Emergence and cosmic evolution of the Kennicutt-Schmidt relation driven by interstellar turbulence

The scaling relations between the gas content and star formation rate of galaxies provide useful insights into processes governing their formation and evolution. We investigate the emergence and the physical drivers of the global Kennicutt-Schmidt (KS) relation at $0.25 \leq z \leq 4$ in the cosmological hydrodynamic simulation NewHorizon capturing the evolution of a few hundred galaxies with a resolution of $\sim$ 40 pc. The details of this relation vary strongly with the stellar mass of galaxies and the redshift. A power-law relation $\Sigma_{\rm SFR} \propto \Sigma_{\rm gas}^{a}$ with $a \approx 1.4$, like that found empirically, emerges at $z \approx 2 - 3$ for the most massive half of the galaxy population. However, no such convergence is found in the lower-mass galaxies, for which the relation gets shallower with decreasing redshift. At the galactic scale, the star formation activity correlates with the level of turbulence of the interstellar medium, quantified by the Mach number, rather than with the gas fraction (neutral or molecular), confirming previous works. With decreasing redshift, the number of outliers with short depletion times diminishes, reducing the scatter of the KS relation, while the overall population of galaxies shifts toward low densities. Using pc-scale star formation models calibrated with local Universe physics, our results demonstrate that the cosmological evolution of the environmental and intrinsic conditions conspire to converge towards a significant and detectable imprint in galactic-scale observables, in their scaling relations, and in their reduced scatter.