7.1.1 Photographic and B-Band Relations

As originally proposed by Tully and Fisher (1977), the observational parameters of the TF relation are: (1) the photographic magnitude corrected for extinction, used as a measure of the luminosity of a galaxy, and (2) the global HI 21-cm line-width corrected for projection, used as a measure of the galaxy's rotational velocity. The raw measurements must be corrected for inclination effects, with the corrections for extinction and projection going in the opposite sense; when extinction corrections to the magnitudes are small (i.e., the galaxy is nearly face-on) the projection corrections for the rotational velocity are large, and vice versa. Consequently, considerable care must be taken to determine the proper corrections to the fundamental observables, and several different prescriptions for these corrections have been proposed (cf. Tully and Fisher 1977; Sandage and Tammann 1976; Fisher and Tully 1977). Nevertheless, any systematics introduced by the use of different correction schemes should in principle scale out, provided that the ``local calibrators'' and the sample galaxies are treated in the same way.

The publication of the Second Reference Catalog of Bright Galaxies by de Vaucouleurs et al. (1976) greatly increased the size of the existing data base of total magnitudes for a wide variety of galaxies. In addition, the completion of extensive HI 21-cm surveys such as that by Fisher and Tully (1981) significantly improved the status of the line-width data. These data were subsequently used by several groups to examine both the utility of the TF relation as a distance indicator and the character of the local Hubble flow (cf. Bottinelli et al. 1983, 1984, 1986; Fouqué et al. 1990; Giraud 1986, 1987; Richter and Huchtmeier 1984). Similar photoelectric data were obtained by Visvanathan (1981, 1983) in the V, r, and IV (₀ ~ 1 µm) bands. These papers, and the references therein, provide a history of the controversies regarding the use of the TF relation.

The introduction of CCDs as the primary optical detector in astronomical use has greatly improved the quality of the surface photometry of galaxies and consequently the TF relations, for with them it is now possible to obtain total magnitudes for galaxies to a precision of ~ 5% (e.g., Pierce 1988). In addition, CCD surface photometry can produce improved and unbiased estimates of galaxy inclinations (e.g., Pierce 1988, Pierce and Tully 1988), which are crucial to correct the observed 21-cm line-widths for line-of-sight projection. Together these developments have prompted an extensive re-examination of the TF relations and their role in the extragalactic distance scale problem (Pierce and Tully 1988; 1992a, b).