A Closed-form Analytical Theory of Nonisobaric Transmission Spectroscopy for Exoplanet Atmospheres

Abstract Analytical models are essential for building physical intuition and guiding the interpretation of exoplanet observations by clarifying the dependencies that shape atmospheric signatures. I present a generalization of the classical isothermal, isobaric transmission model by allowing the opacity to vary with pressure as a power law, κ ∝ P n , and explicitly defining the reference opacity κ 0 at a chosen pressure P 0 . By treating the slant optical depth as an Abel transform of the radial absorption coefficient, I 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 nonisobaric effects and explicitly links the vertical opacity gradient to observable spectral features. I 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 semianalytical retrieval approaches optimized for computational efficiency.