Spatially homogenous cosmology and dynamical systems

Diese Arbeit besteht aus drei Teilen: Teil 1 gibt eine kurze Einleitung in die räumlich homogene Kosmologie und in die Anwendung von Methoden aus der mathematischen Theorie der dynamischen Systeme auf diesem Gebiet. Sie ist an den Leser gerichtet der gerade damit beginnt sich mit der räumlich homogenen Kosmologie vertraut zu machen, und soll ihm helfen einen guten Überblick über dieses Gebiet zu erlangen, und die grundlegenden Ideen und Konzepte zu verstehen. Nach der Lektüre von Teil 1 sollte es dem Leser dann möglich sein Teil 2 zu lesen und zumindest im Kern zu verstehen. Teil 2 ist ein Abdruck meines Aufsatzes 'Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter' welcher 2012 von Springer in der Zeitschrift General Relativity and Gravitation veröffentlicht wurde. Er befasst sich mit der Analyse einer bestimmten Klasse von räumlich homogenen kosmologischen Modellen. Die hierfür gewählten Materieinhalte sind im allgemeinen anisotrop, und umschließen eine größere Familie von Modellen in der etwa auch ideale Flüssigkeiten als Spezialfall enthalten sind. Die Resultate erlauben es Schlüsse darüber zu ziehen in welcher Weise sich der Grad der Anisotropie des Materieinhaltes auf die asymptotische Dynamik in der fernen Vergangenheit und Zukunft auswirkt. Teil 3 gibt eine Anleitung zur Visualisierung der Lösungen der in Teil 2 behandelten Bewegungsgleichungen in einem interaktivem Flussdiagramm mit dem Computer Algebra System Maple. Die so erstellten Diagramme erlauben es dem Benutzer eine Änderung im Verhalten der Lösungen als direkte Reaktion auf eine Änderung der Materieparameter wahrzunehmen, von denen einer im Wesentlichen den Grad der Anisotropie bestimmt. Sie eignen sich daher sehr gut dazu den komplexen Lösungsraum übersichtlich darzustellen und vor allem auch um die aus der Analyse gezogenen physikalischen Schlüsse verständlich zu präsentieren. Teil 3 ist zudem durch ein Maple Dokument ergänzt, welches den Inhalt dieses Teils mit ausführbaren Beispielen wiedergibt.This thesis is organised in three parts: Part 1 is concerned with a short introduction to spatially homogenous cosmology and the use of methods from the mathematical theory of dynamical systems in this research field. It aims to help the reader who is just starting to become acquainted with spatially homogenous cosmology to get a good overview and to become familiar with the basic ideas and concepts. After the lecture of part 1 the reader should then be able to read and understand part 2 at least along general lines. Part 2 is a reprint of my research article Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter which was published by Springer in 2012 in the journal General Relativity and Gravitation. It deals with the analysis of one particular class of spatially homogenous cosmologies. The therefor chosen matter contents are in general anisotropic and comprise a larger family of models in which for instance also perfect fluids are contained as special cases. The results allow to draw conclusions on how the grade of anisotropy of the matter content effects the past and future asymptotic evolution of these models. Part 3 gives a tutorial on how to visualise the solutions of the evolution equations examined in part 2 in an interactive flow diagram with the computer algebra system Maple. The such produced diagrams allow the user to see a change in the behaviour of the solutions as a direct reaction to the change in the matter parameters, where one of them essentially gives the grade of matter anisotropy. They are therefore well suited to clearly represent the complex space of solutions, and most notably to present the physical conclusions which were drawn out of the analysis in a comprehensible fashion. Part 3 is also supplemented by a Maple document, which has the same content than presented in this part, with working examples

Dark Matter reconstruction from stellar orbits in the Galactic Centre

Context. Current constraints on distributed matter in the innermost Galactic Centre (such as a cluster of faint stars and stellar remnants, Dark Matter or a combination thereof) based on the orbital dynamics of the visible stars closest to the central black hole, typically assume simple functional forms for the distributions. Aims. We take instead a general model agnostic approach in which the form of the distribution is not constrained by prior assumptions on the physical composition of the matter. This approach yields unbiased - entirely observation driven - fits for the matter distribution and places constraints on our ability to discriminate between different density profiles (and consequently between physical compositions) of the distributed matter. Methods. We construct a spherical shell model with the flexibility to fit a wide variety of physically reasonable density profiles by modelling the distribution as a series of concentric mass shells. We test this approach in an analysis of mock observations of the star S2. Results. For a sufficiently large and precise data set, we find that it is possible to discriminate between several physically motivated density profiles. However, for data coming from current and expected next generation observational instruments, the potential for profile distinction will remain limited by the precision of the instruments. Future observations will still be able to constrain the overall enclosed distributed mass within the apocentre of the probing orbit in an unbiased manner. We interpret this in the theoretical context of constraining the secular versus non-secular orbital dynamics.Comment: 8 pages, 4 figures, submitted to Astronomy & Astrophysic

The GRAVITY+ Project: Towards All-sky, Faint-Science, High-Contrast Near-Infrared Interferometry at the VLTI

The GRAVITY instrument has been revolutionary for near-infrared interferometry by pushing sensitivity and precision to previously unknown limits. With the upgrade of GRAVITY and the Very Large Telescope Interferometer (VLTI) in GRAVITY+, these limits will be pushed even further, with vastly improved sky coverage, as well as faint-science and high-contrast capabilities. This upgrade includes the implementation of wide-field off-axis fringe-tracking, new adaptive optics systems on all Unit Telescopes, and laser guide stars in an upgraded facility. GRAVITY+ will open up the sky to the measurement of black hole masses across cosmic time in hundreds of active galactic nuclei, use the faint stars in the Galactic centre to probe General Relativity, and enable the characterisation of dozens of young exoplanets to study their formation, bearing the promise of another scientific revolution to come at the VLTI.Comment: Published in the ESO Messenge

The dark mass signature in the orbit of S2

International audienceContext. The Schwarzschild precession of star S2, which orbits the massive black hole at the centre of the Milky Way, has recently been detected with the result of ∼12 arcmin per orbit. The same study also improved the 1σ upper bound on a possibly present dark continuous extended mass distribution (e.g. faint stars, stellar remnants, stellar mass black holes, or dark matter) within the orbit of S2 to ∼4000 M⊙. The secular (i.e. net) effect of an extended mass onto a stellar orbit is known as mass precession, and it runs counter to the Schwarzschild precession.Aims. We explore a strategy for how the Schwarzschild and mass precessions can be separated from each other despite their secular interference, by pinpointing their signatures within a single orbit. From these insights, we then seek to assess the prospects for improving the dark mass constraints in the coming years.Methods. We analysed the dependence of the osculating orbital elements and of the observables on true anomaly, and we compared these functions for models with and without extended mass. We then translated the maximum astrometric impacts within one orbit to detection thresholds given hypothetical data of different accuracies. These theoretical investigations were then supported and complemented by an extensive mock-data fitting analysis.Results. We have four main results. 1. While the mass precession almost exclusively impacts the orbit in the apocentre half, the Schwarzschild precession almost exclusively impacts it in the pericentre half, allowing for a clear separation of the effects. 2. Data that are limited to the pericentre half are not sensitive to a dark mass, while data limited to the apocentre half are, but only to a limited extent. 3. A full orbit of data is required to substantially constrain a dark mass. 4. For a full orbit of astrometric and spectroscopic data, the astrometric component in the pericentre halff plays the stronger role in constraining the dark mass than the astrometric data in the apocentre half. Furthermore, we determine the 1σ dark mass detection thresholds given different datasets on one full orbit. In particular, with a full orbit of data of 50 microarcsec (VLTI/GRAVITY) and 10 km s−1 (VLT/SINFONI) precision, the 1σ bound would improve to ∼1000 M⊙, for example.Conclusions. The current upper dark mass bound of ∼4000 M⊙ has mainly been obtained from a combination of GRAVITY and VLT/NACO astrometric data, as well as from SINFONI spectroscopic data, where the GRAVITY data were limited to the pericentre half. From our results 3 and 4, we know that all components were thereby crucial, but also that the GRAVITY data were dominant in the astrometric components in constraining the dark mass. From results 1 and 2, we deduce that a future population of the apocentre half with GRAVITY data points will substantially further improve the dark mass sensitivity of the dataset, and we note that at the time of publication, we already entered this regime. In the context of the larger picture, our analysis demonstrates how precession effects that interfere on secular timescales can clearly be distinguished from each other based on their distinct astrometric signatures within a single orbit. The extension of our analysis to the Lense-Thirring precession should thus be of value in order to assess future spin detection prospects for the galactic centre massive black hole.Key words: Galaxy: nucleus / stars: individual: S2/S02 / stars: kinematics and dynamics / astrometry / gravitation / black hole physic