| الملخص: | A quarter century after the famous discovery of 51 Peg b, the radial velocity (RV) method remains a key exoplanet detection and characterisation method. For transiting planets, RVs allow us to measure mean densities and draw conclusions about the planets’ compositions. This is particularly valuable for young planets, which are sensitive probes of formation and evolution models. Stellar activity is the main factor limiting RV searches for both young planets and small, temperate planets around older stars. In this thesis, I developed and tested novel approaches to extract RVs from spectra using Gaussian process (GP) regression. I then used a multi-dimensional GP framework to model the impact of stellar activity on those RVs and to disentangle activity-induced and planetary signals in the data from a year-long intensive RV monitoring campaign of the bright, young M-dwarf AU Mic using the HARPS spectrograph. This enabled me and my collaborators to measure the masses of two transiting planets, which have previously been discovered by the TESS satellite, finding Mb = 11.7±5.0 M⊕ and Mc = 22.2±6.7 M⊕. As both planets are similar in size to Neptune, their contrasting densities represent a challenge for current planet formation models, and warrant further investigation. Finally, I also present extensions to the standard Generalised Least-squares Periodogram (GLS), which attempt to account for stellar activity explicitly. I used these to search for additional planets in the AU Mic system using both archival and new HARPS data, excluding the presence of any additional planets with RV semi-amplitudes ≥ 50 ms−1 and periods 20 ≤ P ≤ 1000days.
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