Mass-Radius Relationships for Exoplanets

Swift, D. C.; Eggert, J. H.; Hicks, D. G.; Hamel, S.; Caspersen, K.; Schwegler, E.; Collins, G. W.; Nettelmann, N.; Ackland, G. J.

doi:10.1088/0004-637x/744/1/59

Mass-Radius Relationships for Exoplanets

Journal Article · Tue Dec 13 00:00:00 UTC 2011 · The Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637x/744/1/59· OSTI ID:1830946

Swift, D. C. ^[1]; Eggert, J. H. ^[1]; Hicks, D. G. ^[1]; Hamel, S. ^[1]; Caspersen, K. ^[1]; Schwegler, E. ^[1]; Collins, G. W. ^[1]; Nettelmann, N. ^[2]; Ackland, G. J. ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. Rostock (Germany)
Univ. of Edinburgh (United Kingdom)

For planets other than Earth, particularly exoplanets, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass–radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass–radius and mass–pressure relations for key, relevant materials whose equation of state (EOS) is reasonably well established, and for differentiated Fe/rock. We find that variations in the EOS, such as may arise when extrapolating from low-pressure data, can have significant effects on predicted mass–radius relations and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets, broadly supporting recent inferences about exoplanet structures. Kepler-10b is apparently "Earth-like," likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass–radius curves for H₂O and CH₄, suggesting an "icy" composition with a relatively large core or a relatively large proportion of H₂O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass–radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5^+1.2 – _1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8 TPa, though may be up to 2 TPa. These pressures are accessible by planar shock and ramp-loading experiments at large laser facilities. Furthermore, the center of HAT-P-2b is probably around 210 TPa, in the range of planned National Ignition Facility experiments, and that of CoRoT-3b around 1900 TPa.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1830946

Alternate ID(s):: OSTI ID: 22004341

Report Number(s):: LLNL-JRNL--421766; 383722

Journal Information:: The Astrophysical Journal, Journal Name: The Astrophysical Journal Journal Issue: 1 Vol. 744; ISSN 0004-637X

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Probing the Interiors of the Ice Giants: Shock Compression of Water to 700 GPa and 3.8 g / cm 3 Knudson, M. D.; Desjarlais, M. P.; Lemke, R. W. Physical Review Letters, Vol. 108, Issue 9 https://doi.org/10.1103/physrevlett.108.091102	journal	February 2012
Dynamic Ionic Clusters with Flowing Electron Bubbles from Warm to Hot Dense Iron along the Hugoniot Curve Dai, Jiayu; Kang, Dongdong; Zhao, Zengxiu Physical Review Letters, Vol. 109, Issue 17 https://doi.org/10.1103/physrevlett.109.175701	journal	October 2012
Solid Iron Compressed Up to 560 GPa Ping, Y.; Coppari, F.; Hicks, D. G. Physical Review Letters, Vol. 111, Issue 6 https://doi.org/10.1103/physrevlett.111.065501	journal	August 2013
Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics Daligault, Jérôme; Baalrud, Scott D.; Starrett, Charles E. Physical Review Letters, Vol. 116, Issue 7 https://doi.org/10.1103/physrevlett.116.075002	journal	February 2016
Absolute Equation-of-State Measurement for Polystyrene from 25 to 60 Mbar Using a Spherically Converging Shock Wave Döppner, T.; Swift, D. C.; Kritcher, A. L. Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/physrevlett.121.025001	journal	July 2018
The exoplanet handbook: Book Review Trigo-Rodríguez, Josep M. Meteoritics & Planetary Science, Vol. 47, Issue 3 https://doi.org/10.1111/j.1945-5100.2012.01343.x	journal	March 2012
The search for signs of life on exoplanets at the interface of chemistry and planetary science Seager, Sara; Bains, William Science Advances, Vol. 1, Issue 2 https://doi.org/10.1126/sciadv.1500047	journal	March 2015
Atmosphere-Interior Exchange on Hot, Rocky Exoplanets Kite, Edwin S.; Fegley Jr., Bruce; Schaefer, Laura The Astrophysical Journal, Vol. 828, Issue 2, p. 80 https://doi.org/10.3847/0004-637x/828/2/80	journal	September 2016
Properties and Occurrence Rates for Kepler Exoplanet Candidates as a Function of Host Star Metallicity from the DR25 Catalog Narang, Mayank; Manoj, P.; Furlan, E. The Astronomical Journal, Vol. 156, Issue 5 https://doi.org/10.3847/1538-3881/aae391	journal	October 2018
Threshold Radii of Volatile-rich Planets Lozovsky, M.; Helled, R.; Dorn, C. The Astrophysical Journal, Vol. 866, Issue 1 https://doi.org/10.3847/1538-4357/aadd09	journal	October 2018
Studies of the Core Conditions of the Earth and Super-Earths Using Intense Ion Beams at FAIR Tahir, N. A.; Lomonosov, I. V.; Borm, B. The Astrophysical Journal Supplement Series, Vol. 232, Issue 1 https://doi.org/10.3847/1538-4365/aa813e	journal	August 2017
Ion-beam-driven Planetary Physics Research at FAIR Tahir, N. A.; Shutov, A.; Lomonosov, I. V. The Astrophysical Journal Supplement Series, Vol. 238, Issue 2 https://doi.org/10.3847/1538-4365/aadd4c	journal	October 2018
Dynamical Ionic Clusters with Flowing Electron Bubbles from Warm to Hot Dense Iron along the Hugoniot Curve Dai, Jiayu; Kang, Dongdong; Zhao, Zengxiu arXiv https://doi.org/10.48550/arxiv.1109.4252	text	January 2011
Structure, equation of state, diffusion and viscosity of warm dense Fe under the conditions of giant planet core Dai, Jiayu; Hou, Yong; Kang, Dongdong arXiv https://doi.org/10.48550/arxiv.1303.3361	text	January 2013
Warm Dust around Cool Stars: Field M Dwarfs with WISE 12 or 22 Micron Excess Emission Theissen, Christopher A.; West, Andrew A. arXiv https://doi.org/10.48550/arxiv.1409.0016	text	January 2014
Properties and occurrence rates of $Kepler$ exoplanet candidates as a function of host star metallicity from the DR25 catalog Narang, M.; Manoj, P.; Furlan, E. arXiv https://doi.org/10.48550/arxiv.1809.08385	text	January 2018
Threshold Radii of Volatile-rich Planets Lozovsky, M.; Helled, R.; Dorn, C. IOP Publishing https://doi.org/10.5167/uzh-166681	text	January 2018
The PLATO 2.0 mission Benz, Willy; Alibert, Yann; Heng, Kevin Springer https://doi.org/10.7892/boris.59262	text	January 2014

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