets orbiting other stars in our galaxy. Are these planets water-rich? for how long? Can these sustain life? Even at the scale of our solar system these questions are not fully solved because the clues to their answers are hidden deep inside our nearby planets, their moons, and asteroid bodies. Even if all these objects formed from the same materials that formed our Sun, the hazard of accretion generated very different objects evolving differently.

Accounting for non-ideal mixing effects in the hydrogen-helium equation of state

Context. The equation of state for hydrogen and helium is fundamental for studying stars and giant planets. It has been shown that because of interactions at atomic and molecular levels, the behaviour of a mixture of hydrogen and helium cannot be accurately represented by considering these elements separately. Aims. This paper aims at providing a simple method to account for interactions between hydrogen and helium in interior and evolution models of giant planets. Methods. Using on the one hand ab initio simulations that involve a system of interacting hydrogen and helium particles and pure equations of state for hydrogen and helium on the other, we derived the contributions in density and entropy of the interactions between hydrogen and helium particles. Results. We show that relative variations of up to 15% in density and entropy arise when non-ideal mixing is accounted for. These non-ideal mixing effects must be considered in interior models of giant planets based on accurate gravity field measurements, particularly in the context of variations in the helium-to-hydrogen ratio. They also affect the mass-radius relation of exoplanets. We provide a table that contains the volume and entropy of mixing as a function of pressure and temperature. This table is to be combined with pure hydrogen and pure helium equations of state to obtain an equation of state that self-consistently includes mixing effects for any hydrogen and helium mixing ratio and may be used to model the interior structure and evolution of giant planets to brown dwarfs. Conclusions. Non-linear mixing must be included in accurate calculations of the equations of state of hydrogen and helium. Uncertainties on the equation of state still exist, however. Ab initio calculations of the behaviour of the hydrogen-helium mixture in the megabar regime for various compositions should be performed in order to gain accuracy.

Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons.

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn-Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.

Magnesium oxide-water compounds at megabar pressure and implications on planetary interiors

Magnesium Oxide (MgO) and water (H2O) are abundant in the interior of planets. Their properties, and in particular their interaction, significantly affect the planet interior structure and thermal evolution. Here, using crystal structure predictions and ab initio molecular dynamics simulations, we find that MgO and H2O can react again at ultrahigh pressure, although Mg(OH)2 decomposes at low pressure. The reemergent MgO-H2O compounds are: Mg2O3H2 above 400 GPa, MgO3H4 above 600 GPa, and MgO4H6 in the pressure range of 270–600 GPa. Importantly, MgO4H6 contains 57.3 wt % of water, which is a much higher water content than any reported hydrous mineral. Our results suggest that a substantial amount of water can be stored in MgO rock in the deep interiors of Earth to Neptune mass planets. Based on molecular dynamics simulations we show that these three compounds exhibit superionic behavior at the pressure-temperature conditions as in the interiors of Uranus and Neptune. Moreover, the water-rich compound MgO4H6 could be stable inside the early Earth and therefore may serve as a possible early Earth water reservoir. Our findings, in the poorly explored megabar pressure regime, provide constraints for interior and evolution models of wet planets in our solar system and beyond.

Dynamical tides in Jupiter and the role of interior structure

Context. The Juno spacecraft has obtained highly accurate tidal Love numbers, which provide important constraints on the tidal response and interior structure of Jupiter. Aims. In order to exploit these observations, it is necessary to develop an approach to accurately calculate the tidal response of Jupiter for a given interior model and to investigate the role of the interior structure. Methods. We directly solve the linearized tidal equations of a compressible, self-gravitating, rotating, and viscous fluid body using a pseudo-spectral method. The Coriolis force is fully taken into account, but the centrifugal effect is neglected. We are able to simultaneously obtain the real and imaginary parts of the tidal Love numbers for a given planetary interior model. Results. We calculated the tidal responses for three simplified interior models of Jupiter which may contain a compact rigid core or an extended dilute core. All of the models we consider can explain the fractional correction ∆k22 ≈ −4% due to dynamical tides, but they all have difficulties reconciling the observed ∆k42 ≈ −11% for the high-degree tidal Love number. We show that the Coriolis force significantly modifies gravity modes in an extended dilute core at the tidal frequency relevant to the Galilean satellites. We demonstrate that the existence of a thin stable layer in the outer region would also influence the tidal responses of Jupiter.

Removal of Hot Saturns in Mass–Radius Plane by Runaway Mass Loss

The hot Saturn population exhibits a boundary in mass–radius space, such that no planets are observed at a density less than ∼0.1 g cm−3. Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role X-ray and extreme UV irradiation (XUV)-driven mass loss plays in sculpting the density boundary by constructing interior structure models that include radius inflation, photoevaporative mass loss, and a simple prescription of Roche lobe overflow. We demonstrate that planets puffier than ∼0.1 g cm−3 experience a runaway mass loss caused by adiabatic radius expansion as the gas layer is stripped away, providing a good explanation of the observed edge in mass–radius space. The process is also visible in the radius–period and mass–period spaces, though smaller, high-bulk-metallicity planets can still survive at short periods, preserving a partial record of the population distribution at formation.

Electronic density response of warm dense matter

Matter at extreme temperatures and pressures—commonly known as warm dense matter (WDM)—is ubiquitous throughout our Universe and occurs in astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are probed in x-ray Thomson scattering (XRTS) experiments and are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear response theory and nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques, including path-integral Monte Carlo simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrary complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

A Reanalysis of the Composition of K2-106b: An Ultra-short-period Super-Mercury Candidate

We present a reanalysis of the K2-106 transiting planetary system, with a focus on the composition of K2-106b, an ultra-short-period, super-Mercury candidate. We globally model existing photometric and radial velocity data and derive a planetary mass and radius for K2-106b of M p = 8.53 ± 1.02 M ⊕ and , which leads to a density of g cm−3, a significantly lower value than previously reported in the literature. We use planet interior models that assume a two-layer planet comprised of a liquid, pure Fe core and an iron-free, MgSiO3 mantle, and we determine that the range of the core mass fractions are consistent with the observed mass and radius. We use existing high-resolution spectra of the host star to derive the Fe/Mg/Si abundances ([Fe/H] = −0.03 ± 0.01, [Mg/H] = 0.04 ± 0.02, [Si/H] = 0.03 ± 0.06) to infer the composition of K2-106b. We find that K2-106b has a density and core mass fraction () consistent with that of Earth (CMF⊕ = 32%). Furthermore, its composition is consistent with what is expected, assuming that it reflects the relative refractory abundances of its host star. K2-106b is therefore unlikely to be a super-Mercury, as has been suggested in previous literature.

Rapidly rotating self-gravitating Boussinesq fluid. III. A previously unknown zonal oscillation at the onset of rotating convection

Rotating convection in spheres or spherical shells has been modeled in order to understand dynamics in planetary or stellar interiors. Existing theories have predicted various different types of symmetry for the dynamics at the onset of thermal convection. The only form of global convection not found so far is axisymmetric and equatorially symmetric. In this Letter, we for the first time, report the discovery of a solution bearing such symmetry. It is the geometric oblateness due to rotational flattening that is the key factor, which had not previously been considered.

Kepler-102: Masses and Compositions for a Super-Earth and Sub-Neptune Orbiting an Active Star

Radial velocity (RV) measurements of transiting multiplanet systems allow us to understand the densities and compositions of planets unlike those in the solar system. Kepler-102, which consists of five tightly packed transiting planets, is a particularly interesting system since it includes a super-Earth (Kepler-102d) and a sub-Neptune-sized planet (Kepler-102e) for which masses can be measured using RVs. Previous work found a high density for Kepler-102d, suggesting a composition similar to that of Mercury, while Kepler-102e was found to have a density typical of sub-Neptune size planets; however, Kepler-102 is an active star, which can interfere with RV mass measurements. To better measure the mass of these two planets, we obtained 111 new RVs using Keck/HIRES and Telescopio Nazionale Galileo/HARPS-N and modeled Kepler-102's activity using quasiperiodic Gaussian process regression. For Kepler-102d, we report a mass upper limit M d < 5.3 M ⊕ (95% confidence), a best-fit mass M d = 2.5 ± 1.4 M ⊕, and a density ρ d = 5.6 ± 3.2 g cm−3, which is consistent with a rocky composition similar in density to the Earth. For Kepler-102e we report a mass M e = 4.7 ± 1.7 M ⊕ and a density ρ e = 1.8 ± 0.7 g cm−3. These measurements suggest that Kepler-102e has a rocky core with a thick gaseous envelope comprising 2%–4% of the planet mass and 16%–50% of its radius. Our study is yet another demonstration that accounting for stellar activity in stars with clear rotation signals can yield more accurate planet masses, enabling a more realistic interpretation of planet interiors.

Compression of gaseous hydrogen into warm dense states up to 95 GPa using multishock compression technique

The thermodynamic properties of warm dense hydrogen, such as the equation of state (EOS) and sound velocity, affect our understanding of the evolution and interior structures of gas giant planets. However, for this low-$Z$ gas, obtaining the EOS and sound velocity experimentally under relevant planetary conditions is challenging because the extremely warm states are difficult to reach, characterize, and interrogate. Here, the multishock compression technique is used to generate the thermodynamic states of warm dense hydrogen. This provides a dynamic loading from shock adiabatic to quasi-isentropic compressions, covering wide pressure and density ranges of 0.02--95 GPa and $0.01--0.64 \mathrm{g}/{\mathrm{cm}}^{3}$, which enables us to determine the EOS and infer the high-pressure sound velocities of warm dense hydrogen relevant to planetary interiors. The data obtained in this way are comprehensively compared with several important theoretical models for astrophysics applications. The present experiments provide desirable principal- and off-Hugoniot states for revisiting the thermodynamic space of existing experimental data. These observations and thermodynamic states may be important in guiding future theoretical developments and constructing interior structure models for gas giant planets.

Interior and Evolution of the Giant Planets

The giant planets were the first to form and hold the key to unveiling the solar system’s formation history in their interiors and atmospheres. Furthermore, the unique conditions present in the interiors of the giant planets make them natural laboratories for exploring different elements under extreme conditions. We are at a unique time to study these planets. The missions Juno to Jupiter and Cassini to Saturn have provided invaluable information to reveal their interiors like never before, including extremely accurate gravity data, atmospheric abundances and magnetic field measurements that revolutionised our knowledge of their interior structures. At the same time, new laboratory experiments and modelling efforts also improved, and statistical analysis of these planets is now possible to explore all the different conditions that shape their interiors. We review the interior structure of Jupiter, Saturn, Uranus and Neptune, including the need for inhomogeneous structures to explain the data, the problems unsolved and the effect that advances in our understanding of their internal structure have on their formation and evolution.

A “Floatilla” of Airborne Seismometers for Venus

AbstractBarometers floating on high‐altitude balloons in the relatively clement cloud layer on Venus could detect and characterize acoustic waves generated by seismic activity, avoiding the need for high‐temperature electronics required for surface seismology. Garcia et al. (2022, https://doi.org/10.1029/2022GL098844) recently demonstrated the detection of low‐frequency sound (infrasound) caused by earthquakes of magnitudes 7.3 and 7.5 from stratospheric balloons nearly 3,000 km away from the epicenter. They provided a preliminary demonstration of earthquake magnitude and location inversion, and the determination of S‐ and Rayleigh wave velocities using only their acoustic signature. Large earthquakes produce low‐frequency seismic waves that penetrate the interiors of planets; their detection at continental‐scale distances from a high‐vantage point demonstrates the feasibility of balloon‐based investigations of Venus' interior. We contextualize these results within the effort to perform seismology on Venus from balloons, discuss its limitations, and share perspectives on open research questions in this area.

Shear properties of MgO inferred using neural networks

Abstract. Shear properties of mantle minerals are vital for interpreting seismic shear wave speeds and therefore inferring the composition and dynamics of a planetary interior. Shear wave speed and elastic tensor components, from which the shear modulus can be computed, are usually measured in the laboratory mimicking the Earth's (or a planet's) internal pressure and temperature conditions. A functional form that relates the shear modulus to pressure (and temperature) is fitted to the measurements and used to interpolate within and extrapolate beyond the range covered by the data. Assuming a functional form provides prior information, and the constraints on the predicted shear modulus and its uncertainties might depend largely on the assumed prior rather than the data. In the present study, we propose a data-driven approach in which we train a neural network to learn the relationship between the pressure, temperature and shear modulus from the experimental data without prescribing a functional form a priori. We present an application to MgO, but the same approach works for any other mineral if there are sufficient data to train a neural network. At low pressures, the shear modulus of MgO is well-constrained by the data. However, our results show that different experimental results are inconsistent even at room temperature, seen as multiple peaks and diverging trends in probability density functions predicted by the network. Furthermore, although an explicit finite-strain equation mostly agrees with the likelihood predicted by the neural network, there are regions where it diverges from the range given by the networks. In those regions, it is the prior assumption of the form of the equation that provides constraints on the shear modulus regardless of how the Earth behaves (or data behave). In situations where realistic uncertainties are not reported, one can become overconfident when interpreting seismic models based on those defined equations of state. In contrast, the trained neural network provides a reasonable approximation to experimental data and quantifies the uncertainty from experimental errors, interpolation uncertainty, data sparsity and inconsistencies from different experiments.