Characterization of exoplanetary systems combining transit timing techniques and radial velocities: From secular perturbations to resonant chains

During the past three decades, starting from the first discovery of an exoplanet orbiting a Sun-like star in 1995, the field of exoplanetary science has evolved into a diverse and rapidly expanding discipline. In the early days, the search for new worlds dominated the field, where each new discovery opened unexplored territory of planetary science and challenged existing theories of planet formation and evolution. Today, with more than 6 000 confirmed exoplanets identified through a combination of cutting-edge ground- and space-based facilities (e.g. TESS, CHEOPS, HARPS/-N, ESPRESSO and soon PLATO) the field has entered a new era: an era focused on the detailed characterization of planetary systems and the understanding of their physical and dynamical diversity. Thanks to the continuous monitoring of modern state-of-the-art facilities, the observational baselines of many planetary systems are steadily increasing. This unprecedented temporal coverage is unlocking a new level of characterization, enabling the detection of subtle dynamical effects through timing analyses. These techniques allow to probe the gravitational and tidal interactions that shape planetary architectures and govern their long-term evolution. In this context, this thesis focuses on investigating the dynamical architecture and evolution of exoplanetary systems through complementary observational techniques. By combining Transit Timing Variations (TTVs) and high-precision Radial Velocity (RV) measurements, I provide crucial constraints on planetary masses, orbits, and system architectures. I first explored tidal orbital decay in ultra-hot Jupiters through the analysis of WASP-12 b, using 12 years of ground-based photometry to confirm its decreasing orbital period while revealing intriguing discrepancies that challenge our understanding of stellar evolution and tidal dissipation. I then focus on sub-Neptune characterization in multi-planet systems, notably focusing on the multi-planet system HIP 41378, where I performed a joint dynamical modelling of the TTV and RV signals of the two inner sub-Neptunes using extensive photometric follow-up from CHEOPS, TESS, K2, Spitzer, HST, and high-precision RVs from HARPS. This analysis dynamically confirmed the planetary nature of HIP 41378 g, a non-transiting planet with a period of about 64 days and a mass of about 7 𝑀⊕, located near a 2:1 commensurability with planet c, suggesting a possible mean-motion resonance chain in the system. Finally, I introduce a preliminary study of the young (20 Myr) multi-planet system V1298 Tau, applying a Skew-Normal fitting method to model the cross-correlation function (CCF) and mitigate stellar activity in nearly 400 HARPS-N spectra. Coupling this RV extraction with photodynamical modeling of TTVs+RVs and Gaussian process regression will enable a clearer separation of stellar and planetary signals. Altogether, this work highlights the power of combining diverse techniques to probe the complex dynamical and evolutionary pathways of exoplanetary systems.