Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits

By Jon Fortney, M. Marley, Jason W. Barnes. 2006

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To aid in the physical interpretation of planetary radii constrained through observations of transiting planets, or eventually direct detections, we compute model radii of pure hydrogen-helium, water, rock, and iron planets, along with various mixtures. Masses ranging from 0.01 Earth masses to 10 Jupiter masses at orbital distances of 0.02-10 AU are considered. For hydrogen-helium rich planets, our models are the first to couple planetary evolution to stellar irradiation over a wide range of orbital separations (0.02-10 AU) through a nongray radiative-convective equilibrium atmosphere model. Stellar irradiation retards the contraction of giant planets, but its effect is not a simple function of the irradiation level: a planet at 1 AU contracts as slowly as a planet at 0.1 AU. We confirm the assertion of Guillot that very old giant planets under modest stellar irradiation (like that received by Jupiter and Saturn) develop isothermal atmospheric radiative zones once the planet's intrinsic flux drops to a small fraction of the incident flux. For hydrogen-helium planets, we consider cores up to 90% of the total planet mass, comparable to those of Uranus and Neptune. If "hot Neptunes" have maintained their original masses and are not remnants of more massive planets, radii of ~0.30-0.45 RJ are expected. Water planets are ~40%-50% larger than rocky planets, independent of mass. Finally, we provide tables of planetary radii at various ages and compositions, and for ice-rock-iron planets we fit our results to analytic functions, which will allow for quick composition estimates, given masses and radii, or mass estimates, given only planetary radii. These results will assist in the interpretation of observations for both the current transiting planet surveys as well as upcoming space missions, including COROT and Kepler.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ece6da370ea7406deecbd1ff90a9739e5e29ffa2

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Citations in the corpus

Characterization of exoplanets from their formation - II. The planetary mass-radius relationship (2012, methodology): “For most of the domain of fice, R increases about linearly with the ice fraction, which is in agreement with the results of Fortney et al. (2007).”
EXOPLANET ALBEDO SPECTRA AND COLORS AS A FUNCTION OF PLANET PHASE, SEPARATION, AND METALLICITY (2010, methodology): “D iterative radiative-convective atmo- sphere model previously used in Marley (1997); Burrows et al. (1997); Marley et al. (1999a, 2002); Fortney et al. (2005, 2006, 2007); Fortney & Marley (2007) and Fortney et al. (2008a,b).”
FORMATION AND STRUCTURE OF LOW-DENSITY EXO-NEPTUNES (2011, background): “3R⊕ can be estimated from the mass-radius relationship for rocky (Earth-like composition) planets (e.g., Valencia et al. 2006; Seager et al. 2007; Fortney et al. 2007; Marcus et al. 2010).”
HOW THERMAL EVOLUTION AND MASS-LOSS SCULPT POPULATIONS OF SUPER-EARTHS AND SUB-NEPTUNES: APPLICATION TO THE KEPLER-11 SYSTEM AND BEYOND (2012, methodology): “Here we do expand on that grid to now include a range of incident fluxes, as was done for giant planets in Fortney et al. (2007).”
KEPLER'S FIRST ROCKY PLANET: KEPLER-10b (2011, background): “These finer distinctions will only be possible with measurements of planetary properties better than 5% in radius and 10% in mass (Valencia et al. 2006, 2007; Fortney et al. 2007; Seager et al. 2007; Grasset et al. 2009).”
THE HEAVY-ELEMENT MASSES OF EXTRASOLAR GIANT PLANETS, REVEALED (2011, methodology): “Briefly, planets are composed of up to three components: 1) an inert core, 2) an adiabatic convective envelope (where heavy elements may be mixed in), and 3) a solar-metallicity non-grey atmosphere model (Fortney et al. 2007) that includes the atmospheric extension to the transit radius.”
HAT-P-16b: A 4 MJ PLANET TRANSITING A BRIGHT STAR ON AN ECCENTRIC ORBIT, (2010, methodology): “We have compared HAT-P-16b to the theoretical models from Fortney et al. (2007) by interpolating the models to the solar-equivalent semi–major axis of aequiv = 0.0294±0.0014 AU, the result of which can be seen overplotted in Figure 5.”
THE MASS–METALLICITY RELATION FOR GIANT PLANETS (2015, methodology): “Because planets do most of their cooling, and therefore contraction, early in their lives (see Fortney et al. 2007for a discussion), large uncertainties in age are not a major obstacle in modeling older planets.”
THREE POSSIBLE ORIGINS FOR THE GAS LAYER ON GJ 1214b (2009, methodology): “This is the common general approach for modeling planet interiors (e.g. Valencia et al. 2006; Fortney et al. 2007; Adams et al. 2008; Zeng & Seager 2008; Baraffe et al. 2008; Figueira et al. 2009; Grasset et al. 2009).”
ORBITAL PHASE VARIATIONS OF THE ECCENTRIC GIANT PLANET HAT-P-2b (2013, background): “Planetary radii of 1.13 to 1.22 RJ for 8 MJ planets are expected for 1-10 Gyr ages (Fortney et al. 2007).”
WASP-121 b: a hot Jupiter close to tidal disruption transiting an active F star (2015, methodology): “We note that Rmean should be used when comparing the radius of the planet with theoretical models (e.g. Fortney et al. 2007), while Rcross should rather be employed when interpreting transmission or occultation data.”
KEPLER PLANETS: A TALE OF EVAPORATION (2013, methodology): “Previously, Lopez et al. (2012) have addressed this problem by coupling the Fortney et al. (2007b) and Nettelmann et al. (2011) planetary structure models to a simplistic energylimited estimate for the mass-loss.”
PROBABILISTIC FORECASTING OF THE MASSES AND RADII OF OTHER WORLDS (2016, background): “The suite of models produced by Fortney et al. (2007) for H-/He-rich giant planets, for various insolations and metallicities, peaks at masses between ∼2.5MJ to ∼5.2MJ.”
A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses (2013, methodology): “The models, and their use of approximations and EOS, have evolved since 2005 (Valencia et al. 2006; Fortney et al. 2007; Grasset et al. 2009; Seager et al. 2007), mainly because the more massive solid exoplanets (called Super-Earths) have interior pressures that are far in excess of Earth’s model,…”
Mass-Radius Relationships for Solid Exoplanets (2007, background): “In the past Stevenson (1982) and more recently Fortney et al. (2007) and Sotin et al. (2007) have also investigated mass-radius relationships of rocky and icy exoplanets.”