The KMOS Deep Survey (KDS) II: The evolution of the stellar-mass
  Tully-Fisher relation since z ~ 4
  We use KMOS Deep Survey (KDS) galaxies, combined with results from a range of
spectroscopic studies in the literature, to investigate the evolution of the
stellar-mass Tully-Fisher relation since z ~ 4. We determine the slope and
normalisation of the local rotation-velocity -- stellar-mass (Vc - $M_{\star}$)
relationship using a reference sample of local spiral galaxies; thereafter we
fix the slope, and focus on the evolution of velocity normalisation with
redshift. The rotation-dominated KDS galaxies at z ~ 3.5 have rotation
velocities ~ -0.1 dex lower than local reference galaxies at fixed stellar
mass. By fitting 16 distant comparison samples spanning 0 < z < 3 (containing ~
1200 galaxies), we show that the size and sign of the inferred Vc offset
depends sensitively on the fraction of the parent samples used in the
Tully-Fisher analysis, and how strictly the criterion of 'rotation dominated'
is enforced. Confining attention to subsamples of galaxies that are especially
'disky' results in a consistent positive offset in Vc of ~ +0.1 dex, however
these galaxies are not representative of the evolving-disk population at z > 1.
We investigate the addition of pressure support, traced by intrinsic velocity
dispersion ($\sigma_{int}$) to the KDS dynamical mass budget by adopting a
'total' effective velocity of form $V_{tot} = (Vc^{2} +
4.0\sigma_{int}^{2})^{0.5}$. The rotation-dominated and dispersion-dominated
KDS galaxies fall on the same locus in the total-velocity versus stellar-mass
plane, removing the need for debate over the precise selection threshold for
rotation-dominated galaxies. The comparison sample offsets are in the range
+0.08 to +0.15 dex in total-velocity zero-point (-0.30 to -0.55 dex in
stellar-mass zero-point) from the local Tully-Fisher relation at z > 1,
consistent with steady evolution of the ratio of dynamical to stellar mass with
cosmic time.
