Squeeze the atmosphere into magma: sub-Neptune mass-radius relation
revised by atmosphere-magma interactions
Abstract
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 Mg2SiO4 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.