Analytic Modeling of Tidally Locked Rocky Planet Atmospheres Across Dynamical Regimes

TL;DR

The paper addresses interpreting JWST phase curves for tidally locked rocky planets by relaxing the Weak Temperature Gradient (WTG) assumption and introducing a first-principles four-box framework for day-night heat transport. It formulates hemispheric energy balances and a thermodynamic closure to derive four region temperatures, with heat transport tied to the sound speed via $U \approx \alpha c_s$ and infrared opacity through $\tau = 2 κ p/g$, solved as a nondimensional system. The approach reveals that nightside temperatures can vary by hundreds of kelvin across dynamical regimes and that degeneracies between dayside temperature and surface pressure can bias atmospheric inferences by order-of-magnitude, while remaining fast, interpretable, and consistent with GCM results. Overall, the method provides a practical starting point for rapid interpretation of JWST observations and for exploring a broad dynamical phase space without resorting to computationally intensive simulations.

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-1b, GJ 367b, and TOI-2445b. 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 the atmospheric circulation. Considering the applicable range of atmospheric dynamical regimes, we find that a given planet's nightside temperature can plausibly vary by 100s 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.

Figures (2)

• Figure 1: Estimated values of the WTG parameter $\Lambda$ for planets $r<2R_\oplus$ observed with JWST. $\Lambda\ll1$ implies non-WTG behavior and non-negligible temperature gradients, while $\Lambda\gg1$ implies WTG behavior is likely dominant. The points correspond to an N$_2$ mean molecular weight, while the upper error bars correspond to H$_2$O and the lower to SiO$_2$. Points further from $\Lambda=1$ (or particularly well-known bodies) are labeled with the planet name. The colorbar represents the planet's equilibrium temperature, with zero albedo assumed. Blue starred points are Solar System bodies for comparison.
• Figure 2: Schematic diagram of the dominant mechanisms of heat transport on a tidally locked terrestrial planet in this model: stellar radiation, atmospheric bulk fluid transport, surface heating, and re-radiation.