Thesis (Ph. D.)--University of Wisconsin--Madison, 1959. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 33).

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White dwarfs are among the most common objects in the stellar halo; however, due to their low luminosity and low number density compared to the stars in the discs of the Milky Way, they are scarce in the observable volume. Hence, they are still poorly understood one hundred years after their discovery as relatively few have been observed. They are crucial to the understanding of several fundamental properties of the Galaxy – the geometry, kinematics and star formation history, as well as to the study of the end-stage of stellar evolution for low- and intermediate-mass stars. White dwarfs were traditionally identified by their ultraviolet (UV) excess, however, if they have cooled for a long time, they become so faint in that part of the spectrum that they cannot be seen by the most sensitive modern detectors. Proper motion was then used as a means to identify white dwarf candidates, due to their relatively large space motions compared to other objects with the same colour. The use of proper motion as a selection criterion has proven effective and has yielded large samples of candidates with the SuperCOSMOS Sky Survey and Sloan Digital Sky Survey. In this work I will further increase the sample size with the Panchromatic Synoptic Telescope And Rapid Response System 1 (Pan–STARRS1). To construct luminosity functions for the study of the local white dwarfs, I require a density estimator that is generalised for a proper motion-limited sample. My simulations show that past works have underestimated the density when the tangential velocity was assumed to be a constant intrinsic parameter of an object. The intrinsically faint objects which are close to the upper proper motion limits of the surveys are most severely affected because of the poor approximation of a fixed tangential velocity. The survey volume is maximised by considering the small/intermediate scale variations in the observation properties at different epochs. This type of volume maximisation has not been conducted before because previous surveys did not have multi-epoch data over a footprint area of this size. The tessellation of the 3π Steradian Survey footprint is so complex that the variations are strong functions of position. I continue to demonstrate how a combination of a galactic model and the photometric limits as a function of position can give a good estimate of the completeness limits at different colour and different line-of-sight directions. Finally, I compare the derived white dwarf luminosity function with previous observational and theoretical work. The effect of interstellar reddening on the luminosity functions is also investigated.

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