In this thesis, I develop statistics capable of detecting peculiar features in current observations of the cosmic microwave background (CMB) radiation. Such tools scrutinise the very foundations of standard cosmological models. Evidence of peculiar features in the CMB may require a reassessment of these building blocks. More likely, any features may be artefacts of some non-cosmological signal. Nevertheless, whether the origin of these strange attributes is primordial or local, their discovery would be instructive. Existing statistical tools focus on the amplitude of the spherical harmonic coefficients, I look instead at their phases. The method I form checks for the uniformity of the distribution of phase angles using a non-parametric descriptor, which is known as Kuiper's statistic. The method is applied to the COBE-DMR and WMAP sky maps, and departures from uniformity are found in both. The results probably reflect Galactic contamination or the known variation of signal-to-noise across the sky rather than primordial non-Gaussianity. Next, the statistic is adjusted to probe the topology of the universe. The new method exploits the existence of correlations in the phases of the CMB temperature pattern associated with matched pairs of circles seen in the CMB in universes with non-trivial topologies. After this, I turn our attention to the issue of Galactic foreground signals. A diagnostic of foreground contamination is developed based around the Faraday rotation measures (RM) of extragalactic sources. Statistically significant correlations of RM with the preliminary WMAP individual frequency maps are found. These correlations remain significant in CMB-only maps. Later, I use catalogues of rotation measures to construct a template of the Galactic sky. The RM maps may be used as templates for CMB foreground analysis. This idea is illustrated with a cross-correlation analysis between the WMAP data and our maps. I find a significant cross-correlation, again indicating the presence of significant residual contamination. Problems and future developments are discussed at the end.

This thesis analyses the large scale distribution of galaxies in two recently completed redshift surveys and develops models to infer estimates of redshift-space distortions. These models demonstrate that coherent infall cannot be neglected in analyses of peculiar velocities as previous works have claimed. The clustering statistics of the largest infra-red (IR) redshift survey to date, the PSCz, are measured for the whole survey and also for various sub-samples, split by absolute luminosity and colour. It is found that IR selected galaxies are less strongly clustered than optically selected samples. A weak dependence of clustering on IR colour is found, along with a consistent dependence on IR absolute luminosity. An analysis of the 2dF Galaxy Redshift Survey (2dFGRS), containing about 220,000 galaxy redshifts, is presented. Detailed, high precision measurements are made of both the redshift- and real-space correlation functions. A comprehensive analysis of the measured 2-d correlation function leads to accurate estimates of the redshift-space distortions, including the infall parameter, beta. This measurement is then combined with other recent works to constrain the matter density of the Universe, omega. The 2dFGRS is also split by absolute luminosity and spectral type to look for dependence of clustering on these galaxy properties. A strong dependence on both luminosity and spectral type is found. The 2dF Quasar Redshift Survey (2QZ) is used, along with the 2dFGRS, to look for periodicites in the redshift distributions of QSO's in projected close galaxy-QSO pairs. Recent works have reported such an effect in small samples. No such periodicity is found in the largest, most well defined sample tested to date. These results are entirely consistent with the current cosmological paradigm of a Universe dominated by a cosmological constant and cold dark matter, and also the notion that the large scale distribution of galaxies depends on galaxy type.

This thesis studies a new method of constraining the mass distributions of elliptical galaxies and clusters of galaxies: gravitational redshift. The aim was to determine the types of astrophysical object in which gravitational redshift can be most readily detected and to attempt to observe the effect for the first time in a single object. Longslit stellar kinematics were combined with planetary nebulae kinematics to study the mass distribution of M87. Jeans modelling showed that, although the best-fit model gave too little mass (Upsilon = 5.34+/-0.34, beta = 0.71+/-0.03, M_halo = 2.64+/-0.92 x 10^12 M_sun), by adjusting the orbital anisotropy it was possible to construct a model that was consistent with both the kinematics and existing X-ray gas measurements. Longslit kinematics from the literature were used to attempt to determine the mass-to-light ratio of a sample of elliptical galaxies using gravitational redshift. Models were developed to calculate the expected gravitational redshift from the surface brightness profile. The best-fit mass-to-light ratios were found using this model and also obtained independently using the Jeans equation. The results were not statistically inconsistent with the expected H-band mass-to-light ratios predicted by stellar population models - the Jeans modelling gave a mean mass-to-light ratio of Upsilon_sigma = 1.67+/-0.10, while the gravitational redshift predicted Upsilon_v = 4.84+/-2.67. Integral field spectroscopy of the centre of M60 was undertaken in an attempt to detect gravitational redshift in the centre of an individual galaxy for the first time. The velocity field was summed around the galaxy's isophotes to remove the effect of rotation. Models were constructed to predict the gravitational redshift, which were then compared to the data. It was found that the shallow slope of the light profile made it impossible to detect a gravitational redshift in this case, but that the scatter of the data points suggests that a signal of a few km/s could be detected. Consideration of the models led to a better understanding of the most suitable targets for this kind of study. An analysis of the 2dF groups catalogue was made in order to attempt to determine the strength of the gravitational redshift in clusters of galaxies. A new method was developed for measuring the signal in clusters. As part of the analysis, the density distribution of the clusters was obtained. It was found that they followed an exponential profile, which scaled linearly with the size of the cluster. The gravitational redshift was used to attempt to constrain the mean cluster mass, but it was found that the errors were too large to rule out all but the largest masses with any certainty. Future studies would require either a much larger sample, or one which concentrates specifically on the most uniform, high mass clusters. Gravitational redshift offers a new approach to studying the mass distributions of galaxies and clusters that requires many fewer assumptions regarding the underlying physics than many of the current methods. Unfortunately, it also suffers from a number of potential setbacks. Recent advances in instrument technology, combined with the careful selection of suitable targets should allow gravitational redshift to become a viable tool for studying the nature and distribution of dark matter.

This thesis presents a survey of compact emission-line objects in the Andromeda Galaxy (M31), performed using a novel new instrument, the Planetary Nebula Spectrograph. The final catalogue contains the positions, magnitudes and velocities for 3300 objects displaying [O III] emission at 5007 Angstroms, of which 2615 are found likely to be planetary nebulae (PNe) associated with M31. The survey area covers some 6 square degrees, taking in the whole of M31's disk out to a projected radius of 1.5 degrees, with extensions along the major and minor axes, and the Northern Spur and Southern Stream regions. The calibrated data have been checked for internal consistency and compared with other catalogues. With the exception of the very central, high surface brightness region of M31, this survey is complete to a magnitude limit of m(5007) ~ 23.75, 3.5 magnitudes into the planetary nebula luminosity function. A number of satellite and background galaxies are located within the M31 survey area and emission line objects associated with these have been identified. Analyses of the basic kinematic properties associated with each of these galaxies are presented. The PN catalogue has been analysed for non-kinematic, kinematic and dynamical properties. We have examined the planetary nebula luminosity function across M31, the spatial distribution of PNe, and the luminosity specific PN density. These analyses indicate that apart from a small change in the luminosity specific PN density there are no other non-kinematic differences between the bulge and disk PN populations suggesting that the sample of PNe is not strongly populated by objects whose progenitors are more massive stars. There is no indication of a significant halo PN population. Rotation curves for both the surveyed PNe and H II regions have been produced as well as the PN velocity dispersion profile. The H II rotation curve is seen to be in good agreement with those in the literature, while the PN rotation curve and velocity dispersion profile exhibit some peculiarities. However, under the approximation of an axisymmetric disk these are shown to be mutually consistent, but require the disk to flare with radius if the shape of its velocity ellipsoid remains invariant. The kinematic properties of photometric substructures are examined and kinematic substructures are searched for. A possible kinematic extension of the Southern Stream has been discovered. A new approach is taken in order to search for dynamical streams in the disk of the galaxy, involving an examination of the energy angular momentum plane. This also provides a new way of looking at the distribution function of a tracer population in a disk galaxy.

In this thesis techniques are developed for the simulation of partially ionised plasmas in the fluid approximation. These techniques are used to model the evolution of magnetic fields in the partially ionised regions of the solar atmosphere. Single fluid equations for a partially ionised plasma are derived based on the individual equations for each species. A Lagrangian Remap MHD code is then adapted to simulate a plasma of arbitrary degree of ionisation. The effects of the presence of neutrals on the propagation and damping of Alfv´en waves in the solar atmosphere are investigated. Ion-neutral collisions are shown to be an efficient damping mechanism for outwardly propagating Alfv´en waves of frequencies greater than 0.1 Hz, showing that high frequency waves in the outer solar atmosphere cannot originate at the surface of the Sun. Next simulations to show the effects of neutrals on the emergence of magnetic flux from beneath the solar surface into the outer atmosphere are performed. Results from 2D and 3D numerical experiments show that the presence of neutrals increases the amount of magnetic flux that can emerge into the corona. Furthermore, ion-neutral collisions are strong enough to dissipate currents perpendicular to the magnetic field as it emerges. This shows that ion-neutral collisions are a viable mechanism for the formation of force-free (j ∧B = 0) coronal magnetic field from sub-surface field, which is not the case when the plasma is assumed to be fully ionised.

Over recent years, there has been an increasing level of interest in the cosmological significance of observations of the Sunyaev Zel'dovich (SZ) effect in galaxy clusters. Al though the SZ effect has been known about for around fifty years, observations of it have only become mainstream recently. The SZ effect refers to the redistribution of energy of Cosmic Microwave Background (CMB) photons due to inverse Compton scattering off populations of free electrons, most commonly in galaxy clusters. The SZ acts as an artificial 'emitter' or 'absorber' along the line of sight to a cluster once other back grounds have been removed. SZ measurements suffer from a range of systematic effects that have made observations in the region of the spectrum where the SZ simulates an 'emitter' (above 220 GHz) particularly challenging. Nevertheless, the scientific potential of large-scale SZ surveys is large. In particular, the SZ distortion to the CMB is independent of redshift and limited only by the mass of the clusters being observed. This makes SZ surveys useful for making detailed observations of the evolution of large-scale structure of the Universe, which depends sensitively on cosmological parameters. Knowledge of the spectrum of the SZ effect can also be used to constrain the peculiar velocity of galaxy clusters, which has the potential to provide information about the nature of dark energy. This thesis describes the observation, mapping and detailed analysis of the cluster Abell 1835 at 1.1 mm, where the SZ acts as an 'emitter'. An estimate of the SZ emission from Abell 1835 is obtained and combined with other measurements of the cluster to generate a spectrum, from which one of the most precise limits on a cluster's peculiar velocity to date is obtained.

The intricate analysis of a strong gravitational lens is a complex and computationally demanding problem, requiring the lensed source galaxy's extended light profile to be reconstructed simultaneously with non-linear modeling of the lens galaxy's mass and light. When successful, this analysis gives unrivaled insight into dark matter, cosmology and the most distant Universe. However, such studies remain resigned to small samples, simply due to how long this involved analysis takes. To address this, this thesis presents AutoLens, the first automated framework for comprehensive modeling of a strong gravitational lens's light, mass and source. Reconstruction of the lensed source galaxy uses an adaptive pixel-grid, which is derived in a completely stochastic manner such that a unique pixelization is used for every source reconstruction. This removes biases inherent to pixelized methods associated with the discrete nature of the source-plane. Light profile fitting of the lens galaxy is fully integrated into AutoLens, making it the first method to successfully unify modeling of the lens's light, mass and source into one coherent framework. This allows the method to advocate decomposed mass modeling, which treats separately the lens galaxy's light and dark matter. AutoLens is therefore capable of addressing a diverse range of unique science cases, most notably its ability to determine the central density of a lens galaxy's dark matter halo. These features are incorporated into a fully-automated pipeline, such that the analysis requires no input from the user after an initial setup. This pipeline is tested using a suite of simulated strong lens images which span a variety of source morphologies, lens profiles and lensing geometries. Following the completion of AutoLens's development, the method is ready to analyze the hundreds of archival images of strong gravitational lenses that have been amassed over the past decade, and which are still yet to receive a comprehensive lens analysis. With of order one hundred thousand lenses set to be discovered in the next decade, AutoLens's automated philosophy will be paramount to making analysis of the incoming strong lens samples feasible.

Solar tornado-like prominences have been observed for over 90 years, but their true nature has recently been one of the most hotly debated aspects of prominence research. They have been linked to prominence eruptions, so understanding their stability and the plasma motions seen could provide a link between these dynamic features and the Sun-Earth space weather, which is important to fully understand in modern-day society. This thesis aims to answer some of the open questions on solar ‘tornadoes’, specifically on the plasma behaviour at different temperatures and the magnetic field structure of these apparently-rotating phenomena. Using a range of spectral diagnostic techniques and data from space-based and ground-based instruments, a more complete picture of solar tornadoes is built here. Optically thin emission at coronal temperatures (∼ 1.5 MK) has previously been shown to give anti-symmetric Doppler velocity patterns in a tornado, indicative of rotation. Using the same data set, from 14 September 2013, it has been possible to show that the Doppler pattern is visible in all spectral lines formed above 1 MK, but at lower plasma temperatures the pattern is not present. Electron densities are calculated from density-sensitive line pairs, and it is found that the electron density is lower in the tornado than the surrounding corona. Non-thermal line widths are calculated, showing that there is some additional broadening at the tornado compared to the surrounding corona, which could be due to a turbulent magnetic field component or the presence of unresolved Kelvin-Helmholtz instabilities at the tornado-corona boundary. The temperature structure along an observed line of sight is calculated using the technique of Differential Emission Measure, and this indicates that tornadoes are part of the larger prominence structure that is seen in some wavebands. A dedicated coordinated observation was designed to study tornadoes at lower plasma temperatures (< 1 MK), and to investigate their unknown magnetic structure. An observation of two tornadoes from 15 July 2014 is presented, from which the Mg II h and k lines and the magnetic field are analysed in detail. The optically thick Mg II lines, formed at chromospheric temperatures, show no velocity patterns similar to those seen at higher temperatures. The Mg II lines show a mix of reversed and non-reversed profiles in the prominence. This is the first report of strong central reversal of the h and k lines in a prominence. Comparing to a grid of isothermal isobaric Mg II models reveals that the large central reversals seen in the 15 July 2014 prominence indicates high optical thicknesses and pressures in the prominence slab. The magnetic field in the tornadoes on July has been measured using spectropolarimetry of the He I D3 line, which gives the magnetic field strength and orientation. Field strengths of up to 60 G are found in places, but the average field strength is around 20 − 30 G. The inclination of the magnetic field indicates that it is horizontal, parallel to the solar surface. These observations suggest that the tornado magnetic field is not twisted, but instead horizontal with plasma suspended in dips. An attempt has been made to find correlations between plasma parameters and the observed magnetic field parameters. No correlations are found, but this study has allowed a clearer, statistical investigation into the parameters available from this coordinated observation. These statistics are useful for comparing observations to models, in order to better understand the physical conditions that created the observed line profiles. Finally, this thesis contains an update to a radiative transfer prominence modelling code, PROM, to include calculations of the emergent intensities of Mg II lines. This step was taken to have the ability to freely explore models for larger ranges of model parameters than presented by previous authors, with the scope to investigate more complex (2D, 3D) multi-thread models. The output of the updated code is compared to the results of another Mg ii modelling code, finding good agreement in the recovered optical thickness, but integrated intensities are found to vary by 30−40% for some models. An extended grid of isothermal isobaric and PCTR models is then explored in order to understand the links between observable Mg II h and k line parameters and model parameters. A number of correlations are found, meaning that observed Mg II h and k lines can be used to identify physical parameters in a prominence. These models are compared to observations from 15 July 2014, finding that they can explain some of the observed line profiles, but more complex models are required to fully explain the observations.

In this thesis, I explore the evolution of the brightest cluster galaxies (BCGs) over the last 10 billion years through detailed studies of both local BCGs from SDSS and their high-z progenitors from CANDELS UDS. First, I study a large sample of local BCGs and link their morphologies to their structural properties. We derive visual morphologies for these BCGs and find that ~57% of local BCGs are cD galaxies, ~13% are ellipticals, and ~21% belong to intermediate classes, mostly between E and cD. There is a continuous distribution in the properties of the BCG's envelopes, ranging from undetected (elliptical BCGs) to clearly detected (cD galaxies), with intermediate classes showing increasing degrees of the envelope presence. A minority (~7%) of BCGs have disk morphologies, with spirals and S0s in similar proportions, and the rest (~2%) are mergers. After carefully fitting the galaxy light distributions using Sersic models, I find a clear link between BCG morphology and structure, such that cD galaxies are typically larger than elliptical BCGs, and the visually extended envelope of cD galaxies is a distinct structure differing from the central bulge. Based on this BCG morphology--structure correlation, I develop a statistically robust way to separate cD from non-cD BCGs, by which cD galaxies can be selected with reasonably high completeness and low contamination. Next, I investigate the effect of environment on the properties of local BCGs by studying the relationship between the BCG's internal properties (stellar mass, structure and morphology) and their environment (local density and cluster halo mass). I find that the size of BCGs is determined by the intrinsic BCG stellar mass, with a weak correlation with the cluster environment. Additionally, more massive BCGs tend to inhabit denser regions and more massive clusters than lower mass BCGs. The growth of the BCGs seems to be linked to the hierarchical growth of the structures they inhabit: as the groups and clusters became denser and more massive, the BCGs at their centres also grew. Moreover, I demonstrate that cD galaxies are ~40% more massive than elliptical BCGs, and prefer denser regions and more massive haloes. My results, together with the findings of previous studies, suggest an evolutionary link between elliptical and cD BCGs. I propose that most present-day cDs started their life as ellipticals at z~1, which subsequently grew in stellar mass and size due to mergers. In this process, the cD envelope developed. This process is nearing completion since the majority of the local BCGs have cD morphology. However, the presence of BCGs with intermediate morphological classes suggests that the growth and morphological transformation of BCGs is still ongoing. Finally, I present a new method for tracing the evolution of BCGs from z~2 to z~0. I conclude, on the basis of semi-analytical models, that the best method to select BCG progenitors at z~2 is a hybrid environmental density and stellar mass ranking approach. Ultimately I am able to retrieve 45% of BCG progenitors. Although the selected high-z progenitor sample is a mixture of BCG and non-BCG progenitors, I demonstrate that their properties can be used to trace BCG evolution. Applying this method to the CANDELS UDS data, I construct an observational BCG progenitor sample at z~2. A local BCG comparison sample is constructed using the SDSS data, taking into account the likely contamination from non-BCGs to ensure a fair comparison between high-z and low-z samples. Using these samples I demonstrate that BCG sizes have grown by a factor of ~3.2 since z~2, and BCG progenitors are mainly late-type galaxies, exhibiting less concentrated profiles than their early-type local counterparts. I also find that BCG progenitors have more disturbed morphologies, while local BCGs have much smoother profiles. Moreover, I find that the stellar masses of BCGs have grown by a factor of ~2.5 since z~2, and the SFR of BCG progenitors has a median value of ~14 Msun/yr, much higher than their quiescent local descendants. I demonstrate that at 1 < z < 2 star formation and merging contribute approximately equally to BCG mass growth. However, merging plays a dominant role in BCG assembly at z < 1. I also find that BCG progenitors at high-z are not significantly different from other galaxies of similar mass at the same epoch. This suggests that the processes which differentiate BCGs from normal massive elliptical galaxies must occur at z < 2.

This thesis is structured in two parts. In part 1 we summarise the necessary theoretical background and the numerical tools in order to conduct the research in part 2. In chapter 2 we summarise the 3 + 1 approach to numerical relativity, with a focus on the initial data formalism in the weighted transverse and conformal thin-sandwich decompositions. We then move on to discuss initial data for black hole simulations in chapter 3, where we focus on the moving puncture approach. We note that the standard gauge evolution equations force the initial numerical wormhole slices to evolve into trumpet slices, which suggests the construction of a priori trumpet initial data. We summarise the literature on trumpet research, with a focus on maximal Schwarzschild trumpet initial data in its analytical form. In chapter 4 we provide the necessary numerical tools and techniques, which we use in part 2 to solve the constraint equations numerically. We focus on finite difference methods in connection with the Thomas algorithm and successive over-relaxation to solve boundary value problems in one and two variables. Part 2 contains the novel research of this thesis. In chapter 5 we discuss Kerr in quasi-isotropic coordinates and point out that it represents a maximal trumpet foliation for extreme Kerr, however a wormhole foliation for slow Kerr. We lay out our approach to numerically derive maximal Kerr trumpet initial data. The approach is based on the proposition that two nontrivial impositions on the constraints suffice to construct the data numerically. We propose that these relations can be generalised from Schwarzschild and extreme Kerr to slow Kerr. The main motivation for this stems from the observation that the square of the extrinsic curvature for Bowen-York shows the same behaviour as for Kerr for small radii, and Bowen-York trumpets have been constructed successfully. Our main results are then presented in chapters 6 and 7 in which we test our approach for the special cases of zero and maximal spin, ie for Schwarzschild and extreme Kerr. We succeed with Schwarzschild and present the first ever purely numerical derivation of maximal Schwarzschild trumpet initial data in the weighted transverse decomposition – our first main result. Because of the complexity of the problem for extreme Kerr, we proceed in steps and start out by using more information of the analytical solution to treat the constraints separately. For instance, we provide the conformal metric to the Hamiltonian and momentum constraints, and solve them successfully for the trumpet solution – our second main result. Finally we elaborate on how to relax the assumptions. In particular, we introduce an additional equation which we can solve successfully for the function which describes the deviation of the conformal metric from being flat – our third main result.