Exploring TRAPPIST-1 Climate States with an Energy Balance Model

This paper presents a version of the HEXTOR energy balance model that has been configured for the study of habitable terrestrial planets orbiting low-mass stars. The model is validated for rapidly-rotating Earth-like planets using latitudinal coordinates, which shows expected patterns of bistability. A tidally-locked coordinate transformation is then applied to the model, which is calibrated to match mean values of the minimum, average, and maximum surface temperatures from a general circulation model ensemble of TRAPPIST-1 e. This calibrated energy balance model is used to characterize the possible climate states of such a synchronously rotating planet across a parameter space of instellation and carbon dioxide partial pressure. These calculations suggest a state of partial ice cover for TRAPPIST-1 e and complete ice cover for TRAPPIST-1 f. TRAPPIST-1 e becomes fully ice-free only above ~0.4 bar CO\({\mathstrut}_2\), while TRAPPIST-1 f remains ice-covered unless CO\({\mathstrut}_2\) partial pressure approaches ~1.2 bar. This approach demonstrates the capability of a simplified one-dimensional model to study the climates of terrestrial planets in synchronous rotation, which can help guide more complex models and observations toward the most promising targets of interest.