| Summary: | The relationship first pointed out by Tully and Fisher between the luminosity of spiral galaxies and their maximum rotation velocity, as measured by the 21 cm line-width, continues to be one of the best methods available to measure relative distances. At infrared wavelengths, the observational scatter about this relation is typically 0.35 to 0.50 magnitudes, permitting relative distance estimates with an accuracy of about 20 percent. The Malmquist bias in a magnitude-limited sample is 1.38σ ², and while the solution to the general problem is complex, it is clear that reducing the scatter about the Tully-Fisher relation by even a factor of two would make a large difference in our ability to determine the local velocity field from distances and velocities of individual galaxies. In this dissertation we discuss the scatter in the Tully-Fisher relation at infrared wavelengths, and look for ways to reduce that dispersion through the inclusion of additional observational parameters. The data for this study are derived from a CCD survey of 244 spiral galaxies in twenty clusters falling in the redshift range 3,000 to 11,000 km s⁻¹. From surface brightness profiles and elliptical aperture photometry, we obtained isophotal and total magnitudes at B, R, and I, isophotal diameters, mean and nuclear surface brightnesses, and a concentration parameter indicative of the bulge-to-disk ratio. These quantities were then combined with colors and HI-content measures taken from the literature in a search for correlations with Tully-Fisher residuals. None of the trial second-parameters resulted in a substantial decrease in the scatter about the fiducial Tully-Fisher relation. An examination of the properties of the cluster samples shows that many of the clusters exhibit considerable substructure. While it is possible that the implied depth effects are important to the scatter about the magnitude/line-width relation, calculated lower limits to the dispersion in depth turn out to be rather small.
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