Stellar magnetic activity and rocky planets in cool dwarf stars
Exoplanetary astronomy has entered its Golden Age, with humanity having found over 6000 exoplanets to date. The majority of these discoveries have been achieved through transit-photometry and radial-velocity (RV) techniques. While transit surveys lead in discovery numbers, the RV method persists as a vital and indispensable technique in exoplanetary science, particularly in the most prevalent stellar population -- M dwarfs. Their low masses make them the theoretical favourites for RV detections, since exoplanet signals are stronger over the same period, and are therefore easier to detect and measure accurately. Nevertheless, the stellar activity M dwarfs exhibit introduces significant challenges, particularly when seeking RV semi-amplitudes to the order of 1 m$\,$s$^{-1}$, or lower. Stellar activity is known to mimic or suppress planetary signals, and its effects manifest across all time scales: from short-lived signals due to convective motion (lasting minutes to days), through active regions on the stellar surface (days to months), to long-term magnetic cycles (years to decades). These issues highlight the urgent need for robust methodologies that are capable of reliably disentangling stellar variability from genuine planetary signals. This doctoral dissertation explores these challenges through the application of Gaussian-process (GP) modelling. I present three distinct but interconnected publications that integrate high-precision spectroscopy and photometry with a unified GP-based approach in two cases, and that enable robust disentanglement of planetary signals from stellar activity. Together, these three studies illustrate how observations of different origin can be combined with appropriate statistical machinery for the sake of detecting exoplanets, with the possibility of interpreting stellar activity.