Interior structure models of solid exoplanets using material laws in the infinite pressure limit

Wagner, F.W.; Sohl, F.; Hußmann, H.; Grott, M.; Rauer, H.

doi:10.1016/j.icarus.2011.05.027

Cited by 124 publications

(107 citation statements)

References 64 publications

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“…Planet bulk composition is held fixed to that of the Earth. Using the generalized Rydberg, Keane, and reciprocal K ′ EoS, the resultant surface radii differ by less than 2% from each other (adopted from Wagner et al 2011a). …”

Section: Resultsmentioning

confidence: 99%

“…Calculated models have been used to derive mass-radius relationships for exoplanets assuming a range of chemical compositions to gain insight into the bulk compositions and possible interior structures of these planets (e.g., Valencia 2011, and references therein). Wagner et al (2011a) have reinvestigated mass-radius relationships for rocky exoplanets using equations of state that are compliant with the thermodynamics of the high-pressure limit of a given material.…”

Section: Introductionmentioning

confidence: 99%

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Mass-Radius Relationships of Rocky Exoplanets

2012

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Abstract. Mass and radius of planets transiting their host stars are provided by radial velocity and photometric observations. Structural models of solid exoplanet interiors are then constructed by using equations of state for the radial density distribution, which are compliant with the thermodynamics of the high-pressure limit. However, to some extent those structural models suffer from inherent degeneracy or non-uniqueness problems owing to a principal lack of knowledge of the internal differentiation state and/or the possible presence of an optically thick atmosphere. We here discuss the role of corresponding measurement errors, which adversely affect determinations of a planet's mean density and bulk chemical composition. Precise measurements of planet radii will become increasingly important as key observational constraints for radial density models of individual solid low-mass exoplanets or super-Earths.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mass-Radius Relationships of Rocky Exoplanets

2012

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“…Heat production in the H 2 O shell is set to zero, whereas it accounts for radiogenic heating in the silicate mantle, where a constant value of ε = 7.38 × 10 −12 W kg −1 (appropriate for the Earth, Turcotte & Schubert 2014) is applied. In the iron core, ε is chosen so that the heat flux across the boundary with the silicate mantle (CMB) is Q CMB = −k c (∂T /∂R) CMB (Valencia et al 2006;Wagner et al 2011). For the Earth test considered below, the power through this boundary is ≈ 7 TW, comparable to the lower limit estimated for the Earth (Tateno et al 2009).…”

Section: Appendixmentioning

confidence: 99%

“…The last entry in Table 6 represents the revised release of the 1995 EoS for ordinary water from the International Association for the Properties of Water and Steam (IAPWS, Wagner & Pruß 2002), which already includes temperature dependence and therefore does not apply the second term on the right-hand side of Equation (A11). The EoS in Table 6 are valid up to pressures of at most a few to several times 100 GPa (e.g., Seager et al 2007;Wagner et al 2011), which are easily exceeded in the deep interiors of super-Earths. (The inferred pressure at the center of the Earth is ≈ 360 GPa, e.g., Dziewonski & Anderson 1981.)…”

Section: Appendixmentioning

confidence: 99%

In Situ and Ex Situ Formation Models of Kepler 11 Planets

D’Angelo¹,

Bodenheimer²

2016

ApJ

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We present formation simulations of the six Kepler 11 planets. Models assume either in situ or ex situ assembly, the latter with migration, and are evolved to the estimated age of the system, ≈ 8 Gyr. Models combine detailed calculations of both the gaseous envelope and the condensed core structures, including accretion of gas and solids, of the disk's viscous and thermal evolution, including photo-evaporation and disk-planet interactions, and of the planets' evaporative mass loss after disk dispersal. Planetplanet interactions are neglected. Both sets of simulations successfully reproduce measured radii, masses, and orbital distances of the planets, except for the radius of Kepler 11b, which loses its entire gaseous envelope shortly after formation. Gaseous (H+He) envelopes account for 18% of the planet masses, and between ≈ 35 and ≈ 60% of the planet radii. In situ models predict a very massive inner disk, whose solids' surface density (σ Z ) varies from over 10 4 to ≈ 10 3 g cm −2 at stellocentric distances 0.1 r 0.5 au. Initial gas densities would be in excess of 10 5 g cm −2 if solids formed locally. Given the high disk temperatures ( 1000 K), planetary interiors can only be composed of metals and highly refractory materials. Sequestration of hydrogen by the core and subsequent outgassing is required to account for the observed radius of Kepler 11b. Ex situ models predict a relatively low-mass disk, whose initial σ Z varies from ≈ 10 to ≈ 5 g cm −2 at 0.5 r 7 au and whose initial gas density ranges from ≈ 10 3 to ≈ 100 g cm −2 . All planetary interiors are expected to be rich in H 2 O, as core assembly mostly occurs exterior to the ice condensation front. Kepler 11b is expected to have a steam atmosphere, and H 2 O is likely mixed with H+He in the envelopes of the other planets. Results indicate that Kepler 11g may not be more massive than Kepler 11e.

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“…Asteroseismology can overcome these limitations, but it is only feasible from space for bright targets (see [26][27][28] and, in this volume, the contribution from A. Moya). The uncertainty in the stellar parameters is directly translated into the uncertainty of the planetary parameters, where precisions of a few percent are required to distinguish between different compositions and internal structures [29][30][31][32][33][34][35]. Figure 1 shows the values that different authors get for the quadratic limb darkening coefficients for stars of different effective temperatures.…”

Section: Derivation Of the Planetary Parametersmentioning

confidence: 99%