JWST Transmission Spectroscopy of TOI-3235 b: Challenges in Constraining Giant Planet Atmospheres Around M Dwarfs Amid Stellar Contamination

Giant planets orbiting low-mass M dwarfs challenge current planet formation theories, which predict that such planets are unlikely to form. Characterizing their atmospheres can provide key insight into their origins, but analysis is complicated by stellar contamination in transmission spectra. We present a JWST/NIRSpec PRISM transmission spectrum of TOI-3235 b, a 604 K, 0.665 Jupiter-mass giant planet orbiting a 0.39 Solar-mass M dwarf. We apply a hierarchical retrieval framework incorporating an atmospheric model, a parametric stellar contamination model, and a Gaussian process (GP) to capture residual structure not explained by these deterministic components. We find that the inferred atmospheric properties are model-dependent: retrievals that treat stellar contamination deterministically yield a constrained CH4 abundance corresponding to a sub-solar metallicity that would challenge standard expectations from both core accretion and gravitational instability, along with potentially elevated CO and CO2 abundances that would require chemical disequilibrium. However, residual wavelength-correlated structure suggests the deterministic model is incomplete. Including a GP to marginalize over this structure broadens the atmospheric posterior distributions, preventing robust constraints on the atmospheric composition and highlighting the challenge of characterizing giant planet atmospheres around M dwarfs. We demonstrate that an eclipse observation could clarify these model-dependent ambiguities: detected emission features would constrain the planet's metallicity and test formation scenarios, while a featureless spectrum would confirm stellar contamination dominates the transmission spectrum, providing an empirical M dwarf contamination spectrum.