As discussed above, CCD photometry can reduce the errors in the apparent magnitudes to ~ 5%. It is difficult to reduce errors in W20 much below about 10 km s-1, given that the observed 21-cm profiles often have low intensity ``bumps'' or ``wings''. In addition, inclination errors are currently limited to about 3°, for galaxies with an inclination near 45°. As a result, corrected line-widths (WRi) have a typical rms dispersion of 16 km s-1, or ~ 0.02 in log WRi. This corresponds to an internal error of 0.17 mag or 8% in distance, leaving very little room for intrinsic dispersion in the TF relations. However, there is no assurance that the TF relations are strictly linear. Both the Ursa Major and local calibrating samples are deficient in high luminosity systems and there is some evidence for curvature or a change in slope at the high luminosity end (e.g., Aaronson et al. 1986; Pierce 1988; Mould et al. 1989). However, the available data for a broad range of environments from the local field to the relatively dense core of the Virgo Cluster indicate no sign of any significant variations in slope with local density. It might be expected that low luminosity galaxies would be more sensitive to environmental influences and, if this is the case, a change in slope of the TF relations in differing environments would result. The intrinsic dispersion among galaxies (i.e., any lack of coupling between mass and luminosity) probably adds an uncertainty of ~ 0.15 mag (see Sec. 7.4, 7.5, and Figure 11). It is unclear whether such effects would be random or systematic. In any event, it appears that the internal rms dispersions for the redder TF relations are ~ 0.25 mag, or 12% in distance. In addition, the uncertainty in the physical basis for the TF relations opens the possibility for a subtle systematic variation of the TF relations with environment, although no evidence for such effects has been found. Finally, the distance scale via the TF relations is tied directly to the distance of the LMC and the Galactic calibration of the Cepheid and RR Lyrae variables. Ultimately, the precision of TF relations is limited by this calibration.
7.7 Future Needs and Directions
It is unlikely that the accuracy of visible light CCD photometry will improve much in the future. On the other hand, it is likely that the use of large-format IR arrays will reduce the uncertainties in the estimates of Galactic and internal extinction. With the dispersion in the relations currently being dominated by uncertainties in the corrected line-widths (WRi), significant improvements are most likely to originate from better values of W20, and/or inclinations. The use of two-dimensional velocity field measurements may help in both respects but this would still be somewhat model dependent. A careful investigation of the shape of the TF relations, particularly at the bright end, would help to address current uncertainties regarding the shape and the morphological type dependence of the TF relations.