Squeeze the atmosphere into magma: sub-Neptune mass-radius relation revised by atmosphere-magma interactions

The Kepler mission revealed that sub-Neptunes are about as common as stars, which defied our pre-existing notion of planet demographics. The prevailing view for sub-Neptunes was that they are mostly core by mass and atmosphere by volume (Lopez & Fortney, 2014). However, current formation models do not consider dissolution at the atmosphere-core interface. The temperature and pressure at the magma-atmosphere interface can rise to >3000 K and ~5-30 GPa (Lee et al., 2014; Piso et al., 2015), high enough for dissolution of hydrogen gas into the magma (Chachan & Stevenson, 2018). The dissolution of atmosphere into the magma may explain the drop-off in exoplanet abundance at 3 times Earth radius (Kite et al., 2019), but the puff-up of the magma due to gas dissolution has not previously been included. We propose a simple model to calculate sub-Neptune mass-radius relation, including, for the first time, the puff-up effect. Key assumptions include: (1) nonlinear solubility of gas in magma is constrained by limited laboratory data (Hirschmann et al, 2012); (2) the Fe/core mass fraction is Earth-like, and He/gas mass fraction is Solar-like; (3) ideal mixing between the dissolved gas and magma; (4) the dissolved gas is well mixed within the magma-layer. The EoS used are an Mg 2 SiO 4 for the magma (Stewart et al., 2020); the H/He EoS (Chabrier et al., 2019); and a simple model for Fe (Seager et al., 2007). The model is integrated from the radiative-convective boundary and iterated until atmosphere-magma solubility equilibrium. We have varied the core mass, atmospheric mass and equilibrium temperature in the atmosphere. Our preliminary results are shown in Figures. The critical point for the puff-up of the core due to the dissolved gas corresponds to ~1% solubility at the magma-atmosphere boundary (Fig. 1). The puff-up effect can be important up to 0.3 Earth radius (Fig. 2), much larger than the radius error bars for a single planet in the CKS survey with Gaia DR2 data (Fulton & Petigura, 2018). In future, we will add additional constraints on gas/core mass fraction (Lee, 2019), forward-model the relationship between mass and photospheric radius, and generate predictions for exoplanet masses and radii that can be used to help interpret data from ESA’s PLATO and NASA’s TESS.

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