Mass-Radius Relationships for Solid Exoplanets

By Sara Seager, M. Kuchner, C. Hier-Majumder, B. Militzer. 2007

658 citations recorded by the source corpus.

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial mass planets of all compositions we considered follow a generic functional form that is not a simple power law: log10 Rs = k1 + log10(Ms) - k2M for up to Mp ≈ 20 M⊕, where Ms and Rs are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form ρ = ρ0 + cPn. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found the following: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with ~5% uncertainty water ice planets with ≳25% water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super-Earths" based on the clear distinction in radii between planets with significant gas envelopes and those without.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d4c35ccc3cfa5c88f2ff2e6dd5927c7f9d23bd09

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Citations in the corpus

THREE POSSIBLE ORIGINS FOR THE GAS LAYER ON GJ 1214b (2009, methodology): “At the high pressures found in the solid interior layers, thermal corrections have only a small effect on the mass-density (Seager et al. 2007).”
ON THE LOW FALSE POSITIVE PROBABILITIES OF KEPLER PLANET CANDIDATES (2011, background): “…star. might involve adopting a planet mass distribution according to RV surveys and theoretical mass-radius relations (e.g. Fortney et al. (2007); Seager et al. (2007)), the number of assumptions required for these models and 8 the fact that they do not generally include significant atmospheres…”
Exoplanet Atmospheres: Physical Processes (2010, background): “…to atmospheres, so we show in Figure 7 a generic summary of types of exoplanets via their bulk composition as a function of rock, ice, or gas components (Chambers 2010, Rogers & Seager 2009; see Seager et al. 2007 for a description of mass-radius relations for planet interior compositions).”
A REVISED ESTIMATE OF THE OCCURRENCE RATE OF TERRESTRIAL PLANETS IN THE HABITABLE ZONES AROUND KEPLER M-DWARFS (2013, background): “Planets with radius > 1.4 R⊕ are thought to have either homogeneous composition of water ice, silicate or iron or some differential composition of these compounds (Seager et al. 2007; Rogers et al. 2011; Lopez et al. 2012).”
THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS (2016, methodology): “Regarding additional physics included in the evolutionary model, the radius of the solid core is calculated taking into account its composition (ice mass fraction) and the compression by the surrounding gas using the modified polytropic equation of state of Seager et al. (2007).”
A SUPER-EARTH TRANSITING A NAKED-EYE STAR (2011, background): “To provide a broad view, the left panel of Figure 3 shows the masses and radii of the transiting exoplanets, along with theoretical curves taken from Seager et al. (2007) for “mathematicians’ planets” composed of pure hydrogen, water, rock (MgSiO3 perovskite) and iron.”
HUBBLE SPACE TELESCOPE NEAR-IR TRANSMISSION SPECTROSCOPY OF THE SUPER-EARTH HD 97658B (2014, background): “…sample it is possible to match their measured densities with a broad range of compositions, including both waterrich and water-poor scenarios, simply by varying the amount of hydrogen in their atmospheres (Seager et al. 2007; Valencia et al. 2007, 2013; Rogers & Seager 2010a; Zeng & Sasselov 2013).”
The coronal X-ray - age relation and its implications for the evaporation of exoplanets (2011, methodology): “However models of the interiors of super-Earths (e.g. Seager et al. 2007; Sotin etal.”
MOST 1.6 EARTH-RADIUS PLANETS ARE NOT ROCKY (2014, methodology): “We nominally use the mass-radius relations from Seager et al. (2007) for MgSiO3 perovskite, and phase Fe to define Mrock,min (Rp) and Mrock,max (Rp).”
A POSSIBLE CARBON-RICH INTERIOR IN SUPER-EARTH 55 Cancri e (2012, methodology): “Our model solves the three canonical equations of internal structure for solid planets, namely, (a) mass conservation, (b) hydrostatic equilibrium, and (c) the equation of state (e.g. Fortney et al. 2007; Seager et al. 2007; Sotin et al. 2007; Valencia et al. 2007; Rogers & Seager 2010).”
TESTING IN SITU ASSEMBLY WITH THE KEPLER PLANET CANDIDATE SAMPLE (2013, methodology): “Therefore, we base our mass–radius relation on that of Seager et al. (2007), based on the Perovskite equation of state, to characterize our planetary radii.”
Compositional Imprints in Density–Distance–Time: A Rocky Composition for Close-in Low-mass Exoplanets from the Location of the Valley of Evaporation (2017, methodology): “…other than MgSiO3, 2 These planets can potentially still have (secondary) atmospheres, but not thick primordial H/He envelopes that have the strongest impact on the radius because of the low molecular weight. but these are in comparison of minor importance (Seager et al. 2007, hereafter SKHM07).”
Mantle dynamics in super-Earths: Post-perovskite rheology and self-regulation of viscosity (2012, positive): “(Seager et al., 2007; Sotin et al., 2007; Valencia et al., 2006, 2007b, 2007c).”
HYDROGEN GREENHOUSE PLANETS BEYOND THE HABITABLE ZONE (2011, methodology): “We present results for a 3M⊕ rocky planet with surface gravity g = 17 m s−2 (Seager et al. 2007).”
HAT-P-11b: A SUPER-NEPTUNE PLANET TRANSITING A BRIGHT K STAR IN THE KEPLER FIELD (2009, methodology): “…been granted by NOAO (A285Hr) and NASA (N128Hr). these planets, as has been done by several teams trying to formulate and match theories to the observed bulk properties of known TEPs (e.g. Baraffe et al. 2008; Fortney et al. 2007; Burrows et al. 2007; Seager et al. 2007, and references therein).”