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Tidal Effects on the Oort Cloud Comets and Dynamics of the Sun In Universita` Degli Studi di Padova Dipartimento di Fisica e Astronomia \G. Galilei" SCUOLA DI DOTTORATO DI RICERCA IN ASTRONOMIA CICLO XXVI Doctoral Thesis Tidal Effects on the Oort Cloud Comets and Dynamics of the Sun in the Spiral Arms of the Galaxy PhD School Director: Ch. mo Prof Giampaolo Piotto Supervisor: Ch. mo Prof. Luigi Secco PhD student:Alice De Biasi \If one does not know to which port one is sailing, no wind is favorable.." Lucio Anneo Seneca UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia \G. Galilei" SCUOLA DI DOTTORATO DI RICERCA IN ASTRONOMIA CICLO XXVI Abstract Tidal Effects on the Oort Cloud Comets and Dynamics of the Sun in the Spiral Arms of the Galaxy The Solar System presents a complex dynamical structure and is not isolated from the Galaxy. In particular the comet reservoir of our planetary system, the Oort cloud, is extremely sensitive to the the galactic environment due to its peripheral collocation inside the Solar System. In this framework, the growing evidences about a possible migration of the Sun open new research scenarios relative to the effects that such kind of migration might induce on the cometary motion. Following several previous studied, we identified the spiral arm structure as the main perturbation that is able to produce an efficient solar migration through the disk. Widening the classical model for the spiral arms, provided by Lin& Shu to a 3D formalism, we verified the compatibility between the presence of the spiral perturbation and a significant solar motion for an inner Galactic position to the current one, in agreement with the constrains in position, velocity and metallicity due to the present conditions of our star. The main perturbers of the Oort cloud, the close stellar passages and the tidal field of the Galaxy, might be both affected by the variation of Galactic environment that the solar migration entails. Despite that, in order to isolate the effects to the two different perturbators, we decided to focus our attention only on the Galactic tide. The perturbation due to the spiral structure was included in the study on the cometary motion, introducing the solar migration and adding the direct presence of the non-axisymmetric component in the Galactic potential of the tidal field. The results show a significant influence of the spiral arm in particular on cometary objects belonged to the outer shell of the Oort cloud, for which provides an injection rate three times bigger than the integration performed without the spiral arms. The introduction of the spiral perturbation seems to bolster the planar component of the tide, indeed it produces the most significant variation of the perihelion distance for moderate inclination orbits with respect to the plane. The peak for the cometary injections has been registered between 6 and 7 kpc. If this evidence will be confirmed by more realistic cometary sample, it might involve a redefinition of the habitability edges in the Galaxy (GHZ). In particular regions not precluded to the formation of life, may compromise the development of the life with a high cometary impact risk. UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia \G. Galilei" SCUOLA DI DOTTORATO DI RICERCA IN ASTRONOMIA CICLO XXVI Riassunto Tidal Effects on the Oort Cloud Comets and Dynamics of the Sun in the Spiral Arms of the Galaxy Il Sistema Solare `euna struttura con una dinamica complessa e non isolata da quella galattica. In particolare la riserva cometaria del nostro sistema planetario, la nube di Oort, a causa della sua periferica collocazione all'interno del Sistema Solare, risulta es- tremamente sensibile all'ambiente galattico circostante. In questo contesto, le crescenti evidenze di una possibile migrazione del Sole, aprono un nuovo scenario di indagine rela- tivo ai cambiamenti che tale migrazione potrebbe indurre sul moto cometario. Seguendo un filone di ricerca gi`atracciato, abbiamo identificato nella struttura a spirale la princi- pale perturbazione in grado di produrre un efficace effetto migratorio per il Sole. Am- pliando il classico modello di Lin & Shu con una modellizzazione 3D per i bracci a spirale considerati in regime transiente, siamo stati in grado di verificare la compati- bilit`atra tale perturbazione e un moto solare attraverso il disco, in accordo con i vincoli di posizione, velocit`ae metallicit`aimposti dalla attuale condizione della nostra stella. Malgrado i maggiori perturbatori della nube di Oort, i passaggi stellari ravvicinati e il campo mareale della Galassia, siano entrambi potenzialmente sensibili alla variazione di ambiente galattico che una migrazione solare comporta, abbiamo concentrato il nostro studio unicamente sulla marea galattica. La perturbazione dovuta alla spirale, `estata incorporata nello studio dei moti cometari, sia attraverso l'introduzione della migrazione solare, che come effetto diretto sulle comete grazie alla presenza della componente non- assisimmetrica nel campo mareale. I risultati mostrano un’influenza significativa della spirale, in particolar modo sulla popolazione cometaria del guscio pi`uesterno della nube, per la quale si sono registrati tassi di immissione cometaria 3 volte maggiori rispetto al caso senza tale perturbazione. La spirale sembra rinforzare l'azione della compo- nente piana della marea, producendo infatti le maggiori variazioni sui perieli cometari in corrispondenza di orbite con inclinazioni moderate rispetto al piano galattico. Si `e inoltre rilevato che il picco di immissione cometaria si trova in corrispondenza di dis- tanze galattiche per il Sole comprese tra 6 e 7 kpc. Se tale evidenza fosse confermata anche da campioni cometari pi`urealistici, potrebbe comportare un vincolo ulteriore alla definizione della zona di abitabilit`agalattica (GHZ). In particolare, regioni del disco vi Contents non attualmente precluse alla formazione della vita, potrebbero risultare inadatte allo sviluppo della stessa per un rischio di impatto cometario troppo elevato. Contents Abstract iii Riassuntov List of Figures xi List of Tables xv Abbreviations xvii Introduction1 1 Comets: a brief overview5 1.1 Comets in general: the trans-Neptunian population.............5 1.2 Comets in particular: different comet families................8 1.2.1 Short period comets.......................... 10 1.2.1.1 Jupiter family comets.................... 11 1.2.1.2 Halley-type comets..................... 13 1.3 The Oort cloud: the long period comets reservoir.............. 14 1.3.1 Origin and evolution of Long period comets............. 14 1.3.2 Perturbers of the Oort cloud..................... 15 1.3.2.1 Cometary Fading and Destruction............. 20 1.4 The formation of the Oort cloud....................... 20 1.5 Exo Oort cloud................................. 26 1.5.1 \Oort-type comet Cloud" structure around different stars..... 26 1.5.2 Constraints for the formation of Oort-type comet clouds...... 26 1.5.3 Applications.............................. 31 2 The Galactic Environment 35 2.1 The model for the Milky Way......................... 35 2.1.1 The Bulge................................ 36 2.1.2 The Disk................................ 36 vii viii Contents 2.1.3 The DM Halo.............................. 38 2.1.4 The Galactic mass distributions.................... 40 2.2 The solar motion in an axisymmetric potential............... 41 3 The Spiral Arms Effects on the Solar Path 43 3.1 The solar migration: a new framework of research............. 43 3.1.1 Metallicity gradient.......................... 44 3.1.1.1 Starting Sun's position................... 46 3.2 Spiral arms theory............................... 47 3.2.1 The long-live density waves model.................. 48 3.2.1.1 Instabilities on the disk................... 49 3.2.1.2 Formation of Spiral Arms.................. 52 3.2.2 Spiral arms associated with the solar environment......... 54 3.2.3 Results for a 2D fixed spiral arms................... 59 3.3 3D extension for the spiral arms....................... 61 3.3.1 Summary for the 3D spiral arms model............... 66 3.4 Overlapping vs separate spiral arms perturbations............. 67 3.4.1 The epicycle parameters........................ 68 3.4.2 Joined vs separate spiral arms code.................. 72 3.4.2.1 Joined perturbations..................... 72 3.4.2.2 Separate perturbations................... 73 3.4.3 Runs................................... 74 3.4.3.1 Trends for two infinitely separated encounters...... 75 3.4.3.2 Effect of finite separation.................. 78 3.4.4 A statistical measure of the difference in distributions....... 81 3.4.5 The spiral arms perturbation on the solar path........... 83 4 Solar motion on the Galactic Habitable Zone 93 4.1 The Galactic Habitable Zone......................... 93 4.2 Sun position on the GHZ........................... 100 5 The Spiral Arms Effects on the Oort Cloud 105 5.1 Cometary Orbits................................ 105 5.2 Integration in an axisymmetric potential................... 106 5.2.1 Results for the cometary integration in a 2D axisymmetric potential108 5.3 Integration in a non-axisymmetric potential................. 111 5.3.1 The relative form and the perturbative function ......... 112 R 5.3.1.1 Numerical problems..................... 115 5.3.2 Initial conditions for Sun and comets................. 117 5.3.2.1 The solar path........................ 117 5.3.2.2 The 3D cometary samples.................. 119 5.3.3 Results for the cometary integration in a 3D non-axisymmetric potential................................ 119 5.3.3.1
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