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We present dynamical measurements from the KMOS (K-band Multi-ObjectSpectrograph) Deep Survey (KDS), which is comprised of 77 typical star-forminggalaxies at z $\simeq$ 3.5 in the mass range 9.0 < log(M$_{\star}$/M$_{\odot}$)< 10.5. These measurements constrain the internal dynamics, the intrinsicvelocity dispersions ({\sigma}$_{int}$) and rotation velocities (V$_{C}$) ofgalaxies in the high redshift Universe. The mean velocity dispersion of thegalaxies in our sample is {\sigma}$_{int}$ = $70.8^{+3.3}_{-3.1}$ km s$^{-1}$,revealing that the increasing average {\sigma}$_{int}$ with increasingredshift, reported for z $\lesssim2$, continues out to z $\simeq$ 3.5. Only 34$\pm$ 8% of our galaxies are rotation-dominated (V$_{C}$/{\sigma}$_{int}$ > 1),with the sample average V$_{C}$/{\sigma}$_{int}$ value much smaller than atlower redshift. After carefully selecting comparable star-forming samples atmultiple epochs, we find that the rotation-dominated fraction evolves withredshift with a z$^{-0.2}$ dependence. The rotation-dominated KDS galaxies showno clear offset from the local rotation velocity-stellar mass (i.e.V$_{C}$-M$_{\star}$) relation, although a smaller fraction of the galaxies areon the relation due to the increase in the dispersion-dominated fraction. Theseobservations are consistent with a simple equilibrium model picture, in whichrandom motions are boosted in high redshift galaxies by a combination of theincreasing gas fractions, accretion efficiency, specific star-formation rateand stellar feedback and which may provide significant pressure support againstgravity on the galactic disk scale.

The KMOS Deep Survey (KDS) I: dynamical measurements of typical star-forming galaxies at z $\simeq$ 3.5