The Tully-Fisher Relation, its residuals, and a comparison to theoretical predictions for a broadly selected sample of galaxies

We target 234 galaxies for Hα spectroscopy, selected from the Sloan Digital Sky Survey spectroscopic galaxy catalog, and successfully obtain rotation curves for 162 galaxies using the Calar Alto and MDM telescopes. No morphological cuts were applied to the sample, except an i-band isophotal axis ratio of < 0.7. We fit arc-tangent functions to the rotation curves, and evaluate the circular velocity at a radius containing 80% of the total i-band light. The g, r, i, and z-band Tully-Fisher relations are determined using a maximum likelihood fitting procedure that leaves the slope, intercept, and intrinsic scatter as free parameters. The Tully-Fisher relations have slopes between -5.4 and -7.7 ± 0.2 mag/log₁₀(kms^-1), and intercepts between -18.95 and -19.88 ± 0.04 mag at 100 kms^-1, and an intrinsic scatter of 0.42 ± 0.04 mag independent of wavelength. We find correlations between TF residuals and color and half-light radius residuals in the expected sense. The data weakly follow the trend expected if the stellar mass-to-light ratio was approximated by the color.

We investigate the correlations among stellar mass (M_*), disk scale length (R_d), and rotation velocity at 2.2 disk scale lengths (V_2.2) for a sample of 81 disk-dominated galaxies. We find a logarithmic slope of 2.60 ± 0.13 for the L_i-V_2.2 relation, somewhat shallower than most previous studies, with intrinsic scatter of 0.13 dex. Our direct estimates of the total-to-stellar mass ratio yield a median ratio of 2.4 to 4.4, with large scatter at a given M_* and R_d. The stellar mass accounts for 65% of the rotation within 2.2R_d. The distribution of scale lengths at fixed 0M_* is broad, but we find no correlation between disk size and the residual from the M_*-V_2.2 relation. This result implies that stellar disks do not dominate the mass within 2.2R_d and have m_d < 0.1. A model with a disk-to-halo mass ratio m_d=0.05 provides a reasonable match to the R_d-M_* distribution for spin parameters λ ranging from ∼ 0.04 - 0.08, and it yields a reasonable match to the mean M_*-V_2.2 relation.