The Tully-Fisher Relation and its Residuals for a Broadly Selected Sample of Galaxies

We measure the relation between galaxy luminosity and disk circular velocity (the Tully-Fisher [TF] relation), in the g , r , i , and z bands, for a broadly selected sample of galaxies from the Sloan Digital Sky Survey, with the goal of providing well-defined observational constraints for theoretical models of galaxy formation. The input sample of 234 galaxies has a roughly flat distribution of absolute magnitudes in the range -18.5 > M r > -22, and our only morphological selection is an isophotal axis ratio cut b / a < 0.6 to allow accurate inclination corrections. Long-slit spectroscopy from the Calar Alto and MDM observatories yields usable Hα rotation curves for 162 galaxies (69%), with a representative color and morphology distribution. We define circular velocities V 80 by evaluating the rotation curve at the radius containing 80% of the i -band light. Observational errors, including estimated distance errors due to peculiar velocities, are small compared to the intrinsic scatter of the TF relation. The slope of the forward TF relation steepens from -5.5 ± 0.2 mag (log 10 km s -1 ) -1 in the g band to -6.6 ± 0.2 mag (log 10 km s -1 ) -1 in the z band. The intrinsic scatter is σ ≈ 0.4 mag in all bands, and residuals from either the forward or inverse relations have an approximately Gaussian distribution. We discuss how Malmquist-type biases may affect the observed slope, intercept, and scatter. The scatter is not dominated by rare outliers or by any particular class of galaxies, although it drops slightly, to σ ≈ 0.36 mag, if we restrict the sample to nearly bulgeless systems. Correlations of TF residuals with other galaxy properties are weak: bluer galaxies are significantly brighter than average in the g -band TF relation but only marginally brighter in the i band; more concentrated (earlier type) galaxies are slightly fainter than average, and the TF residual is virtually independent of half-light radius, contrary to the trend expected for gravitationally dominant disks. The observed residual correlations do not account for most of the intrinsic scatter, implying that this scatter is instead driven largely by variations in the ratio of dark to luminous matter within the disk galaxy population.