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3.3. The TF Scatter

Of great importance to applications of the TF relation is its scatter sigmaTF, the rms magnitude dispersion about the mean relation M(eta). This scatter is composed of three basic contributions: magnitude and velocity width measurement errors, and intrinsic or ``cosmic'' scatter. Of the three, recent analyses have suggested that the second and third are about equally important, contributing ~ 0.25-0.30 mag each (Willick et al. 1996). Photometric measurement errors are quite small in comparison. Thus, the overall TF scatter is about 0.4 mag. It is significant that sigmaTF determines not only random distance errors (deltad / d appeq 0.46 sigmaTF), but also systematic errors associated with statistical bias effects (Section 9). Knowing sigmaTF is therefore crucial for assessing the reliability of TF studies. (An analogous statement applies to the scatter of the other DIs discussed in this Chapter as well.)

I would be remiss if I did not mention that the TF scatter remains controversial. Estimates of sigmaTF have varied widely in the last decade. Bothun & Mould (1987) suggested that sigmaTF could be made as small as ltapprox 0.25 mag with a velocity width-dependent choice of photometric aperture. Pierce & Tully (1988) also found sigmaTFappeq 0.25 using CCD data in the Virgo and Ursa Major clusters. Willick (1991) and Courteau (1992) found somewhat higher but still small values of the TF scatter (sigmaTF = 0.30-0.35 mag). Bernstein et al. (1994) found the astonishing value of 0.1 mag for the Coma Cluster TF relation using I-band CCD magnitudes and carefully measured H I velocity widths.

Unfortunately, these relatively low values have not been borne out by later studies using more complete samples. Willick et al. (1995, 1996, 1997) calibrated TF relations for six separate samples comprising nearly 3000 spiral galaxies, and found typical values of sigmaTFappeq 0.4 mag for the CCD samples. Willick et al. (1996) argued that the large sample size and a relatively conservative approach to excluding outliers drove up earlier, optimistically low estimates of the TF scatter. Other workers, notably Sandage and collaborators (e.g., Sandage 1994; Federspiel et al. 1994) have taken an even more pessimistic view of the accuracy of the TF relation, suggesting that typical spirals scatter about the TF expectation by 0.6-0.7 mag.

How can one reconcile this wide range of values? At least part of the answer lies in different workers' preconceptions and preferences. Those excited at the possiblity of finding a more accurate way of estimating distances tend to find low (sigmaTF ltapprox 0.3 mag) values. Those who doubt the credibility of TF distances tend to find high (sigmaTF gtapprox 0.5 mag) ones. It is possible to arrive at such discrepant results in part because the samples differ so dramatically. Perhaps it is only justified to speak of a particular value of the TF scatter for a given set of sample selection criteria; hopefully, this issue will be clarified in the years to come.

There is one galaxian property with which the TF scatter demonstrably appears to vary, however, and that is luminosity (velocity width). Brighter galaxies exhibit a smaller TF scatter than fainter ones (Federspiel et al. 1994; Freudling et al. 1995; Willick et al. 1997). Part of this effect is undoubtedly due to the fact that the errors in eta = log Deltav -2.5 go as (Deltav)-1, if errors in Deltav itself are roughly constant as is most likely the case. Such velocity width errors translate directly into a TF scatter that increases with decreasing luminosity. A careful study of whether the intrinsic TF scatter varies with luminosity has not yet been carried out.

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