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We present the $0.6<z<2.6$ evolution of the ionized gas velocity dispersionin 175 star-forming disk galaxies based on data from the full KMOS$^{\rm 3D}$integral field spectroscopic survey. In a forward-modelling Bayesian frameworkincluding instrumental effects and beam-smearing, we fit simultaneously theobserved galaxy velocity and velocity dispersion along the kinematic major axisto derive the intrinsic velocity dispersion $\sigma_0$. We find a reduction ofthe average intrinsic velocity dispersion of disk galaxies as a function ofcosmic time, from $\sigma_0\sim45$ km s$^{-1}$ at $z\sim2.3$ to$\sigma_0\sim30$ km s$^{-1}$ at $z\sim0.9$. There is substantial intrinsicscatter ($\sigma_{\sigma_0, {\rm int}}\approx10$ km s$^{-1}$) around thebest-fit $\sigma_0-z$-relation beyond what can be accounted for from thetypical measurement uncertainties ($\delta\sigma_0\approx12$ km s$^{-1}$),independent of other identifiable galaxy parameters. This potentially suggestsa dynamic mechanism such as minor mergers or variation in accretion beingresponsible for the scatter. Putting our data into the broader literaturecontext, we find that ionized and atomic+molecular velocity dispersions evolvesimilarly with redshift, with the ionized gas dispersion being $\sim10-15$ kms$^{-1}$ higher on average. We investigate the physical driver of the onaverage elevated velocity dispersions at higher redshift, and find that ourgalaxies are at most marginally Toomre-stable, suggesting that their turbulentvelocities are powered by gravitational instabilities, while stellar feedbackas a driver alone is insufficient. This picture is supported through comparisonwith a state-of-the-art analytical model of galaxy evolution.

The Evolution and Origin of Ionized Gas Velocity Dispersion from $z\sim2.6$ to $z\sim0.6$ with KMOS$^{\rm 3D}$