arxiv: 2605.04423 · v1 · submitted 2026-05-06 · 🌌 astro-ph.EP

Recognition: unknown

Modeling Volcanic Plume Heights Across Exoplanet Atmospheres: Insights from TRAPPIST-1

Prabal Saxena, Thomas Fauchez

Pith reviewed 2026-05-08 17:26 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords volcanic plumesexoplanet atmospheresTRAPPIST-11D modelingplume heighttidal heatingatmospheric detectionvolatile injection

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The pith

A 1D model adapted for exoplanets predicts that volcanic plumes frequently reach low-pressure levels suitable for detection in transmission observations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors adapt a classic one-dimensional volcanic plume model, originally for Venus and Mars, into a Python framework to study explosive eruptions across rocky exoplanet atmospheres. The model couples vent thermodynamics with buoyant entrainment and height-varying stability to forecast how high plumes rise and whether they overshoot into low-pressure regions. This matters because many close-in rocky worlds experience strong tidal heating that can drive volcanism, injecting volatiles that alter atmospheric composition and climate in ways potentially visible to telescopes. Sensitivity tests across gravity, composition, temperature, and vent conditions map regions where plumes routinely reach detectable altitudes. The result supplies concrete predictions for when volcanic emissions could appear in spectra of planets like those in the TRAPPIST-1 system.

Core claim

We have created and benchmarked a flexible 1D plume model that integrates vent thermodynamics, buoyant entrainment, and vertically varying static stability to compute plume rise, neutral-buoyancy height, and overshoot. After confirming mass conservation and agreement with prior codes and scaling laws, the model is applied to exoplanet background states including CO2-rich atmospheres under strong irradiation. Systematic exploration shows plume height depends strongly on surface gravity, mean molecular weight, background stratification, vent overpressure, and volatile loading, with identifiable parameter regimes where plumes penetrate to low-pressure levels.

What carries the argument

The 1D volcanic plume model that couples vent thermodynamics, buoyant entrainment, and vertically varying static stability to predict plume rise, neutral-buoyancy height, and overshoot.

If this is right

Plume heights increase with lower surface gravity and higher vent overpressure across the tested parameter space.
CO2-rich atmospheres under strong irradiation allow plumes to reach higher altitudes more readily than other compositions.
Distinct regions of parameter space exist where plumes routinely penetrate to low-pressure levels, maximizing potential detectability in transmission or emission spectra.
The framework supplies direct predictions for volcanic emission detectability on tidally heated rocky exoplanets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

These height predictions could be combined with atmospheric retrieval codes to forecast the strength of volcanic spectral features in data from upcoming telescopes.
The same model structure might be tested against plume observations on solar-system bodies with known volcanism to further constrain entrainment parameters before exoplanet application.
Time-variable or three-dimensional extensions could reveal how plume material disperses horizontally and affects global atmospheric chemistry beyond the neutral-buoyancy level.

Load-bearing premise

The vent thermodynamics, buoyant entrainment, and static stability assumptions from the original Venus and Mars model apply without major revision to the range of exoplanet atmospheric conditions examined.

What would settle it

An observation of actual plume height or volcanic gas distribution on a known rocky exoplanet that lies outside the model's predicted range for the measured planetary gravity, atmospheric composition, and vent conditions would falsify the model's transferability.

Figures

Figures reproduced from arXiv: 2605.04423 by Prabal Saxena, Thomas Fauchez.

**Figure 1.** Figure 1: Plume height H dependency on temperature for isothermal profiles at VEI–4 and VEI–6. In our experiments, the pressure profile (and therefore the vertical stratification) is held fixed across the different isothermal atmospheres, so N remains nearly unchanged. As a result, variations in plume height are primarily driven by changes in F0, which depend both on the density contrast between the hot eruptive mix… view at source ↗

**Figure 2.** Figure 2: Top Panel: Background 2 bar CO2 column extracted from our ExoCAM simulation of TRAPPIST-1e used in the temperature-offset experiments. Bottom x-axis: temperature T (K). Left y-axis: pressure (Pa; logarithmic, inverted). Top x-axis: specific humidity Q (kg kg−1 ). Right y-axis: altitude (km), placed at the pressures that correspond to those altitudes so ticks align with the pressure grid. Bottom Panel: Ambi… view at source ↗

**Figure 3.** Figure 3: Plume buoyancy diagnostic for our TRAPPIST-1e, 2 bar CO2 single column. Centerline density contrast ρa − ρp (green), neutral-buoyancy line (black), diagnosed NBH at zNBH ≃ 1.2 km (green dashed), and plume-top H ≃ 20 km (red dotted). Above NBH the contrast is weakly positive, and the large overshoot ∆z is explained by finite momentum at NBH rising through a soft mid-column, followed by arrest in a stiff upp… view at source ↗

**Figure 4.** Figure 4: Similar figure to the bottom panel of view at source ↗

**Figure 5.** Figure 5: Plume height H dependency on surface pressure for VEI–4 and VEI–6. The temperature profile of view at source ↗

**Figure 6.** Figure 6: Plume height H dependency on atmospheric temperature for VEI–4 and VEI–6. The pressure profile of view at source ↗

**Figure 7.** Figure 7: Interior pressure profiles as a function of depth for rocky bodies with varying surface gravities. Pressure increases linearly with depth according to P(z) = ρmantle × g × z, assuming a uniform mantle density of 3300 kg/m3 . The vertical green dashed line marks the 2 GPa pressure threshold for decompression melting onset in peridotite mantles. Colored circles indicate the depth at which each body reaches t… view at source ↗

**Figure 8.** Figure 8: Schematic figure of exovolcanic plume detectability in transmission for TRAPPIST-1e (left) and emission for TRAPPIST-1d (right). The refraction limit at λ = 1 µm has been computed using the PSG (Villanueva et al. 2022) ray-tracing calculation. The emission layers of TRAPPIST-1d have been estimated using the ExoCAM 0.5 bar CO2 profile at the substellar point and the Eddington–Barbier approximation, i.e., th… view at source ↗

read the original abstract

Explosive volcanic eruptions play a fundamental role in the evolution and observability of rocky exoplanets, serving as a key mechanism for injecting volatiles into planetary atmospheres and potentially modifying their climate and composition. This process may be particularly important for close-in exoplanets where tidal forcing can drive substantial internal heating, analogous to (but often exceeding) Io's volcanism. In this work, we adapt and extend a classic 1D volcanic plume model originally developed in IDL by Glaze and Baloga for Venus and Mars applications, and port it into a flexible, open Python framework suitable for exoplanet studies. The model explicitly couples vent thermodynamics, buoyant entrainment, and vertically varying static stability to predict plume rise, neutral-buoyancy height, and overshoot for a wide range of planetary and atmospheric conditions. We first benchmark the Python implementation against the original IDL code and analytic scaling laws to ensure adequate momentum budgets and strict mass conservation. We then apply the model to a suite of exoplanet-relevant background states, including CO2-rich atmospheres under strong irradiation and diverse surface conditions. A systematic sensitivity analysis explores how plume height depends on surface gravity, bulk atmospheric composition (and mean molecular weight), background temperature and stratification, vent overpressure, and volatile loading. We identify regions of parameter space where plumes routinely penetrate to low-pressure levels, maximizing their potential detectability in transmission or emission. These results provide a physically grounded framework for predicting whether and how volcanic emissions might be detected on rocky exoplanets, including-but not limited to-those experiencing strong tidal heating.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Ports a Venus/Mars 1D plume model to Python and sweeps TRAPPIST-1 parameters, but keeps the original entrainment and stability assumptions fixed without re-deriving them for low-g or high-MMW cases.

read the letter

The paper takes the Glaze and Baloga 1D plume model, ports it to an open Python framework, and runs sensitivity tests across exoplanet-relevant conditions with a focus on TRAPPIST-1 analogs. The new piece is the mapping of how neutral-buoyancy and overshoot heights change with gravity, mean molecular weight, stratification, and vent properties, plus the identification of regimes where plumes reach low-pressure levels that could affect transmission spectra. They benchmark the Python version against the original IDL code and analytic scalings, which is the right first step for checking momentum and mass budgets. The code being public and flexible is a practical plus for anyone who needs quick estimates of volcanic injection on tidally heated rocky worlds. The sensitivity runs are systematic enough to scope out the problem space without overclaiming. The soft spot is the direct transfer of the entrainment formulation and axisymmetric, non-condensing assumptions from the Venus/Mars calibration. Varying g, temperature, and composition while holding the functional form fixed does not test whether the coefficients themselves shift in lower-gravity or different-density regimes, which is exactly the concern in the stress-test note. The abstract claims strict mass conservation and adequate momentum budgets, but without the full error analysis or regime-specific checks visible here, it is hard to judge how much those claims constrain the exoplanet predictions. This is aimed at atmospheric modelers and observers who want a ready tool to link internal heating to observable plume heights on rocky exoplanets. Readers working on JWST-era spectra or habitability assessments get a concrete framework they can run themselves. The work is coherent on its own terms and shows honest engagement with the prior literature, so it deserves a serious referee to pressure-test the generalization step and any validation details in the full text. I would send it to peer review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript adapts the classic 1D volcanic plume model of Glaze and Baloga (originally for Venus and Mars) to exoplanet atmospheres, with a focus on TRAPPIST-1-like planets. The authors port the model to an open Python framework, benchmark it against the original IDL implementation and analytic scaling laws to verify momentum budgets and mass conservation, and conduct sensitivity analyses varying surface gravity, mean molecular weight, background temperature/stratification, vent overpressure, and volatile loading. The central claim is that the resulting neutral-buoyancy and overshoot heights identify regions of parameter space where volcanic plumes can reach low-pressure levels, thereby providing a physically grounded framework for predicting detectability of volcanic emissions in transmission or emission observations on rocky exoplanets, including those with strong tidal heating.

Significance. If the 1D assumptions hold across the explored regimes, the work supplies a reproducible, extensible tool for assessing volcanic volatile injection on rocky exoplanets and its potential observational signatures. The benchmarking against the established code and analytic laws, together with the open Python implementation, are clear strengths that support reproducibility and future extensions. The sensitivity study usefully maps how tidal heating and atmospheric properties affect plume rise, offering a starting point for target selection in future observations.

major comments (2)

[§3 (Model Description and Assumptions)] §3 (Model Description and Assumptions): The entrainment formulation (constant or weakly varying coefficient) and axisymmetric Gaussian plume assumptions are taken directly from the Glaze & Baloga Venus/Mars calibration and held fixed while sweeping g, T, and mean molecular weight. Because neutral-buoyancy height is set by the competition between buoyancy flux and entrainment, this fixed functional form is load-bearing for the detectability predictions; no test is presented of coefficient dependence on density contrast or turbulence regime in low-g/high-MMW states.
[§4.2–4.3 (Sensitivity Analysis)] §4.2–4.3 (Sensitivity Analysis): While parameter sweeps are shown, the manuscript reports no quantitative uncertainty propagation (e.g., Monte Carlo on vent overpressure and volatile loading) or comparison against 3D plume simulations for the exoplanet cases; without these, the identification of 'regions of parameter space' where plumes routinely penetrate to low-pressure levels remains qualitative and limits the strength of the central framework claim.

minor comments (2)

The abstract states that 'strict mass conservation' is verified, but the main text would benefit from a short table or plot quantifying conservation residuals across the benchmark cases and exoplanet runs.
Figure captions should explicitly label which curves correspond to TRAPPIST-1 g and composition values versus the broader parameter sweeps.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped clarify the scope and limitations of our modeling approach. We address each major comment below and have made targeted revisions to improve the manuscript.

read point-by-point responses

Referee: §3 (Model Description and Assumptions): The entrainment formulation (constant or weakly varying coefficient) and axisymmetric Gaussian plume assumptions are taken directly from the Glaze & Baloga Venus/Mars calibration and held fixed while sweeping g, T, and mean molecular weight. Because neutral-buoyancy height is set by the competition between buoyancy flux and entrainment, this fixed functional form is load-bearing for the detectability predictions; no test is presented of coefficient dependence on density contrast or turbulence regime in low-g/high-MMW states.

Authors: We agree that the entrainment coefficient is held fixed from the original calibration and that this choice influences the neutral-buoyancy height. In the revised manuscript we have added a new paragraph in §3 that justifies retaining the constant coefficient by referencing its prior use across a range of density contrasts and by noting that our analytic benchmarking confirms conservation properties remain intact. We also explicitly state the limitation for extreme low-g or high-MMW regimes and identify variable entrainment as a natural extension for future work. This addition clarifies the assumption without changing the reported results. revision: partial
Referee: §4.2–4.3 (Sensitivity Analysis): While parameter sweeps are shown, the manuscript reports no quantitative uncertainty propagation (e.g., Monte Carlo on vent overpressure and volatile loading) or comparison against 3D plume simulations for the exoplanet cases; without these, the identification of 'regions of parameter space' where plumes routinely penetrate to low-pressure levels remains qualitative and limits the strength of the central framework claim.

Authors: We acknowledge that the original sensitivity analysis consisted of deterministic sweeps. In the revision we have incorporated a Monte Carlo ensemble in §4.2 that samples vent overpressure and volatile loading from observationally motivated distributions; the resulting plume-height distributions are now shown and used to delineate the parameter regions with quantitative uncertainty bounds. Direct comparison with 3D simulations lies outside the present scope, which prioritizes an efficient 1D tool for broad exploration; we have added a brief discussion paragraph citing relevant 3D studies and noting this as a future validation step. revision: partial

Circularity Check

0 steps flagged

No circularity; derivation uses externally validated 1D plume model ported from Glaze & Baloga

full rationale

The paper's core chain ports an established 1D volcanic plume model (vent thermodynamics, buoyant entrainment, vertically varying static stability) originally developed by Glaze and Baloga for Venus/Mars, implements it in Python, benchmarks against the original IDL code and analytic scalings for momentum and mass conservation, then applies it to exoplanet parameter sweeps. No equation reduces a prediction to a parameter defined by the same exoplanet outputs, no self-citation bears the load of the central claims, and no uniqueness theorem or ansatz is smuggled in from the authors' prior work. The sensitivity analysis varies g, composition, temperature, and vent conditions while holding the functional form fixed; this is standard model application, not circular re-derivation. The framework is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is inferred from described components: the model inherits standard 1D plume assumptions and explores but does not invent new entities.

free parameters (2)

vent overpressure
Listed as a variable in the sensitivity analysis; specific values not provided in abstract.
volatile loading
Explored as a parameter affecting plume height; no fitted values given.

axioms (2)

domain assumption The 1D buoyant entrainment and static stability assumptions from the original Glaze and Baloga model hold for exoplanet atmospheres.
Invoked when porting the model to new planetary conditions.
domain assumption Background atmospheric states (CO2-rich, strong irradiation) are representative of TRAPPIST-1 planets.
Used to define the suite of cases studied.

pith-pipeline@v0.9.0 · 5590 in / 1394 out tokens · 28772 ms · 2026-05-08T17:26:15.609762+00:00 · methodology

discussion (0)

Reference graph

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