Surface photometry is one area of extragalactic studies in which information is urgently needed by optical as well as radio astronomers. The aim of this thesis is to supply some of the photometric parameters for 48 galaxies in two international colour systems. The reader will notice that descriptions are included of many detailed aspects of the work and little attention is paid to the more basic problems. This is because the discussion of the basic problems in photo-graphic photometry of galaxies formed the contents of an M.Sc. thesis. Volume one is devoted to a detailed description of the methods used for the reduction techniques together with a discussion of the results, while volumes two and three contain the photometric data. In the first volume, the first chapter is concerned with previous investigations and the following chapter contains detailed descriptions of the instruments and methods used in the preliminary plate reductions. The subject of isophotometry is dealt with in the third chapter, while in the fourth and fifth chapters respectively, mention is made of the reduction techniques, together with conclusions which may be deduced from the photometric data. This information is given in volume two for those galaxies with NGC catalogue numbers from 4189 to 4459, while the data for objects from NGC 4461 to NGC 4762 are listed in the third volume of the thesis.

The magnetic rotator model has long been the favored explanation for coherent photometric modulations in the DQ Herculis class of cataclysmic variables. However, to date, all evidence supporting this model has been of the indirect variety. Unlike their synchronously rotating cousins, the AM Herculis objects, DQ Herculis stars have not yet been discovered to emit polarized radiation. Therefore, in light of this crucial lack, the evidence used to place these objects in the magnetic cataclysmic variable category has been strictly circumstantial, based primarily on the coherence of the photometric periodicities. In this work, time-resolved spectroscopy of four long-period DQ Herculis stars is performed. In addition, two of the same objects are observed with a new, sensitive circular polarimeter. Chapters II and III describe these observations and the results of each. To summarize, coherent variations in the wavelength of emission lines were found with the spectroscopic observations. A model is put forth, explaining this phenomenon as being due to varying illumination from a bright spot on the primary. This, of course, adds strength to the magnetic rotator model. Secondly, circular polarization was definitely found in one object studied, and possibly in a second. Therefore, for the first time, there is direct evidence of the magnetic nature of these binaries. In Chapter IV, the model of the rotating bright spot illuminating the disk is explored in further detail, including modeling with a minicomputer. Afterward, a problem brought out by the low polarization coupled with large amplitude photometric variations and a cool spectrum is investigated, namely, is it possible to produce large amounts of cyclotron radiation without producing large amounts of circular polarization? The results tend to show that, for a large emitting area, the answer is yes. Chapter V is a summary of the rest of the work.

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D.Phil. / During the last few years the number of known variable stars which show periodic light level changes has grown by several tens of thousands. The aim of the research reported here was to extend the suite of statistical methods available for the analysis of periodic variable star time series. Solution techniques for five problems are discussed. The first is an automated method for detecting periodic variable stars from a database containing of the order of 100 000 time series of observations. Typically only 100-200 brightness measurements of each star were obtained, spread irregularly over an interval of about 3 years. The proposed method is based on a signal to noise ratio. Percentiles for the statistic are found by studying randomisations of a large number of the observed time series. It is shown that the percentiles depend strongly on the number of observations in a given dataset, and the dependence is calibrated empirically. The estimation of the frequency, amplitude and phase of a sinusoid from observations contaminated by correlated noise is the second problem considered. The study of the observational noise properties of nearly 200 real datasets of the relevant type is reported: noise can almost always be characterised as a random walk with superposed white noise. A scheme for obtaining weighted nonlinear least squares estimates of the parameters of interest, as well as standard errors of these estimates, is described. Simulation results are presented for both complete and incomplete data, and an application to real observations is also shown. In the third topic discussed it is assumed that contemporaneous measurements of the light in-tensity of a pulsating star is obtained in several colours. There is strong theoretical interest in a comparison of the amplitudes and phases of the variations in the different colours. A general scheme for calculating the covariance matrix of the estimated amplitude ratios and phase differences is described. The first step is to fit a time series model to the residuals after subtracting the best-fitting sinusoid from the observations. The residuals are then crosscorrelated to study the interdependence between the errors in the different colours. Once the multivariate time series structure can be modelled, the covariance matrix can be found by bootstrapping. An illustrative application is described in detail. The times between successive instances of maximum brightness, or the times between successive brightness minima, serve as estimates for the periods of the so-called "long period variables" (stars with pulsation periods of the order of months). The times between successive maxima (or minima) vary stochastically, and are also subject to measurement errors, which poses a problem for tests for systematic period changes — the topic of the fourth problem studied. A simple statistical model for the times between successive maxima, or minima, of such stars is used to calculate the auto-correlation properties of a new time series, which is non-stationary in its variance. The new series consists of an alternation of cycle lengths based on respectively the times between maxima, and those between minima of the light curve. Two different approaches to calculating the theoretical spectrum of the non-stationary time series, as required in the proposed statistical hypothesis test, are given. Illustrative applications complete the relevant chapter.

Large stellar surveys are revealing the chemodynamical structure of the Galaxy across a vast spatial extent. However, the many millions of low-resolution spectra observed to date have not yet been fully leveraged. In chapters 2 and 3, we employ data-driven spectroscopic models to the low-resolution LAMOST survey (𝑅 = 1800). In chapter 2, we employ The Cannon, a data-driven approach for estimating chemical abundances, to obtain detailed abundances, using the GALAH survey as our reference. We deliver five (for dwarfs) or six (for giants) estimated abundances representing five different nucleosynthetic channels, for 3.9 million stars, to a precision of 0.05 - 0.23 dex. Using wide binary pairs, we demonstrate that our abundance estimates provide chemical discriminating power beyond metallicity alone. We show the coverage of our catalogue with radial, azimuthal and dynamical abundance maps, and examine the neutron capture abundances across the disk and halo, which indicate different origins for the in-situ and accreted halo populations. LAM- OST has near-complete Gaia coverage and provides an unprecedented perspective on chemistry across the Milky Way. Stars with unusual levels of enrichment in a particular element are of great interest, but often pose a problem for data-driven methods. In chapter 2, we present a simple method, for the de- tection of 𝑋-enriched stars, for arbitrary elements ?, even from blended lines. Our method does not require stellar labels, but instead directly estimates the counterfactual unrenriched spectrum from other unlabelled spectra. We apply this method to the 6708 Å Li doublet in LAMOST DR5, identifying 8,428 Li-enriched stars seamlessly across evolutionary state. We comment on the ex- planation for Li-enrichement for different subpopulations, including planet accretion, nonstandard mixing, and youth. The Galactic disk exhibits complex chemical and dynamical substructure thought to be induced by the bar, spiral arms, and satellites. In chapter 4, rather than calculating spectroscopic quantities, we use them to understand the Milky Way. We explore the chemical signatures of bar resonances in action and velocity space and characterize the differences between the signatures of corotation and higher-order resonances using test particle simulations. Thanks to recent surveys, we now have large datasets containing metallicities and kinematics of stars outside the solar neighborhood. We compare the simulations to the observational data from Gaia EDR3 and LAMOST DR5 and find weak evidence for a slow bar with the “hat” moving group (250 km s⁻¹ ≲ 𝑣_𝜑i ≲ 270 km s⁻¹) associated with its outer Lindblad resonance and “Hercules” (170 km s⁻¹ ≲ 𝑣_𝜑 ≲ 195 km s⁻¹) with corotation. While constraints from current data are limited by their spatial footprint, stars closer in azimuth than the Sun to the bar’s minor axis show much stronger signatures of the bar’s outer Lindblad and corotation resonances in test particle simulations. Future datasets with greater azimuthal coverage, including the final Gaia data release, will allow reliable chemodynamical identification of bar resonances. Finally, in chapter 5, we present KORG, a new package for 1D LTE (local thermal equilib- rium) spectral synthesis, which computes theoretical spectra from the near-ultraviolet to the near- infrared, and implements both plane-parallel and spherical radiative transfer. It is compatible with automatic differentiation libraries, and easily extensible, making it ideal for statistical inference and parameter estimation applied to large data sets. We outline the inputs and internals of KORG, and compare its output spectra to those produced by other codes. We use five example wavelength regions across 3660 Å – 15050 Å to show that the residuals between KORG and the other codes are no larger than that between existing codes themselves. We show that KORG is 1–100 times faster than other codes in typical use.

Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively.

The aim of this work has been to increase our understanding of the surface brightness distributions of late-type stars through Doppler imaging and eclipse mapping techniques. Combining spectroscopic and photometric observations with the technique of Doppler Imaging, I have reconstructed surface images of the G2V star He 699 (for 08 October 2000), which show high latitude and polar structures. In the case of the KOV star AB Dor, the Doppler images for January 1992 and November 1993 show a large polar cap with small dark features also present at intermediate to high latitudes. As the phase sampling of the observations was insufficient to apply the sheared-image method it was not possible to detect any differential rotation. In the second part of my thesis I determine the surface brightness distribution of the primary component of the RS CVn eclipsing binary SV Cam. I have used extrapolated size distributions of sunspots to an active star to synthesize images of stellar photospheres with high spot filling factors. The resulting surface images, reconstructed with the Maximum Entropy eclipse mapping technique, show large spurious spot features at the quadrature points. It is concluded that two-spot modelling or chi-squared minimisation techniques are more susceptible to spurious structures being generated by systematic errors, arising from incorrect assumptions about photospheric surface brightness, than simple Fourier analysis of the light-curves. Spectrophotometric data from 9 HST orbits, observed in November 2001, have been used to eclipse-map the primary component of SV Cam. In combination with its HIPPAR- COS parallax it is found that the surface flux in the eclipsed low-latitude region is about 30% lower than computed from the best fitting PHOENIX model atmosphere. This flux deficit can only be accounted for if about a third of the primary's surface is covered with unresolved spots. However, when the spottedness from the eclipsed region is applied to the entire surface of the primary star, there still remains an unaccounted flux deficit. The remaining flux deficit is explained by the presence of a large polar spot extending down to latitude 48+/-6 deg. When the Maximum Entropy eclipse mapping technique is used to fit SV Cam's lightcurve, the observed minus computed residuals show strong spurious peaks at the quadrature points. It is only possible to reduce these peaks with the addition of a polar cap and the reduction of the primary star's temperature, to account for the star being peppered with unresolvable spots. Motivated by this result we investigate the limb darkening of the primary component of SV Cam. The wavelength dependence of the limb darkening is analysed by sub-dividing the HST lightcurve into 10 bands of equal emission flux. Flux variations between the first and fourth contact of the primary eclipse indicate that the limb darkening decreases towards longer wavelengths, in accordance with published limb darkening laws. Comparing fits of ATLAS and PHOENIX model atmospheres we find a wavelength dependence of the best fitting model. Due to its smooth cutoff at the stellar limb, the spherical geometry of the PHOENIX model atmosphere gives the best fit during partial eclipse. Between the second and third contact the difference between spherical and plane-parallel geometry is less important.

D.Phil. / We propose solutions to two statistical problems using the frequency domain approach to time series analysis. In both problems the data at hand can be described by the well known signal plus noise model. The first problem addressed is the estimation of the underlying variance of a process for the use in a Shewhart or CUSUM control chart when the mean of the process may be changing. We propose an estimator for the underlying variance based on the periodogram of the observed data. Such estimators have properties which make them superior to some estimators currently used in Statistical Quality Control. We also present a CUSUM chart for monitoring the variance which is based upon the periodogram-based estimator for the variance. The second problem, stimulated by a specific problem in Variable Star Astronomy, is to test whether or not the mean of a bivariate time series is constant over the span of observations. We consider two periodogram-based tests for constancy of the mean, derive their asymptotic distributions under the null hypothesis and under local alternatives and show how consistent estimators for the unknown parameters in the proposed model can be found

Stars, and collections of stars, encode rich signatures of stellar physics and galaxy evolution. With properties influenced by both their environment and intrinsic nature, stars retain information about astrophysical phenomena that are not otherwise directly observable. In the time-domain, the observed brightness variability of a star can be used to investigate physical processes occurring at the stellar surface and in the stellar interior. On a galactic scale, comparatively fixed properties of stars, including chemical abundances and stellar ages, serve as a multi-dimensional record of the origin of the galaxy. In the Milky Way, together with orbital properties, this informs the details of the subsequent evolution of our Galaxy since its formation. Extending beyond the Local Group, the attributes of unresolved stellar populations allow us to study the diversity of galaxies in the Universe. By examining the properties of stars, and how they vary across a range of spatial and temporal scales, this Dissertation connects the information residing within stars, to global processes in galactic formation and evolution. We develop new approaches to determine stellar properties, including rotation and surface gravity, from the variability that we directly observe. We offer new insight into the chemical enrichment history of the Milky Way, tracing different stellar explosions, that capture billions of years of evolution. We advance knowledge and understanding of how stars and galaxies are linked, by examining differences in the initial stellar mass distributions comprising galaxies, as they form. In building up this knowledge, we highlight current tensions between data and theory. By synthesizing numerical simulations, large observational data sets, and machine learning techniques, this work makes valuable methodological contributions to maximize insights from diverse ensembles of current and future stellar observations.

Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively.