| Summary: | In this thesis are presented the Tully-Fisher (TF) relations for a sample of 99 galaxies within the four nearby dusters; Coma, Abell 2199. Abell 2634 and Abell 194. Each cluster was compromised of two samples. The first sample was drawn from either Zwicky or UGC catalogues based on a combination of magnitude, type and ellipticity. These provided spiral duster member candidates over the entire duster region to a magnitude limit of 16 in the b-band. The second sample was selected from published photographic plate scans of the central areas of each duster. This sample had a fainter magnitude limit of 18 b-band mags but covered a much smaller area (approx. 2ºx2º). The galaxies were observed over two observing runs in May and August of 1993 on the JKT and INT Isaac Newton Group Telescopes simultaneously. I-band CCD images and optical long-slit spectra were taken of 65% of the sdected objects. Isophotal ellipse fitting of the images was used to produce surface brightness profiles. From these, isophotal magnitudes and diameters woe extracted. From, consideration of the surface brightness, ellipticity and position angle a "disk region" of each profile was selected and used to calculate extrapolated total magnitudes. Gaussian fitting of Ha emission lines of the long-split spectra produced optical rotation curves for each galaxy. Maximum rotation velocities were calculated from these curves. Corrections found in the literature were applied to the total magnitude and rotation velocity of each galaxy. These compensated for internal dust extinction and the inclination of the disk to the line-of sight. Numerical simulations of the fitting procedures demonstrated that an inverse regression of log-rotation velocity on magnitude provided a fit tothe relationship free from selection bias. Residuals around this fit woe used to choose forms of the corrections that produced the minimum scatter. A fullerror budget was compiled and an error weighted fit to the data yielded relationships with a mean scatter of 0.35 mags rms. A combination of all sources of measurement error, considering inter-correlation, produced a value of 027 mags rms, as an estimate of the contribution to the scatter. It was shown that uncertain cluster membership was not a significant source of scatter. In addition, the "expanding duster" model correction suggested in the literature did not significantly reduce the scatter. The most important source of scatter in the relationship was found to be the symmetry and extent of rotation curves used. A significant correlation was shown to exist between rotation curve extent in terms of disk scale lengths and the TF fit residuals. When only the highest quality data were used, the typical scatter was reduced to 020 mags rms. Consideration of the remaining measurement errors produced an upper limit of 0.12 mags rms for the intrinsic scatter within the TF relation. Monte-Carlo modelling indicated that the observed difference in TF slope between the Coma and Abell 2634 samples was significant, The possibility that this difference is the result of systematic errors in the dataset was ruled out It is concluded that the change in gradients is due to real variations in the underlying slope influenced by differences in duster environment.
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