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,
