Following the first detection of gravitational waves from a binary coalescence, the study of the formation and evolution of these gravitational-wave sources and the recovery and analysis of any detected event will be crucial for the newly realised field of observational gravitational wave astrophysics. This thesis covers a wide range of these topics including simulating the dense environments where compact binaries are likely to form, focusing on binaries containing an intermediate mass black hole (IMBH). It is shown that such binaries do form, are able to merge within a ∼ 100 Myr simulation, and that the careful treatment of the orbital evolution (including post-Newtonian effects) implemented here was crucial for correctly describing the binary evolution. The later part of the thesis covers the analysis of the gravitational waves emitted by such a binary, and shows it is possible to identify the IMBH with high confidence, together with most other parameters of the binary, despite the short-duration signals and assumed uncertainties in the available waveform models. Finally a method for rapid parameter estimation of gravitational wave sources is presented and shown to recover source parameters with comparable accuracy using only a small fraction ∼ 0.1% of the computational resources required by conventional methods.

The revolutionary discoveries of the last few years have opened a new era of astronomy. With the detection of gravitational-waves, we now have the opportunity of investigating new phenomena, such as mergers of black-holes. Furthermore, multi-messenger observations now allow us to combine information from different channels, providing insight into the physics involved. With this rapid evolution and growth of the field, many challenges need to be faced. In this thesis we propose three data analysis strategies to efficiently study the coalescences of compact binaries. First we propose an algorithm to reduce the computational cost of Bayesian inference on gravitational-wave signals. Second we prove that machine-learning signal classification could enhance the significance of gravitational-wave candidates in unmodelled searches for transients. Finally we develop a tool, saprEMo, to predict the number of electromagnetic events, which according to a specific emission model, should be present in a particular survey.

N-body simulations are used to investigate the dynamics of planetary systems based on the observed period-radius distribution by Kepler. The stability of the distri- bution is tested using integrations of 2,000 systems and with the addition of a Jupiter-like perturber in an aligned and inclined configuration sufficient for Lidov- Kozai (LK) oscillations. ∼ 67% of planetary systems are found stable, falling to ∼ 62% and ∼ 48% with an aligned or inclined giant perturber. Planet ejections are rare. Instability timescales of systems are predicted by spacing and multiplicity of planets, but exceptions are common. Evolution of select individual systems are investigated and classified. The dynamics of stellar binaries on eccentric orbits around a massive black hole (MBH) in the empty loss cone (LC) are also explored. The LK mechanism is sup- pressed by two-body relaxation from stars in galactic nuclei whilst tidal perturba- tions from the MBH excite the eccentricity of the binary to produce mergers in ∼ 75% of simulations. Stellar tides circularise the binaries and produce low velocity mergers. Enhanced magnetic fields in merger products could explain relativistic jet formation in tidal disruption events (TDEs). A method is presented for rapidly calculating the stellar evolution of stars with masses \[m=8.0-300.0M_\odot\] and metallicities \[-4.0\leq [Z/H]\leq 0.5\] that can be incorporated into future n-body simulations.

It has been long known that galaxy properties are strongly connected to their environment; however, a complete picture is still missing. This work's aim is to better understand the role of environment in shaping the galaxy properties, using a sample of 25 redshift-selected galaxy groups at 0.060 < z < 0.063, for which 30 multi-wavelength parameters are available. Given the wide variety of group dynamical states, it was fundamental to try and identify different classes of groups performing a statistical clustering analysis using all the available parameters independently of their physical meaning, which resulted in two classes distinct by their mass. To move beyond mass driven correlations, a new clustering analysis was performed removing the mass dependent properties, this approach provided a categorisation in four classes with distinctive group properties. Based on this, the galaxy properties were investigated and the classes interpreted as follows: a class of field-like galaxies in the early stage of structure formation; a class of low-mass groups either still in formation phase, or evolved, but small because they are isolated; a class of massive groups with no, or very little, ongoing star formation, likely in a more evolved stage of structure formation; and a class of massive groups possibly experiencing merger events. The result obtained have shown that it is possible to distinguish between classes of groups and thus be able to study the property of galaxies in systems with homogeneous properties. The method developed applied to data sets with larger statistics and good data quality could be a powerful tool to study galaxy evolution in galaxy groups.

The subject of this thesis is the simulation of X-ray cluster surveys and related issues, with a focus on the research that can be conducted with the International X-ray Observatory (IXO), or a similar next-generation X-ray observatory. A general purpose X-ray image simulator has been developed. It uses a modern cosmological simulation and cluster scaling relations to produce simulated cluster images that are well motivated by theory and observation. A distribution of point sources and various instrumental effects are also included. The simulator is complemented by a source identification method. The IXO selection function is mapped over a varying surface brightness parameter space. Simulated IXO surveys are used to explore the biases present in X-ray cluster surveys. These reveal that it is necessary to correct for biases using a detailed and carefully applied selection function to recover the true evolution of the luminosity-temperature relation. This is crucial for shallow surveys. Simulations of IXO using different angular resolutions are found to have only a minor effect on the number and distribution of detected clusters.

Advanced ground based laser interferometer gravitational wave detectors are due to come online in late 2015 and are expected to make the first direct detections of gravitational waves, with compact binary coalescence widely regarded as one of the most promising sources for detection. In Chapter I I compare two techniques for predicting the uncertainty of sky localization of these sources with full Bayesian inference. I find that timing triangulation alone tends to over-estimate the uncertainty and that average predictions can be brought to better agreement by the inclusion of phase consistency information in timing-triangulation techniques. Gravitational wave signals will provide a testing ground for the strong field dynamics of GR. Bayesian data analysis pipelines are being developed to test GR in this new regime, as presented in Chapter 3 Appendix B. In Chapter II and Appendix C I compare the predicted from of the Bayes factor, presented by Cornish et al. and Vallisneri, with full Bayesian inference. I find that the approximate scheme predicts exact results with good accuracy above fitting factors of ~ 0.9. The expected rate of detection of Compact Binary Coalescence signals has large associated uncertainties due to unknown merger rates. The tool presented in Chapter III provides a way to estimate the expected rate of specified CBC systems in a selected detector.

In this thesis I describe a statistically robust multi-wavelength study on 21 X-ray luminous cluster cores at 0.15<z<0.3, spanning X-ray to near Infra-Red (NIR) wavelengths, and using weak lens analysis of SNAPSHOT data from the Hubble Space Telescope Advanced Camera for Surveys. Substructures found in the "non-parametric" lensing mass maps are compared with K-band luminosity and Chandra X-ray flux maps. I construct parameterised mass models using a Bayesian statistics based method. Mass-observable scaling relations are used to explore segregation in cluster properties between cool core and non cool core clusters. The spatial mass distribution is better constrained than the weak lens mass, which suffers a low mass bias due to smoothing systematics. Assuming a constant bias for a constant smoothing scale, the K-band luminosity scales with mass similarly to the X-ray luminosity. I also demonstrate the detection of the weak lens signal of a galaxy group outside the HST:ACS field of view (A3192). I conclude that the analysis algorithm in this thesis could be useful in the analysis of cluster observations from future surveys such as PANSTARRS and DES.

The NA62 experiment at CERN is designed to perform a precision measurement of the ultra-rare K+ -> π+vv_ branching fraction. The experiment relies on a kinematic background rejection using the missing -10 mass-squared signatures of the contributing background components. As the signal is of the order (10 ) smaller than that of the most common kaon decays, the tracking performance of the detector must be exceptional in order to achieve a large signal to background ratio of S/B « 10. In this thesis, two tools to aid with the tracking procedure have been developed. Firstly, a field map which describes the fringe field of the spectrometer magnet has been created, tested and implemented in the NA62 Monte-Carlo software. Additionally, an analysis procedure to improve the precision and accuracy of track momentum in data was developed. Such tools are essential, not only for the K+ -> π+vv_ decay, but also for all decays containing tracks. In particular, they have been used to aid the measurement of the branching fraction and the form factor for the Standard Model decay K+ -> π+μ+μ- which is described here. The measurement has been performed using the data collected by the NA62 experiment in 2016 and 2017. The event selection, trigger efficiency determination and the analysis techniques used for the measurement are presented. The analyses of the two data sets are provided separately to demonstrate the progressing sensitivity of the detector. The final results are compatible with literature, and the 2017 measurement is currently the world’s most precise for this channel. This demonstrates the future potential of NA62 for when larger data sets become available in the next few years.

The dominant noise source in aLIGO is Brownian thermal noise, due to mechanical losses in the atomic structure of the amorphous titania doped tantala end test-mass mirror coatings. This thesis investigates the structural source of these losses. The effect of titania doping and thermal annealing upon the atomic structure of amorphous tantalum pentoxide coating preparations are studied using advanced electron diffraction techniques. Significant differences between the coating atomic structures have been identified for the first time in detail. The tantala based coatings studied have been demonstrated as better described by a heterogeneous phase separated model, rather than the continuous random network model for covalently bonded amorphous metal-oxides. The short-range ordering (SRO) of the coating atomic structures was investigated using pair-distribution function analyses, with an upper limit found to be ~4 Å. Correlations spanned ~9 Å, and have been related to model structures; between 4 - 5 Å, correlations were identified as signatures for 3D structural ordering. Fluctuation Electron Microscopy (FEM) was employed to investigate the MRO of the coating atomic structures. A novel approach to FEM was developed by the author during this PhD, in which the structural variance was computed using normalised cross-correlation coefficients. This made absolute intensity irrelevant, with the shape and the spatial distribution of the diffracted intensity taking precedence. The method is insensitive to poor SNR, illumination conditions, slight differences in experimental facility, and slight thickness variations in the samples. Virtual Dark-Field (VDF) imaging was adapted to amorphous structures in novel ways for the first time in this thesis. Simultaneous representation of the FEM data in real and reciprocal space, spatially resolved the structures responsible for the FEM signal. Correlation analyses were performed between VDF images of the structural ordering that relate to specific atom-pair correlations, including the use of novel annular variance images. The images and correlations clearly highlight the heterogeneous ordering and phase separation within the structures. Mechanisms responsible for the coating mechanical losses have been proposed, relating to the MRO, tensile-stress, as well as its reduction by titanium doping.

Quasi-periodic pulsations (QPPs) are a phenomenon commonly observed in solar flares, and are also occasionally observed in stellar flares. They are time variations in the intensity of the flare emission that repeat with approximately constant timescales, or timescales that increase or decrease monotonically in the special case of non-stationary QPPs. There are two main reasons for the interest in QPPs. First is the potential for the diagnosis of plasma parameters in the corona, such as the magnetic field strength and plasma density, which are otherwise difficult to observe directly. If the mechanism causing the QPPs can be inferred, then they would join MHD oscillations of coronal loops as a coronal seismology tool (e.g. Nakariakov & Ofman 2001). Secondly, since QPPs have been found to be a common phenomenon in flares, flares cannot be fully understood without knowing the origin of QPPs. This thesis presents statistical studies of QPPs in both solar and stellar flares, with the aim of learning more about the nature of this phenomenon. The robust detection of QPPs in solar and stellar flares has been the topic of recent debate. In light of this, this thesis shows how a statistical method described by Vaughan (2005), originally developed to test for the presence of periodic variations of the X-ray emission from Seyfert galaxies, can be adapted to aid with the search for QPPs in are time series data. The method identifies statistically significant periodic signals in power spectra, and properly accounts for red noise as well as the uncertainties associated with the data. The method has been further developed to be used with rebinned power spectra, allowing QPPs whose signal is spread over more than one frequency bin to be detected. An advantage of this method is that there is no need to detrend the data prior to creating the power spectrum. Examples are given where the method has been applied to synthetic data, as well as real flare data from the Nobeyama Radioheliograph (NoRH). These show that, despite the transient nature of QPPs, peaks corresponding to the QPPs can be detected at a significant level in the power spectrum without any processing of the original time series data, providing the background trends are not too steep. The properties of a set of solar flares originating from a single active region (AR) that exhibit QPPs were investigated. In particular, any indication of QPP periods relating to AR properties was searched for, as might be expected if the characteristic timescale of the pulsations corresponds to a characteristic length scale of the flaring structure. The three AR properties used for this study were the area, bipole separation distance, and average magnetic field strength, which were all measured at the photosphere using SDO/HMI magnetogram data. The AR studied, best known as NOAA 12192, was unusually long-lived and persisted for over three Carrington rotations. During this time a total of 181 flares were observed by GOES. Data from the GOES, SDO/EVE, Fermi, Vernov and NoRH observatories were used to determine if QPPs were present in the flares. For the soft X-ray GOES and EVE data, the time derivative of the signal was used so that any variability in the impulsive phase of the flare was emphasised. Power spectra of the time series data, without any form of detrending, were inspected and flares with a peak above the 95% confidence level in the power spectrum were labelled as having candidate QPPs. The confidence levels were determined taking full account of data uncertainties and the possible presence of red noise. A total of 37 flares (20% of the sample) showed good evidence of having stationary or weakly non-stationary QPPs, and some of the pulsations can be seen in data from multiple instruments and in different wavebands. Because of the conservative detection method used, this may be a lower bound for the true number of flares with QPPs. The fact that a substantial fraction of the flare sample showed evidence of QPPs, using a strict detection method with minimal processing of the data, demonstrates that these QPPs are a real phenomenon that cannot be explained by the presence of red noise or the superposition of multiple unrelated flares. No correlations were found between the QPP periods and the AR area, bipole separation distance, or average magnetic field strength. This lack of correlation with the AR properties implies that the small-scale structure of the AR (which was not accounted for in this study) is important and/or that different QPP mechanisms act in different cases. Flares that are orders of magnitude larger than the most energetic solar flares have been observed on Sun-like stars, raising the question of whether the same physical processes are responsible for both solar and stellar flares, and hence whether the Sun is capable producing a devastating superflare. A study of QPPs in the decline phase of white-light stellar flares observed by Kepler was embarked upon. Out of the 1439 flares on 216 different stars detected in the short-cadence data using an automated search, 56 flares were found to have QPP-like signatures in the light curve, of which 11 had stable decaying oscillations. No correlation was found between the QPP period and the stellar temperature, radius, rotation period, or surface gravity, suggesting that the QPPs are independent of global stellar parameters. Hence they are likely to be the result of processes occurring in their local environment. There was also no significant correlation between the QPP period and flare energy, while there was evidence that the period scales with the QPP decay time for the Gaussian damping scenario, but not to a significant degree for the exponentially damped case. This same scaling has been observed for MHD oscillations on the Sun, suggesting that they could be the cause of the QPPs in those flares. Scaling laws of the flare energy were also investigated, supporting previous reports of a strong correlation between the flare energy and stellar temperature/radius. Additional analysis was performed on one flare with a rare multi-period QPP pattern. Two periodic signals were identified using the wavelet and autocorrelation techniques. The presence of multiple periods is an indication that the QPPs might have been caused by magnetohydrodynamic oscillations, and suggests that the physical processes operating during stellar flares could be the same as those in solar flares.