Planetary Climate Dynamics

Abstract:

Following seminal studies such as Muñoz’s 2007 work on HD 209458b, which simulated heavy element escape beyond the Roche lobe, one-dimensional hydrocodes have flourished, routinely solving the Euler equations to model transonic outflows across an increasingly diverse population of exoplanets. However, the modelling frontier of escape is often shaped by the hand-off from continuum to rarefied flow (Kn ≳ 0.1) and non-equilibrium processes. Molecular-kinetic techniques, long the workhorse of Solar-System aeronomy, naturally bridge this gap, providing a self-consistent description of collisional, transitional and free-molecular regimes in a single framework. Here we make the case for a concerted push toward large-scale molecular-kinetic simulations of exoplanet outflows, highlighting two end-member scenarios along the escape spectrum where forthcoming observations may allow the theory to be tested and refined.Cosmic Shoreline. Characterising the transition from Jeans (particle-by-particle) escape to subsonic and ultimately transonic bulk outflow remains an open problem in escape theory. The onset of rapid escape (~1 bar Myr⁻¹) as ionising irradiation increases is a key parameter defining the phase boundary between airless and airy rocky worlds—the “Cosmic Shoreline” (Zahnle & Catling 2017; Ji et al. 2025). Johnson et al. (2013) combined an analytic treatment with Direct Simulation Monte Carlo (DSMC; Bird 1994) to derive a critical heating rate for triggering transonic flow, working with the ansatz that the scaling of this transition extends smoothly from Pluto- to Earth-sized bodies. We will present new DSMC simulations that probe this transition for high-molecular-weight atmospheres on Earth-mass and super-Earth planets, refining the dynamics of rapid escape across this regime.Helium triplet and fractionation. Fractionation may help explain some of the non-detections of the neutral-helium triplet (1083 nm) in giant-planet outflows (Schulik & Owen 2024). Multi-fluid hydrodynamics simulations have found that the neutral helium can actually be accelerated by gravity to accrete out of the flow at a downward velocity of ~1 km s⁻¹ (Xing et al. 2023; Schulik & Owen 2024). We note that the ratio of the slip velocity to the thermal speed of the outflow scales with the Knudsen number for collisionality, ΔU/ Vth~ KnHe . Thus, we will discuss how a significant slip velocity may require Kn ≳ 0.1, a regime in which the fractionation process may be better described with molecular-kinetics, possibly with implications for predictions of the transit depth of the helium triplet.Moreover, the Direct Simulation Monte Carlo (DSMC) method offers some desirable properties over hydrocodes: it scales naturally to fully three-dimensional geometries, albeit at significant computational cost, and naturally treats non-equilibrium phenomena such as photoelectron heating and excited-state populations.

Abstract:

Larger-than-Earth exoplanets are sculpted by strong stellar irradiation, but it is unknown whence they originate. Two propositions are that they formed with rocky interiors and hydrogen-rich envelopes (‘gas-dwarfs’), or with bulk compositions rich in water-ices (‘water-worlds’) . Multiple observations of super-Earth L 98-59 d have revealed its low bulk-density, consistent with substantial volatile content alongside a rocky/metallic interior, and recent JWST spectroscopy evidences a high mean molecular weight atmosphere. Its density and composition make it a waymarker for disentangling the processes which separate super-Earths and sub-Neptunes across geological timescales. We simulate the possible pathways for L 98-59 d from birth up to the present day using a comprehensive evolutionary modelling framework. Emerging from our calculations is a novel self-limiting mechanism between radiative cooling, tidal heating, and mantle rheology, which we term the 'radiation-tide-rheology feedback'. Coupled numerical modelling yields self-limiting tidal heating estimates that are up to two orders of magnitude lower than previous calculations, and yet are still large enough to enable the extension of primordial magma oceans to Gyr timescales. Our analysis indicates that the planet formed with a large amount (>1.8 mass%) of sulfur and hydrogen, and a chemically-reducing mantle; inconsistent with both the canonical gas-dwarf and water-world scenarios. A thick atmosphere and tidal heating sustain a permanent deep magma ocean, allowing the dissolution and retention of volatiles within its mantle. Transmission features can be explained by in-situ photochemical production of SO2 in a high-molecular weight H2-H2S background. These results subvert the emerging gas-dwarf vs. water-world dichotomy of small planet categorisation, inviting a more nuanced classification framework. We show that interactions between planetary interiors and atmospheres shape their observable characteristics over billions of years.

Abstract:

The “cosmic shoreline”, a semi-empirical relation that separates airless worlds from worlds with atmospheres as proposed by Zahnle & Catling (2017), is now guiding large-scale JWST surveys aimed at detecting rocky exoplanet atmospheres. We expand upon this framework by revisiting the shorelines using existing hydrodynamic escape models applied to Earth-like, Venus-like, and steam atmospheres for rocky exoplanets, and we estimate energy-limited escape rates for CH4 atmospheres. We determine the critical instellation required for atmospheric retention by calculating time-integrated atmospheric mass loss. Our analysis introduces a new metric for target selection in the Rocky Worlds DDT and refines expectations for rocky planet atmosphere searches in Cycle 4. Exploring initial volatile inventory ranging from 0.01% to 1% of planetary mass, we find that its variation prevents the definition of a unique clear-cut shoreline, though non-linear escape physics can reduce this sensitivity to initial conditions. Additionally, uncertain distributions of high-energy stellar evolution and planet age further blur the critical instellations for atmospheric retention, yielding broad shorelines. Hydrodynamic escape models find atmospheric retention is markedly more favorable for higher-mass planets orbiting higher-mass stars, with carbon-rich atmospheres remaining plausible for 55 Cancri e despite its extreme instellation. Dedicated modelling efforts are needed to better constrain the escape dynamics of secondary atmospheres, such as the role of atomic line cooling, especially for Earth-sized planets. Finally, we illustrate how density measurements can be used to statistically test the existence of the cosmic shorelines, emphasizing the need for more precise mass and radius measurements.

Abstract:

The atmospheric circulation of Jupiter is shaped by a complex interplay between deep internal processes and cloud-level dynamics. Numerical simulations and observational analyses have suggested that Jupiter’s mid-latitude jets are strongly influenced by baroclinic instability [1], which is governed by the planet’s atmospheric thermal structure. Jupiter emits a substantial intrinsic heat flux originating from its interior. Past modelling efforts [2, 3] have demonstrated that this internal energy plays a key role in shaping large-scale atmospheric dynamics.Our previous work [4] showed that latitudinal variations in interior heat flux can significantly impact the structure and behaviour of Jupiter’s mid-latitude jets in a General Circulation Model (GCM).  Such an impact is best illustrated by the relative vorticity snapshots from two simulations with the lowest and highest latitudinal flux gradient (see Figure 1). In this study, we present a more detailed analysis linking these jet modifications to changes in the atmospheric thermal structure and, consequently, to the strength and distribution of baroclinic eddy activity. In particular, we use the Lorenz energy cycle framework to diagnose how variations in deep thermal forcing influence baroclinic energy conversion and eddy-mean flow interactions. We further examine the implications for meridional transport and the water cycle within Jupiter’s weather layer.Additionally, we present a control simulation in which the potential temperature at the model’s lower boundary is forced toward a fixed value (a deep adiabat setup). We compute the equivalent upward heat flux associated with this forcing to place it in the context of previous models that impose constant or latitudinally varying interior heat flux. This allows a direct comparison of how different representations of deep thermal forcing affect upper-atmospheric dynamics.Finally, we discuss the broader implications of these findings for future weather-layer models of Jupiter and other gas giant planets, especially on the effect of bottom boundary conditions in representing the coupling between deep and observable atmospheric dynamics. Figure 1: Mollweide projection of the relative vorticity at 1 bar at the end of two simulations.Reference:[1] Read, P. L. (2023). The dynamics of Jupiter’s and Saturn’s weather layers: a synthesis after Cassini and Juno. Annual Review of Fluid Mechanics, 56(1), 271–293. https://doi.org/10.1146/annurev-fluid-121021-040058[2] Liu, J., & Schneider, T. (2011). Convective Generation of Equatorial Superrotation in Planetary Atmospheres. Journal of the Atmospheric Sciences, 68(11), 2742-2756. https://doi.org/10.1175/JAS-D-10-05013.1[3] Young, R. M. B., Read, P. L., & Wang, Y. (2018). Simulating Jupiter’s weather layer. Part I: Jet spin-up in a dry atmosphere. Icarus, 326, 225–252. https://doi.org/10.1016/j.icarus.2018.12.005[‌4] Hu, X. and Read, P.: Latitudinal Variation in Internal Heat Flux in Jupiter's Atmosphere: Effect on Weather Layer Dynamics, Europlanet Science Congress 2024, EPSC2024-669, https://doi.org/10.5194/epsc2024-669, 2024.

Abstract:

This talk will cover the state of the art in whole-planet subNeptune modelling, and needs for the future.  Inferences about the composition of the deep envelope can be made on the basis of the way chemical transformations in the deep envelope may be evidenced in the observable atmosphere, such as has been attempted, for example, regarding the presence or absence of NH3 in the observable atmospheres of subNeptunes.  Such inferences require an understanding not only of deep envelope chemistry, but also of vertical mixing processes. The mixing process engages a number of poorly understood phenomena, such as mixing rates through stably stratified (nonconvective) internal radiative layers.  The occurrence of such radiative layers can be induced by compositional suppression of convection (e.g. due to high molecular weight H2O in an H2-rich atmosphere). We will review our modelling studies regarding this phenomenon.  Typically, the envelope-silicate interface is hot enough that the interface takes the form of a magma ocean, so compositional interchange with the magma ocean becomes crucial. This exchange includes rock vapours as well as lower molecular weight volatiles.  Our work on magma ocean exchanges will be reviewed. We highlight the importance of mineral physics experiments and molecular dynamics to provide crucially needed (and largely absent) thermodynamic parameters, particularly at high pressure.  At sufficiently high temperatures, silicate itself can become supercritical so that the distinction between silicate melt and silicate vapour disappears and the silicate substance becomes completely miscible with the lower molecular weight envelope.  Modeling and experiment regarding this novel and largely unexplored regime is particularly needed.