Refining Exoplanet Escape Predictions with Molecular-Kinetic Simulations

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/ V_th~ Kn_He . 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.