Calibrated Tully-Fisher relations for improved estimates of disc rotation velocities

In this paper, we derive scaling relations between photometric observable quantities and disc galaxy rotation velocity V rot or Tully-Fisher relations (TFRs). Our methodology is dictated by our purpose of obtaining purely photometric, minimal-scatter estimators of V rot applicable to large galaxy samples from imaging surveys. To achieve this goal, we have constructed a sample of 189 disc galaxies at redshifts z < 0.1 with long-slit Hα spectroscopy from Pizagno et al. and new observations. By construction, this sample is a fair subsample of a large, well-defined parent disc sample of ∼170 000 galaxies selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). The optimal photometric estimator of V rot we find is stellar mass M ★ from Bell et al., based on the linear combination of a luminosity and a colour. Assuming a Kroupa initial mass function (IMF), we find: log [V 80/(km s−1)] = (2.142 ± 0.004) + (0.278 ± 0.010)[log (M ★/M⊙) − 10.10], where V 80 is the rotation velocity measured at the radius R 80 containing 80 per cent of the i-band galaxy light. This relation has an intrinsic Gaussian scatter dex and a measured scatter σmeas= 0.056 dex in log V 80. For a fixed IMF, we find that the dynamical-to-stellar mass ratios within R 80, (M dyn/M ★)(R 80), decrease from approximately 10 to 3, as stellar mass increases from M ★≈ 109 to 1011 M⊙. At a fixed stellar mass, (M dyn/M ★)(R 80) increases with disc size, so that it correlates more tightly with stellar surface density than with stellar mass or disc size alone. We interpret the observed variation in (M dyn/M ★)(R 80) with disc size as a reflection of the fact that disc size dictates the radius at which M dyn/M ★ is measured, and consequently, the fraction of the dark matter 'seen' by the gas at that radius. For the lowest M ★ galaxies, we find a positive correlation between TFR residuals and disc sizes, indicating that the total density profile is dominated by dark matter on these scales. For the highest M ★ galaxies, we find instead a weak negative correlation, indicating a larger contribution of stars to the total density profile. This change in the sense of the correlation (from positive to negative) is consistent with the decreasing trend in (M dyn/M ★)(R 80) with stellar mass. In future work, we will use these results to study disc galaxy formation and evolution and perform a fair, statistical analysis of the dynamics and masses of a photometrically selected sample of disc galaxies.