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 Ha 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 similar to 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-star from Bell et al., based on the linear combination of a luminosity and a colour. Assuming a Kroupa initialmass function (IMF), we find: log [V-80/(km s(-1))]=(2.142 +/- 0.004) + (0.278 +/- 0.010)[log (M-star/M-circle dot) - 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 <(sigma)over tilde>s = 0.036 +/- 0.005 dex and a measured scatter sigma(meas) = 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-star)(R-80), decrease from approximately 10 to 3, as stellar mass increases from M-star approximate to 10(9) to 10(11)M(circle dot). At a fixed stellar mass, (M-dyn/M-star)(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-star)(R-80) with disc size as a reflection of the fact that disc size dictates the radius at which M-dyn/M-star is measured, and consequently, the fraction of the dark matter 'seen' by the gas at that radius. For the lowest M-star 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-star 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-star)(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.