Star formation in the Milky Way is confined to star-forming regions (OB association, HII regions, and open clusters) in the Galactic plane. It is usually assumed that these regions are found preferably along spiral arms, as is observed in other spiral galaxies. However, young early-type stars are often found at high Galactic latitudes, far away from their birthplaces in the Galactic disc. These stars are called runaway stars, and it is believed that they were ejected from their birth- places early in their lifetimes by one of two mechanisms: ejection from a binary system following the destruction of the massive companion in a supernova type II event (the binary ejection mechanism), or ejection from a dense cluster following a close gravitational encounter between two close binaries (the dynamical ejection mechanism). The aims of our study were: to improve the current understanding of the nature of high Galactic latitude runaway stars, in particular by investigating whether the theoretical ejection mechanisms could explain the more extreme cases; to show the feasibility of using high Galactic latitude stars as tracers of the spiral arms. The main technique used in this investigation was the tracing of stellar orbits back in time, given their present positions and velocities in 3D space. This technique allowed the determination of the ejection velocities, flight times and birthplaces of a sample of runaway stars. In order to obtain reasonable velocity estimates several recent catalogues of proper motion data were used. We found that the evolutionary ages of the vast majority of runaway stars is consistent with the disc ejection scenario. However, we identified three outliers which would need flight times much larger then their estimated ages in order to reach their present positions in the sky. Moreover, the ejection velocity distribution appears to be bimodal, showing evidence for two populations of runaway stars: a “low” velocity population (89 per cent of the sample), with a maximum ejection velocity of about 300 kms−1, and a “high” velocity population, with ejection velo- cities of 400 – 500 kms−1. We argue that the observed bimodality and maximum ejection velocity of 500 kms−1 can be interpreted as a natural consequence of a variation of the binary ejection mechanism. A possible connection between the “high” velocity population and the so-called hypervelocity stars is also explored, resulting in the conclusion that some stars previously identified as hypervelocity may be in fact runaway stars. The feasibility of using stars as tracers of the spiral arms was tested on a local sample, in order to obtain better quality data and larger numbers. We found that the spiral arms pattern speeds estimated from this sample (24.9±5.2 kms−1 kpc−1) and from a selected sample of runaways (22.8 ± 7.8 kms−1 kpc−1) are consistent within the errors and also consistent with other published estimates. We concluded that our estimates combined with the ones obtained in other studies suggest a value in the range 20 − 25 kms−1 kpc−1 for the pattern speed. Moreover, we concluded that an adequate representation of the spiral arms is obtained given the former pattern speed estimate, even when applied to the sample of runaway stars.

No description available.

Our work has two recherchive parts. The first is devoted to the shell galaxies and we describe the observational facts here, different models of origin and the possibility of determining the gravitational potential with the use of shells. The second part is on the modified Newtonian dynamics (MOND). We explain what it consists in, its implications and its experimental tests. The third part is devoted to our numerical simulations of a shell system evolution both in the classical and modified dynamics. Our mission is to explain the differences in the two simulation theoretically and to verify, whether the result of the modified simulation oppose the observed shells around the galaxy NGC 3923. The conclusion is it doesn't, but our test is not very strong.

We investigate the orbital evolution of an initially thin stellar disc around a supermassive black hole, considering various perturbative sources of gravity. By means of direct numerical N-body modelling, we first focus on the case when the disc is embedded in an extended spherically symmetric star cluster. We find that the gravitational influence of the disc triggers formation of macroscopic non- spherical substructure in the cluster which, subsequently, significantly affects the evolution of the disc itself. In another approximation, when the cluster is emu- lated by an analytic spherically symmetric potential, we further consider pertur- bative gravitational influence of a distant axisymmetric source. Using standard perturbation methods, we derive a simple semi-analytic model for such a config- uration. It turns out that the additional axisymmetric potential leads to mutual gravitational coupling of the individual orbits from the disc. Consequently, the dense parts of the disc can, for some period of time, evolve coherently. Finally, we apply some of our results to the young stellar disc which is observed in the innermost parsec of the Galactic Centre. 1

Orientador: Prof. Dr. Maximiliano Ujevic Tonino / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015. / Neste trabalho, estudamos uma série de estruturas bidimensionais como discos finos e varios tipos de anéis finos, que possam representar objetos astrofísicos, usando a func¸ão de distribuição de partículas. Como primeiro passo, resolvemos a equação de Fokker-Planck estacionária, ajustando os parâmetros de modo que a função de distribuição satisfação, simultaneamente, a equação de Fokker-Planck e a equação de Poisson para um determinado potencial gravitacional conhecido dos modelos. A seguir fazemos uma análise da evolução temporal da função de distribuição de partículas, de alguns destes sistemas, após as estruturas sofrerem uma perturbação em seu campo gravitacional. As soluções e evoluções da equação de Fokker-Planck são encontradas usando diretamente m'etodos numéricos, primeiramente fazemos uma discretização da equação de Fokker-Planck usando o método das diferenc¸as finitas, e resolvendo o sistema de equações lineares resultante através de métodos que possam reduzir o tempo de processamento computacional e que resultem em soluções robustas quanto a convergência do sistema de equaçõess lineares, como o método GMRES (método do resíduo mínimo generalizado) e LCD (método das direções conjugadas a esquerda), que tornam viávell o estudo das evoluções temporais de estruturas bidimensionais que estamos interessados. / In this work we study, using the particle distribution function, several thin structures like thin disks and thin rings that may represent astropysical objects. As a first step, we solve the stationary Fokker-Planck equation adjusting the parameters of the system so that the particles distribution function satisfies simultaneously the Fokker-Planck and Poisson equations for a determined gravitational potential model. Then, we make an analysis of the temporal evolution of the particle distribution function for some of these systems under a perturbation on the gravitational field. The solutions and evolutions of the Fokker-Planck equation are found using direct numerical methods, first we use a finite difference scheme discretization method for a Fokker-Planck equation, and then we solve the resulting linear system through robust numerical methods that reduce the computational processing time, as the GMRES method (generalized minimum residual method) and the LCD method (left conjugated direction method).

Star clusters are thought to be the birthplaces of stars as well as the building blocks of galaxies. They typically consist of thousands to millions of stars bound together by self-gravity. These systems evolve on the scale of Myr to Gyr, there- fore, it is impossible for us to see any change in their global evolution even within hundreds of human lifetimes. Although the equations of motion of stars in a star cluster are simple New- tonian, it is impossible to predict precisely history of any star within them to any point in the future. Therefore, we may either compare the observations of different star clusters at different age, we may invent theoretical approaches and analytical predictions, or we must follow their evolution numerically (e.g. with direct N-body integrators) which is the main focus of my research and this thesis. First, we follow the evolution of star clusters in general while coming up with a novel method to estimate their characteristic timescale (i.e. the time of core collapse) based on global parameters. The core collapse is directly linked to the formation of hard binary stars, thus, we focus on their analysis as well. We also follow several recent observational results: (i) ALMA observations of the Serpens South star-forming region indicate that star clusters are born mass...

Globular clusters are dense and massive star clusters that are an integral part of any major galaxy. Careful studies of their stars, a single cluster may contain several millions of them, have revealed that the ages of many globular clusters are comparable to the age of the Universe. These remarkable ages make them valuable probes for the exploration of structure formation in the early universe or the assembly of our own galaxy, the Milky Way. A topic of current research relates to the question whether globular clusters harbour massive black holes in their centres. These black holes would bridge the gap from stellar mass black holes, that represent the final stage in the evolution of massive stars, to supermassive ones that reside in the centres of galaxies. For this reason, they are referred to as intermediate-mass black holes. The most reliable method to detect and to weigh a black hole is to study the motion of stars inside its sphere of influence. The measurement of Doppler shifts via spectroscopy allows one to carry out such dynamical studies. However, spectroscopic observations in dense stellar fields such as Galactic globular clusters are challenging. As a consequence of diffraction processes in the atmosphere and the finite resolution of a telescope, observed stars have a finite width characterized by the point spread function (PSF), hence they appear blended in crowded stellar fields. Classical spectroscopy does not preserve any spatial information, therefore it is impossible to separate the spectra of blended stars and to measure their velocities. Yet methods have been developed to perform imaging spectroscopy. One of those methods is integral field spectroscopy. In the course of this work, the first systematic study on the potential of integral field spectroscopy in the analysis of dense stellar fields is carried out. To this aim, a method is developed to reconstruct the PSF from the observed data and to use this information to extract the stellar spectra. Based on dedicated simulations, predictions are made on the number of stellar spectra that can be extracted from a given data set and the quality of those spectra. Furthermore, the influence of uncertainties in the recovered PSF on the extracted spectra are quantified. The results clearly show that compared to traditional approaches, this method makes a significantly larger number of stars accessible to a spectroscopic analysis. This systematic study goes hand in hand with the development of a software package to automatize the individual steps of the data analysis. It is applied to data of three Galactic globular clusters, M3, M13, and M92. The data have been observed with the PMAS integral field spectrograph at the Calar Alto observatory with the aim to constrain the presence of intermediate-mass black holes in the centres of the clusters. The application of the new analysis method yields samples of about 80 stars per cluster. These are by far the largest spectroscopic samples that have so far been obtained in the centre of any of the three clusters. In the course of the further analysis, Jeans models are calculated for each cluster that predict the velocity dispersion based on an assumed mass distribution inside the cluster. The comparison to the observed velocities of the stars shows that in none of the three clusters, a massive black hole is required to explain the observed kinematics. Instead, the observations rule out any black hole in M13 with a mass higher than 13000 solar masses at the 99.7% level. For the other two clusters, this limit is at significantly lower masses, namely 2500 solar masses in M3 and 2000 solar masses in M92. In M92, it is possible to lower this limit even further by a combined analysis of the extracted stars and the unresolved stellar component. This component consists of the numerous stars in the cluster that appear unresolved in the integral field data. The final limit of 1300 solar masses is the lowest limit obtained so far for a massive globular cluster. / Kugelsternhaufen sind dichte, gravitativ gebundene Ansammlungen von teilweise mehreren Millionen Sternen, die ein fester Bestandteil jeder massiven Galaxie sind. Aus der Untersuchung der Kugelsternhaufen in der Milchstraße weiß man, dass das Alter von vielen dieser Objekte vergleichbar ist mit jenem des Universums. Dies macht sie zu wertvollen Forschungsobjekten, beispielsweise um die Entstehung der Milchstraße und die Strukturbildung im frühen Universum zu verstehen. Eine aktuelle wissenschaftliche Fragestellung befasst sich damit, ob Kugelsternhaufen massive schwarze Löcher beherbergen. Diese würden eine Brücke schlagen von den stellaren schwarzen Löchern, die durch den Kollaps massereicher Sterne entstehen, zu den supermassiven schwarzen Löchern, welche man in den Zentren massiver Galaxien beobachtet. Man bezeichnet sie daher auch als mittelschwere schwarze Löcher. Die sicherste Diagnostik, um schwarze Löcher zu detektieren und ihre Masse zu bestimmen ist, die Bewegung der Sterne innerhalb ihrer gravitativen Einflusssphäre zu vermessen. Spektroskopische Untersuchungen vermögen dies über die Dopplerverschiebung von Spektrallinien, sind jedoch in dichten stellaren Feldern wie Kugelsternhaufen schwierig. Aufgrund der Turbulenz in der Atmosphäre und dem endlichen Auflösungsvermögen des Teleskops erscheinen die Sterne in den Beobachtungen nicht punktförmig, sondern mit einer durch die Punktspreizfunktion (PSF) gegebenen Breite. In dichten stellaren Feldern führt dies dazu, dass die Sterne überlappen. Da klassische spektroskopische Verfahren nicht bildgebend sind, lassen sich die Beiträge der Einzelsterne zu einem beobachteten Spektrum nicht trennen und die Geschwindigkeiten der Sterne können nicht vermessen werden. Bildgebende spektroskopische Verfahren, wie etwa die Integralfeld-Spektroskopie, bieten jedoch die Möglichkeit, die PSF zu rekonstruieren und basierend darauf die Spektren überlappender Sterne zu trennen. Im Rahmen der vorgelegten Arbeit wird das Potential der Integralfeld-Spektroskopie in der Beobachtung dichter stellarer Felder zum ersten Mal systematisch analysiert. Hierzu wird eine Methodik entwickelt, die das Extrahieren von Einzelsternspektren über eine Rekonstruktion der PSF aus den vorhandenen Daten erlaubt. Anhand von Simulationen werden Voraussagen darüber gemacht, wie viele Sternspektren aus einem gegebenen Datensatz extrahiert werden können, welche Qualität diese Spektren haben und wie sich Ungenauigkeiten in der rekonstruierten PSF auf die Analyse auswirken. Es zeigt sich hierbei, dass die entwickelte Methodik die spektroskopische Analyse von deutlich mehr Sternen erlaubt als klassische Verfahren. Parallel zu dieser systematischen Studie erfolgt die Entwicklung einer dezidierten Analysesoftware, welche im zweiten Teil der Arbeit auf Daten von drei Kugelsternhaufen angewendet wird, die mit dem PMAS Integralfeld-Spektrographen am Calar Alto Observatorium aufgenommen wurden: M3, M13 und M92. Die Auswertung dieser Daten liefert Spektren für eine Stichprobe von ungefähr 80 Sternen pro Kugelsternhaufen, weit mehr als bisher im Zentrum eines der drei Haufen verfügbar waren. In der weiteren Analyse werden Jeans Modelle für jedes der drei Objekte gerechnet. Diese erlauben basierend auf einer angenommenen Massenverteilung innerhalb des Kugelsternhaufens eine Vorhersage der Geschwindigkeitsdispersion der Sterne. Der Vergleich mit den gemessenen Geschwindigkeiten zeigt, dass in keinem der drei Haufen ein schwarzes Loch benötigt wird, um die Dynamik der zentrumsnahen Sterne zu erklären. Im Gegenteil, die Beobachtungen können zu 99,7-prozentiger Sicherheit ausschließen, dass sich in M13 ein schwarzes Loch mit einer Masse größer 13000 Sonnenmassen befindet. In den anderen beiden Haufen liegt diese Grenze noch bei deutlich geringeren Massen, nämlich bei 2500 Sonnenmassen in M3 und 2000 Sonnenmassen in M92. In M92 ist es außerdem möglich, das Limit noch weiter herabzusetzen durch eine zusätzliche Analyse der unaufgelösten stellaren Komponente. Diese Komponente besteht aus dem integrierten Licht all jener Sterne, die zu schwach und zahlreich sind als dass sie aus den verfügbaren Daten einzeln extrahiert werden könnten. Das endgültige Limit von 1300 Sonnenmassen ist das geringste, welches bisher in einem massiven Kugelsternhaufen gemessen wurde.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.