Richard Chatterjee

Abstract:

Rocky exoplanets accessible to characterization often lie on close-in orbits where tidal heating within their interiors is significant, with the L 98-59 planetary system being a prime example. As a long-term energy source for ongoing mantle melting and outgassing, tidal heating has been considered as a way to replenish lost atmospheres on rocky planets around active M-dwarfs. We simulate the early evolution of L 98-59 b, c, and d using a time-evolved interior-atmosphere modelling framework, with a self-consistent implementation of tidal heating and redox-controlled outgassing. 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’. Our coupled 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 time-scales. Comparisons with a semi-analytic model demonstrate that this negative feedback is a robust mechanism which can probe a given planet’s initial conditions, atmospheric composition, and interior structure. The orbit and instellation of the sub-Venus L 98-59 b likely place it in a regime where tidal heating has kept the planet molten up to the present day, even if it were to have lost its atmosphere. For c and d, a long-lived magma ocean can be induced by tides only with additional atmospheric regulation of energy transport.

Abstract:

Survive or not survive, that is the question of the 500-hour JWST Rocky Worlds DDT Program. Whether a terrestrial planets’ atmosphere can suffer under the intense XUV of its host, or if it completely escapes, these are the questions we explore. Zahnle & Catling (2017) defined the Cosmic Shoreline, but recent observations from JWST reveal airless worlds around M-stars, calling for a refinement of this “receding” shoreline (Pass et al. 2025). M-stars spend a longer time in pre-main sequence, subjecting their orbiting worlds to some higher intensity XUV activity. This complicates our present understanding of this shoreline. Investigating chemical effects of planet-star interactions could be the key to a more complete picture of this shoreline.  We investigate the interplay between photochemistry, mixing, and escape of carbon dioxide atmospheres under intense and mild XUV fluxes as follow on work to both Johnstone et al. (2018) and Nakayama et al. (2022). We expand on this work by adopting thermal structure models from Nakayama et al. (2022) and apply them to identify key chemical pathways for escape. We create a reduced C-O chemical network including neutral and ionic species to identify these pathways. As photochemistry simulations take into account many reactions, these 1D calculations are too computationally expensive to be done in 3D. Although rudimentary at best, the mixing parameter– eddy diffusion term, K_zz, comprises the dynamical element of 1D photochemical simulations. Here, we consider the mixing of photochemical products in competition with escape to explore the chemical pathways of retention and loss. We compare the photochemical model results for active and inactive cases for the Trappist-1 system planets. Then, using the resulting composition-dependent heating and cooling rates for Trappist-1 planets, we assess their propensity for efficient atomic line cooling versus escape. We follow the work of Chatterjee & Pierrehumbert (2024) in this assessment.  Finally, using our pathway analysis, we find an analytical formula for calculating an energy-limited escape boundary for these planets based on composition.  It is important here to note the limitations of 1D work. First, there exists an exchange of rigor between modelling chemistry and dynamics. Insights from this work are ripe for implementation into 3D GCMs, especially in response to incorporating UV-driven processes for thermospheric modelling mentioned in Ding and Wordsworth (2019). Second, interaction with the interior is important in the early phase of planetary formation, i.e., the magma ocean phase. Due to exchange between atmosphere and magma early in the planet’s formation, incorporation with an interior-atmosphere model would better constrain higher pressure chemical abundances. Although this work focuses on the upper atmosphere, extrapolation to the surface environment is a key goal for understanding a planet.  Considering planet-star interaction is imperative for the selection of targets for observation. However, it is also important when considering anomalous detections of atmospheres around planets predicted to not have an atmosphere. This could be a first step in determining an atmosphere as non-primary and/or distinguishing between an airless planet and one with high altitude haze.

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.