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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 sigmaTF 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 sigmaTF(eta) = sigma0 - geta, with different values of sigma0 (the scatter for a typical, eta = 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 sigma0 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 sigmaTF, we are actually referring to the sigma0 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 betaI was essentially unchanged. The mock catalogs were generated and analyzed with g = 0.