Recent developments of dynamic x-ray characterization experiments of dense matter are reviewed, with particular emphasis on conditions relevant to interiors of terrestrial and gas giant planets. These studies include characterization of compressed states of matter in light elements by x-ray scattering and imaging of shocked iron by radiography. Several applications of this work are examined. These include the structure of massive "Super Earth" terrestrial planets around other stars, the 40 known extrasolar gas giants with measured masses and radii, and Jupiter itself, which serves as the benchmark for giant planets.
This article deals with the most recent developments in the field of exoplanetary science connecting the interior of the planets with their habitability. In this issue, I have specified the importance of interior dynamics and briefly reviewed some of the main factors by which interior of a planet can effect the habitability of extra-solar planets.
In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. Variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying this principle to planetary interior can beautifully summa…
The recently adopted Ariel ESA mission will measure the atmospheric composition of a large number of exoplanets. This information will then be used to better constrain planetary bulk compositions. While the connection between the composition of a planetary atmosphere and the bulk interior is still being investigated, the combination of the atmospheric composition with the measured mass and radius of exoplanets will push the field of exoplanet characterisation to the next level, and provide new insights of the nature of planets in our galaxy. In this white paper, we outline the ongoing activiti…
Interior characterization traditionally relies on individual planetary properties, ignoring correlations between different planets of the same system. For multi-planetary systems, planetary data are generally correlated. This is because, the differential masses and radii are better constrained than absolute planetary masses and radii. We explore such correlations and data specific to the multiplanetary-system of TRAPPIST-1 and study their value for our understanding of planet interiors. Furthermore, we demonstrate that the rocky interior of planets in a multi-planetary system can be preferenti…
Jupiter's radio emission has been linked to its planetary-scale magnetic field, and spacecraft investigations have revealed that most planets, and some moons, have or had a global magnetic field. Generated by internal dynamos, magnetic fields are one of the few remote sensing means of constraining the properties of planetary interiors. For the Earth, its magnetic field has been speculated to be partially responsible for its habitability, and knowledge of an extrasolar planet's magnetic field may be necessary to assess its habitability. The radio emission from Jupiter and other solar system pla…
We now know that the outer solar system is host to at least six diverse planetary ring systems, each of which is a scientifically compelling target with the potential to inform us about the evolution, history and even the internal structure of the body it adorns. These diverse ring systems represent a set of distinct local laboratories for understanding the physics and dynamics of planetary disks, with applications reaching beyond our Solar System. We highlight the current status of planetary rings science and the open questions before the community to promote continued Earth-based and spacecr…
In this review, I briefly summarize the present status of experimental and theoretical investigations of the properties of matter under conditions characteristic of planetary interiors, from terrestrial to jovian planets. I first focus on the two lightest elements, hydrogen and helium, and discuss recent theoretical and experimental investigations of their properties at high pressure and temperature. Then, I discuss the impact of these properties, as well as of the equation of state of heavier elements, on planetary interiors. Finally, I highlight the importance of exoplanet transit observatio…
Giant gaseous planets often reside on orbits in sufficient proximity to their host stars for the planetary quadrupole gravitational field to become non-negligible. In presence of an additional planetary companion, a precise characterization of the system's orbital state can yield meaningful constraints on the transiting planet's interior structure. However, such methods can require a very specific type of system. This paper explores the dynamic range of applicability of these methods and shows that interior structure calculations are possible for a wide array of orbital architectures. The HAT-…
Recently there has been tremendous increase in the number of identified extra-solar planetary systems. Our understanding of their formation is tied to exoplanet internal structure models, which rely upon equations of state of light elements and compounds like water. Here we present shock compression data for water with unprecedented accuracy that shows water equations of state commonly used in planetary modeling significantly overestimate the compressibility at conditions relevant to planetary interiors. Furthermore, we show its behavior at these conditions, including reflectivity and isentrop…
Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics
UC Berkeley（加州大学伯克利分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；The Institute of Science and Technology Austria（奥地利科学技术研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Bakar Institute of Digital Materials for the Planet, UC Berkeley（加州大学伯克利分校巴卡尔地球数字材料研究所）
A monomodal model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of rotation rate as well as with thermal and viscous diffusivities. The convection model is used as a boundary condition for a linearization of the equations of motion in the transition region between convectively unstable and stably-stratified regions, yielding the depth to which convection penetrates into the stable region and establishing a relationship between that depth and the local convective Rossby number, di…
This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we will discuss the various types of planets appearing in this diagram and describe internal structures for each type. The review will summarize the status of theoretical and experimental works performed in the field of equation of states (EOS) for materials relevant to planetary interiors and will address the main theoretical and experimental uncertainties and ch…
Using ab initio molecular dynamics simulations, we calculate the physical properties of MgO at conditions extending from the ones encountered in the Earth mantle up to the ones anticipated in giant planet interiors such as Jupiter. We pay particular attention to the high pressure melting temperature throughout this large density range as this is a key ingredient for building accurate planetary interior models with a realistic description of the inner core. We compare our simulation results with previous ab initio calculations that have been so far limited to the pressure range corresponding to…
Here it is shown how to find the interior structure of a variety of rock-and-iron planetary bodies by using the rock density and some aspects of the core density as known for the Earth and using a convection principle for the iron-rich core. Convection minimizes both the density and temperature gradients inside the core fluid. This is achieved if the density of the core fluid is close to pure iron melting density at the core-mantle boundary, and the density has the smallest value possible for iron-rich melt at the inner core boundary. The critical iron densities for both pure iron and iron wit…
Hot Jupiters are generally observed to lack close planetary companions, a trend that has been interpreted as evidence for high-eccentricity migration. We present the discovery and validation of WASP-132 c (TOI-822.02), a 1.85 $\pm$ 0.10 $R_{\oplus}$ planet on a 1.01 day orbit interior to the hot Jupiter WASP-132 b. Transiting Exoplanet Survey Satellite (TESS) and ground-based follow-up observations, in conjunction with vetting and validation analysis, enable us to rule out common astrophysical false positives and validate the observed transit signal produced by WASP-132 c as a planet. Running …
In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination and the harmonic arguments are l…
The coupled interior-atmosphere system of terrestrial exoplanets remains poorly understood. Exoplanets show a wide variety of sizes, densities, surface temperatures, and interior structures, with important knock-on effects for this coupled system. Many exoplanets are predicted to have a "stagnant lid" at the surface, with a rigid stationary crust, sluggish mantle convection, and only minor volcanism. However, if exoplanets have Earth-like plate tectonics, which involves several discrete, slowly moving plates and vigorous tectono-magmatic activity, then this may be critical for planetary habita…
Using a generalized Bayesian inference method, we aim to explore the possible interior structures of six selected exoplanets for which planetary mass and radius measurements are available in addition to stellar host abundances: HD~219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55~Cnc~e, and HD~97658b. We aim to investigate the importance of stellar abundance proxies for the planetary bulk composition (namely Fe/Si and Mg/Si) on prediction of planetary interiors. We performed a full probabilistic Bayesian inference analysis to formally account for observational and model uncertainties while obtaini…
Although carbon monoxide (CO) is an abundant molecule and may have great importance for planetary interiors, measurements of its properties are difficult due to its extreme volatility. We calculate the equation of state for CO over a range of temperature and density that is applicable to the conditions in planetary interiors. Previous experimental and theoretical studies cover only a limited temperature-density range. Our calculations match these early results well, but now cover the full range of relevance. The method of calculation is based on the general-purpose quotidian equation of state …
A major goal in the discovery and characterisation of exoplanets is to identify terrestrial-type worlds that are similar to (or otherwise distinct from) our Earth. Recent results have highlighted the importance of applying devolatilisation -- i.e. depletion of volatiles -- to the chemical composition of planet-hosting stars to constrain bulk composition and interiors of terrestrial-type exoplanets. In this work, we apply such an approach to a selected sample of 13 planet-hosting Sun-like stars, for which high-precision photospheric abundances have been determined in the first paper of the seri…
'Empirical' models (pressure vs. density) of Uranus and Neptune interiors constrained by the gravitational coefficients J_2, J_4, the planetary radii and masses, and Voyager solid-body rotation periods are presented. The empirical pressure-density profiles are then interpreted in terms of physical equations of state of hydrogen, helium, ice (H_2O), and rock (SiO_2) to test the physical plausibility of the models. The compositions of Uranus and Neptune are found to be similar with somewhat different distributions of the high-Z material. The big difference between the two planets is that Neptune…
Water content and the internal evolution of terrestrial planets and icy bodies are closely linked. The distribution of water in planetary systems is controlled by the temperature structure in the protoplanetary disk and dynamics and migration of planetesimals and planetary embryos. This results in the formation of planetesimals and planetary embryos with a great variety of compositions, water contents and degrees of oxidation. The internal evolution and especially the formation time of planetesimals relative to the timescale of radiogenic heating by short-lived 26Al decay may govern the amount…
Context: The long-term carbonate-silicate cycle plays an important role in the evolution of Earth's climate and, therefore, may also be an important mechanism in the evolution of the climates of Earth-like exoplanets. Aims: We investigate the effects of radiogenic mantle heating, core size, and planetary mass on the evolution of the atmospheric partial $CO_2$ pressure, and the ability of a long-term carbon cycle driven by plate tectonics to control the atmospheric $CO_2$ pressure. Methods: We developed a box-model which connects carbon cycling to parametrized mantle convection. The carbon cycl…
The melt productivity of a differentiated planet's mantle is primarily controlled by its iron content, which is itself approximated by the planet's core mass fraction (CMF). Here we show that estimates of an exo-planet's CMF allows robust predictions of the thickness, composition and mineralogy of the derivative crust. These predicted crustal compositions allow constraints to be placed on volatile cycling between surface and the deep planetary interior, with implications for the evolution of habitable planetary surfaces. Planets with large, terrestrial-like, CMFs ($\geq$0.32) will exhibit thin…
Ice-rich planets are formed exterior to the water ice-line and thus are expected to contain a substantial amount of ices. The high ice content leads to unique conditions in the interior, under which the structure of a planet is affected by ice interaction with other metals. We apply experimental data of ice-rock interaction at high pressure, and calculate detailed thermal evolution for possible interior configurations of ice-rich planets, in the mass range of super-Earth to Neptunes (5-15 Earth masses). We model the effect of migration inward on the ice-rich interior by including the influence…
We present the first investigation of Th abundances in Solar twins and analogues to understand the possible range of this radioactive element and its effect on rocky planet interior dynamics and potential habitability. The abundances of the radioactive elements Th and U are key components of a planet's energy budget, making up 30% to 50% of the Earth's (Korenaga 2008; Allègre et al. 2001; Schubert et al. 1980; Lyubetskaya & Korenaga 2007; The KamLAND Collaboration 2011; Huang et al. 2013). Radiogenic heat drives interior mantle convection and surface plate tectonics, which sustains a deep carb…
A large fraction of known Jupiter like exoplanets are inflated as compared to Jupiter. These "hot" Jupiters orbit close to their parent star and are bombarded with intense starlight. Many theories have been proposed to explain their radius inflation and several suggest that a small fraction of the incident starlight is injected in to the planetary interior which helps to puff up the planet. How will such energy injection affect the planetary dynamo? In this Letter, we estimate the surface magnetic field strength of hot Jupiters using scaling arguments that relate energy available in planetary …
The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are ca…
Thermal history calculations provide important insights into the interior evolution of planets, but incorporate simplified dynamics from the systems they represent. Planetary interiors typical incorporate complex rheologies, viscous layering, lateral heterogeneities, and time delays in processes, which have not been traditionally represented by parameterised approaches. Here we develop numerical models for planetary evolution, incorporating the physical complexity of Earth's interior, and use them to generate statistically-based Nu-Ra scalings. These encapsulate the main effects of tectonic tr…
Observations from the Juno and Cassini missions provide essential constraints on the internal structures and compositions of Jupiter and Saturn, resulting in profound revisions of our understanding of the interior and atmospheres of Gas Giant planets. The next step to understand planetary origins in our Solar System requires a mission to their Ice Giant siblings, Uranus and Neptune.
Aims: The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk composition on the interior--atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres. Methods: We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO2) following the crystallization of a magma ocean after planet formation, predicting a compositional profile …
Magrathea v2: A planetary interior modeling platform in C++
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Department of Physics and Astronomy, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校物理与天文学系）；Department of Physics, Ariel University（阿里埃勒大学物理系）；Department of Astronomy, University of Wisconsin–Madison（威斯康星大学麦迪逊分校天文学系）；Department of Earth and Space Science, University of Washington（华盛顿大学地球与空间科学系）；Astrophysics Research Center (ARCO), Department of Natural Sciences, The Open University of Israel（以色列开放大学自然科学学院天体物理研究中心）
Magrathea v2 是一个开源的 C++ 行星内部建模平台，扩展了成分支持，新增成分反演工具，并提高了用户自定义模型的灵活性。
We discuss the interior structure and composition of giant planets, and how this structure changes as these planets cool and contract over time. Here we define giant planets as those that have an observable hydrogen-helium envelope, which includes Jupiter-like planets, which are predominantly H/He gas, and Neptune-like planets which are predominantly composed of elements heavier than H/He. We describe the equations of state of planetary materials and the construction of static structural models and thermal evolution models. We apply these models to transiting planets close to their parent star…
Probing the interiors of the gas giant planets in our Solar System is not an easy task. It requires a set of accurate measurements combined with theoretical models that are used to infer the planetary composition and its depth dependence. The masses of Jupiter and Saturn are 317.83 and 95.16 Earth masses, respectively, and since a few decades, we know that they mostly consist of hydrogen and helium. It is the mass of heavy elements (all elements heavier than helium) that is not well determined, as well as their distribution within the planets. While the heavy elements are not the dominating ma…
Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter …
We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape.…
We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from…
