Impact of Subsurface Temperature Gradients on Emission Spectra of Airless Exoplanets: the Solid-state Greenhouse and Anti-Greenhouse

Abstract

An emerging goal of exoplanet science is to constrain the surface composition of airless exoplanets. Without the protection of an atmosphere, these planets are likely covered by a powder-like regolith, similar to the Moon. Laboratory studies show that, under vacuum conditions, such regoliths can develop subsurface temperature gradients, also known as the solid-state greenhouse effect. This effect can significantly modify the emission features of airless bodies, but its potential impact on exoplanets is still unexplored. Here we derive analytic solutions of the two-stream radiative transfer equations with scattering, absorption, plus emission, and combine them with Mie theory calculations to model subsurface temperature gradients and emission spectra of airless exoplanets. The results show exo-regoliths can develop strong solid-state greenhouse or anti-greenhouse effects, with temperature gradients $>200$~K in the upper-most subsurface ($\mathcal{O}(100)μ$m). These temperature gradients alter surface emission features, modify secondary eclipse depths by up to $\sim50\%$, and can produce higher-than-blackbody emission at some wavelengths. In addition, we study whether subsurface temperature gradients can be disentangled from other microscopic effects, such as changes in space weathering or particle size. At least in some cases, the co-existence of these effects makes it essentially impossible to distinguish different surface compositions within the precisions achievable by JWST. Overall, subsurface temperature gradients thus open potentially new ways to characterize surfaces of airless exoplanets, but they also complicate the interpretation of airless exoplanet spectra. In either case, their effect can be important and should be included in future modeling studies.