A new convection scheme for GCMs of temperate sub-Neptunes

Atmospheric characterisation of temperate sub-Neptunes is the new frontier of exoplanetary science with recent JWST observations of possible Hycean world K2-18b. Accurate modelling of atmospheric processes is essential to interpreting high-precision spectroscopic data given the wide range of possible conditions in the sub-Neptune regime, including on potentially habitable planets. Notably, convection is an important process which can operate in different modes across sub-Neptune conditions. Convection can act very differently in atmospheres with a high condensible mass fraction (non-dilute atmospheres) or with a lighter background gas, e.g. water convection in a H$_2$-rich atmosphere, and can be much weaker or even shut down entirely in the latter case. We present a new mass-flux scheme which can capture these variations and simulate convection over a wide range of parameter space for use in 3D general circulation models (GCMs). We validate our scheme for two representative cases, a terrestrial-like atmosphere and a mini-Neptune atmosphere. In the terrestrial case, considering TRAPPIST-1e with an Earth-like atmosphere, the model performs near-identically to Earth-tuned models in an Earth-like convection case. In the mini-Neptune case, considering the bulk properties of K2-18b and assuming a deep H$_2$-rich atmosphere, we demonstrate the capability of the scheme to reproduce non-condensing convection. We find convection occurring at pressures greater than 0.3 bar and the dynamical structure shows high-latitude prograde jets. Our convection scheme will aid in the 3D climate modelling of a wide range of exoplanet atmospheres, and enable further exploration of temperate sub-Neptune atmospheres.