An ab initio study of the rovibronic spectrum of sulphur monoxide (SO): diabatic vs. adiabatic representation

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Sulfur dioxide in the mid-infrared transmission spectrum of WASP-39b

The recent inference of sulfur dioxide (SO2) in the atmosphere of the hot (approximately 1,100 K), Saturn-mass exoplanet WASP-39b from near-infrared JWST observations1-3 suggests that photochemistry is a key process in high-temperature exoplanet atmospheres4. This is because of the low (<1 ppb) abundance of SO2 under thermochemical equilibrium compared with that produced from the photochemistry of H2O and H2S (1-10 ppm)4-9. However, the SO2 inference was made from a single, small molecular feature in the transmission spectrum of WASP-39b at 4.05 μm and, therefore, the detection of other SO2 absorption bands at different wavelengths is needed to better constrain the SO2 abundance. Here we report the detection of SO2 spectral features at 7.7 and 8.5 μm in the 5-12-μm transmission spectrum of WASP-39b measured by the JWST Mid-Infrared Instrument (MIRI) Low Resolution Spectrometer (LRS)10. Our observations suggest an abundance of SO2 of 0.5-25 ppm (1σ range), consistent with previous findings4. As well as SO2, we find broad water-vapour absorption features, as well as an unexplained decrease in the transit depth at wavelengths longer than 10 μm. Fitting the spectrum with a grid of atmospheric forward models, we derive an atmospheric heavy-element content (metallicity) for WASP-39b of approximately 7.1-8.0 times solar and demonstrate that photochemistry shapes the spectra of WASP-39b across a broad wavelength range.

Photochemically produced SO2 in the atmosphere of WASP-39b

Photochemistry is a fundamental process of planetary atmospheres that regulates the atmospheric composition and stability1. However, no unambiguous photochemical products have been detected in exoplanet atmospheres so far. Recent observations from the JWST Transiting Exoplanet Community Early Release Science Program2,3 found a spectral absorption feature at 4.05 μm arising from sulfur dioxide (SO2) in the atmosphere of WASP-39b. WASP-39b is a 1.27-Jupiter-radii, Saturn-mass (0.28 MJ) gas giant exoplanet orbiting a Sun-like star with an equilibrium temperature of around 1,100 K (ref. 4). The most plausible way of generating SO2 in such an atmosphere is through photochemical processes5,6. Here we show that the SO2 distribution computed by a suite of photochemical models robustly explains the 4.05-μm spectral feature identified by JWST transmission observations7 with NIRSpec PRISM (2.7σ)8 and G395H (4.5σ)9. SO2 is produced by successive oxidation of sulfur radicals freed when hydrogen sulfide (H2S) is destroyed. The sensitivity of the SO2 feature to the enrichment of the atmosphere by heavy elements (metallicity) suggests that it can be used as a tracer of atmospheric properties, with WASP-39b exhibiting an inferred metallicity of about 10× solar. We further point out that SO2 also shows observable features at ultraviolet and thermal infrared wavelengths not available from the existing observations.

Early Release Science of the exoplanet WASP-39b with JWST NIRSpec G395H

Measuring the abundances of carbon and oxygen in exoplanet atmospheres is considered a crucial avenue for unlocking the formation and evolution of exoplanetary systems1,2. Access to the chemical inventory of an exoplanet requires high-precision observations, often inferred from individual molecular detections with low-resolution space-based3-5 and high-resolution ground-based6-8 facilities. Here we report the medium-resolution (R ≈ 600) transmission spectrum of an exoplanet atmosphere between 3 and 5 μm covering several absorption features for the Saturn-mass exoplanet WASP-39b (ref. 9), obtained with the Near Infrared Spectrograph (NIRSpec) G395H grating of JWST. Our observations achieve 1.46 times photon precision, providing an average transit depth uncertainty of 221 ppm per spectroscopic bin, and present minimal impacts from systematic effects. We detect significant absorption from CO2 (28.5σ) and H2O (21.5σ), and identify SO2 as the source of absorption at 4.1 μm (4.8σ). Best-fit atmospheric models range between 3 and 10 times solar metallicity, with sub-solar to solar C/O ratios. These results, including the detection of SO2, underscore the importance of characterizing the chemistry in exoplanet atmospheres and showcase NIRSpec G395H as an excellent mode for time-series observations over this critical wavelength range10.