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Richard Chatterjee

Graduate student

Research theme

  • Climate physics
  • Exoplanets and planetary physics

Sub department

  • Atmospheric, Oceanic and Planetary Physics

Research groups

  • Planetary Climate Dynamics
richard.chatterjee@physics.ox.ac.uk
Atmospheric Physics Clarendon Laboratory, room 206
ORCID iD
Google Scholar
  • About
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  • Publications

Novel Physics of Escaping Secondary Atmospheres May Shape the Cosmic Shoreline

arXiv:2412.05188 [astro-ph.EP]

Authors:

Richard D. Chatterjee, Raymond T. Pierrehumbert

Abstract:

Recent James Webb Space Telescope observations of cool, rocky exoplanets reveal a probable lack of thick atmospheres, suggesting prevalent escape of the secondary atmospheres formed after losing primordial hydrogen. Yet, simulations indicate that hydrodynamic escape of secondary atmospheres, composed of nitrogen and carbon dioxide, requires intense fluxes of ionizing radiation (XUV) to overcome the effects of high molecular weight and efficient line cooling. This transonic outflow of hot, ionized metals (not hydrogen) presents a novel astrophysical regime ripe for exploration. We introduce an analytic framework to determine which planets retain or lose their atmospheres, positioning them on either side of the cosmic shoreline. We model the radial structure of escaping atmospheres as polytropic expansions - power-law relationships between density and temperature driven by local XUV heating. Our approach diagnoses line cooling with a three-level atom model and incorporates how ion-electron interactions reduce mean molecular weight. Crucially, hydrodynamic escape onsets for a threshold XUV flux dependent upon the atmosphere's gravitational binding. Ensuing escape rates either scale linearly with XUV flux when weakly ionized (energy-limited) or are controlled by a collisional-radiative thermostat when strongly ionized. Thus, airlessness is determined by whether the XUV flux surpasses the critical threshold during the star's active periods, accounting for expendable primordial hydrogen and revival by volcanism. We explore atmospheric escape from Young-Sun Mars and Earth, LHS-1140 b and c, and TRAPPIST-1 b. Our modeling characterizes the bottleneck of atmospheric loss on the occurrence of observable Earth-like habitats and offers analytic tools for future studies.
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The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape

arXiv:2504.19872 [astro-ph.EP]

Authors:

Xuan Ji, Richard D. Chatterjee, Brandon Park Coy, Edwin S. Kite

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 modeling 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.
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Photochemistry versus Escape in the Trappist-1 planets.

(2025)

Authors:

Sarah Blumenthal, Richard Chatterjee, Harrison Nicholls, Louis Amard, Shang-Min Tsai, Tad Komacek, Raymond Pierrehumbert

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. 
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Refining Exoplanet Escape Predictions with Molecular-Kinetic Simulations

(2025)

Authors:

Richard Chatterjee, Shane Carberry Mogan, Robert Johnson

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.
More details from the publisher

The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape

(2025)

Authors:

Xuan Ji, Richard Chatterjee, Brandon Park Coy, Edwin Kite

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.
More details from the publisher

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