In this thesis we investigate the development and use of numerical methods to study astrophysical problems, particularly the formation and evolution of objects via gravitational instability in circumstellar discs. We begin with a comprehensive overview of the development, validation and optimisation of numerical tools. These formed the basis of SEREN, a Smoothed Particle Hydrodynamics (SPH) code for modelling self-gravitating fluid dynamics. SEREN has been rigorously tested and optimised, and is now being used for high-performance research in various areas of star formation. We then consider in some depth the problems associated with shocks, instabilities and shear flows in numerical simulations, detailing why such problems arise and what can be done to alleviate them. Finally we model circumstellar discs, investigating the influence of both physical and computational parameters upon the formation of objects via gravitational instability. We then model the interaction of discs with stars and other disc systems, investigating the influence of the orbital parameters upon the evolution of a marginally stable disc. Ultimately we find that gravitational instability in massive extended circumstellar discs is a viable mechanism for the formation of brown dwarfs and massive planets, and provides an explanation for the "brown dwarf desert" and free-floating planets. We also find that while disc-star and disc-disc interactions might produce accretion bursts and exert an influence over the disc evolution, they are not a likely mechanism for triggering fragmentation in marginally stable discs.

In this thesis, we employ two numerical tools - semi- analytical models and N-body plus hydrodynamical simulations of large scale structure and individual galaxies - to explore the underlying physics governing the formation and evolution of groups of galaxies, and the role of environment in generating polar structures around disk galaxies. Using phenomenological models of baryonic physics imposed upon large-scale dissipationless simulations of the Universe, semi-analytic models (SAMs) are one of the principal methods used to model large samples of model galaxies. We sought to examine the properties of groups of galaxies with a range of densities using SAMs applied specifically to the industry-standard Millennium Run; for this work, we make use of the well-known Munich and Durham models, and their descendants. We are especially interested in how group properties change as we change the linking length of our Friends- of-Friends group finder. We compare the group populations and richness in these models and compare them both with observations and high-resolution N- body simulations. This leads us to the conclusion that the Durham models produce a much larger population of compact objects than the Munich models. We also explore the group dynamics and morphology as a function of density. We compare the luminosity distributions of galaxy groups using publicly available SAMs in order to explore

This work investigates the properties of Early-Type Galaxies (ETGs; elliptical and lenticulars) containing thermal dust emission, with aims of linking the formation and evolution of these galaxies with their current dust properties. Three different proxies for morphology are considered for selecting ETGs, and these are tested against three sets of visually classified galaxies. We find that classifying ETGs as those galaxies in the optical Red Sequence results in samples with ≳35% contamination by late-types, and ≲82% completeness. Concentration and Sérsic index proxies result in slightly improved contamination levels of ≳30% and ~60-70% completeness. These results lead to the conclusion that morphological proxies cannot be used to create fully robust samples of ETGs. Therefore, we choose to use visual inspection to identify ETGs at low redshifts.

With the development of more and more elegant and sensitive interferometric gravitational wave detectors, we are expecting the first direct detection of gravitational waves in a short time. This triggers huge interest to develop more powerful tools to perform data analysis on these signals, and to develop a good understanding of the analysis so that confident conclu- sions can be made. A further step would be to view into the future, as the first detections will boost the scientific demands for more powerful future generation detectors, which identifies the task of optimising the site of such detectors. Bayesian Inference plays a vital role in data analysis, and one excellent example that demon- strates its usefulness is its ability to resolve the tension between multiple models using the methodology of Bayesian Model Selection. In this thesis we apply this methodology to the timing data of pulses from the pulsar 1E 2259+586. With a set of different choices for the prior range, a fair and quantitative comparison can be made between two competing models: that of so-called successive anti-glitches and an anti-/normal glitch pair. Our analysis of the data shows a consistent support for the successive anti-glitches model, with a Bayes Factor of ∼ 45, where the uncertainty has been estimated from nested sampling and from multiple runs that are slightly different, but still within a factor of two, showing a general consistency. Simplifying the timing model will only make the Bayes Factor even bigger, while the two event model is overwhelmingly supported over the one event model. In gravitational wave data analysis, posteriors are generally complicated structures contain- ing multiple modes. A novel algorithm to achieve efficient sampling for multi-modal pos- teriors, known as mixed MCMC, is proposed in this thesis. This enables communication between multiple regions within the parameter space by adopting a novel jump proposal. We present the mixed MCMC algorithm and first apply it to a toy model problem, where the likelihood may be determined theoretically. By comparing the theoretical and empiri- cally sampled values of 2 log(L) for credible regions that correspond to 68.27%, 95.45% and 99.73%, we conclude that for our illustrative model the sampling result of mixed MCMC is consistent with the theoretical prediction with small uncertainty. Since it does not re- quire multiple chains with different temperatures, mixed MCMC can boost the efficiency of sampling by design, compared with (for example) parallel tempering MCMC. The sampling strategy of mixed MCMC can be helpful for not only Bayesian Inference, but also more general problems like the global optimisation of future generations of Gravita- tional Wave Detectors. As we expect such problem to be intrinsically high dimensional and multi-modal, mixed MCMC is a suitable sampling method, and we develop and apply it in this thesis. Based on our analysis it is concluded that for both a 3-detector-network and a 5-detector-network, Australia hosts the “best” site, in the sense that such site is most flex- ible, i.e. it can be involved in the largest number of detector networks, involving different component sites, that have a high ‘Figure of Merit’. The work of gravitational wave data analysis leads to the ultimate goal of making a direct detection of gravitational waves, which in turn requires the ability of distinguish astronomi- cal signals from a noisy background, and assess the significance of each gravitational wave ‘trigger’ (i.e. candidate event) appropriately. There are two types of method for estimating significance and these differ by the key distinction of either removing the foreground events from the background estimation or keeping them in the analysis. This thesis presents the results of a Mock Data Challenge (MDC), carried out within the LIGO Scientific Collabo- ration using different data analysis pipelines, designed to investigate these two methods for estimating significance. It contains a variety of background complexity ranging from simple, realistic to complex, and foreground event rate ranging from zero, low, medium and high. Analysis of the MDC results illustrated that generally all methods for determining the sig- nificance agree well with each other, irrespective of the background complexity. However, a discrepancy became apparent between the results for removal or non-removal of foreground events, for events below a significance level of < 10−3. Our results demonstrated that the removal method is an unbiased estimator for the mean of the significance. However, as the most scientifically interesting events are likely to have a very small numerical value for their significance, such method would overestimate that significance for most of the realisations.

In this thesis I bring together three projects that comprise my postgraduate studies; using numerical simulations of galaxy formation in a cosmological context. The first of these projects involves the simulation of a suite of galaxies in loose group and field environments. This suite of galaxies is used to compare properties such as the metallicity gradients and morphology to determine if systematic differences are apparent as a function of subtle environmental differences. Almost no distinction is seen between galaxies in the field and the loose group environments: individual assembly histories of the galaxies dominate over ambient environmental effects with the exception of the vertical velocity dispersion of the stellar disc where loose group galaxies tend to exhibit a greater number of instances of impulsive heating of the disc. In the second project I present further analysis of this suite of galaxies and a comparison with other galaxies simulated using contrasting methodologies, in ad- dition to several semi-numerical galaxy formation models. The focus of this work is the evolution of metallicity gradients and star formation profiles, finding that galaxies form in an inside-out fashion. This leads to steeper metallicity gradients in young stellar populations at high redshift compared with the present day. By considering present day stellar populations with different ages in these galaxies the converse is found, older populations have flatter gradients. This suggests that while the metallicity gradient starts out steep, it flattens over time due to stellar migra- tion/mixing. This flattening due to stellar migration happens at a faster rate than the flattening of the gas phase metallicity gradient. Finally, I present an update to the N-body and adaptive mesh refinement hydrodynamical code ramses that introduces a more sophisticated feedback treatment, this code is dubbed ramses-ch. Under the new scheme, energetic and elemental feedback is contributed by stars throughout their lifetime rather than (as previously) in a single burst. This relaxation of the ‘instantaneous feedback approximation’ in ramses-ch opens up the opportunity for studying chemical evolution using adaptive mesh refinement hydrodynamics where previous studies were limited to smoothed particle hydrodynamical codes or semi-numerical models. The new code is applied to the simulation of a typical disc galaxy using different stellar initial mass functions and supernovae type-Ia progenitor models. The influence of these model inputs on the ratio of elemental abundances and supernovae rates in the simulated galaxies are compared as a means of constraining chemical evolution models. The conclu- sions drawn from this work are discussed in the broader context of galaxy formation simulations.

Near-Earth Asteroids (NEAs) can provide useful resources in terms of feedstock for spacecraft propellant, crew logistic support and a range of useful metals. The possibility of capturing small NEAs using low energy transfers would therefore be of significant scientific and commercial interest. Although NEAs may make close approaches to the Earth, and so represent a potential impact threat, the exploitation of their resources has long been proposed as a necessary element for future space exploration. The objective of the research presented in this thesis is to develop methodologies for the trajectory design of capturing NEAs in the neighbourhood of the Earth. Firstly aimed at capturing NEAs around the Earth-Moon L2 point, a new type of lunar asteroid capture is defined, termed direct capture. In this capture strategy, the transfer trajectory for capturing an NEA into the Earth-Moon system is modelled in the Sun-Earth-Moon restricted four-body. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid’s initial obit to the stable manifold associated with Earth-Moon L2 point. The direct asteroid capture strategy requires a shorter flight time compared to an indirect asteroid capture strategy, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system. As ideal locations for space science missions and candidate gateways for future crewed interplanetary missions, the Sun-Earth libration points L1 and L2 are also preferred locations for the captured asteroids. Therefore, the concept of coupling together a flyby of the Earth and then capturing small NEAs onto Sun–Earth L1 or L2 periodic orbits is proposed. A periapsis map is then employed to determine the required perigee of the Earth flyby. Moreover, depending on the perigee distance of the flyby, Earth flybys with and without aerobraking are investigated to design a transfer trajectory capturing a small NEA from its initial orbit to the stable manifolds associated with Sun-Earth L1 and L2 periodic orbits. NEA capture strategies using an Earth flyby with and without aerobraking both have the potential to be of lower cost in terms of energy requirements than a direct NEA capture strategy without the Earth flyby. Moreover, NEA capture with an Earth flyby also has the potential for a shorter flight time compared to the NEA capture strategy without the Earth flyby. Following by this work, a more general analysis of aerobraking is undertaken and the low energy capture of near-Earth asteroids into bound orbits around the Earth using aerobraking is then investigated. Two asteroid capture strategies utilizing aerobraking are defined, termed single-impulse capture and bi-impulse capture, corresponding to two approaches to raising the perigee height of the captured asteroid’s orbit after the aerobraking manoeuvre. A Lambert arc in the Sun-asteroid two-body problem is again used as an initial estimate for the transfer trajectory to the Earth and then a global optimization is undertaken, using the total transfer energy cost and the retrieved asteroid mass ratio (due to ablation) as objective functions. It is shown that aerobraking can in principle enable candidate asteroids to be captured around the Earth with, in some cases, extremely low energy requirements. The momentum exchange theory is also applied to the capture of small near-Earth asteroids into bound periodic orbits at the Sun-Earth L1 and L2 points. A small asteroid is first manoeuvred to engineer a flyby with a larger asteroid. Two strategies are then considered: when the small asteroid approaches the vicinity of the large asteroid, it will either impact the large asteroid or connect to it with a tether. In both strategies, momentum exchange can be used to effect the capture of one of the asteroids. Then, a two-impulse Lambert arc is utilized to design a post-encounter transfer trajectory to the stable manifolds of the Sun-Earth L1 or L2 points. By investigating the outcome of the impact on the small asteroid, or the tension of the tether, the maximum velocity increment available using these momentum exchange strategies is investigated. Again the capture strategies using momentum exchange in principle have the potential to deliver low-energy capture of asteroids. The methods presented in this thesis are intended to be used as a preliminary analysis for these asteroid capture strategies. Although some significant practical challenges remain, the transfer in the CRTBP models can serve as a good approximation for the trajectory in a more accurate dynamical model.

Across cosmic time, stars have contributed most of the radiant energy found in the Universe and have created nearly all the chemical elements heavier than helium. Understanding the evolution of the Universe requires understanding the history of star formation. Stars form in galaxies, which are in essence huge aggregations of stars, dust and gas. Understanding star formation requires, among other things, measuring the rate at which interstellar gas is being converted into stars in a given galaxy. Star formation, a critical driver of galaxy evolution, responds both to external influences (local and global environment) and internal factors (e.g. dust).For several decades, the properties of star formation have been studied in galaxies residing in the dense environments of galaxy clusters and compared to those in the sparsely populated field. In this thesis we aim to bridge this gap in the study of the star formation-density relation by studying the evolution of galaxy properties, particularly their star formation rate (SFR) in the critical intermediate region on the periphery of rich galaxy clusters. Using photometric and spectroscopic data from the Sloan Digital Sky survey (SDSS) we show how common observables, such as colour, SFR, and SFR/M* are influenced when galaxies are assembled into clusters via large-scale filaments. We discover that complex galaxy populations (e.g. blue passive galaxies and [optically] red star-forming galaxies) are commonly found in and around rich clusters in the nearby (z ~ 0.1) universe. While the blue passive galaxies are the progenitors of passive red cluster galaxies, the (optically) red star-forming galaxies are a mix of at least two different populations. One set of red star-forming galaxies are dust obscured star-forming x galaxies, while the rest of them are normal star-forming galaxies whose colour is a result of metal-rich dominant stellar populations.

In this work, the transverse momentum spectra of Λ and K\(^0\)\(_S\) measured with the ALICE experiment at the LHC are discussed. Measurements are presented for colliding systems of protons, at centre of mass energies 2.76 TeV and 7 TeV, and for lead ions at a centre of mass energy of 2.76 TeV per nucleon. The spectra are discussed within a theoretical framework of a thermally equilibrated, hydrodynamically evolving system, which serves to explain the shape of the spectra for p\(_T\) < 2 GeV/c. For p\(_T\) > 6 GeV/c jet quenching is evident, but no evidence of particle species dependance in jet quenching is observed. The Λ/K\(^0\)\(_S\) ratio shows an enhancement for 2 < p\(_T\) < 6 GeV/c, peaking at 1.5 for the 5% most central Pb–Pb collisions compared to 0.6 for pp. This is discussed in terms of a coalescence model. It cannot be explained purely by enhanced baryon production, but must also involve a redistribution of particles within p\(_T\). This supports the hydrodynamical picture of hadron production. A brief comparison to the results presently available in p–Pb collisions at the LHC is also given.

This thesis focuses on gravitational wave (GW) astrophysics with Pulsar Timing Arrays (PTAs). Firstly it is shown that anisotropy in the GW background may be present, and that its characterization at different angular scales carries important information. The standard analysis for isotropic backgrounds is then generalized by decomposing the angular distribution of the GW energy density into multipole moments. Generalized overlap reduction functions (ORFs) are computed for a generic level of anisotropy and PTA configuration. A rigorous analysis is then done of the assumptions made when calculating ORFs. It is shown that correlated phase changes introduce previously unmodeled effects for pulsars pairs separated by less than a radiation wavelength. The research then turns to the study of continuous GW sources from supermassive black hole binaries (SMBHBs). Here it shown that the detection of GWs from SMBHB systems can yield direct information about the masses and spins of the black holes, provided that the GW-induced timing fluctuations both at the pulsar and at Earth are detected. This in turn provides a map of the nonlinear dynamics of the gravitational field and a new avenue to tackle open problems in astrophysics connected to the formation and evolution of SMBHs.

Gravitational waves (GWs) have been detected for the first time in 2015 by the LIGO-Virgo Scientific Collaboration. The source of the GWs was a binary black hole (BBH). The observation caught the final fraction of a second as the two black holes spiralled together and merged. This observation (and the others to follow) marked the beginnings of GW astronomy, ‘a new window on the dark universe’, providing a means to observe astronomical phenomena which may be completely inaccessible via other avenues as well as a new testing ground for Einstein’s theory of general relativity (GR). However, this is just the beginning – like electromagnetic astrophysics, there is a full spectrum of GW frequencies to explore. At very low frequencies, pulsar timing arrays (PTAs) are being used to search for the GW background from the merging population of massive black hole binaries (MBHBs). No detection has yet been made, but upper limits have been placed. Here we present results on what inference on the MBHB population can be learnt from present and possible future PTA results, and also compare current upper limits with astrophysical predictions, finding them to be fully consistent so far. We also present a generic method for testing the consistency of a theory against experimental evidence in the situation where there is no strong viable alternative (for example GR). We apply this to BBH observations, finding them to be fully consistent with GR and also to Newton’s constant of gravitation, where there is considerable inconsistency between measurements.