Robustness of C/O and mean molecular weight under disequilibrium chemistry

Abstract: Transmission spectroscopy increasingly reduces exoplanet spectra to derived compositional metrics, such as C/O, O/H, and mean molecular weight (MMW), but these quantities do not carry molecular abundance uncertainties in the same way. We assessed the reliability of these metrics for hot Jupiters and sub-Neptunes, by combining analytic uncertainty propagation with photochemical VULCAN forward models and representative published retrieval constraints. Propagating molecular abundance uncertainties produced substantially larger fractional uncertainties in elemental abundance ratios than in MMW. The fractional uncertainties in C/O and O/H were typically comparable to the inferred ratios, whereas the fractional uncertainty in MMW was more than two orders of magnitude smaller in H2/He-dominated atmospheres. Photochemistry and vertical mixing redistributed individual molecules but produced only minor changes in C/O and MMW at the pressures probed by transmission spectroscopy. C/O remains an important diagnostic of atmospheric chemistry and planetary formation history, but its interpretation requires careful uncertainty propagation. Mean molecular weight may provide a comparatively stable population-level diagnostic for linking observable atmospheres to bulk composition, especially across the sub-Neptune radius valley.