A theory of transmission spectroscopy of hydrodynamic outflows from planetary atmospheres: Spectral-line saturation and limits on mass-loss constraints

Abstract

Transmission spectroscopy is a key technique in the characterization of exoplanet atmospheres and has been widely applied to planets undergoing hydrodynamic escape. While a robust analytic theory exists for transmission spectra of hydrostatic atmospheres, the corresponding interpretation for escaping atmospheres has so far relied on numerical modeling, despite the growing number of observations of planetary winds. In this work, a theory of transmission spectroscopy in hydrodynamically escaping atmospheres is developed by coupling the standard transmission geometry to a steady-state, spherically symmetric, isothermal outflow. This approach yields closed-form expressions for the chord optical depth and effective transit radius of a planetary wind and allows the optical depth inversion problem to be examined. The analytic solution reveals that transmission spectroscopy of planetary winds naturally separates into two regimes. In an opacity-limited regime, transmission depths retain sensitivity to the atmospheric mass-loss rate $\dot{M}$. Beyond a critical threshold, however, spectral-line cores become saturated and no longer provide a unique constraint on the escape rate. This transition is marked by a sharp analytic boundary of the form $\sigma (\lambda )\dot{M}\le C_{\mathrm{sat}}$, where $\sigma (\lambda )$ is the line absorption cross-section and $C_{\mathrm{sat}}$ is a constant set by the thermodynamic and geometric properties of the wind. This condition specifies when the inversion between transmission depth and mass-loss rate admits a real solution. Once it is violated, the effective transit radius is no longer controlled by opacity or mass loss, but by the geometric extent of the absorbing wind.

Accepted for publication in Astronomy \& Astrophysics

References in corpus (11)

• Atmospheric Escape from Hot Jupiters
• Atmospheric Retrieval for Super-Earths: Uniquely Constraining the Atmospheric Composition with Transmission Spectroscopy
• Rayleigh scattering in the transit spectrum of HD 189733b
• p-winds: an open-source Python code to model planetary outflows and upper atmospheres
• The fundamentals of Lyman-alpha exoplanet transits
• Characterisation of the upper atmospheres of HAT-P-32 b, WASP-69 b, GJ 1214 b, and WASP-76 b through their He I triplet absorption
• Constraining planetary mass-loss rates by simulating Parker wind profiles with Cloudy
• Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications
• Expanding the inventory of spectral lines used to trace atmospheric escape in exoplanets
• Interior redox state effects on the stability of secondary atmospheres and observational manifestations: LP 791-18 d as a case study for outgassing rocky exoplanets
• A Closed-Form Analytical Theory of Non-Isobaric Transmission Spectroscopy for Exoplanet Atmospheres