Characterisation of cool stellar atmospheres for PLATO

M dwarfs are the most abundant stars in our Galaxy, but they are not well studied. This is changing as observational capabilities improve and M dwarfs have become important targets in the search for exoplanets. These cool and small stars are therefore key targets in many current and upcoming missions. One such mission is the future ESA telescope PLATO, which aims to find exoplanets using light curves. Thousands of M dwarfs are part of the mission's sample, and all these stars need to be accurately characterised. Obtaining accurate atmospheric parameters for M dwarfs using spectroscopy is no easy task. This is because their spectrum is filled with molecular lines due to the low effective temperatures. It is especially challenging in the optical wavelength region, where molecular lines obscure the atomic lines. The situation improves in the near-infrared, which also allows for the benefit of receiving more light. In the last decade, many papers deriving M dwarf parameters have been published. These parameters mostly agree within uncertainties, but some discrepancies remain. The first paper presented in this thesis explores these differences while also investigating non-LTE effects in M dwarfs. It finds an insignificant effect for iron but a significant effect for potassium. To characterise the thousands of M dwarfs in the PLATO sample, new methods using machine learning have been developed. In the second paper of this thesis, we present a pipeline capable of analysing APOGEE spectra. The pipeline is a modification of an existing FGK version. We trained a new neural network, added a pseudo-continuum correction method, and implemented evolutionary models created for the PLATO mission to obtain the surface gravity. The modified pipeline was tested on a sample of M dwarfs with good results. In the final paper presented in this thesis, we provide abundances of Fe, Ti, and Ca for a small sample of well-known M dwarfs using differential abundance analysis. Our results mostly agree within uncertainties when compared to literature values. However, there are few studies to compare with, and there is generally a spread between the available studies.