Quantification of abundance uncertainties in chemical models of exoplanet atmospheres

TL;DR

This work delivers a rigorous uncertainty quantification for 1D chemical models of exoplanet atmospheres across six well-studied planets, using a lognormal perturbation framework to propagate uncertainties in reaction kinetics, photodissociation cross sections, and vertical mixing. By separating chemistry and mixing effects and applying Pearson/Spearman correlations, it identifies both robust observable species (e.g., H$_2$O, CO, CO$_2$, SiO) and species with large uncertainties (e.g., HCN, SO$_2$, PH$_3$, TiO), and highlights the dominant role of vertical mixing alongside kinetics in shaping abundances. The analysis reveals that planets near chemical equilibrium exhibit smaller uncertainties, while photochemistry-dominated atmospheres show larger dispersion, with many critical reactions involving S-, P-, Si-, and Ti-bearing species needing improved kinetic or cross-section data. These findings offer a concrete roadmap for improving exoplanet atmospheric models and for interpreting observations within quantified uncertainty limits.

Abstract

Chemical models are routinely used to predict the atmospheric composition of exoplanets and compare it with the composition retrieved from observations, but little is known about the reliability of the calculated composition. We carried out a sensitivity analysis to quantify the uncertainties in the abundances calculated by a state-of-the-art chemical atmosphere model of the widely observed planets WASP-33b, HD209458b, HD189733b, WASP-39b, GJ436b, and GJ1214b. We found that the abundance uncertainties in the observable atmosphere are relatively small, below one order of magnitude and in many cases below a factor of two, where vertical mixing is a comparable or even larger source of uncertainty than (photo)chemical kinetics. In general, planets with a composition close to chemical equilibrium have smaller abundance uncertainties than planets whose composition is dominated by photochemistry. Some molecules, such as H2O, CO, CO2, and SiO, show low abundance uncertainties, while others such as HCN, SO2, PH3, and TiO have more uncertain abundances. We identified several critical albeit poorly constrained processes involving S-, P-, Si-, and Ti-bearing species whose better characterization should lead to a global improvement in the accuracy of models. Some of these key processes are the three-body association reactions S + H2, Si + O, NH + N, and N2H2 + H; the chemical reactions S + OH --> SO + H, NS + NH2 --> H2S + N2, P + PH --> P2 + H, and N + NH3 --> N2H + H2; and the photodissociation of molecules such as P2, PH2, SiS, CH, and TiO.

Figures (5)

• Figure 1: Left panel: Random lognormal distribution of the rate coefficient of the reaction H + H + M $\rightarrow$ H$_2$ + M, evaluated at 1 mbar and 1000 K, for the models where (photo)chemical kinetics is perturbed. Right panel: Random lognormal distribution of $K_{zz}$ around the nominal value for the HD 189733b models where vertical mixing is perturbed, where the black histogram refers to the whole set of 3000 runs, the blue one to the set of converged runs, and the red one excludes those runs with a relaxed convergence (see text). The runs actually considered for the sensitivity analysis are those converged but excluding the right wing to have a symmetric distribution (blue area). In both panels, the vertical dotted line indicates the nominal value and the shaded gray area the range $\pm$ 1 $\sigma$ around it.
• Figure 2: Calculated pressure-temperature profiles (solid lines referred to the bottom $x$-axis) and adopted $K_{zz}$ vertical profiles (dashed lines referred to the top $x$-axis) for the six exoplanets investigated.
• Figure 3: Calculated vertical distribution of abundances in the ultra-hot Jupiter WASP-33b and the hot Jupiters HD 209458b, HD 189733b, and WASP-39b. The solid lines correspond to the mean abundance, the shaded areas to the range around the mean $\pm$$\sigma$, and the dotted lines to the abundances resulting from the unperturbed model. The panels on the left show the effect on the calculated abundances of the uncertainties on (photo)chemical kinetics, while the right panels correspond to the effect on the abundances of the uncertainty in $K_{zz}$.
• Figure 4: Same as in Fig. \ref{['fig:hot_jupiters']}, but for the warm Neptunes GJ 436b and GJ 1214b.
• Figure 5: Impact of the reaction S + H$_2$ + M $\rightarrow$ H$_2$S + M on the abundances of selected species in GJ 436b. The shaded areas show the variation in the calculated abundances when the adopted rate coefficient is ten times below and above the nominal value.