abstract: In this thesis I model the thermal and structural evolution of Kuiper Belt Objects (KBOs) and explore their ability to retain undifferentiated crusts of rock and ice over geologic timescales. Previous calculations by Desch et al. (2009) predicted that initially homogenous KBOs comparable in size to Charon (R ~ 600 km) have surfaces too cold to permit the separation of rock and ice, and should always retain thick (~ 85 km) crusts, despite the partial differentiation of rock and ice inside the body. The retention of a thermally insulating, undifferentiated crust is favorable to the maintenance of subsurface liquid and potentially cryovolcanism on the KBO surface. A potential objection to these models is that the dense crust of rock and ice overlying an ice mantle represents a gravitationally unstable configuration that should overturn by Rayleigh-Taylor (RT) instabilities. I have calculated the growth rate of RT instabilities at the ice-crust interface, including the effect of rock on the viscosity. I have identified a critical ice viscosity for the instability to grow significantly over the age of the solar system. I have calculated the viscosity as a function of temperature for conditions relevant to marginal instability. I find that RT instabilities on a Charon-sized KBO require temperatures T > 143 K. Including this effect in thermal evolution models of KBOs, I find that the undifferentiated crust on KBOs is thinner than previously calculated, only ~ 50 km. While thinner, this crustal thickness is still significant, representing ~ 25% of the KBO mass, and helps to maintain subsurface liquid throughout most of the KBO's history. / Dissertation/Thesis / M.S. Astrophysics 2013

Mean motion resonances (MMRs) play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system and in. exoplanetary systems. Most previous theoretical analyses have focused on the low- to moderate-eccentricity regime, but with new discoveries of high-eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high-eccentricity regime. Here we report on a study of the high-eccentricity regime of MMRs in the circular planar restricted three-body problem. Numerical analyses of the 2: 1 and the 3: 2 interior resonances are carried out for a wide range of planet-to-star mass ratio mu, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We find that new stable libration zones appear at higher eccentricity at libration centers that are. shifted from those at low eccentricities. We provide physically intuitive explanations for these transitions in phase space, and we present novel results on the mass and eccentricity dependence of the resonance widths. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.

Orientador: Ernesto Vieira Neto / Resumo: O estudo da formação e evolução do Sistema Solar é uma fonte de informação para entender sob quais condições a vida poderia surgir e evoluir. Nós apresentamos, nesta Tese de doutorado, um estudo numérico da fase final de acresção dos planetas gigantes do Sistema Solar durante e após a fase do disco de gás protoplanetário. Em nossas simulações, utilizamos um modelo recente e confiável para a formação de Urano e Netuno para esculpir as propriedades do disco trans-Netuniano original (Izidoro et al. , 2015a). Nós fizemos este estudo de uma maneira autoconsistente considerando os efeitos do gás e da evolução dos embriões planetários que formam Urano e Netuno por colisões gigantescas. Consideramos diferentes histórias de migração de Júpiter, devido a incerteza de como Júpiter migrou, durante a fase de gás. As nossas simulações permitiram obter pela primeira vez as propriedades orbitais do disco trans-Netuniano original. Então, calculamos o tempo de instabilidade dos planetas gigantes a partir de sistemas planetários que formam similares Urano e Netuno. Nossos resultados indicam fortemente que a instabilidade dos planetas gigantes acontecem cedo em até 500 milhões de anos e mais provável ainda ter acontecido em 136 milhões de anos após a dissipação do gás. Nós também realizamos simulações para discutir alguns efeitos dinâmicos que acontecem na região do cinturão de Kuiper. Estes efeitos acontecem quando Netuno esteve em alta excentricidade durante a instabilidade planetária. Para es... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: A study of the formation and evolution of the Solar System is a source of information for an understanding of what conditions life could arise and evolve. We present a numerical study of the final stage of accretion of the giant planets of the Solar System during and after the protoplanetary gas disc phase. In our simulations, we use a recent and reliable model for the formation of Uranus and Neptune to sculpt the properties of the original trans-Neptunian disk (Izidoro et al. , 2015a). We have done this study in a self-consistent way considering the effects of gas and the evolution of planetary embryos which form Uranus and Neptune by mutual giant collisions. We considered different Jupiter migration stories due to the uncertainty of how Jupiter’s migration was during the gas phase. Our simulations provide for the first time to obtain the orbital properties of the original trans-Neptunian disk. We then calculate the instability time of the giant planets from planetary systems which form similar Uranus and Neptune. Our results strongly indicate that the instability of the giant planets occurs early within 500 million years and even more likely to happen at 136 million years after gas dissipation. We also perform simulations to discuss some dynamical effects that happen in the Kuiper belt region. These effects happen when Neptune was in high eccentricity during planetary instability. For this problem, we use the simulations performed by Gomes et al. (2018) who investigated the... (Complete abstract click electronic access below) / Doutor

Les petits corps du système solaire riches en volatiles incluent plusieurs populations d’objets : les astéroïdes de la ceinture principale, les astéroïdes troyens des planètes géantes, les objets trans-neptuniens (OTNs) et les comètes. Au cours de ces dernières années, l'’idée que leur position actuelle résulte de migrations orbitales plutôt qu’elle ne reflète leur région de formation a progressivement émergée. Spécifiquement, certains astéroïdes pourraient être des comètes, et certaines comètes pourraient être des OTNs. Je présente ici les travaux réalisés au cours de ma thèse pour contraindre la composition (minéralogie de surface et structure interne) de ces différentes populations afin i) de déterminer les liens qui les unissent, ii) comprendre leurs migrations passées et donc, iii) apporter de nouvelles contraintes aux modèles dynamiques décrivant la formation et l’évolution de notre système solaire. À cet effet, j’ai principalement utilisé comme méthode d’analyse l’observation spectroscopique, ainsi que la modélisation des données obtenues et leur comparaison aux données spectrales de météorites et poussières cosmiques étudiées en laboratoire. / The icy small bodies of our solar system encompass several populations of objects : the main belt asteroids, the giant planets Trojans, the Trans-Neptunian Objects (TNOs) and the comets. During recent years, the idea that their present location is the result of orbital migrations rather than their true formation location has progressively emerged. Specifically, some asteroids could be comets, and some comets could be TNOs. Here, I present the studies carried out along my PhD aiming to constrain the physical properties of all these populations in order ultimately i) to determine the link between these populations, ii) bring key constraints to their past orbital evolution and thus iii) key constraints to the formation and evolution models for our Solar System. For that purpose, I have used spectroscopy as a main tool, as well as data modelling using a radiative transfert code and comparison of our astronomical data to laboratory measurements of meteorites and cosmic dust.

Planetary systems are not only composed of planets, but also of km-sized rocky and icy bodies that are confined within belts similar to the Asteroid and Kuiper belt in the Solar System. Mutual collisions within these belts grind down solids producing dust and giving rise to debris discs. Primitive asteroids and comets likely played a major role in the emergence of life on Earth through their delivery of volatiles early in the lifetime of our planet. Cometary impacts, therefore, could be a necessary condition for the emergence of life in exoplanets and the study of debris discs essential to determine the ubiquity of such phenomenon. Moreover, exocometary discs provide a unique window into the origins and outer regions of planetary systems as comets do within our Solar System. Initially, in Chapter 1 I present an overview of the study of exoplanetary systems, focusing on debris discs. I discuss the basics of planet formation, its connection with debris discs, and how these evolve and interact with planets. I also describe how we observe these discs and probe their volatile component that is locked inside exocomets, and some evidence supporting the idea of exocomets venturing into the inner regions of planetary systems. Then, in Chapters 2, 3, 4 and 5 I present new ALMA observations of the systems HD 181327, η Corvi, the multiplanet system 61 Vir and HD 107146, which host debris discs. In the first two, I highlight the derivation of the density structure of their discs and the detection of volatiles being released by exocomets; while in the third and fourth I compare the observations with simulations, which I use to set constraints on the underlying planetesimal distribution and mass and orbital distance of unseen planets. Finally, in Chapter 6 I present result obtained from N-body simulations to study the process of inward transport of comets by a multiplanetary system and how these can deliver material to inner planets and explain the frequently observed exozodiacal dust. To conclude, in Chapter 7 I summarise the results and conclusions of this dissertation and discuss ongoing and future work.

Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden. / This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader.

Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden. / This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.