ii Riassunto Rivelazione e caratterizzazione dell'architettura orbitale di sistemi planetari intorno a stelle fredde Le nane M si sono dimostrate dei target affascinanti per la ricerca di esopianeti, grazie alla crescente evidenza dalle survey di transiti (ad esempio Kepler) e di velocit`aradiali (ad esempio HARPS ed HARPS-N), anche se diversi ostacoli intralciano la ricerca e l'analisi di sistemi planetari intorno ad esse. Per queste ragioni, `edi fondamentale importanza intensificare gli sforzi rivolti alla rive- lazione e caratterizzazione di pianeti extrasolari intorno a nane M, poich´ele nuove scoperte contribuiranno a portare il supporto statistico necessario allo studio di classi peculiari di pianeti, mentre la precisa caratterizzazione orbitale sia di sistemi noti che appena scoperti aiuter`aa vincolare meglio i processi di for- mazione e migrazione planetaria. Le molte domande aperte sulle nane M ospiti e sui loro sistemi planetari, e lo sviluppi di nuove metodologie per investigarle, sono la base delle motivazioni del mio lavoro di Dottorato. Nella mia tesi, per prima cosa presento la tematica dei sistemi esoplane- tari intorno a nane M, sia dal punto di vista osservativo che statistico. Poi riporto il mio lavoro di analisi delle prestazioni di tre diverse tipi di anal- isi di periodogramma, il \Generalised Lomb-Scargle periodogram" (GLS), la sua versione modificata che sfrutta la statistica bayesiana (BGLS), ed il pe- riodogramma multifrequenza chiamato FREquency DEComposer (FREDEC), motivato dall’ubiquit`adi sistemi multipli di pianeti di piccola massa. I risultati illustrati sostengono la necessit`adi rafforzare e sviluppare ulteriormente le pi`u aggressive ed efficaci strategie per la robusta identificazione di segnali planetari di piccola ampiezza nei dati di velocit`aradiale. In seguito descrivo gli algoritmi ad alte prestazioni usati dal gruppo di ricerca di cui sono parte per la model- lizazione di segnali Kepleriani singoli e multipli, e la loro applicazione sia su dati simulati di velocit`aradiale analizzati alla cieca, e contenenti rappresentazioni realistiche di segnali stellari e planetari, che su dati HARPS ad alta precisione di archivio di una stella M con un sistema multiplo di super Terre. Riporto quindi i primi risultati che ho ottenuto nell'analisi di dati di ve- locit`aradiale raccolti come parte del progetto HADES (HArps-n red Dwarf Exoplanet), cio`ela rivelazione di un pianeta di piccola massa e lungo periodo intorno alla nana M1 GJ15A, una delle stelle pi`uvicine al Sole, che era gi`anota ospitare una super Terra di corto periodo. Poich´ela stella ospite `eparte di un sis- tema binario con la nana M GJ15B, ho derivato una soluzione orbitale migliorata per GJ15B e studiato un set di simulazioni numeriche dell'evoluzione a lungo termine del sistema planetario affetto da oscillazioni eccentriche di Lidov-Kozai, iii iv RIASSUNTO che provano che l'interazione dinamica pu`ofacilmente aumentare l'eccentricit`a del pianeta esterno, anche al di sopra dei livelli osservati. Per concludere, de- scrivo la strategia e i risultati preliminari dell'analisi bayesiana ancora in corso del campione HADES, che mira a calcolare la frequenza di pianeti intorno a stelle di piccola massa e la rivelabilit`aglobale della survey. Abstract Detection and Orbital Architecture Characteri- zation 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 pre- cise 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 method- ologies 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 v vi ABSTRACT observed value. Finally, I describe the strategy and preliminary results of the ongoing Bayesian analysis of the full HADES sample, aiming to compute the occurrence rates of planets around small mass stars and the global detectability of the survey. Contents Riassunto iii Abstract v 1 Introduction 1 1.1 Historical and scientific context . .1 1.2 Chapter summaries . .4 2 M dwarfs planetary systems: detection techniques and statis- tical properties 7 2.1 Detection techniques . .7 2.1.1 The radial velocity method . .8 2.1.2 The transit method . 13 2.1.3 The gravitational microlensing method . 14 2.2 M dwarfs stellar noise . 15 2.2.1 Identifying stellar signals . 15 2.2.2 Correcting stellar signals . 17 2.2.3 Examples of systems affected by stellar activity . 18 2.2.4 Activity relationships . 19 2.3 Properties of M-dwarf planetary systems . 20 2.3.1 Population analysis . 21 2.3.2 M dwarfs habitability . 25 3 Periodogram tools 29 3.1 Introduction . 29 3.2 Simulation setup . 31 3.2.1 Assumptions and Caveats . 31 3.2.2 Synthetic catalogs . 31 3.3 Results . 34 3.3.1 Sanity check on white noise . 35 3.3.2 Single-planet circular orbits catalog . 37 3.3.3 Single-planet eccentric orbits catalog . 39 3.3.4 Additional experiment: correlated noise . 41 3.3.5 Multi-planet circular orbits catalog . 44 3.3.6 Multi-planet eccentric orbits catalog . 47 3.4 Summary and discussion . 48 vii viii CONTENTS 4 High-performance algorithms: tests and applications 51 4.1 Radial velocity fitting challenge . 51 4.1.1 Simulated data sets . 52 4.1.2 Implemented analysis techniques . 53 4.1.3 Results . 57 4.2 GJ 273: a very low-mass planet in a compact multiple system . 60 4.2.1 The known system . 60 4.2.2 Candidate planet detection . 63 4.2.3 Statistical validation . 66 5 Global Architecture of Planetary Systems 69 5.1 HARPS-N@TNG . 69 5.2 The GAPS project . 71 5.2.1 Results overview . 74 5.3 The HADES programme . 77 6 GJ15A: A multiple wide planetary system sculpted by binary interaction 81 6.1 Introduction . 81 6.2 Observations and catalog data . 82 6.3 Stellar Properties of GJ15A and GJ15B . 85 6.3.1 Photometric analysis . 85 6.4 Spectroscopic data analysis . 87 6.4.1 The MCMC model . 87 6.4.2 Analysis of the activity indexes . 88 6.4.3 Analysis of the combined RV time series . 89 6.5 Binary orbital interaction . 96 6.5.1 Orbital modeling from astrometry and RV data . 99 6.5.2 Lidov-Kozai Interaction modeling . 104 6.6 Discussion and conclusions . 106 7 HADES statistical analysis - occurrence rate and global de- tectability 113 7.1 Stellar sample statistics . 113 7.2 Observation strategy statistical study . 121 7.3 Complete HADES statistical study . 123 7.3.1 Landmark Bayesian analysis . 123 7.3.2 HADES team approach . 124 7.3.3 Preliminary results . 125 8 Summary and conclusions 129 8.1 Summary of results . 129 8.1.1 Tools for data analysis . 129 8.1.2 Study of M dwarfs planetary systems . 131 8.2 Future prospects . 133 8.2.1 Further application of analysis techniques . 133 8.2.2 Future opportunities . 133 List of Figures 2.1 The period distribution of exoplanets orbiting M dwarfs: in yel- low are shown those from transit observations and in orange those from radial velocity. 21 2.2 The m sin i distribution of RV exoplanets orbiting M dwarfs. 22 2.3 The Rp distribution of transit exoplanets orbiting M dwarfs. 23 2.4 Planetary occurrence rate in the period-radius parameter space. The upper number in each cell indicates the occurrence rate, while the lower number indicates the Kepler pipeline sensitivity. (Dressing and Charbonneau, 2015). 24 2.5 Circustellar habitable zone as function of stellar mass for zero- age main sequence stars, with the assumption of Earth-like planet and atmosphere.