This thesis concerns inferring core collapse supernova physics using gravitational waves. The mechanism through which the supernova is re-energised is not well understood and there are many theories of the physical processes behind the so called supernova mechanism. Gravitational waves provide an opportunity to see through to the core of a collapsing star. This thesis provides an algorithm that will analyse a detected gravitational waveform from a core collapse supernova and identify the supernova mechanism. This is achieved through the use of Bayesian model selection and a nested sampling algorithm. This Bayesian data analysis algorithm is called the Supernova Model Evidence Extractor (SMEE). SMEE is designed to classify detected gravitational waveforms from core-collapse supernovae and 3 different versions which employ different types of data have been developed. These 3 versions utilise time domain (which has been fast Fourier transformed into the frequency domain), power spectrum domain and spectrogram data and the success of each version is investigated. Firstly, results for a simplified idealised version of SMEE are discussed. In this scenario only a single gravitational wave detector is considered and the effect of the sky position of the source are ignored. Next, techniques which can be employed to improve SMEE are investigated. Finally, SMEE is tested using 3 gravitational wave detectors and the full effect of the time delay between detectors and the antenna response on each detector is included. As well as this, recoloured detector noise from the Science runs from both LIGO and Virgo are utilised here. This thesis demonstrates that each version of SMEE is successful and are able to infer the supernova mechanism for a galactic supernova. The spectrogram version of SMEE is deemed the most accurate and it is recommended that this technique should be further explored in the future.

This thesis is primarily concerned with the atmospheric structure of footpoints during the impulsive phase of a solar flare. Through spectroscopic diagnostics in Extreme- Ultraviolet wavelengths we have made significant progress in understanding the depth of flare heating within the atmosphere, and the energy transport processes within the footpoint. Chapter 1. introduces the Sun and its outer atmosphere, forming the necessary background to understand the mechanisms behind a solar flare and their observational characteristics. The standard flare model is presented which explains the energy source behind a flare, through to the creation of the EUV and X-ray emission. In Chapter 2 the basics of atomic emission line spectroscopy are introduced, covering the processes driving electron excitation and de-excitation, the formation of Gaussian line profiles, and the formation of density sensitive line ratios. The concept of a differ-ential emission measure is also derived from first principles, followed by a description of all of the instruments used throughout this thesis. Chapter 3 presents measurements of electron density enhancements in solar flare footpoints using diagnostics from Hinode/EIS. Using RHESSI imaging and spectroscopy, the density enhancements are found at the location of hard X-ray footpoints and are interpreted as the heating of layers of increasing depth in the chromosphere to coronal temperatures. Chapter 4 shows the first footpoint emission measure distributions (EMD) obtained from Hinode/EIS data. A regularised inversion method was used to obtain the EMD from emission line intensities. The gradient of the EMDs were found to be compatible with a model where the flare energy input is deposited in an upper layer of the flare chromosphere. This top layer then cools by a conductive flux to the denser plasma below which then radiates to balance the conductive input. The EUV footpoints are found to be not heated directly by the injected flare energy. In Chapter 5 electron densities of over 1013 cm−3 were found using a diagnostic at transition region temperatures. It was shown to be difficult to heat plasma at these depths with a thick-target flare model and several suggestions are made to explain this; including optical depth effects, non-ionisation equilibrium, and model inaccuracies. Finally, Chapter 6 gathered together both the density diagnostic and EMD results to attempt to forward fit model atmospheres to observations using a Genetic Algorithm. The results are preliminary, but progress has been made to obtain information about the T (z) and n(z) profiles of the atmosphere via observation.

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

The main aim of this thesis is to understand and investigate some essential phys- ical processes leading to dust grain growth and their interactions in plasmas. This is achieved by applying both analytic and numerical models. Three main situations are explored: dust grains growth in presence of electrostatic and electromagnetic fields, dust grains interaction in submicron scales, and collective effects of dust grains above thundercloud. The evolution and character of plasma dust has wide-ranging implications for astro- physics and laboratory plasmas, including plasma processes and fusion devices. The local electromagnetic fields can influence the conditions for dust growth, leading in some cases to naturally occurring prolate-spheroidal dust shapes. However, presence of magnetic fields can have significant effects on dust growth. Results for dust growth by ion accretion under the combined influence of an applied magnetic field and the evolving electrostatic field arising from the charged grain in 1D and 3D have been presented. The calculations show that most ions starting near the grain surface ulti- mately collide with it, while those starting further away execute orbital motion around the magnetic field lines and drift toward the grain. Moreover, the energy spectrum for impacting ions shows discrete structure in presence of a parallel oriented magnetic field. Finally, we note that the magnetic field influences the spatial deposition pattern of ions, leading to increasing ions fluxes at the grain ends. Microdischarge plasmas is an electrical discharges which occurs in geometries in range of sub-millimetre length scales. However, a much extreme situation than mi- crodischarge plasma where small size charged dust grains can cause breakdown for the neutral gas when dust inter space reach to sub-micro scales. The interactions of charged dust grains in plasma where molecules of Oxygen gas are present and the ef- fect on the discharge of the ambient gas is investigated in presence of magnetic field. The particle in cell model was used to simulate electrons motion in addition to using Monte Carlo method to simulate the electrons collisions with neutrals. The importance of the magnetic field was explored by varying the parameter (p) which gives the rela- tive size of the electric field to the magnetic field. The distribution of electrons kinetic energies was investigated in two cases when (p = 103) and (p = 102). At the first case the gained energy increased dramatically, however, the gained energy did not ex- ceed further than the metastables threshold as a result of consuming electrons energy in metastable collisions. When magnetic field is increased (p = 102), gained energy is fluctuated as a results of contribution in gyromotion orbits and electrons only involved in metastable collisions. However, a number of metastable in this case is lower than (p = 103) case. The electron beam can occur just after sprites. The presence of charged dust above thundercloud are thought to have a basic role in the electron beam formation in which the electrons avalanche in sprite event leaving an environment of negative charged dust and positive ions. This environment was simulated in a model like hollow cathode with a column of positive ions inside. The particle in cell method was used to simulate particles motion. Results for electrons evolution in such this environment with and without presence of positive ions were presented. Electrons in environment without positive ions evolve upwards gaining lower final energy. For the case when positive column is presented, electrons evolve upwards in a long path and do not biased to sidewalls. The trajectory of the electron shows an oscillator motion. The period of such motion depends on the electron’s original position. Electrons gain higher energy in a shorter time comparing to the case when the ions column is not simulated.

This thesis is an account of the research carried out by the author in developing a range of necessary components for future gravitational wave detectors, between October 2009 and September 2013 in the Institute for Gravitational Research at the University of Glasgow. The aims of this thesis were to design, develop and test technologies which enable future space-borne interferometric gravitational wave detectors. The research was as part of a large international collaboration focused on developments for a space-borne gravitational wave detector by the name of LISA an all of her variants. At the university of Glasgow this collaboration included H.Ward, D.I. Robertson, C. J. Killow, E. D. Fitzsimons, M. Perreur-Lloyd and the author.

For last decades, magnetohydrodynamic (MHD) waves arise to a hot topic of solar physics. With modern instruments, MHD wave modes are reliably detected, not only for their potential to heat the solar corona, but also as a new tool to diagnose the plasma parameters remotely (MHD seismology). In this thesis, we use space-borne EUV/UV imagers and ground-based observatories to study compressive MHD waves in coronal loops and sunspots. We identify several instrumental artifacts and formulate the scheme to estimate the imager data noise. The diagnostic potential of MHD waves in various plasma structures are also investigated. The orbit-related long periodicities (30-96 min) in the TRACE images and the derotation-induced short periodicy (3-9 min) in the SDO/AIA images are studied and quantified. The methods are proposed to mitigate the effects of such artificial periodicities. The noise level of AIA images is formulated. In sunspots, the 5–min oscillation power usually forms a ring structure enclosing the sunspot umbra. The phase variation was found to display high-order MHD azimuthal body modes. The mode numbers were measured and justified by significance tests. A multi-level observation of magnetoacoustic waves in sunspot was performed. The variation of the magnetoacoustic cut-off frequency over sunspot cross-sectional geometry and sunspot atmosphere was quantified and exploited to diagnose the inclination angle of the magnetic field. To automatically measure the propagating speed of compressive MHD waves, we designed cross-fitting technique (CFT), 2D coupled fitting (DCF) and best similarity measure (BSM). Parametric studies were performed to confirm the validity and robustness of these methods. Distinct propagating fast wave trains were found to be associated with radio bursts that were generated by the flare-accelerated non-thermal electrons. The stretching wavelength along the waveguide implies that the wave trains were impulsively triggered. The wave parameters are measured to probe the properties of guided fast waves. The connectivity between different levels of sunspots and the associated active regions were studied. The long period oscillations were found in both the chromosphere and the corona. The periodicity was close to typical solar interior g-modes.

The detection of Gravitational Waves using the Laser Interferometer Space Antenna (LISA) will open whole new areas of physics and astrophysics for exploration. The lower frequency signals detected by the antenna will allow us to probe gravitational wave sources that are inaccessible with current and future ground based detectors. However, the ability of LISA to detect gravitational wave signals is dependent on the removal of the laser frequency noise realisations from the optical bench measurements, that would otherwise dominate the signal data streams. Time Delay Interferometry (TDI) provides a method for removing the laser noise contributions by time shifting the individual optical bench measurements. The cancellation of the noise is achieved by identifying the individual optical bench measurements that contain equal numbers of identical realisations of the laser noise but with opposing signs. Although the TDI combinations produce signal datastreams that are free from the laser frequency noise contributions, the time shifting of the optical bench measurements means that the TDI combination data streams defined at different time stamps will nevertheless contain identical realisations of the remaining detector noise terms. Independent TDI combinations (denoted A, E and T) can be constructed from the simpler laser-noise cancelling combinations by diagonalising the correlation matrix of the combination data streams at any given timestamp. This ensures that the optimal combinations are independent with respect to each other at this particular timestamp, but this result does not apply when the optimal combinations are compared at different timestamps. As the time shifting of the optical bench measurements introduces within them identically equal realisations of the remaining detector noise terms, the A, E and T data streams could therefore be correlated in time. The presence, and potential impact, of these time correlations has been investigated for the first time within this thesis. This work has been carried out by identifying the time stamps and optical bench designations of the individual optical bench terms in the algebraic expression for each TDI combination. The resultant configuration of non-zero off-diagonal terms in the covariance matrix for the TDI combination data streams has been investigated for simplified models of the LISA constellation. The presence of non-zero correlations between the combination datastreams could pose a serious problem to a number of signal parameter search methods that rely on the datastreams being independent. The effects on the parameter recovery for a gravitational wave signal containing two sinusoids has been investigated for a simplified LISA model and for the combination datastreams produced using the data from the second Mock LISA Data Challenge. In both cases, the presence of identically equal detector noise realisations in different time stamps of the signal data streams introduces auto and cross correlations between the combinations. When the non-zero covariances were explicitly accounted for within the likelihood function, the confidence intervals, reflecting the uncertainty in our inference of the unknown parameters, were found to be significantly smaller - indicating significantly tighter constraints on the true signal parameters, in comparison to the results obtained with a likelihood function that assumed the data streams to be independent in time.

The past few decades of solar observations have seen an increase in both the spatial and temporal resolution of data. The recent launch of the Solar Dynamics Observatory is the next step in a digital era and provides so much data that the satellite has its own Feature Finding Team tasked with creating automated detection algorithms to ease the burden on human analysis. This thesis will present some methods of automated solar feature recognition with the aim of finding a consistent method that can be reliably used on long term datasets (the Michelson Doppler Imager data from 1996-2010 will be used as the example in this thesis). We show methods for detecting sunspots in white light intensity data as well as a method for detecting magnetic fragments in magnetogram data. By applying these methods to a long term dataset we build a sunspot catalogue which is then used to investigate the evolution of sunspot properties over solar cycle 23. We find that the International Sunpot Number does not accurately represent the number of sunspots present on the visible solar disk although the trend does follow the number of sunspots. We also find that the umbral area of sunspots is between 20 and 40% of the total sunspot area and that this exhibits smooth variation over the solar cycle indicating there may be some change in how sunspots are formed at different points in the cycle. We then use the catalogue to investigate the Wilson depression effect and use Monte Carlo simulations along with sunspot models to show that the tau = 1 layer of the photosphere is recessed by 500-1000 km inside sunspots. Next, we examine the magnetic fields inside sunspot umbrae to investigate claims of a long term secular decrease in sunspot magnetic fields that could point to a long term solar minimum spanning many cycles. We do not see evidence of this decrease although we only analyse one cycle of data. Next, five active regions are analysed using an automated magnetic fragment detection and tracking algorithm. We also examine quiet Sun magnetic fields and note that at field strengths of 5 Gauss from the HMI/SDO instrument, the orbital motion of the satellite can be detected as a fluctuation in the measured magnetic field strength with the period of a satellite in geosynchronous orbit. We also calculate the diffusion and drift velocities of fragments in three of the observed active regions and find that our diffusion coefficients are higher than previous studies but our drift speeds are lower than those from the same studies.

The work in this thesis charts the revival and development of research that tests some of the core fundamental assumptions that characterise the study of magnitude-redshift surveys for the estimation of galaxy luminosity functions (LF). Estimating LFs, either parametrically or non-parametrically, generally requires the assumption of separability between the LF, and the density function. The work carried out initially by Rauzy (2001) amounts to a test statistic, Tc, constructed from the cumulative luminosity function (CLF). It is a direct probe of separability and therefore is rendered a magnitude completeness test to identify the presence of potential systematics and/or evolution within a particular survey sample. We originally applied Rauzy's test of completeness to the Millennium Galaxy Catalogue (MGC), the Two Degree Field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS). We then extended the Tc statistic for data-sets characterised by two distinct faint and bright apparent magnitude limits. Following on from this we have developed a variant on Tc that we have named, Tv, which was constructed instead from the cumulative density function (CDF) and can be considered a differential form of the much celebrated, Schmidt (1968) V/Vmax statistic. The completeness analysis of data-sets such as the 2dFGRS and the Clowes Campusano Large Quasar Group Survey (CCLQG) have also lead to developing a procedure that will optimise our estimators based on the signal-to-noise of our sampling technique. Finally, we have developed a new, robust statistical probe to constrain evolutionary models applied to current and future redshift surveys. This probe exploits the fundamental assumption of separability coupled with a maximum entropy technique to constrain the evolutionary parameter that characterises, in particular, pure luminosity evolution.

For work on my thesis dissertation, we have been studying some energetic processes in solar flares. On our work on hard X-ray (HXR) emission from flares, we have shown that non-thermal recombination emission can compare with the bremsstrahlung HXR flux for certain flare conditions. In this thesis, we show spectral features characteristic of non-thermal recombination HXR emission and suggest how it plays a signicant role in the flare HXR continuum, something that has been ignored in the past. It is important to note that these results could demand a reconsideration of the numbers of accelerated electrons since recombination can be much more efficient in producing HXR photons than bremsstrahlung. We go on to show that although nonthermal recombination is not likely to dominate the total HXR flux unless we consider extreme parameter regimes, it can still form a signicant proportion of the HXR flux for typical flare conditions, thereby remaining important for both spectral inversion and low energy electron cut-off diagnostic capabilities. In related work on diagnosing particle acceleration in flares, we also have an interest in studying solar neutrons. To this end, this thesis presents our work done with new-age neutron detectors developed by our colleagues at the University of New Hampshire. Using laboratory and simulated data from the detector to produce its response matrix, we then employ regularisation and deconvolution techniques to produce encouraging results for data inversion. As a corollary, we have been reconsidering the role of inverse Compton scattering (ICS) of photospheric photons. Gamma-ray observations clearly show the presence of 100 MeV electrons and positrons in the solar corona, by-products of GeV energy ions. We present results of ICS of solar flare photons taking proper account of radiation field geometry near the solar surface. If observed, such radiation would let us determine the number of secondary positrons produced in large flares, contributing to a full picture of ion acceleration and to predicting neutron fluxes to be encountered by future inner heliosphere space missions.