LAUSR

Context. Observationally constraining the atmospheric temperature-pressure (TP) profile of exoplanets is an important step forward for improving planetary atmosphere models, thus further enabling one to place the detection of spectral features and the measurement of atomic and molecular abundances through transmission and emission spectroscopy on solid ground. Aims. The aim is to constrain the TP profile of the ultra-hot Jupiter KELT-9b by fitting synthetic spectra to the observed Hα and Hβ lines and identify why self-consistent planetary TP models are unable to fit the observations. Methods. We constructed 126 one-dimensional TP profiles varying the lower and upper atmospheric temperatures, as well as the location and gradient of the temperature rise. For each TP profile, we computed the transmission spectra of the Hα and Hβ lines employing the Cloudy radiative transfer code, which self-consistently accounts for non-local thermodynamic equilibrium (NLTE) effects. Results. The TP profiles, leading to best fit the observations, are characterised by an upper atmospheric temperature of 10 000–11 000 K and by an inverted temperature profile at pressures higher than 10−4 bar. We find that the assumption of local thermodynamic equilibrium (LTE) leads one to overestimate the level population of excited hydrogen by several orders of magnitude and hence to significantly overestimate the strength of the Balmer lines. The chemical composition of the best fitting models indicate that the high upper atmospheric temperature is most likely driven by metal photoionisation and that FeII and FeIII have comparable abundances at pressures lower than 10−6 bar, possibly making the latter detectable. Conclusions. Modelling the atmospheres of ultra-hot Jupiters requires one to account for metal photoionisation. The high atmospheric mass-loss rate (>1011 g s−1), caused by the high temperature, may have consequences on the planetary atmospheric evolution. Other ultra-hot Jupiters orbiting early-type stars may be characterised by similarly high upper atmospheric temperatures and hence high mass-loss rates. This may have consequences on the basic properties of the observed planets orbiting hot stars.