The Radial Velocity (RV) community has made tremendous leaps forward in the past decades detecting and characterising ever smaller and lighter exoplanets. In recent years, this trend has been broken as planet-induced RV signals smaller than 1 m/s are drowned out by the stars' activity. The detection of Earth analogues causing an RV effect of about 10 cm/s is, therefore, out of reach at the time of writing. A few avenues are being explored to resume the trend to detect ever lighter planets. These include improving (a) instruments, (b) observation strategies, (c) RV extraction techniques, (d) the monitoring of stellar activity, and (e) the stellar activity models.

This thesis is subdivided into three interconnected topics. First, I present my contribution to problem (c). I implemented a technique called Least-Squares Deconvolution (LSD) to estimate precise stellar RVs. Instead of using a template-based mask, I inferred the average stellar line profile based on laboratory data and extracted the RV from this profile. I analysed the dependence of the RVs on the quality thresholds and found a suitable optimisation scheme. We call this method the Multi-Mask Least-Squares Deconvolution technique (MM-LSD), and I have made it publicly available on GitHub. MM-LSD can be a valuable tool if observations are spread out over time and have not been reduced with the same pipelines or CCF masks, as can be the case in archival data. I expect the multi-mask approach to be adopted in tandem with the CCF technique, which will then provide more stable RVs, reducing method-induced RV variations. These variations are not the aim of the current modelling efforts focused on mitigating stellar-induced RV variations and are essential to eliminate.

The flexibility and transparency of the MM-LSD pipeline enable one to extend it easily. For the second part of my PhD, I have implemented a magnetic flux estimation technique built on MM-LSD. This extension is aimed to contribute to solving the problem (d) above. I modelled the Zeeman effect in intensity spectra for which it can be parameterised in a way suitable for the LSD approach. Through this method, the information contained in thousands of lines can be harnessed simultaneously. This approach suppresses noise within the spectra and leads to the averaging out of many other effects affecting the absorption lines. The approach and the results are published in Lienhard et al. (2023). The extracted indicator shows higher correlations with the RVs than any classical indicators and is thus a very promising tool for mitigating stellar activity in solar-type stars.

Lastly, I led the observation campaign for TOI-1774 carried out with the HARPS-N spectrograph. For this star, we initiated a collaboration with CHEOPS to share the data and run a joint analysis on the photometric (CHEOPS) and RV data (HARPS-N). I tested the two approaches above on this target, estimating the planetary mass to 7.14 +/- 2.08 Earth masses and the radius to 2.836 +/- 0.036 Earth radii. The orbital period of this planet was known from the transits observed by TESS and is equal to 16.71 days. Lastly, I assessed the probability of the existence of other planets in the system.