Analytic Modeling of Tidally Locked Rocky Planet Atmospheres across Dynamical Regimes

Abstract We present a new first-principles analytic approach to interpreting eclipses and phase curves of rocky planets. Observations with JWST have reported nondetections of atmospheres around the majority of hot rocky planets orbiting M dwarfs. However, most of these “bare rock” inferences are based on models that are ill-suited to many currently observable planets, as they were developed for use on cooler, slower-rotating bodies. In particular, these models rely on the weak temperature gradient assumption, in which rotation is neglected and temperature gradients can be simply related to wind speeds. We find that this assumption may not be valid for over 40% of terrestrials observed with JWST, including TRAPPIST-1 b, GJ 367 b, and TOI-2445 b. Our simple new four-box model does not rely on this assumption, and instead allows the heat transport efficiency to be specified or follow scalings derived herein. This method is fast, interpretable, physically motivated, reproduces previous general circulation model results, and can be used as a starting point for more detailed modeling. We observe that the longitudinal temperature structure of tidally locked terrestrials depends strongly on atmospheric circulation. Considering the applicable range of atmospheric dynamical regimes, we find that a given planet’s nightside temperature can plausibly vary by hundreds of kelvin (from detectable to undetectable). Furthermore, a planet’s dayside energy balance can display complex behavior, with degeneracies between surface pressure and dayside temperature. Illustrating an application to observations, we find that assumptions about atmospheric dynamics and longitudinal temperature structure can bias atmospheric constraints at the order-of-magnitude level.