4.2. Velocity Width Dependence of TF Scatter

It has been noted by a number of authors (Federspiel, Sandage, & Tammann 1994; Willick et al. 1997; Giovanelli et al. 1997a, 1997b) that _TF exhibits a velocity width (or, equivalently, a luminosity) dependence: luminous, rapidly rotating galaxies have smaller TF scatter than faint, slowly rotating ones. Willick et al. (1997) showed that this effect could be parameterized by _TF() = ₀ - g, with different values of ₀ (the scatter for a typical, = 0, galaxy) and g for each sample. For the MAT sample, they found g = 0.33, while for A82, they found g = 0.14. In the VELMOD analysis, we treated ₀ as a free parameter for both samples but fixed the values of g to the Willick et al. (1997) values. For the remainder of this paper, when we refer to _TF, we are actually referring to the ₀ for the respective samples. We note that a significant likelihood increase was achieved by adopting this variable TF scatter, but that the derived value of _I was essentially unchanged. The mock catalogs were generated and analyzed with g = 0.