Context. KELT-9 b exemplifies a newly emerging class of short-period gaseous exoplanets that tend to orbit hot, early type stars – termed ultra-hot Jupiters. The severe stellar irradiation heats their atmospheres to temperatures of ~4000 K, similar to temperatures of photospheres of dwarf stars. Due to the absence of aerosols and complex molecular chemistry at such temperatures, these planets offer the potential of detailed chemical characterization through transit and day-side spectroscopy. Detailed studies of their chemical inventories may provide crucial constraints on their formation process(es) and evolution history. Aims. We aim to search the optical transmission spectrum of KELT-9 b for absorption lines by metals using the cross-correlation technique. Methods. We analysed two transit observations obtained with the HARPS-N spectrograph. We used an isothermal equilibrium chemistry model to predict the transmission spectrum for each of the neutral and singly ionized atoms with atomic numbers between three and 78. Of these, we identified the elements that are expected to have spectral lines in the visible wavelength range and used those as cross-correlation templates. Results. We detect (>5σ) absorption by Na I, Cr II, Sc II and Y II, and confirm previous detections of Mg I, Fe I, Fe II, and Ti II. In addition, we find evidence of Ca I, Cr I, Co I, and Sr II that will require further observations to verify. The detected absorption lines are significantly deeper than predicted by our model, suggesting that the material is transported to higher altitudes where the density is enhanced compared to a hydrostatic profile, and that the material is part of an extended or outflowing envelope. There appears to be no significant blue-shift of the absorption spectrum due to a net day-to-night side wind. In particular, the strong Fe II feature is shifted by 0.18 ± 0.27 km s−1, consistent with zero. Using the orbital velocity of the planet we derive revised masses and radii of the star and the planet: M* = 1.978 ± 0.023 M⊙, R* = 2.178 ± 0.011 R⊙, mp = 2.44 ± 0.70 MJ and Rp = 1.783 ± 0.009 RJ.

We introduce a fast and versatile computer code, GGchem, to determine the chemical composition of gases in thermo-chemical equilibrium down to 100 K, with or without equilibrium condensation. We review the data for molecular equilibrium constants, k p (T ), from several sources and discuss which functional fits are most suitable for low temperatures. We benchmark our results against another chemical equilibrium code. We collect Gibbs free energies, ∆G• − f , for about 200 solid and liquid species from the NIST-JANAF database and the geophysical database SUPCRTBL. We discuss the condensation sequence of the elements with solar abundances in phase equilibrium down to 100 K. Once the major magnesium silicates Mg 2 SiO 4 [s] and MgSiO 3 [s] have formed, the dust/gas mass ratio jumps to a value of about 0.0045 which is significantly lower than the often assumed value of 0.01. Silicate condensation is found to increase the carbon/oxygen ratio (C/O) in the gas from its solar value of ∼ 0.55 up to ∼ 0.71, and, by the additional intake of water and hydroxyl into the solid matrix, the formation of phyllosilicates at temperatures below ∼ 400 K increases the gaseous C/O further to about 0.83. Metallic tungsten (W) is the first condensate found to become thermodynamically stable around 1600 − 2200 K (depending on pressure), several hundreds of Kelvin before subsequent materials like zirconium dioxide (ZrO 2 ) or corundum (Al 2 O 3 ) can condense. We briefly discuss whether tungsten, despite its low abundance of ∼ 2 × 10 −7 times the silicon abundance, could provide the first seed particles for astrophysical dust formation. The GGchem code is publicly available at https://github.com/pw31/GGchem.

For the calculation of complex neutral/ionized gas phase chemical equilibria, we present a semi-analytical versatile and efficient computer program, called FastChem. The applied method is based on the solution of a system of coupled nonlinear (and linear) algebraic equations, namely the law of mass action and the element conservation equations including charge balance, in many variables. Specifically, the system of equations is decomposed into a set of coupled nonlinear equations in one variable each, which are solved analytically whenever feasible to reduce computation time. Notably, the electron density is determined by using the method of Nelder and Mead at low temperatures. The program is written in object-oriented C++ which makes it easy to couple the code with other programs, although a stand-alone version is provided. FastChem can be used in parallel or sequentially and is available under the GNU General Public License version 3 at https://github.com/exoclime/FastChem together with several sample applications. The code has been successfully validated against previous studies and its convergence behavior has been tested even for extreme physical parameter ranges down to 100 K and up to 1000 bar. FastChem converges stable and robust in even most demanding chemical situations, which posed sometimes extreme challenges for previous algorithms.