Exoplanets, -moons, -comets

A Closed-Form Analytical Theory of Non-Isobaric Transmission Spectroscopy for Exoplanet Atmospheres

By Keith Cowing

Status Report

astro-ph.EP

November 13, 2025

Filed under Ariel, astronomy, atmosphere, exoplanet, hot jupiter, JWST, Spectroscopy, WASP-39b

A Closed-Form Analytical Theory of Non-Isobaric Transmission Spectroscopy for Exoplanet Atmospheres — Comparison between the analytical transmission models and the empirical spectra. Top: Earth’s transmission spectrum from Macdonald & Cowan (2019, 2023) derived from ACE-FTS solar-occultation measurements. The empirical spectrum is shown as a solid black line, the isobaric analytical model as a blue curve, and the generalized non-isobaric model as an orange curve. Bottom: JWST transmission spectrum of WASP-39b from the ERS program (Rustamkulov et al. 2023; Tsai et al. 2023), shown as black points with 1σ error bars, compared with the same analytical models (blue: isobaric; orange: non-isobaric). In both cases the non-isobaric formulation reproduces the relative depths and shapes of the major molecular bands, notably the SO2 and CO2 features, more faithfully than the classical isobaric approximation. — astro-ph.EP

Analytical models are essential for building physical intuition and guiding the interpretation of exoplanet observations by clarifying the dependencies that shape atmospheric signatures.

We present a generalization of the classical isothermal, isobaric transmission model by allowing the opacity to vary with pressure as a power law, κ∝Pn, and explicitly defining the reference opacity κ0 at a chosen pressure P0. By treating the slant optical depth as an Abel transform of the radial absorption coefficient, we derive a closed-form expression for the effective transit radius in a hydrostatic, isothermal atmosphere with pressure-dependent opacity.

The solution provides a compact framework for exploring non-isobaric effects and explicitly links the vertical opacity gradient to observable spectral features. We benchmark the model against empirical transmission spectra of Earth and the hot Jupiter WASP-39b, finding a significantly improved fit relative to the isobaric formula.

This generalized expression offers a physically interpretable foundation for analyzing high-precision spectra from JWST and upcoming ARIEL observations, and can serve as a basis for semi-analytical retrieval approaches optimized for computational efficiency.

Leonardos Gkouvelis

Comments: Submitted to The Astrophysical Journal
Subjects: Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:2511.07656 [astro-ph.EP] (or arXiv:2511.07656v1 [astro-ph.EP] for this version)
https://doi.org/10.48550/arXiv.2511.07656
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Submission history
From: Leonardos Gkouvelis
[v1] Mon, 10 Nov 2025 22:04:33 UTC (1,013 KB)
https://arxiv.org/abs/2511.07656
Astrobiology,

Keith Cowing

Explorers Club Fellow, ex-NASA Space Station Payload manager/space biologist, Away Teams, Journalist, Lapsed climber, Synaesthete, Na’Vi-Jedi-Freman-Buddhist-mix, ASL, Devon Island and Everest Base Camp veteran, (he/him) 🖖🏻

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