NLTE atmospheric modelling of the ultra-hot Jupiter WASP-178b and comparison with UV and optical observations

We model the atmosphere of the ultra-hot Jupiter (UHJ) WASP-178b accounting for NLTE effects and compare synthetic transmission spectra with NUV and optical observations. We use the HELIOS code (LTE) in the lower and the Cloudy code (LTE or NLTE) in the middle and upper atmosphere to compute the temperature-pressure (TP) and abundance profiles. We further use Cloudy to compute the theoretical planetary transmission spectrum both in LTE and NLTE for comparison with observations. We find an isothermal TP profile at pressures higher than 10 mbar and lower than 10$^{-8}$ bar, with an almost linear increase from about 2200 K to about 8100 K in between. The temperature structure is driven by NLTE effects, particularly in the form of increased heating resulting from the overpopulation of long-lived FeII levels with strong transitions in the NUV band, where the stellar emission is strong, and of decreased cooling due to the underpopulation of MgI and MgII levels that dominate the cooling. The planetary atmosphere is hydrostatic up to pressures of about 1 nbar, and thus accurately modelling spectral lines forming at pressures lower than about 1 nbar requires accounting for both hydrodynamics and NLTE effects. The NLTE synthetic transmission spectrum overestimates the observed H$α$ and H$β$ absorption, while the LTE model is in good agreement, which is surprising as the opposite has been found for the other UHJs for which NLTE modelling has been performed. Instead, in the NUV we find an excellent match between the NLTE transmission spectrum and the HST/UVIS data, contrary to the LTE model. This contrasts previous LTE results requiring SiO absorption to fit the observations. The accurate characterisation of the atmosphere of UHJs is possible only accounting for NLTE effects, and particularly for the level population of Fe and Mg, which dominate heating and cooling, respectively.