Beyond Plane-Parallel: Modelling the Atmospheres of Young Sub-Neptunes in the JWST Era

In the era of JWST, high-precision transmission spectra are now available for a growing number of sub-Neptunes, shedding light on the present-day atmospheric compositions of these planets. Many of these spectra have been flat, with a degeneracy between possible high mean molecular weight or cloudy atmospheres. There remain key questions surrounding the sub-Neptune regime, including the formation and evolution processes that sculpt the population. Observations of young sub-Neptunes are an important avenue for understanding such processes, with distinct diagnostics of water-rich versus water-poor formation scenarios. The larger scale heights of young sub-Neptunes yield larger signals in transmission spectroscopy than mature sub-Neptunes, providing confident detections and avoiding degeneracies from flat spectra. The recent observations of V1298 Tau b revealed strong detections of key molecules in its thick hydrogen-rich atmosphere, including CO₂, CO, H₂O, and CH₄, the latter at significantly lower abundance than predicted by equilibrium chemistry. High internal temperatures (T_int ~ 600 K) and strong vertical mixing were invoked to explain these findings. However, this extreme T_int is difficult to reconcile with predictions of planetary evolution models and the planet’s energy budget; the planet’s bulk measurements and constraints on atmospheric escape require a low internal temperature consistent with boil-off. This therefore points to a problem with the assumptions behind either atmospheric or interior models. A common simplifying assumption in radiative transfer modelling is the plane-parallel set-up, valid for atmospheric scale heights much less than the planetary radius – a condition that is violated for the highly extended atmospheres of young sub-Neptunes. This could have significant implications for interpreting the thermal structure and chemistry of their atmospheres and interiors. We explore the effect of relaxing this assumption on the inferred T_int and predicted methane abundances for young sub-Neptunes, demonstrated using V1298 Tau b. Using a radiative transfer model configured in both plane-parallel and spherical coordinates we compare the resulting atmospheric pressure-temperature profiles for equivalent internal luminosities. We proceed to consider the implications of using spherical coordinates on models of atmospheric chemistry, by modifying the photochemical code VULCAN, and self-consistently including our updated temperature structures. Due to geometric dilution, a spherical atmosphere has a higher temperature at deeper pressures for fixed internal temperature compared to a plane-parallel one, suppressing the methane. Young sub-Neptunes are crucial windows into the origins of the most abundant planetary population and closely linked to the origin of the radius valley. Our results demonstrate the importance of challenging modelling assumptions when interpreting observations of young and low-gravity exoplanets with JWST.