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UM ESTUDO SOBRE O Momentum ANGULAR UNIVERSIDADE FEDERAL DO RIO GRANDE DO NORTE CENTRO DE CIÊNCIAS EXATAS E DA TERRA DEPARTAMENTO DE FÍSICA TEÓRICA E EXPERIMENTAL JULIANA CERQUEIRA DE SANTANA UM ESTUDO SOBRE O Momentum ANGULAR TOTAL DE ESTRELAS COM PLANETAS DISSERTAÇÃO DE MESTRADO NATAL, RN NOVEMBRO DE 2011 JULIANA CERQUEIRA DE SANTANA UM ESTUDO SOBRE O Momentum ANGULAR TOTAL DE ESTRELAS COM PLANETAS Trabalho apresentado ao Programa de Pós- graduação em Física do Departamento de Física Teórica e Experimental da UNIVER- SIDADE FEDERAL DO RIO GRANDE DO NORTE como requisito parcial para obtenção do grau de Mestre em Física. Orientador: Prof. Dr. José Renan de Medeiros NATAL, RN NOVEMBRO DE 2011 Aos meus queridos pais Nilza e Roque, a quem eu tanto amo e que me inspiram a cada dia que acordo. ii Agradecimentos Assim como em nossa formação enquanto sujeito fomos orientados a agradecer por algum feito realizado em prol de nosso bem estar, nesse momento não é diferente. Agradeço a Deus, fonte de força espiritual, onde sempre busquei carregar minhas energias e toda esperança, pois o indivíduo não é feito só de razão. Agradeço aos meus pais Nilza e Roque, pelo seu amor in- condicional e por sua compreensão em todas minhas ausências. Ao professor José Renan pelos conhecimentos transmitidos e mais ainda que isso, pelos ensinamentos que ultrapassam as fron- teiras da Universidade. A sua figura de grande cientista que desperta o respeito e admiração de muitos. Aos meus irmãos Cida, Sérgio e André, que sempre me apoiaram em minhas esco- lhas. Agradeço ao professor Marildo pelo incentivo em todo momento da minha graduação, principalmente nos períodos iniciais deste curso. Ele também foi de fundamental importân- cia para minha formação acadêmica. Aos colegas Sânzia e Carlos Eduardo, que dispuseram de seu tempo e conhecimentos no desevolvimento preliminar deste trabalho. A Sumaia pela sua atenção e disponibilidade sempre. Agradeço aos meus amigos, uns pelos grupos de estudo realizados e conhecimentos compartilhados outros pelo apoio oferecido e por sempre estarem disponíveis a ajudar. A todos os amigos e familiares que me apoiaram e alimentaram minha esperança, meus sinceros agradecimentos. Agradeço ao CNPq, que contribuiu com o lado fin- canceiro proporcionando minha dedicação exclusiva neste trabalho e à UFRN que me acolheu para o desenvolvimento do mesmo. “Toda a nossa ciência, comparada com a realidade, é primitiva e infantil - e, no entanto, é a coisa mais preciosa que temos.” —ALBERT EINSTEIN (1879-1955) iv Resumo Desde o anuncio pioneiro de Michel Mayor e seu então estudante Didier Queloz, em 1995, da existência de um planeta orbitando a estrela 51 Peg, até a presente data, 695 planetas extra- solares foram descobertos, orbitando estrelas do tipo espectral F, G, K e M. Um estudo sobre o comportamento do momentum angular total dos sistemas planetários, conhecidos até o mo- mento, torna-se relevante quando conhecemos que cerca de 98% do momentum angular do Sis- tema Solar está associado aos planetas, embora esses representem apenas 0,15% da massa de todo o Sistema. Na presente dissertação de mestrado estudamos o comportamento do momen- tum angular estelar, do momentum angular orbital e do momentum angular total numa amostra de 282 estrelas, abrigando planetas, incluindo 40 sistemas multiplos. Observamos que os siste- mas planetários contendo mais de 1 planeta conhecido possuem tanto momentum angular orbital quanto momentum angular total mais elevado, comparado àqueles sistemas que possuem apenas 1 planeta. Esta análise mostra que sistemas planetários múltiplos tendem a ter momenta mais elevado, sugerindo que em tais sistemas os planetas que contribuem com maior parcela para o momenta já foram descobertos. Sendo assim, sistemas planetários com menores valores para o momenta representam melhores candidatos para a descoberta de novos planetas. Palavras-chave: Estrelas, Momentum Angular, Planeta extra-solar, v Abstract Since Michel Mayor and his student Didier Queloz’s pioneer announcement, in 1995, of the existence of a planet orbiting the star 51 Peg, up to present date, 695 extrasolar planets orbiting stars of spectral type F, G, K and M have been discovered. A study on the behavior of the total angular momentum of the planetary systems known up to present date becomes relevant when we know that about 98% of the angular momentum of the solar system is associated with the planets, although they represent only 0.15 percent of the mass of the whole system. In this dissertation we study the behavior of stellar angular momentum, orbital angular momentum and total angular momentum in a sample of 282 stars harboring planets, including 40 multiple systems. We observed that planetary systems containing more than one known planet have both higher orbital angular momentum and total angular momentum compared to those who have only one planet. This analysis shows that multiplanet systems tend to have higher momenta, suggesting that the planets in such systems that contribute to the greater portion momenta have been found. Thus, planetary systems with lower values for the momenta represent the best candidates to the discovery of new planets. Keywords: Stars, Angular Momentum, Extra-solar Planet, vi Sumário Resumo iv Abstract v Lista de Figuras viii Lista de Tabelas x 1 Introdução 1 1.1 Métodos de Detecção de Planetas . 2 1.1.1 Velocidade Radial . 2 1.1.2 Trânsito Planetário . 3 1.1.3 Imagem Direta . 4 1.1.4 Micro-lentes Gravitacionais . 4 1.1.5 Cronometragem . 4 1.2 Proposta deste Trabalho . 4 2 Amostra de Dados 6 2.1 Base de Dados . 6 2.2 Parâmetros Estelares . 7 2.3 Parâmetros Planetários . 8 3 Resultados e Discussões 9 3.1 Massa Estelar . 9 3.2 Velocidade de Rotação . 10 3.3 Parâmetros Planetários . 12 3.4 Momentum Angular de Estrelas Hospedeiras de Planetas . 14 3.5 Momentum Angular Total de Sistemas Planetários . 15 4 Considerações Finais 20 A Parâmetros Orbitais Planetários 22 B Parâmetros Estelares 33 SUMÁRIO vii C Símbolos 48 Referências Bibliográficas 50 viii Lista de Figuras 1.1 Diagrama esquemático da variação de brilho de uma estrela quando o planeta transita frente a linha de visão. 3 2.1 Distribuição percentual do tipo espectral das 282 estrelas, das quais apenas 281 possuem tipo espectral conhecido na literatura. 7 3.1 Análise da frequência estelar em função de sua massa, das quais, apenas 280 possuem massas conhecidas na literatura. As cores em preto, azul e vermelho são respectivamente estrelas em sistemas planetários simples, binários e múltiplos. 10 3.2 Frequência dos valores da velocidade de rotação estelar. Em azul, preto, ver- melho e verde são indicadas, respectivamente, estrelas com tipo espectral F, G, KeM........................................ 11 3.3 Comportamento da velocidade de rotação, Vsini, das estrelas hospedeiras de planetas extra-solares em função do seu índice de metalicidade. 12 3.4 Distribuição dos 341 planetas em função de seus valores mínimos de massa. 13 3.5 Distribuição dos 177 planetas em função de suas massas efetivas. 13 3.6 Distribuição dos planetas em função do seu período orbital. 14 3.7 Comportamento do momentum angular rotacional para 182 estrelas com tipo espectral F e G pertencentes à amostra, em função de suas massas. Os círcu- los pretos e rosa são, respectivamente, estrelas hospedeiras de planetas e sem planetas conhecidos até o momento [12]. A linha vermelha representa o me- lhor ajuste linear para a relação de Kraft com parâmetros livres: a = 1,87 e b = 5,25 para intervalos de massa com log ( M ) < 0,1 e a = 5,66 e b = 2,25 para M intervalos de massas com log( M ) ≥ 0,1, no diagrama acima. 16 M 3.8 Distribuição do momentum angular orbital dos sistemas planetários em função da massa dos planetas. 17 3.9 Distribuição da razão entre o momentum angular orbital dos sistemas planetá- rios orbitando estrelas com massas compreendidas entre 0,9 e 1,10 M , e o momentum angular orbital dos planetas do Sistema Solar. 18 3.10 Distribuição do momentum angular total dos sistemas planetários em função da massa da estrela central. 19 LISTA DE FIGURAS ix 3.11 Distribuição do momentum angular total dos sistemas planetários em função da massa do sistema planetário. 19 x Lista de Tabelas A.1 Parâmetros Orbitais Planetários. 22 B.1 Parâmetros Estelares. 34 C.1 Simbolos e constantes utilizados ao longo do trabalho. 48 C.2 Nomenclatura usada para referenciar os planetas do Sistema Solar. 49 1 CAPÍTULO 1 Introdução “A vida sem ciência é uma espécie de morte.” —SÓCRATES (470 A.C. - 399 A.C.) A descoberta pioneira de um planeta orbitando a estrela 51 Pegasus, anunciada em ou- tubro de 1995 por Michel Mayor e seu então estudante Didier Queloz [55], astrônomos da Universidade de Genebra, Suíça, representou um dos maiores eventos científicos do século XX, também de grande impacto filosófico. De um lado, estava aberto o caminho para a busca efetiva de resposta para uma questão fundamental do pensamento humano, qual seja sobre a origem do Sistema Solar e da própria Terra. Por outro lado, a descoberta de um planeta fora do Sistema Solar quebrou o paradigma sobre a existência ou não de novos mundos, fato que se confirmou pelas sucessivas descobertas de planetas extra-solares acontecidas desde então. Dezesseis anos após a pioneira descoberta dos dois astrônomos suíços, cerca de 700 novos planetas extra-solares estão catalogados na enciclopédia de planetas extra-solares mantida por Jean Schneider [3]. Destes, 643 foram detectados pelo método de velocidade radial, 184 através do trânsito planetário, 26 por imagem direta, 13 por micro-lentes gravitacionais e 12 por cronometragem. Associadas a tais descobertas, devemos sublinhar ainda os milhares de planetas extra-solares ora em tratamento nas missões espaciais CoRoT [1] e Kepler [2]. Os planetas até então descobertos orbitam os mais variados tipos de estrelas, em tipo espectral e estágios evolutivos, desde a Pré-Sequência e Sequência Principal, até os estágios de Subgigantes e Gigantes, com massa variando entre 0,3 e 4,5 massa solar.
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