2026ApJ...997..307G

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 κ₀ at a chosen pressure P₀. 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.