A Simple Analytical Model for Rocky Planet Interiors

Zeng, Li; Jacobsen, S. B.

doi:10.3847/1538-4357/aa6218

Cited by 39 publications

(15 citation statements)

References 39 publications

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“…Colors represent the assumed mass of the planet in each run. The empirical scaling relation of CRF ≈ CMF 0.5 proposed inZeng and Jacobsen (2017) is shown as a red dashed line. (b) Comparison of our calculated mass and radius values (symbols as inFigure 3) to the Z16 model for CMF = 0.25 (red dashed line), 0.33 (dashed green line), and 0.45 (dashed black line).…”

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confidence: 99%

The Pressure and Temperature Limits of Likely Rocky Exoplanets

Unterborn

Panero

2019

JGR Planets

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The interior composition of exoplanets is not observable, limiting our direct knowledge of their structure, composition, and dynamics. Recently described observational trends suggest that rocky exoplanets, that is, planets without significant volatile envelopes, are likely limited to <1.5 Earth radii. We show that given this likely upper limit in the radii of purely rocky super‐Earth exoplanets, the maximum expected core‐mantle boundary pressure and adiabatic temperature are relatively moderate, 630 GPa and 5000 K, while the maximum central core pressure varies between 1.5 and 2.5 TPa. We further find that for planets with radii less than 1.5 Earth radii, core‐mantle boundary pressure and adiabatic temperature are mostly a function of planet radius and insensitive to planet structure. The pressures and temperatures of rocky exoplanet interiors, then, are less than those explored in recent shock‐compression experiments, ab initio calculations, and planetary dynamical studies. We further show that the extrapolation of relevant equations of state does not introduce significant uncertainties in the structural models of these planets. Mass‐radius models are more sensitive to bulk composition than any uncertainty in the equation of state, even when extrapolated to terapascal pressures.

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confidence: 99%

The Pressure and Temperature Limits of Likely Rocky Exoplanets

Unterborn

Panero

2019

JGR Planets

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“…But for internally differentiated rocky planets, its value is a little lower. In this sense, Zeng & Jacobsen (2017) showed that for both the Earth and Earth-like rocky planets, its value is approximately equal to 1/3. In consequence, we can take ξ 1 = 2/5 and ξ 2 = 1/3.…”

Section: Initial Conditions and Physical Parametersmentioning

confidence: 97%

The dynamical evolution of close-in binary systems formed by a super-Earth and its host star

Luna

Navone

Melita

2020

A&A

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Aims. The aim of this work is to develop a formalism for the study of the secular evolution of a binary system which includes interaction due to the tides that each body imparts on the other. We also consider the influence of the J2-related secular terms on the orbital evolution and the torque, caused by the triaxiality, on the rotational evolution, both of which are associated only to one of the bodies. We apply these set of equations to the study of the orbital and rotational evolution of a binary system composed of a rocky planet and its host star in order to characterize the dynamical evolution at work, particularly near spin-orbit resonances. Methods. We used the equations of motion that give the time evolution of the orbital elements and the spin rates of each body to study the dynamical evolution of the Kepler-21 system as an example of how the formalism that we have developed can be applied. Results. We obtained a set of equations of motion without singularities for vanishing eccentricities and inclinations. This set gives, on one hand, the time evolution of the orbital elements due to the tidal potentials generated by both members of the system as well as the oblateness of one of them. On the other hand, it gives the time evolution of the stellar spin rate due to the corresponding tidal torque and of the planet’s rotation angle due to both the tidal and triaxiality-induced torques. We found that for the parameters and the initial conditions explored here, the tidally and triaxiality-induced modifications of the tidal modes can be more significative than expected and that the time of tidal synchronization strongly depends on the values of the rheological parameters.

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“…The model then calculates the minimum and maximum core radius fractions for which a marginal CRF can be sampled. The core radius fraction is related (Zeng & Jacobsen 2017) This translates to a CMF of 78% ± 11% using this model. As an alternative method, we characterized the internal structure of HD 137496 b considering a pure-iron core, a silicate mantle, and a pure-water layer using a Bayesian inference analysis.…”

Section: Modeling Of the Internal Structure Of Hd 137496 Bmentioning

confidence: 99%

The HD 137496 system: A dense, hot super-Mercury and a cold Jupiter

Silva

Barros

Otegi

et al. 2022

A&A

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Context. Most of the currently known planets are small worlds with radii between that of the Earth and that of Neptune. The characterization of planets in this regime shows a large diversity in compositions and system architectures, with distributions hinting at a multitude of formation and evolution scenarios. However, many planetary populations, such as high-density planets, are significantly under-sampled, limiting our understanding of planet formation and evolution. Aims. NCORES is a large observing program conducted on the HARPS high-resolution spectrograph that aims to confirm the planetary status and to measure the masses of small transiting planetary candidates detected by transit photometry surveys in order to constrain their internal composition. Methods. Using photometry from the K2 satellite and radial velocities measured with the HARPS and CORALIE spectrographs, we searched for planets around the bright (Vmag = 10) and slightly evolved Sun-like star HD 137496. Results. We precisely estimated the stellar parameters, M* = 1.035 ± 0.022 M⊙, R* = 1.587 ± 0.028 R⊙, Teff = 5799 ± 61 K, together with the chemical composition (e.g. [Fe/H] = −0.027 ± 0.040 dex) of the slightly evolved star. We detect two planets orbiting HD 137496. The inner planet, HD 137496 b, is a super-Mercury (an Earth-sized planet with the density of Mercury) with a mass of Mb = 4.04 ± 0.55 M⊕, a radius of Rb = 1.31−0.05+0.06 R⊕, and a density of ρb = 10.49−1.82+2.08 g cm-3. With an interior modeling analysis, we find that the planet is composed mainly of iron, with the core representing over 70% of the planet’s mass (Mcore / Mtotal = 0.73−0.12+0.11). The outer planet, HD 137496 c, is an eccentric (e = 0.477 ± 0.004), long period (P = 479.9−1.1+1.0 days) giant planet (Mc sinic = 7.66 ± 0.11 MJup) for which we do not detect a transit. Conclusions. HD 137496 b is one of the few super-Mercuries detected to date. The accurate characterization reported here enhances its role as a key target to better understand the formation and evolution of planetary systems. The detection of an eccentric long period giant companion also reinforces the link between the presence of small transiting inner planets and long period gas giants.

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A Simple Analytical Model for Rocky Planet Interiors

Cited by 39 publications

References 39 publications

The Pressure and Temperature Limits of Likely Rocky Exoplanets

The Pressure and Temperature Limits of Likely Rocky Exoplanets

The dynamical evolution of close-in binary systems formed by a super-Earth and its host star

The HD 137496 system: A dense, hot super-Mercury and a cold Jupiter

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