Where does the simplified stellar contamination model fail in exoplanet transmission spectroscopy?

¹ Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA
² Center for Radio Astronomy and Astrophysics Mackenzie (CRAAM), Mackenzie Presbyterian University, Rua da Consolacão, 930, São Paulo, São Paulo 01302-907, Brazil

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 July 2025
Accepted: 5 January 2026

Abstract

Stellar photospheric heterogeneities (e.g., starspots and faculae) distort the apparent stellar spectrum during a transit and imprint wavelength-dependent biases on the measured planet–to–star radius ratio. This transit light source effect (TLSE) must be accounted for to obtain reliable atmospheric properties. A widely used approach is the Rackham–TLSE (R–TLSE) prescription, which applies a disk-averaged contamination correction based solely on the filling factor and spectral contrast. However, accurate transmission-spectroscopy interpretations require models that also account for limb darkening, the spatial distribution of active regions, and transit geometry. In this work, we incorporated these effects into a self-consistent, pixel-resolved framework, ECLIPSE-Xλ, and performed idealized, noise-free model–model comparisons against the R–TLSE approximation. Using three archetypal systems – the super-Earth LHS 1140 b, the mini-Neptune K2-18 b, and the hot Jupiter WASP-69 b – we show that disk-averaged TLSE corrections can differ from the self-consistent model by up to ~400 ppm in the optical for active hosts and non-equatorial transits, while remaining below ~10 ppm at near-infrared wavelengths where limb darkening is weaker. We then applied both approaches to the JWST/NIRISS SOSS transmission spectrum of LHS 1140 b. When limb darkening is artificially set to zero, ECLIPSE-Xλ recovers stellar-contamination parameters that closely match the reference R–TLSE solution, confirming that the two frameworks are consistent in the disk-averaged limit. With wavelength-dependent limb darkening included, however, reproducing the observed short-wavelength slope through stellar contamination alone requires very hot faculae (ΔT_fac ≃ 600 K) covering f_fac ≃ 0.35 of the visible hemisphere, corresponding to an equivalent circular facular region with radius ≃0.6 R_⋆ (i.e., about 60% of the stellar radius) on the stellar disk. Such an extended, unocculted active region would be physically unlikely even for an active M dwarf. In this context, a purely stellar-contamination explanation for any residual optical slope would demand rather extreme facular populations; scenarios in which a genuine atmospheric contribution helps complement a more modest facular signal appear more physically plausible. Taken together, these results delineate the regime of validity of the R–TLSE approximation and underscore the need for geometry-aware stellar-heterogeneity models that explicitly account for limb darkening in high-precision transmission spectroscopy.