The KMOS Deep Survey (KDS) - I. Dynamical measurements of typical star-forming galaxies at z ≃ 3.5

We present dynamical measurements from the KMOS (K-band multi-object spectrograph) Deep Survey (KDS), which comprises 77 typical star-forming galaxies at z similar or equal to 3.5 in the mass range 9.0 < log (M-*/M circle dot) < 10.5. These measurements constrain the internal dynamics, the intrinsic velocity dispersions (sigma(int)) and rotation velocities (VC) of galaxies in the high-redshift Universe. The mean velocity dispersion of the galaxies in our sample is sigma(int) = 70.8(-3.1)(+3.3) km s(-1), revealing that the increasing average sint with increasing redshift, reported for z less than or similar to 2, continues out to z similar or equal to 3.5. Only 36 +/- 8 per cent of our galaxies are rotation-dominated (V-C/sigma(int) > 1), with the sample average VC/sint value much smaller than at lower redshift. After carefully selecting comparable star-forming samples at multiple epochs, we find that the rotation-dominated fraction evolves with redshift with a z(-0.2) dependence. The rotation-dominated KDS galaxies show no clear offset from the local rotation velocity-stellar mass (i.e. VC-M-*) relation, although a smaller fraction of the galaxies are on the relation due to the increase in the dispersion-dominated fraction. These observations are consistent with a simple equilibrium model picture, in which random motions are boosted in high-redshift galaxies by a combination of the increasing gas fractions, accretion efficiency, specific star formation rate and stellar feedback and which may provide significant pressure support against gravity on the galactic disc scale.