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Evolution of the Eccentricity and Orbital Inclination Caused by Planet-Disc Interactions Jean Teyssandier

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Evolution of the Eccentricity and Orbital Inclination Caused by Planet-Disc Interactions Jean Teyssandier Evolution of the eccentricity and orbital inclination caused by planet-disc interactions Jean Teyssandier To cite this version: Jean Teyssandier. Evolution of the eccentricity and orbital inclination caused by planet-disc interac- tions. Galactic Astrophysics [astro-ph.GA]. Université Pierre et Marie Curie - Paris VI, 2014. English. NNT : 2014PA066205. tel-01081966 HAL Id: tel-01081966 https://tel.archives-ouvertes.fr/tel-01081966 Submitted on 12 Nov 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité : Physique École doctorale : ASTRONOMIE ET ASTROPHYSIQUE D’ÎLE-DE-FRANCE réalisée à l’Institut d’Astrophysique de Paris présentée par Jean TEYSSANDIER pour obtenir le grade de : DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse : Évolution de l’excentricité et de l’inclinaison orbitale due aux interactions planètes-disque soutenue le 16 Septembre 2014 devant le jury composé de : Bruno Sicardy Président Carl Murray Rapporteur Sean Raymond Rapporteur Alessandro Morbidelli Examinateur Clément Baruteau Examinateur Caroline Terquem Directrice de thèse Une mathématique bleue Dans cette mer jamais étale D’où nous remonte peu à peu Cette mémoire des étoiles Léo Ferré, La mémoire et la mer 2 Remerciements Mes remerciements vont tout d’abord à Caroline, pour avoir accepté de diriger cette thèse. Ca a été un plaisir de pouvoir profiter du large spectre de ses con- naissances, et de tant apprendre à son contact. Je lui suis aussi redevable pour la rigueur qu’elle a imposée à mon travail et qui ne pourra que m’être bénéfique pour la suite. Je la remercie enfin de m’avoir laissé une grande liberté dans mes recherches, m’encourageant à explorer mes propres pistes et développer mes idées, et de toujours avoir laissé sa porte ouverte à la discussion. C’est aussi grâce à elle et Steve Balbus que j’ai pu passer deux si belles années à Oxford. Les aléas de la recherche ont parfois du bon! Je remercie aussi Carl Murray et Sean Raymond d’avoir accepté de servir en tant que rapporteurs de cette thèse, ainsi que Bruno Sicardy, Alessandro Mor- bidelli et Clément Baruteau pour avoir accepté d’en être les examinateurs. Je remercie aussi Frederic Rasio et Smadar Naoz de m’avoir accueilli à l’Université de Northwestern durant les stages qui ont précédé ma thèse. Ce sont eux qui m’ont définitivement donné le goût pour la dynamique des exoplanètes. Je remercie aussi John Papaloizou pour la collaboration qu’il a apportée à l’un des papiers publiés dans cette thèse. Cette thèse n’aurait pas été une si belle expérience sans toutes les rencon- tres qu’elle a occasionnées en chemin. Il y a d’abord les anciens du M2 de l’Observatoire, Élodie, Andy, Jessica, Claire-Line, Alex, Élise et les autres. À l’IAP, c’est toujours un plaisir de revenir passer du temps avec Vincent, Flavien et tous les autres doctorants. À Oxford, je remercie Suzanne Aigrain de m’avoir accueilli dans son groupe, avec à la clé les fameux déjeuners du vendredi! C’est un plaisir d’avoir côtoyé ses étudiants, en particulier Tom, Ed et Ruth. Enfin, la vie à Oxford n’aurait pas été la même sans Thibaut, Rich et Shravan. Un grand merci au passage à Rich, pour avoir relu quelques bouts de ma thèse. Plus généralement, ce fut un plaisir de partager durant deux ans la vie du groupe d’astrophysique d’Oxford. 3 4 Peu de choses durant mon séjour à Oxford m’ont fait plus plaisir que de recevoir la visite de mon frère et ma soeur. J’espère qu’ils auront l’occasion de venir à Cambridge voir si les pubs sont si différents de ceux d’Oxford. Enfin, cette thèse est dédiée à mes parents, pour leur soutien inconditionnel durant toute la poursuite de mes études. Si j’en suis arrivé là, c’est surtout grâce à eux. Abstract Since the discovery of the first planet orbiting a main-sequence star outside the solar system in 1995, the field of exoplanet studies has grown rapidly, both from the observational and theoretical sides. Despite the fact that we are still lacking a global picture for the formation and evolution of planetary systems, it is now commonly accepted that planets form in protoplanetary discs and interact with them in the early stages of their evolution. This thesis aims at studying some of these interactions. The observations of extrasolar planets have brought several puzzling results to the attention of the community. One of them is the existence of hot Jupiters, giant gaseous planets which orbit their parent star with a period of a few days only. The commonly accepted scenario is that they formed in the outer parts of the disc and migrated inward. Furthermore, a significant number of planets detected so far, especially by the method of radial velocities, have high eccen- tricities. This is in contrast with our own solar system where giant planets have quasi-circular orbits. Such a distribution of eccentricities may be the signature of strong dynamical interactions between the different components of a same planetary system. Finally, there are short-period planets whose orbits is mis- aligned with the axis of rotation of their host star, which could possibly argue against the smooth migration of planets in their disc. Therefore, it is important to disentangle between the orbital characteristics that planets acquired through mutual dynamical interactions, and the ones they acquired when they interacted with the disc. Firstly, it gives constraints on the physical parameters of protoplanetary discs. Secondly, it is interesting to know the properties of the system of planets after the disc has dissipated, and what sort of initial conditions one can expect when planets start to interact freely one with each other. For instance, one can ask if it is possible for planets to reach large eccentricities and inclinations when the disc was still present, and whether they could maintain them or not. 5 6 The first topic that we study in this thesis is the interaction between a planet and a disc, when the orbit of the planet has a large inclination with respect to the mid-plane of the disc. If the initial inclination of the orbit is larger than some critical value, the gravitational force exerted by the disc on the planet leads to a Kozai cycle in which the eccentricity of the orbit is pumped up to large values and oscillates with time in antiphase with the inclination. On the other hand, both the inclination and the eccentricity are damped by the frictional force that the planet is subject to when it crosses the disc. Typically, Neptune or lower mass planets would remain on inclined and eccentric orbits over the disc lifetime, whereas orbits of Jupiter or higher mass planets would align and circularize. A mechanism that could explain this primordial misalignment between plan- ets and discs, and more generally, the population of planets with large spin-orbit misalignments, is that of resonant migration. When two planets migrate in a disc, it is possible that they enter a configuration where the ratio of their orbital periods is equal to the ratio between two small integers. This configuration is referred to as mean motion resonance. If the resonance is maintained during the migration, the eccentricities can grow to high values. Simulations have shown that, in some cases, the inclinations could also grow to high values. However, the disc tends to damp the eccentricities and inclinations and keep them to low values. In this thesis we study, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion res- onance to enter an inclination–type resonance. We show that this resonance can be achieved only after the eccentricities have reached a critical value. However the maximum value reached by the eccentricities is limited by the disc damp- ing. We show that the criterion for triggering an inclination–type resonance is a function of the ratio between the eccentricity damping timescale and the or- bital migration timescale. If this ratio is larger than a few tenths, the system can enter an inclination–type resonance. However, both observations and theory suggest that this ratio probably cannot exceed a few hundredths. We conclude that excitation of inclinations through the type of resonance described here is very unlikely to happen in a system of two planets migrating in a disc. Résumé Depuis la découverte de la première planète orbitant une étoile de la séquence principale autre que le Soleil en 1995, ce champ de recherche a connu une crois- sance vertigineuse, tant au niveau des observations, que des modèles théoriques développés en parallèle. Même si la formation et l’évolution des systèmes planétaires restent encore mal comprises dans leur globalité, Il est à peu près certain que les planètes se forment dans des disques protoplanétaires et inter- agissent avec ces derniers durant la phase primordiale de leur évolution. Cette thèse s’attache à décrire certains aspects de ces interactions. Parmi les problèmes soulevés par les nombreuses observations d’exoplanètes, on peut citer l’existence des Jupiter chaudes, géantes gazeuses dont la révolu- tion autour de leur étoile s’effectue en quelques jours à peine.
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