Often in statistics it is of interest to investigate whether or not a trend is significant. Methods for testing such a trend depend on the assumptions of the error terms such as whether the distribution is known and also if the error terms are independent. Likelihood ratio tests may be used if the distribution is known but in some instances one may not want to make such assumptions. In a time series, these errors will not always be independent. In this case, the error terms are often modelled by an autoregressive or moving average process. There are resampling techniques for testing the hypothesis of interest when the error terms are dependent, such as, modelbased bootstrapping and the wild bootstrap, but the error terms need to be whitened. In this dissertation, a bootstrap procedure is used to test the hypothesis of no trend for variable stars when the error structure assumes a particular form. In some cases, the bootstrap to be implemented is preferred over large sample tests in terms of the level of the test. The bootstrap procedure is able to correctly identify the underlying distribution which may not be χ2.

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This dissertation describes a new detailed abundance study of field red horizontal branch stars, RR Lyrae stars and blue horizontal branch stars. To carry out this study, we obtained high-resolution and high signal-to-noise ratio echelle spectra at the McDonald observatory and Las Campanas Observatory. In addition, new pulsational emphemerides were derived to analyze the spectra of RR Lyrae stars throughout the pulsational cycles. We find that the abundance ratios are generally consistent with those of field stars of similar metallicity in different evolutionary stages and throughout the pulsational cycles for RR Lyrae stars. We also estimated the red and blue edges of the RR Lyrae instability strip using the derived effective temperatures of RHB and BHB stars. New variations between microturbulence and effective temperature are found among the HB population. For the first time the variation of microturbulence as a function of phase is empirically shown to be similar to the theoretical calculations. Finally, through the study of a rare eclipsing sdB and M dwarf binary, we discovered an unusually low mass for this type of HB star, which observationally proved the existence of a new group of low-mass sdB stars that was theoretically predicted in the past. / text

The Best M.Phil Thesis in the Faculties of Dentistry, Engineering, Medicine and Science (University of Hong Kong), Li Ka Shing Prize,1993-1995 / published_or_final_version / Physics / Master / Master of Philosophy

The study of variable stars is extremely important to the astronomical field of scientific research. Variable stars must be methodically studied, usually by amateur astronomers over a long period of time, in order to provide professional astronomers important data that allows them to further analyze variable star behavior.Variable stars are unique because their pulsation produces visible changes in luminosity. This pulsation allows amateur astronomers to visually observe and identify variable stars. This type of research and study is special because amateurs can make a real contribution to the field.My objective was to become an amateur astronomer in the hopes that I could discover variable stars and contribute my findings to the greater astronomical scientific community. In completing this task, my overall goal was to better understand the true nature of science in order to improve my teaching in a secondary science classroom.

The detailed observational analysis of three massive B- and O-type stars was carried out in this study in order to characterize their fundamental, magnetic, and variability properties. The bulk of the data acquired were obtained with the high-resolution ESPaDOnS spectropolarimeter at the Canada-France-Hawaii telescope, within the context of the Magnetism in Massive Stars (MiMeS) project. Two of these stars (HR5907 and HD57682) are newly detected magnetic stars, discovered from observations acquired as part of the broader survey component of the MiMeS program, while the last star, ω Ori, was previously reported as magnetic in the literature. The rotation periods of HR5907 and HD57682 were inferred from photometric, Hα emission and longitudinal field variations. A period of 0.508276 was inferred for HR5907, making this the shortest period, non-degenerate, magnetic massive star identified to date. Furthermore, ultraviolet and optical spectroscopy were combined to infer the fundamental properties of HR5907 and HD57682. Direct modelling of the Least-Squares Deconvolved line profiles and the longitudinal magnetic field measurements were used to infer the magnetic properties of HR5907, HD57682, and ω Ori. A detailed investigation of the newly obtained and archival polarimetric data of ω Ori revealed no convincing evidence for a magnetic field, despite evidence of variability in some emission quantities in this dataset, which had been previously attributed to a large-scale magnetic field. The strength and variability of the optical photospheric helium lines of HR5907 suggests that this star is He-rich, with a non-uniform distribution of its surface chemistry. Lastly, the emission variations in the hydrogen lines of HR5907 suggest this star hosts a highly-structured, rigidly-rotating, centrifugally supported magnetosphere. Similarly, line profile variations throughout the optical spectrum of HD57682 are attributed to emission variations caused by a rotationally-modulated, dynamical magnetosphere. As magnetism in massive stars is a relatively rare and poorly-studied phenomenon, these studies comprise the bulk of the detailed investigations of magnetic massive stars carried out to date. The results of these investigations are also discussed in the context of addressing the current outstanding issues related to magnetism in massive stars. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-09-28 17:22:35.115

Hyperflares from Soft Gamma Repeaters have revealed quasi-periodic oscillations, suggested to be torsional modes of the neutron star crust produced during starquakes. We study how a magnetic field affects these modes. We make a plane-parallel model of the neutron star crust with a vertical and non-vertical field and solve for the eigenvalues and eigenfunctions. In the vertical field case we find a discrete set of modes comparable to the observed frequencies giving evidence for this theory. We find that the lower order modes do not depend on B while the higher order modes do when the field strength is low or extremely high. We make a simple analytic model of a non-vertical field in a closed box representing the neutron star crust. The mode spectrum in this model is continuous rather than discrete, raising the puzzle of why only specific modes are excited during the hyperflare.

Despite considerable progress in recent years, a complete description of the physical drivers of galaxy formation and evolution remains elusive, in part because of our poor understanding of star formation, and how star formation in galaxies is regulated by feedback from supernovae and massive stellar winds. Insight into the star formation histories of galaxies, and the interplay between star formation and feedback, can be gained by measuring their chemical abundances, which until recently has only been possible for galaxies in the nearby universe. However, reliable star formation and abundance calibrations have been hampered by various systematic uncertainties, and the lack of a suitable spectrophotometric sample with which to develop better calibrations. To address the limitations of existing surveys, we have obtained integrated optical spectra for a diverse sample of more than four hundred nearby star-forming galaxies. Using these data, in conjunction with observations from the Sloan Digital Sky Survey, we conduct a detailed analysis of optical star formation indicators, and develop empirical calibrations for the [O II] 3727 and H-beta 4861 nebular emission lines. Next, we investigate whether integrated spectroscopy of star forming galaxies can be used to infer their gas-phase oxygen abundances in the presence of radial abundance gradients, diffuse-ionized gas emission, and dust attenuation. We conclude that the integrated R23 parameter is generally insensitive to these systematic effects, enabling the gas-phase metallicity to be measured with a precision of +/-0.1 dex. We apply these methods to study the evolution in the luminosity-metallicity relation at 0<z<1 based on an analysis of more than 3500 I-band selected galaxies observed as part of the AGN and Galaxy Evolution Survey, and data culled from the literature. Our principal results are that, at fixed luminosity, the mean gas-phase metallicity of luminous (MB<-19 mag), star-forming galaxies at z=1 is a factor of two lower than the gas-phase metallicity in comparably luminous galaxies at z=0. However, after accounting for the effects of luminosity evolution, we find that the amount of chemical evolution for luminous galaxies corresponds to an increase of only 10%-20% since z1⁺ё, assuming a direct evolutionary connection between nearby and distant star-forming galaxies.

Neutron stars in mass-transferring binaries accrete hydrogen and helium rich matter from their companions. Unstable nuclear burning of this matter results in Type I X-ray bursts every few hours to days. Theoretical models propose three regimes of unstable burning on neutron star surfaces and also define the critical accretion rate above which the neutron star burns fuel stably without bursting. Currently, the theoretical value for this stability boundary is comparable to the Eddington limit whereas the observational limit is estimated to 0.3 m&dot;Edd. In this dissertation, we examine the boundary between stable and unstable thermonuclear burning at the surface of an accreting neutron star for a range of initial compositions. We compute different steady-state equilibrium models and use them to conduct a linear perturbation analysis. The main results of this analysis are plots of the critical accretion rates as a function of the initial helium mass fraction which were never produced before.