Detection and Orbital Architecture Characterization of Planetary Systems Around Cool Stars

M dwarfs have proven to be fascinating targets for exoplanetary search, from the growing evidence from transit (e.g., Kepler) and radial-velocity (e.g, HARPS, HARPS-N) surveys, even if several complex obstacles hamper the analysis and detection of planetary systems around them. For these reasons, it is pivotal to intensify the efforts towards the detection and characterization of extrasolar planets around M dwarfs, since new discoveries will help bring the statistical support still needed for the study of peculiar classes of planets, while the precise orbital characterization of both known and new systems will tighten the constraints on formation and migration processes. The many open issues on M dwarfs host and their planetary systems, and the development of new methodologies to investigate them, are the foundation of the motivation for my PhD work. In my thesis I first present the topic of M dwarfs exoplanetary systems, both from the observational and statistical point of view. I then report my work on performance analysis of three periodogram tools, the Generalised Lomb-Scargle Periodogram (GLS), its modified version based on Bayesian statistics (BGLS), and the multi-frequency periodogram scheme called FREquency DEComposer (FREDEC), motivated by the ubiquitousness of multiple systems with low-mass components. The results illustrated reinforce the need for the strengthening and further developing of the most aggressive and effective ab initio strategies for the robust identification of low-amplitude planetary signals in RV data sets. I describe the high-performance algorithms for single and multiple Keplerian signals modeling used by the research group I am part of, and their applications both on blindly analyzed simulated RV measurements including realistic stellar and planetary signals, and on high- precision HARPS archive data of an M dwarf star with a multiplanet system of Super Earths. I then report the first results I obtained from the analysis of RV data collected as part of the HADES (HArps-n red Dwarf Exoplanet Survey) project, that is the detection of a long-period low-mass planet orbiting the M1 dwarf GJ15A, one of the nearest stars to the Sun, which was already known to host a short-period Super Earth. Since the host star is part of a binary system with the M dwarf GJ15B, I derived an improved orbital solution for GJ15B and studied a suite of numerical simulations of the long-term evolution of the planetary system under eccentric Lidov-Kozai oscillations, which proved that this dynamical interaction can easily enhance the eccentricity of the outer planet, up to and even above the observed value. Finally, I describe the strategy and preliminary results of the ongoing Bayesian analysis of the full HADES survey, aiming to compute the occurrence rates of planets around small mass stars and the global detectability of the survey.