Interior structure models of GJ436b

Abstract

Context. GJ436b is the first extrasolar planet discovered that resembles Neptune in mass and radius. Two more are known (HAT-P-11b and Kepler-4b), and many more are expected to be found in the upcoming years. The particularly interesting property of Neptune-sized planets is that their mass M p and radius R p are close to theoretical M − R relations of water planets. Given M p , R p , and equilibrium temperature, however, various internal compositions are possible. Aims. A broad set of interior structure models is presented here that illustrates the dependence of internal composition and possible phases of water occurring in presumably water-rich planets, such as GJ 436b on the uncertainty in atmospheric temperature profile and mean density. We show how the set of solutions can be narrowed down if theoretical constraints from formation and model atmospheres are applied or potentially observational constraints for the atmospheric metallicity Z 1 and the tidal Love number k 2 . Methods. We model the interior by assuming either three layers (hydrogen-helium envelope, water layer, rock core) or two layers (H/He/H 2 O envelope, rocky core). For water, we use the equation of state H 2 O-REOS based on finite temperature -density functional theory -molecular dynamics (FT-DFT-MD) simulations. Results. Some admixture of H/He appears mandatory for explaining the measured radius. For the warmest considered models, the H/He mass fraction can reduce to 10 −3 , still extending over ∼0.7 R ⊕ . If water occurs, it will be essentially in the plasma phase or in the superionic phase, but not in an ice phase. Metal-free envelope models have 0.02 < k 2 < 0.2, and the core mass cannot be determined from a measurement of k 2 . In contrast, models with 0.3 < k 2 < 0.82 require high metallicities Z 1 < 0.89 in the outer envelope. The uncertainty in core mass decreases to 0.4M p , if k 2 ≥ 0.3, and further to 0.2M p , if k 2 ≥ 0.5, and core mass and Z 1 become sensitive functions of k 2 . Conclusions. To further narrow the set of solutions, a proper treatment of the atmosphere and the evolution is necessary. We encourage efforts to observationally determine the atmospheric metallicity and the Love number k 2 .

ATMOSPHERIC CIRCULATION OF ECCENTRIC HOT NEPTUNE GJ436b

“…Since the discovery of its transit and subsequent secondary eclipse, GJ436b has become a popular target for Hubble (Bean et al 2008;Pont et al 2009) and Spitzer (Gillon et al 2007a;Deming et al 2007;Demory et al 2007;Stevenson et al 2010) observations as well as modeling efforts (Spiegel et al 2010;Madhusudhan & Seager 2010). Given GJ436b's mass (M p = 0.0729M J ) and radius (R p = 0.3767R J ), its interior must contain significant quantities of heavy elements in addition to hydrogen and helium (Adams et al 2008;Figueira et al 2009;Rogers & Seager 2010;Nettelmann et al 2010). This raises the possibility that, like Uranus and Neptune, whose atmospheric C/H ratios lie between 20 and 60 times solar (Gautier et al 1995), the atmosphere of GJ436b is highly enriched in heavy elements.…”

Constraining planetary interiors with the Love number k2

“…However, k 2 is not a unique function of the planet's core mass. For three-layer models we find a degeneracy with respect to the density discontinuity in the envelope (Kramm et al 2010).…”

“…Further constraints could be made if there was more precise knowledge about the envelope's temperature profile and/or metallicity. We also performed calculations for the Love numbers of GJ 436b (Nettelmann et al 2010a, Kramm et al 2010, GJ 1214b (Nettelmann et al 2010b) and Saturn (Kramm et al 2010).…”

Constraining the volatile fraction of planets from transit observations

“…It is therefore more logical, from an observational point of view, to compare the evolution of two planets with the same mass and radius at a given epoch (5 Gyr in what follows). In this case, the two planets (volatile-poor and volatile-rich planet) cannot have the same gas fraction, and the difference in the evolution will be the result of both the change in volatile fraction (as demonstrated in the previous section) and of the change in gas fraction (as has been demonstrated in many papers, e.g., Nettelmann et al 2010;Valencia et al 2013;Lopez et al 2013, for planets in the mass range we consider here).…”

“…The effect of the gas fraction on the radius evolution of low-mass planets has been discussed elsewhere (see, e.g., Nettelmann et al 2010;Valencia et al 2013;Lopez et al 2013 among others). We focus in this section on the differential evolution of the two planets with the same gas fraction, but different volatile fraction.…”