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

Abstract

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 À18:5 > M r > À22, 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 H 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 À5:5 AE 0:2 mag ( log 10 km s À1 ) À1 in the g band to À6:6 AE 0:2 mag ( log 10 km s À1 ) À1 in the z band. The intrinsic scatter is % 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 % 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.

The Dawes Review 1: Kinematic Studies of Star-Forming Galaxies Across Cosmic Time

“…The rotators at < z > 1.2 show consistency with a small scatter stellar mass Tully-Fisher relationship, whilst the non-rotators depart radically from this. The question of evolution depends on which local Tully-Fisher relationship is assumed (an issue also highlighted by Puech et al 2008), but the comparison with Pizagno et al (2007) suggests a −0.36 dex evolution of the zeropoint fairly similar to that found by SINS (Cresci et al 2009) at z ß2, consistent with the idea of discs increasing their stellar mass with time at a fixed v c . Consistent gas fractions were found using both the Kennicutt-Schmidt relationship and the difference between dynamical and stellar mass.…”

“…The Tully-Fisher relationship was explored in more detail by Puech et al (2008) who reaffirmed the earlier conclusion that the increase in scatter about the mean relation was due to the 'non-relaxed' PR and CK classes (the scatter increases from 0.1 to 0.8 dex from RDs to CKs; shown in Figure 6). However, with a bigger sample and an improved analysis and a revised local reference, 13 they now found a modest amount of zeropoint evolution in the K-band Tully-Fisher relationship (about 0.34 dex or a factor of two 13 The local stellar mass relation was based on the K-band, one of Hammer et al (2007), which they derive from the SDSS relation of Pizagno et al (2007). Hammer et al examine the Verheijen relation (which is also the basis of the Bell & de Jong (2001) relation) and conclude that it is biased and the SDSS relation is more reliable.…”

Dynamical properties of AMAZE and LSD galaxies from gas kinematics and the Tully-Fisher relation atz ~ 3

“…There are still discrepant results on a possible evolution at intermediate redshifts of the tight relation observed in local galaxies (e.g., Haynes et al 1999;Pizagno et al 2007). For example Vogt et al (1996) reported very little evolution of the B-band TFR up to z ∼ 1, but other groups (e.g.…”

In-N-Out: The Gas Cycle From Dwarfs to Spiral Galaxies

“…The Pizagno et al (2007) data are for the tangental rotational velocities, while the data from Geha et al (2006) employ the H I line width and thus should be interpreted as lower limits to the circular velocities. The simulated galaxies follow both the baryonic and standard Tully-Fisher relations across nearly an order of magnitude velocity range.…”