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

We present the $0.6<z<2.6$ evolution of the ionized gas velocity dispersion in 175 star-forming disk galaxies based on data from the full KMOS$^{\rm 3D}$ integral field spectroscopic survey. In a forward-modelling Bayesian framework including instrumental effects and beam-smearing, we fit simultaneously the observed galaxy velocity and velocity dispersion along the kinematic major axis to derive the intrinsic velocity dispersion $\sigma_0$. We find a reduction of the average intrinsic velocity dispersion of disk galaxies as a function of cosmic 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 intrinsic scatter ($\sigma_{\sigma_0, {\rm int}}\approx10$ km s$^{-1}$) around the best-fit $\sigma_0-z$-relation beyond what can be accounted for from the typical measurement uncertainties ($\delta\sigma_0\approx12$ km s$^{-1}$), independent of other identifiable galaxy parameters. This potentially suggests a dynamic mechanism such as minor mergers or variation in accretion being responsible for the scatter. Putting our data into the broader literature context, we find that ionized and atomic+molecular velocity dispersions evolve similarly with redshift, with the ionized gas dispersion being $\sim10-15$ km s$^{-1}$ higher on average. We investigate the physical driver of the on average elevated velocity dispersions at higher redshift, and find that our galaxies are at most marginally Toomre-stable, suggesting that their turbulent velocities are powered by gravitational instabilities, while stellar feedback as a driver alone is insufficient. This picture is supported through comparison with a state-of-the-art analytical model of galaxy evolution.