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This thesis is concerned with the dynamical evolution of globular star clusters modelled as the classical gravitational N-body problem. The models in this thesis are idealised in order to allow the detailed study of particular dynamical aspects of the cluster evolution. Examples of properties which tend to be omitted are stellar evolution, primordial binaries and the effect of an external tidal gravitational field. The methods used in this thesis are gas models, N-body models and physical arguments. One of the main topics in this thesis is gravothermal oscillations in multicomponent star clusters. The evolution of one-component globular clusters, systems with equal particle masses, is quite well understood. However, the evolution of more realistic globular clusters, with a range of particle masses, is a much more complicated matter. The condition for the on-set of gravothermal oscillations in a one-component system is simply that the number of stars is greater than a certain number ( ≈7000). In a multi-component system the relationship between the number of stars at which the gravothermal oscillations first appear and the stellar mass distribution of a cluster is a complex one. In order to investigate this phenomenon two different types of multi-component systems were studied: two-component systems (the simplest approximation of a mass spectrum, Chapter 2) and ten-component systems (which were realisations of continuous power law IMFs, Chapter 3). In both cases the critical number of stars at which gravothermal oscillations first appear are found empirically for a range of stellar mass distributions. The nature of the oscillations themselves are investigated and it is shown that the oscillations can be understood by focusing on the behaviour of the heavier stars within the cluster. A parameter Nef (de nined Mtot/mmax where Mtot is the total mass and mmax is the maximum stellar mass) acts as an approximate stability boundary for multicomponent systems.The stability boundary was found to be at Nef ~- 12000. In this Chapter 4, globular star clusters which contain a sub-system of stellar-mass black holes (BH) are investigated. This is done by considering two-component models, as these are the simplest approximation of more realistic multi-mass systems, where one component represents the BH population and the other represents all the other stars. These systems are found to undergo a long phase of evolution where the centre of the system is dominated by a BH sub-system. After mass segregation has driven most of the BH into a compact sub-system, the evolution of the BH sub-system is found to be in uenced by the cluster in which it is contained. The BH sub-system evolves in such a way as to satisfy the energy demands of the whole cluster, just as the core of a one component system must satisfies the energy demands of the whole cluster. The BH sub-system is found to exist for a significant amount of time. It takes approximately 10trh;i, where trh;i is the initial half-mass relaxation time, from the formation of the compact BH sub-system up until the time when 90% of the sub-system total mass is lost (which is of order 103 times the half-mass relaxation time of the BH sub-system at its time of formation). Based on theoretical arguments the rate of mass loss from the BH sub-system (M2) is predicted to be (βζM)/(αtrh): where M is the total mass, trh is the half-mass relaxation time, and α, β, ζ are three dimensionless parameters. (see Section 4.3 for details). An interesting consequence of this is that the rate of mass loss from the BH sub-system is approximately independent of the stellar mass ratio (m2/m1) and the total mass ratio (M2/M1) (in the range m2/m1 ≥ 10 and M2/M1 ≈ 10-2, where m1, m2 are the masses of individual low-mass and high-mass particles respectively, and M1, M2 are the corresponding total mass). The theory is found to be in reasonable agreement with most of the results of a series of N-body simulations, and all of the models if the value of ζ is suitable adjusted. Predictions based on theoretical arguments are also made about the structure of BH sub-systems. Other aspects of the evolution are also considered such as the conditions for the onset of gravothermal oscillation. The final chapter (Chapter 5) of the thesis contains some concluding comments as well as a discussion on some possible future projects, for which the results in this thesis would be useful.

Most star formation in galaxies takes place in embedded clusters, within Giant Molecular Clouds (GMCs). Stars also generally form as part of binary star systems, with almost all massive stars having at least one close companion. Binaries shape the physical properties of older star clusters by setting their central density and ejecting low-mass stars, but also play a role during cluster formation by modifying the mechanical and radiative feedback from massive stars and shedding enriched material in the cluster’s gas reservoir. Conversely, dynamical interactions between stars in dense stellar environments are known to form, modify, and destroy binary systems. In consequence, the populations of binaries observed in the Galactic field and in old stellar clusters are understood to be shaped by a combination of the physics of star formation and subsequent dynamical interactions in embedded clusters, although the relative importance of these processes remains unknown. In this thesis, we implement a prescription for an initial population of binaries in the coupled N-body and radiation hydrodynamics star cluster formation code Torch, and investigate how this initial population is modified in the earliest stages of cluster formation, while gas and stars coexist. As an ansatz for the initial population of binaries, we use the properties of main-sequence binaries in the Galactic field. We first perform a suite of simulations initialized from a 10^4 M⦿ cloud, in which the simulations only differ by their stellar content (i.e. presence or absence of an initial population of binaries, and stochasticity of star formation). We compare the populations of binaries identified 1.2–2 Myr after the onset of star formation and find that an initial population of binaries is needed at all masses to reproduce the multiplicity fraction observed in main-sequence stars. We also show that this initial population is modified in a systematic manner before the effects of feedback from massive stars shape the gas. We further find evidence of both preferential formation and preferential destruction of binaries via dynamical interactions. The net effect of these interactions shifts the distributions of primary masses and semi-major axes to lower values, and the distributions of mass ratios and eccentricities to larger values. In a second time, we perform simulations with different virial parameters and initial turbulent velocity patterns, and find that the trends previously identified are robust to those changes in our initial conditions. We however find that both the virial parameter and the initial turbulent velocity pattern have a strong influence on the star formation rate, and therefore on the rapidity with which the distributions are modified. We conclude that dynamical interactions in embedded clusters are important for shaping the populations of binaries observed in the MilkyWay, thus opening the floor to future investigations of the impact of binaries on star cluster formation. / Thesis / Master of Science (MSc)

I present an overview of the tools and methods of gravitational dynamics motivated by a variety of dynamics problems. Particular focus will be given to the development of dynamic phase-space configurations as well as the distribution functions of collisionless systems. Chapter 1 is a short review of the descriptions of a gravitational system examining Poisson's equations, the probability distribution of particles, and some of the most popular model groups before working through the challenges of introducing anisotropy into a model. Chapter 2 covers the work of Barber2014b which looks at the relations between quantities in collisionless systems. Analytical methods are employed to describe a model that can violate the GDSAI, a well-known result connecting the density slope to the velocity anisotropy. We prove that this inequality cannot hold for non-separable systems and discuss the result in the context of stability theorems. Chapter 3 discusses the background for theories of gravity beyond Newton and Einstein. It covers the `dark sector' of modern astrophysics, motivates the development of MOND, and looks at some small examples of these MONDian theories in practice. Chapter 4 discusses how to perform detailed numerical simulations covering code methods for generating initial conditions and simulating them accurately in both Newtonian and MONDian approaches. The chapter ends with a quick look at the future of N-body codes. Chapters 5 and 6 contain work from Barber 2012 and Barber 2014a which look at the recent discovery of an attractor in the phase-space of collisionless systems and present a variety of results to demonstrate the robustness of the feature. Attempts are then made to narrow down the necessary and sufficient conditions for the effect while possible mechanisms are discussed. Finally, the epilogue is a short discussion on how best to communicate scientific ideas to others in a lecturing or small group setting. Particular focus is given to ideas of presentation and the relative importance of formality versus personality.

<p dir="ltr"> This article-based dissertation provides an account of two distinct classes of expansive astrophysical outflows and techniques to interpret their observations using numerical modeling. The primary purpose of this dissertation is to provide an extensive description of the research projects I undertook during my tenure as a Graduate Research Assistant, under the guidance of my advisor Prof. Paul Duffell.</p><p dir="ltr">Chapter 1 provides a brief introduction to numerical hydrodynamics and techniques of modeling expanding flows numerically. I also introduce the aforementioned classes of astrophysical outflows, namely relativistic jets from Active Galactic Nuclei (AGN), and supernova remnants (SNRs). I provide a general overview of the theoretical picture, and the general strategy used in this work to model them.</p><p dir="ltr">Chapter 2 describes my investigation on the connection of kiloparsec scale AGN jet properties to their intrinsic parameters and surroundings, based on an article published in The Astrophysical Journal. Using a suite of over 40 relativistic hydrodynamic jet models, we find that the dynamics of relativistic jets can be described in terms of only two parameters, the jet to ambient medium energy density ratio, and the jet opening angle. The former is found to strongly control the Fanaroff-Riley (FR) morphological dichotomy, which was previously thought to be tied to the magnitude of the jet luminosity. We also suggest a purely hydrodynamical origin of bright spots observed in some AGN jets. Our models were tested against and found to be consistent with the observations of the jets in M87 and Cygnus A.</p><p dir="ltr">In chapter 3, I present my moving-mesh hydrodynamics code Sprout, also described in an article published in The Astrophysical Journal Supplements. Sprout solves the equations of ideal hydrodynamics on an expanding Cartesian mesh. The expanding mesh can follow fluid outflows for several orders of magnitude with very little numerical diffusion. This allows Sprout to capture expanding flows with very high dynamic range. Sprout is thus particularly suitable for studying expanding outflows such as supernova remnants and active galactic nuclei. Relative to other moving mesh codes, the simple mesh structure in Sprout is also convenient for implementing additional physics or algorithms. I discuss many code tests that were performed to test the accuracy and performance of the numerical scheme.</p><p dir="ltr">Chapter 4 details my study of hydrodynamic instabilities in supernova remnants (SNRs) as they expand against the circumstellar medium (CSM). This is based on an article published in The Astrophysical Journal. A suite of 3D hydrodynamical SNR models, generated using my hydro code \sprout, was used to study the impact of the stellar ejecta density profile and seed anisotropies in the ejecta and the CSM on formation of turbulent structures in the SNRs. We found that most of the turbulent power in these models resides at a typical angular mode or scale that is determined by the ejecta density structure. It was also found that clumps or anisotropies in either the ejecta or CSM do not imprint upon these turbulence structures unless they are massive and form large-scale coherent structures.</p><p dir="ltr">In chapter 5, I discuss the implementation of a technique to measure anisotropies in observed SNRs just using 2D high-resolution images. This technique is calibrated using 3D hydro SNR models and synthetic images derived from them. As seen in Chapter 4, we find a similar dominant angular scale of turbulent structures dictated by the ejecta density structure. Both the 3D models and the synthetic images yield the same value of this scale, which validates the image analysis technique used in this work. As an example of how this technique can be applied to observations, we analyze observations of a known supernova remnant (Tycho's SNR) and compare with our models. Our technique picks out the angular scale of Tycho's fleece-like structures and also agrees with the small-scale power seen in Tycho.</p><p dir="ltr">PhChapter 6 summarizes the results, conclusions, and future prospects of all the research work described so far. It is followed by a bibliography, my curriculum vita, and a list of publications.</p>

This dissertation describes the current version of GenASiS and reports recent progress in its development. GenASiS is a new computational astrophysics code built for large-scale and multi-dimensional computer simulations of astrophysical phenomena, with primary emphasis on the simulations of neutron star mergers and core-collapse supernovae. Neutron star mergers are of high interest to the astrophysics community because they should be the prodigious source of gravitation waves and the most promising candidates for gravitational wave detection. Neutron star mergers are also thought to be associated with the production of short-duration, hard-spectral gamma-ray bursts, though the mechanism is not well understood. In contrast, core-collapse supernovae with massive progenitors are associated with long-duration, soft-spectral gamma-ray bursts, with the `collapsar' hypothesis as the favored mechanism. Of equal interest is the mechanism of core-collapse supernovae themselves, which has been in the forefront of many research efforts for the better half of a century but remains a partially-solved mystery. In addition supernovae, and possibly neutron star mergers, are thought to be sites for the emph{r}-process nucleosynthesis responsible for producing many of the heavy elements. Until we have a proper understanding of these events, we will have only a limited understanding of the origin of the elements. These questions provide some of the scientific motivations and guidelines for the development of GenASiS. In this document the equations and numerical scheme for Newtonian and relativistic magnetohydrodynamics are presented. A new FFT-based parallel solver for Poisson's equation in GenASiS are described. Adaptive mesh refinement in GenASiS, and a novel way to solve Poisson's equation on a mesh with refinement based on a multigrid algorithm, are also presented. Following these descriptions, results of simulations of neutron star mergers with GenASiS such as their evolution and the gravitational wave signals and spectra that they generate are shown. In the context of core-collapse supernovae, we explore the capacity of the stationary shock instability to generate magnetic fields starting from a weak, stationary, and radial magnetic field in an initially spherically symmetric fluid configuration that models the stalled shock in the post-bounce supernova environment. Our results show that the magnetic energy can be amplified by almost 4 orders of magnitude. The amplification mechanisms for the magnetic fields are then explained.

Στο πρώτο μέρος της διατριβής περιγράφεται η "στρατηγική του μιγαδικού επιπέδου" (cxps) και εξηγείται ο λόγος για τον οποίο προκρίνεται αυτή. με την cxps συνεργάζεται στενά η "τεχνική της πολλαπλής διαμερισης" (MTP), η οποία χρησιμοποιείται στους σχετικούς υπολογισμούς. κατασκευάζεται το μοντέλο ενός διαφορικά περιστρεφόμενου πολυτρόπου αστέρα υπό την επίδραση τυροειδούς μαγνητικού πεδίου. εισάγεται η ποσότητα h σαν παράμετρος διαταραχής και u παράμετρος διαφορικής περιστροφής. αναπτύσσεται η θεωρία που περιλαμβάνει όρους μέχρι και πρώτης τάξης στις παραμέτρους διαταραχής u, h και ευρίσκονται οι διαφορικές εξισώσεις, στις οποίες, υπακούουν οι συναρτήσεις του προβλήματος. ακολούθως γίνεται αριθμητική εφαρμογή των προηγούμενων για όλες τις ενδιαφέρουσες καταστάσεις περιστροφής. το δεύτερο μέρος της διατριβής διαπραγματεύεται μοντέλα, στα οποία η διαφορική περιστροφή προκύπτει από το ιξώδες υλικό του αστέρα με επίλυση της λεγόμενης "εξισώσεως ζεύξης", η οποία είναι συνέπεια της εξισώσεως Navier-Stokes για ιξωδοπολυτροπικούς αστέρες. παρουσιάζονται αριθμητικά αποτελέσματα για τη δομή διαφόρων μοντέλων με ασθενές, μέτριο και ισχυρό μαγνητικό πεδίο. δίνεται έμφαση στον υπολογισμό της "ενεργειακής απώλειας" λογω ιξώδους τριβής. ακολουθει σχολιασμός των αριθμητικών αποτελεσμάτων με έμφαση στο γεγονός ότι η ύπαρξη του μαγνητικού πεδίου περιορίζει δραστικά την ενεργειακή απώλεια. στην περίπτωση αυτή το μαγνητικό πεδίο δρα ως "λιπαντικό" και προστατεύει τον αστέρα από την υπερβολική απώλεια ενέργειας λογά ιξώδους τριβής των διαφορικώς περιστρεφόμενων φλοιών του. / In the first part, it has primarily been described the "complex plane strategy"(cxps) and has also been explained the reason of implementing this method in the present investigation. With the cxps collaborates the "multiple partition technique" (MTP) which is involved in the corresponding computations. In particular, the model of a differentially rotating polytropic star is constructed, which is under the cooperating influence of a toroidal magnetic field. To this purpose, perturbation theory is used on the basis of the fundamental magnetic perturbation parameter h. the theory including terms up to the first order in both the perturbation parameters u (rotation) and h (magnetic field),is developed and the corresponding differential equations are set up. Our computation concerns mainly critical rotations. In the second part of the thesis, we consider models with differential rotation owing to the viscous material of the star, on the basis of the so called "coupling equation" that is consequence of the Navier-Stokes equation for viscous polytropic stars. Emphasis is given on the study of dissipative effects due to viscous friction, as they are determined by the combined action of rotation and magnetic field. The computations show that a toroidal magnetic field can play the role of an efficient "lubricant" injected into the material of the particular magnetic model, thus reducing drastically the energy dissipated due to viscous friction.