Universidade Federal Do Rio Grande Do Norte Centro De Ciências Exatas E Da Terra Departamento De Física Teórica E Experimental Programa De Pós-Graduação Em Física

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Universidade Federal Do Rio Grande Do Norte Centro De Ciências Exatas E Da Terra Departamento De Física Teórica E Experimental Programa De Pós-Graduação Em Física universidade federal do rio grande do norte centro de ciências exatas e da terra departamento de física teórica e experimental programa de pós-graduação em física ESTUDO DA TOPOLOGIA DE MICROLENTES GRAVITACIONAIS E A DESCOBERTA DE EXOPLANETAS DO TIPO TERRA NA ZONA HABITÁVEL Leandro de Almeida natal-rn 2017 Leandro de Almeida ESTUDO DA TOPOLOGIA DE MICROLENTES GRAVITACIONAIS E A DESCOBERTA DE EXOPLANETAS DO TIPO TERRA NA ZONA HABITÁVEL Dissertação de mestrado apresentada ao Programa de Pós-Graduação em Física do Departamento de Física Teó- rica e Experimental da Universidade Federal do Rio Grande do Norte como requisito parcial para a obtenção do grau de mestre em Física. Orientador: Prof. Dr. José Dias do Nascimento Jr. natal-rn 2017 Universidade Federal do Rio Grande do Norte – UFRN Sistema de Bibliotecas – SISBI Catalogação da Publicação na Fonte - Biblioteca Central Zila Mamede Almeida, Leandro de. Estudo da topologia de microlentes gravitacionais e a descoberta de exoplanetas do tipo Terra na zona habitável / Leandro de Almeida. - 2017. 101f.: il. Dissertação (mestrado) - Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Programa de Pós- Graduação em Física. Natal, RN, 2017. Orientador: José Dias do Nascimento Júnior. 1. Microlentes gravitacionais - Dissertação. 2. Exoplanetas - Dissertação. 3. Detecção - Dissertação. I. Nascimento Júnior, José Dias do. II. Título. RN/UF/BCZM CDU 524.3:520.3 À minha família i Agradecimentos • Agradeço em primeiro lugar à minha querida mãe Lúcia, por todo o suporte emoci- onal e físico nesses 5 anos longe de casa que me trouxeram até aqui. • Ao meu orientador, Dr. José Dias do Nascimento Jr. pelos aconselhamentos e por me guiar durante essa jornada que foi escrever essa dissertação. • Ao Professor e bom amigo João Leão, pelas críticas construtivas e pelo apoio que vem desde a graduação. • Aos meus colegas da pós-graduação de física da UFRN e aos muitos cafés que to- mamos. E também à todos os meus companheiros e companheiros do Grupo de Estrutua e Evolução Estelar (GE3). • Ao meu querido irmão Martin Cruisk por todas as discussões científicas e momentos de ping = 10ms . E também ao outro irmão Juninho por mais 1 ano de café e arroz (com cebola dessa vez). • À linda Alexia Thamy pelo companheirismo e principalmente pelos ótimos debates (e os muitos jantares gourmet que inventamos). • À minha amiga Mariana e ao meu amigo Apollo por esses mais de 10 anos de muitos papos e aventuras. • À Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) pelo apoio financeiro. i Eu não quero acreditar, eu quero conhecer. Carl Sagan Resumo Na última década, o número de exoplanetas descobertos cresceu exponencialmente, principalmente devido as observações realizadas pela missão Kepler e K2, que no ano de 2016, anunciou 1284 planetas confirmados de uma só vez. Estas descobertas foram feitas utilizando o método de trânsito planetário, que não possui sensibilidade para planetas de baixa massa muito distantes de suas estrelas. A maioria destas descobertas apresentam planetas gigantes com órbitas próximas às suas estrelas. Por outro lado, a técnica de detecção através de microlentes gravitacionais é sensível à planetas de baixa massa em órbitas de 0:5 AU até 10 AU. Esta técnica pode detectar planetas em estrelas de baixa luminosidade pois, depende apenas do campo gravitacional combinado da estrela-planeta, o que seria difícil para as outras técnicas que dependem da luz emitida pela estrela. Até o momento, foram descobertos 47 planetas através desta técnica, que é uma quantidade relativamente pequena comparada com os outros métodos. Nesta dissertação mostramos de maneira detalhada as equações por detrás da teoria de microlentes gravitacionais e suas aplicações na detecção de planetas de baixa massa. Nos focamos na caracterização e análise de sistemas com topologia fechada, em que o planeta tem entre 10−5 e 10−6 da massa da estrela e com seu semi-eixo maior em torno de 1 AU, que são sistemas com carac- terísticas de massa e distância parecidos com o sistema Sol-Terra. Também apresentamos uma sugestão de parametrização para o parâmetro de impacto µ0 e o ângulo de impacto α de forma a reduzir o tempo de busca em curvas de luz geradas a partir de sistemas com topologia fechada. Apresentamos ainda os principais passos para o desenvolvimento de dois códigos que utilizam o método semi-analítico de resolução da equação da lente e o método de simulação por força bruta "Inverse Ray Shooting"(IRS) respectivamente. Esses códigos simulam a topologia e curva de luz de eventos de microlentes gravitacionais, e foram usados para produzir todas as figuras e gráficos apresentados nesta dissertação. Ao final, demonstramos a capacidade do modelo semi-analítico na simulação de curvas teóricas e comparamos essas curvas com eventos reais de microlentes gravitacionais. Palavras-chave: Microlentes Gravitacionais, Exoplanetas, detecção. iii Abstract In the last decade, the number of exoplanets discovered has grown exponentially, mainly due to Kepler observations which, along with observations of the K2 mission, announced the discovery of 1284 planets at once in 2016. These discoveries were done using the planetary transit method, which has low sensitivity for low-mass planets far away from their stars. Thus most of the discoveries of giant planets was of orbits close to their stars. In contrast, the gravitational microlensing technique is sensitive to low-mass planets orbiting between 0:5 AU and 10 AU. Because it depends only on the combi- ned gravitational field of the star-planet, this technique can detect planets around low brightness stars, which would be difficult for other techniques that depend on star emitted light. Until now, astronomers have discovered 47 planets through this technique, which is relatively low number, when compared to the other methods like transit and radial velocity. In this dissertation we show in detail the equations behind the gravitational microlensing theory and its applications to detect distant low-mass planets. We focus on the characterization of systems with closed topology, where the planet has between 10−5 and 10−6 of the mass of the star and with a semi-major axis about 1 AU (planet with Earth-like mass around 1AU of a star with Sun-like mass). We also present a sugges- tion of parameterization for the impact parameter µ0 and the impact angle α in order to reduce the search time consuming for light curves generated from systems with close topology. We present the main steps for the development of two algorithms that use the semi-analytical method of solution of the lens equation and the brute force of simula- tion method Inverse Ray Shooting (IRS) respectively. These codes simulate the topology and light curve of microlensing events, and were used to simulate our systems presen- ted in this dissertation. As a main result, we demonstrate the hability of the model to generate theoretical curves and compared these light curves with real microlensing events. Keywords: Gravitational Microlensing, Exoplanets, Detection iv Lista de Figuras 1.1 Planetas descobertos por método por ano...................3 2.1 Diagrama do caminho da luz..........................9 2.2 Diagrama da luz Detalhe............................9 2.3 Anel de Einstein................................ 10 2.4 Diagrama Luz Offset.............................. 11 2.5 Diagrama da luz Offset detalhe........................ 12 2.6 Projeção das imagens.............................. 13 2.7 Projeção das imagens 2............................. 14 2.8 Diagrama de Magnificação Single Lens.................... 15 2.9 Magnificação de M± .............................. 15 2.10 Trajeto da fonte para lente singular...................... 18 2.11 OGLE-2012-BLG-0371............................. 20 2.12 Parametrização do trajeto da fonte para n lentes............... 24 3.1 Distribuição de pontos randômicos...................... 35 3.2 Tipos de Distribuição.............................. 36 3.3 Mapa de Magnificação Randômico....................... 37 3.4 Mapa de Magnificação de Vogel........................ 37 3.5 Mapa de Magnificação para várias Curvas de Luz.............. 38 4.1 Imagens formadas para n = 1 ......................... 40 4.2 Trajetória das imagens para n = 1 ....................... 41 4.3 Topologia de sistema binário.......................... 42 4.4 Trajeto das Imagens para n = 2........................ 42 4.5 Paridade das imagens ao cruzar a linha da caustica............. 43 4.6 Topologia geral de sistemas binários A.................... 44 4.7 Topologia geral de sistemas binários B.................... 45 4.8 Topologias aberta, ressonante e fechada.................... 45 v LISTA DE FIGURAS 4.9 Topologia de um sistema aberta........................ 46 4.10 Topologia de um sistema aberta com q < 1 .................. 47 4.11 Topologia fechada de um sistema....................... 48 4.12 Topologia de um sistema fechada (s << 1) .................. 49 4.13 Topologia de um sistema ressonante A.................... 50 4.14 Topologia de um sistema ressonante B.................... 50 4.15 Degenerescência do trajeto........................... 51 4.16 Curva de luz com detecção de planeta..................... 52 4.17 Topologia e Região de Interesse para q << 1 ................. 53 4.18 Evolução da área de influência com s ..................... 56 4.19 Diagrama µ0 x α ................................ 57 4.20 Curvas de Luz de um sistema de topologia fechada............. 58 5.1 Curva de Luz OGLE 2003–BLG–235/MOA 2003–BLG–53........
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