Assessing the Interior Structure of Terrestrial Exoplanets with Implications for Habitability

Assessing the Interior Structure of Terrestrial Exoplanets with Implications for Habitability 

Authors: 

Dorn et al 

Abstract: 

Astrophysical observations reveal a large diversity of radii and masses of exoplanets. It is important to characterize the interiors of exoplanets to understand planetary diversity and further determine how unique, or not, Earth is. Assessing interior structure is challenging because there are few data and large uncertainties. Thus, for a given exoplanet a range of interior structure models can satisfy available data. Typically, interior models aim to constrain the radial structure and composition of the core and mantle, and additionally ice, ocean, and gas layer if appropriate. Constraining the parameters of these layers may also inform us about interior dynamics. However, it remains challenging to constrain interior dynamics using interior structure models because structure models are relatively insensitive to the thermal state of a planet. Nevertheless, elucidating interior dynamics remains a key goal in exoplanetology due to its role in determining surface conditions and hence habitability. Thus far, Earth-like habitability can be excluded for super-Earths that are in close proximity to their stars and therefore have high surface temperatures that promote local magma oceans.

Structure and Evolution of Internally Heated Hot Jupiters

Structure and Evolution of Internally Heated Hot Jupiters

Authors:

Komacek et al

Abstract:
Hot Jupiters receive strong stellar irradiation, producing equilibrium temperatures of 1000−2500 Kelvin. Incoming irradiation directly heats just their thin outer layer, down to pressures of ∼0.1 bars. In standard irradiated evolution models of hot Jupiters, predicted transit radii are too small. Previous studies have shown that deeper heating -- at a small fraction of the heating rate from irradiation -- can explain observed radii. Here we present a suite of evolution models for HD 209458b where we systematically vary both the depth and intensity of internal heating, without specifying the uncertain heating mechanism(s). Our models start with a hot, high entropy planet whose radius decreases as the convective interior cools. The applied heating suppresses this cooling. We find that very shallow heating -- at pressures of 1−10 bars -- does not significantly suppress cooling, unless the total heating rate is ≳10% of the incident stellar power. Deeper heating, at 100 bars, requires heating at only 1% of the stellar irradiation to explain the observed transit radius of 1.4RJup after 5 Gyr of cooling. In general, more intense and deeper heating results in larger hot Jupiter radii. Surprisingly, we find that heat deposited at 104 bars -- which is exterior to ≈99% of the planet's mass -- suppresses planetary cooling as effectively as heating at the center. In summary, we find that relatively shallow heating is required to explain the radii of most hot Jupiters, provided that this heat is applied early and persists throughout their evolution.

Internal Structure of Giant and Icy Planets: Importance of Heavy Elements and Mixing

Internal Structure of Giant and Icy Planets: Importance of Heavy Elements and Mixing

Authors: 

Helled et al

Abstract:
In this chapter we summarize current knowledge of the internal structure of giant planets. We concentrate on the importance of heavy elements and their role in determining the planetary composition and internal structure, in planet formation, and during the planetary long-term evolution. We briefly discuss how internal structure models are derived, present the possible structures of the outer planets in the Solar System, and summarise giant planet formation and evolution. Finally, we introduce giant exoplanets and discuss how they can be used to better understand giant planets as a class of planetary objects.

Constraining the Interiors of SuperEarths and Mini Neptunes

A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

Authors:

Dorn et al

Abstract:

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied

Trying to Figure out Which Exoplanets are Earth-like

Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies

Authors:

Dorn et al

Abstract:

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 obtaining confidence regions of structural and compositional parameters of core, mantle, ice layer, ocean, and atmosphere. We determined how sensitive our parameter predictions depend on (1) different estimates of bulk abundance constraints and (2) different correlations of bulk abundances between planet and host star. [...] Although the possible ranges of interior structures are large, structural parameters and their correlations are constrained by the sparse data. The probability for the tested exoplanets to be Earth-like is generally very low. Furthermore, we conclude that different estimates of planet bulk abundance constraints mainly affect mantle composition and core size.

The Interaction of Terrestrial Exoplanet Oceans and Mantle

Effect of surface-mantle water exchange parameterizations on exoplanet ocean depths

Authors:

Komacek et al

Abstract:

Terrestrial exoplanets in the canonical habitable zone may have a variety of initial water fractions due to random volatile delivery by planetesimals. If the total planetary water complement is high, the entire surface may be covered in water, forming a "waterworld." On a planet with active tectonics, competing mechanisms act to regulate the abundance of water on the surface by determining the partitioning of water between interior and surface. Here we explore how the incorporation of different mechanisms for the degassing and regassing of water changes the volatile evolution of a planet. For all of the models considered, volatile cycling reaches an approximate steady-state after ∼2 Gyr. Using these steady-states, we find that if volatile cycling is either solely dependent on temperature or seafloor pressure, exoplanets require a high abundance (≳0.3% of total mass) of water to have fully inundated surfaces. However, if degassing is more dependent on seafloor pressure and regassing mainly dependent on mantle temperature, the degassing rate is relatively large at late times and a steady-state between degassing and regassing is reached with a substantial surface water fraction. If this hybrid model is physical, super-Earths with a total water fraction similar to that of the Earth can become waterworlds. As a result, further understanding of the processes that drive volatile cycling on terrestrial planets is needed to determine the water fraction at which they are likely to become waterworlds.

A Simple Analytical Model for Rocky Planet Interior

A Simple Analytical Model for Rocky Planet Interior

Authors:

Zeng et al

Abstract:

Based on the PREM~\citep{Dziewonski:1981}, the internal gravity of the Earth increases approximately linearly in the core and stays approximately constant in the mantle. Tested with numerical calculations in~\citet{Zeng:2016}, this behavior of internal gravity can be generalized to any two-layer (iron-silicate) rocky exoplanet with core mass fraction (CMF) in between 0.2∼0.35 and mass in between 0.1 and 30 M⊕. Based on this fact, (1) CMF ≈ CRF2 (core radius fraction squared), (2) Pc∼g2s (interior pressure scales as surface gravity squared), (3) energy released of core formation is ∼110 the total gravitational energy, (4) effective heat capacity of the mantle ≈(MpM⊕)⋅7.5⋅1027J/K, (5) moment of inertia ≈13⋅Mp⋅R2p, and some other results can be derived. These results, though approximate, are handy to use owing to their simplicity and lucidity. They lead us deeper into the understanding of the interior structures of those planets.

Possible Internal Structures and Compositions of Proxima Centauri b

Possible Internal Structures and Compositions of Proxima Centauri b

Authors:

Brugger et al

Abstract:

We explore the possible Proxima Centauri b's interiors assuming the planet belongs to the class of dense solid planets (rocky with possible addition of water) and derive the corresponding radii. To do so, we use an internal structure model that computes the radius of the planet along with the locations of the different layers of materials, assuming that its mass and bulk composition are known. Lacking detailed elementary abundances of the host star to constrain the planet's composition, we base our model on solar system values. We restrained the simulations to the case of solid planets without massive atmospheres. With these assumptions, the possible radius of Proxima Centauri b spans the 0.94--1.40 R⊕ range. The minimum value is obtained considering a 1.10 M⊕ Mercury-like planet with a 65% core mass fraction, whereas the highest radius is reached for 1.46 M⊕ with 50% water in mass, constituting an ocean planet. Although this range of radii still allows very different planet compositions, it helps characterizing many aspects of Proxima Centauri b, such as the formation conditions of the system or the current amount of water on the planet. This work can also help ruling out future measurements of the planet's radius that would be physically incompatible with a solid planetary body.

Variational Principle for Planetary Interiors

Variational Principle for Planetary Interiors

Authors:

Zeng et al

Abstract:

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 summarize the set of differential equations into one, which provides us some insight into the problem. From it, a universal mass-radius relation, an estimate of error propagation from equation of state to mass-radius relation, and a form of virial theorem applicable to planetary interiors are derived.

New approach to scaling rules for stellar and planetary dynamos

New approach to scaling rules for stellar and planetary dynamos

Authors:

Barrois

Abstract:

Glorified dimensional analysis is used to derive scaling rules for internal and external magnetic field strengths and various time scales. Naive dimensional analysis is inconclusive because of multiple time scales, but physical arguments serve to weed out irrelevant parameters. Time scales can be derived from linearized instability analysis instead of ill-founded assumptions of Magnetic-Archimedean-Coriolis (MAC) balance. Further relationships can be derived from high-level models of coupled main field components and differential rotation. The ratios of the external dipole field to internal magnetic fields and of differential to overall rotation depend on details of the dynamo mechanism.

Revising the Kepler-10 System for Exoplanet Characteristics & Adding Kepler-10d (KOI-72.X)

Revised Masses and Densities of the Planets around Kepler-10

Authors:

Weiss et al

Abstract:

Determining which small exoplanets have stony-iron compositions is necessary for quantifying the occurrence of such planets and for understanding the physics of planet formation. Kepler-10 hosts the stony-iron world Kepler-10b (K10b), and also contains what has been reported to be the largest solid silicate-ice planet, Kepler-10c (K10c). Using 220 radial velocities (RVs), including 72 precise RVs from Keck-HIRES of which 20 are new from 2014-2015, and 17 quarters of Kepler photometry, we obtain the most complete picture of the Kepler-10 system to date. We find that K10b (Rp=1.47 Re) has mass 3.72±0.42 Me and density 6.46±0.73 g/cc. Modeling the interior of K10b as an iron core overlaid with a silicate mantle, we find that the iron core constitutes 0.17±0.11 of the planet mass. For K10c (Rp=2.35 Re) we measure Mp=13.98±1.79 Me and ρ=5.94±0.76 g/cc, significantly lower than the mass computed in Dumusque et al. (2014, 17.2±1.9 Me). Internal compositional modeling reveals that at least 10% of the radius of Kepler-10c is a volatile envelope composed of hydrogen-helium (0.2% of the mass, 16% of the radius) or super-ionic water (28% of the mass, 29% of the radius). Analysis of only HIRES data yields a higher mass for K10b and a lower mass for K10c than does analysis of the HARPS-N data alone, with the mass estimates for K10c formally inconsistent by 3σ. Splitting the RVs from each instrument leads to inconsistent measurements for the mass of planet c in each data set. This suggests that time-correlated noise is present and that the uncertainties in the planet masses (especially K10c) exceed our formal estimates. Transit timing variations (TTVs) of K10c indicate the likely presence of a third planet in the system, KOI-72.X. The TTVs and RVs are consistent with KOI-72.X having an orbital period of 24, 71, or 101 days, and a mass from 1-7 Me.

The Exotic Mantle Materials Hypothesized for SuperEarths

Using mathematical models, scientists have 'looked' into the interior of super-Earths and discovered that they may contain compounds that are forbidden by the classical rules of chemistry -- these substances may increase the heat transfer rate and strengthen the magnetic field on these planets. The findings have been presented in a paper published in the journal Scientific Reports.

The authors of the paper are a group of researchers from MIPT led by Artem Oganov, a professor of the Skolkovo Institute of Science and Technology and the head of the MIPT Laboratory of Computer Design. In a previous study, Oganov and his colleagues used an algorithm created by Oganov called USPEX to identify new compounds of sodium and chlorine, as well as other exotic substances.

In their latest paper, the researchers attempted to find out which compounds may be formed by silicon, oxygen, and magnesium at high pressures. These particular elements were not chosen by chance.

"Earth-like planets consist of a thin silicate crust, a silicate-oxide mantle -- which makes up approximately 7/8 of the Earth's volume and consists more than 90% of silicates and magnesium oxide -- and an iron core. We can say that magnesium, oxygen, and silicon form the basis of chemistry on Earth and on Earth-like planets," says Oganov.

Using the USPEX algorithm, the researchers investigated various structural compositions of Mg-Si-O that may occur at pressures ranging from 5 to 30 million atmospheres. Such pressures may exist in the interior of super-Earths -- planets with a solid surface mass several times greater than the mass of the Earth. There are no planets like this in the solar system, but astronomers know of planets orbiting other stars that are not as heavy as the gas giants, but are considerably heavier than the Earth. They are called super-Earths. These planets include the recently discovered Gliese 832c, which is five times heavier than the Earth, or the mega-Earth Kepler-10c, which is 17 times heavier than the Earth.

The results of the computer modelling show that the interior of these planets may contain the "exotic" compounds MgSi3O12 and MgSiO6. They have many more oxygen atoms than the MgSiO3 on Earth.

In addition, MgSi3O12 is a metal oxide and a conductor, whereas other substances consisting of Mg-Si-O atoms are dielectrics or semiconductors. "Their properties are very different to normal compounds of magnesium, oxygen, and silicon - many of them are metals or semiconductors. This is important for generating magnetic fields on these planets. As magnetic fields produce electrical currents in the interiors of a planet, high conductivity could mean a significantly more powerful magnetic field," explains Oganov.

A more powerful magnetic field means more powerful protection from cosmic radiation, and consequently more favourable conditions for living organisms. The researchers also predicted new magnesium and silicon oxides that do not fit in with the rules of classical chemistry -- SiO, SiO3, and MgO3, in addition to the oxides MgO2 and Mg3O2 previously predicted by Oganov at lower pressures.

link.

Hydrogen-Water Mixtures in Giant Planet Interiors

Hydrogen-Water Mixtures in Giant Planet Interiors Studied with Ab Initio Simulations

Authors:

Soubiran et al

Abstract:

We study water-hydrogen mixtures under planetary interior conditions using ab initio molecular dynamics simulations. We determine the thermodynamic properties of various water-hydrogen mixing ratios at temperatures of 2000 and 6000 K for pressures of a few tens of GPa. These conditions are relevant for ice giant planets and for the outer envelope of the gas giants. We find that at 2000 K the mixture is in a molecular regime, while at 6000 K the dissociation of hydrogen and water is important and affects the thermodynamic properties. We study the structure of the liquid and analyze the radial distribution function. We provide estimates for the transport properties, diffusion and viscosity, based on autocorrelation functions. We obtained viscosity estimates of the order of a few tenths of mPa.s for the conditions under consideration. These results are relevant for dynamo simulations of ice giant planets.

Kepler-36b's Planetary Interior is Probably Similar to Earth's

Scaling the Earth: A Sensitivity Analysis of Terrestrial Exoplanetary Interior Models

Authors:

Unterborn et al

Abstract:

An exoplanet's structure and composition are first-order controls of the planet's habitability. We explore which aspects of bulk terrestrial planet composition and interior structure affect the chief observables of an exoplanet: its mass and radius. We apply these perturbations to the Earth, the planet we know best. Using the mineral physics toolkit BurnMan to self-consistently calculate mass-radius models, we find that core radius, presence of light elements in the core and an upper-mantle consisting of low-pressure silicates have the largest effect on the final calculated mass at a given radius, with mantle composition being secondary. We further apply this model to determine the interior composition of Kepler-36b, finding that it is likely structurally similar to the Earth with Si/Fe = 1.14 compared to Earth's Si/Fe = 1 and Sun's Si/Fe = 1.19. We expand these results provide a grid of terrestrial mass-radius models for determining whether exoplanets are indeed "Earth-like" as bound by their composition and structure.

Demographics and Characteristics of Exoplanets

Maps and Masses of Transiting Exoplanets: Towards New Insights into Atmospheric and Interior Properties of Planets

Author:

de Wit

Abstract:

With over 1800 planets discovered outside of the Solar System in the past two decades, the field of exoplanetology has broadened our perspective on planetary systems. Research priorities are now moving from planet detection to planet characterization. In this context, transiting exoplanets are of special interest due to the wealth of data made available by their orbital configuration. Here, I introduce two methods to gain new insights into the atmospheric and interior properties of exoplanets.

The first method aims to map an exoplanet's atmosphere based on the scanning obtained while it is occulted by its host star. I introduce the basics of eclipse mapping, its caveats, and a framework to mitigate their effects via global analyses including transits, phase curves, and radial velocity measurements. I use this method to create the first 2D map and the first cloud map of an exoplanet for the hot-Jupiters HD189733b and Kepler-7b, respectively. Ultimately temperature, composition, and circulation patterns could be constrained in 3D, a significant asset for informing atmospheric models.

The second method, MassSpec, aims to determine transiting planet masses and atmospheric properties solely from transmission spectra. Determination of an exoplanet's mass is key to understanding its basic properties, including its potential for supporting life. To date, mass constraints for exoplanets are mainly based on radial velocity measurements, which are not suited for planets with low masses, large semi-major axes, or those orbiting faint or active stars. I demonstrate that a planet's mass has to be accounted for by atmospheric retrieval methods to avoid biases and that JWST could determine the mass and atmospheric properties of half a dozen Earth-sized planets in their host's habitable zones over its lifetime, which could lead to the first identification of a habitable exoplanet.

Equilibrium Rotation of Semiliquid Exoplanets and Satellites

Equilibrium rotation of semiliquid exoplanets and satellites

Author:

Makarov

Abstract:

A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures. Unlike planets with solid mantles and Earth-like rheology, semiliquid bodies can be captured into stable pseudosynchronous spin resonance, where the average rate of rotation is higher than the synchronous 1:1 resonance. Two basic conditions are derived for capture of planets with a triaxial figure into pseudosynchronous rotation, one related to the characteristic tidal wave number (the product of the tidal frequency by the Maxwell time), and the other to the orbital eccentricity. If a semiliquid object does not satisfy either of the two conditions, it is captured into the synchronous resonance. For nearly axially symmetric bodies, only the first condition is in place, and the other is much relaxed, so they should predominantly be pseudosynchronous. It is also pointed out that the equilibrium pseudosychronous rotation rate can not reach the widely used asymptotic value from the constant time lag model but is in reality closer to the synchronous spin.

Surface/atmospheric Abundances of Bio-Necessary Materials may be VERY Variable in Terrestrial Exoplanets

Tracing the Ingredients for a Habitable Earth from Interstellar Space through Planet Formation

Authors:

Bergin et al

Abstract:

We use the C/N ratio as a monitor of the delivery of key ingredients of life to nascent terrestrial worlds. Total elemental C and N contents, and their ratio, are examined for the interstellar medium, comets, chondritic meteorites and terrestrial planets; we include an updated estimate for the Bulk Silicate Earth (C/N = 49.0 +/- 9.3). Using a kinetic model of disk chemistry, and the sublimation/condensation temperatures of primitive molecules, we suggest that organic ices and macro-molecular (refractory or carbonaceous dust) organic material are the likely initial C and N carriers. Chemical reactions in the disk can produce nebular C/N ratios of ~1-12, comparable to those of comets and the low end estimated for planetesimals. An increase of the C/N ratio is traced between volatile-rich pristine bodies and larger volatile-depleted objects subjected to thermal/accretional metamorphism. The C/N ratios of the dominant materials accreted to terrestrial planets should therefore be higher than those seen in carbonaceous chondrites or comets. During planetary formation, we explore scenarios leading to further volatile loss and associated C/N variations owing to core formation and atmospheric escape. Key processes include relative enrichment of nitrogen in the atmosphere and preferential sequestration of carbon by the core. The high C/N BSE ratio therefore is best satisfied by accretion of thermally processed objects followed by large-scale atmospheric loss. These two effects must be more profound if volatile sequestration in the core is effective. The stochastic nature of these processes hints that the surface/atmospheric abundances of biosphere-essential materials will likely be variable.

Water, Hydrogen and the Internal Structure of Gas Giants

Miscibility calculations for water and hydrogen in giant planets

Authors:

Soubiran et al

Abstract:

We present results from ab initio simulations of liquid water-hydrogen mixtures in the range from 2 to 70 GPa and from 1000 to 6000 K, covering conditions in the interiors of ice giant planets and parts of the outer envelope of gas giant planets. In addition to computing the pressure and the internal energy, we derive the Gibbs free energy by performing a thermodynamic integration. For all conditions under consideration, our simulations predict hydrogen and water to mix in all proportions. The thermodynamic behavior of the mixture can be well described with an ideal mixing approximation. We suggest a substantial fraction of water and hydrogen in giant planets may occur in homogeneously mixed form rather than in separate layers. The extend of mixing depends on the planet's interior dynamics and its conditions of formation, in particular on how much hydrogen was present when icy planetesimals were delivered. Based on our results, we do not predict water-hydrogen mixtures to phase separate during any stage of the evolution of giant planets. We also show that the hydrogen content of an exoplanet is much higher if the mixed interior is assumed.

Simulating the Interiors of Giant Planets

Can we Figure out the Internal Structure of Rocky Exoplanets From Their Mass and Radius?

Can we constrain interior structure of rocky exoplanets from mass and radius measurements?

Authors:

Dorn et al

Abstract:

We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii as well as to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Our main conclusions are: (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are key constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structure
including hydrogen- and water-rich exoplanets.