Cosmic evolution of the star formation efficiency in Milky Way-like galaxies

Current star formation models are based on the local structure of the interstellar medium (ISM), yet the details on how the small-scale physics propagates up to global galactic-scale properties are still under debate. To investigate this we use {\small VINTERGATAN}, a high-resolution (20 pc) cosmological zoom-in simulation of a Milky Way-like galaxy. We study how the velocity dispersion and density structure of the ISM on 50-100 pc scales evolve with redshift, and quantify their impact on the star formation efficiency per free-fall timescale, $\epsilon_{\rm ff}$. During starbursts the ISM can reach velocity dispersions as high as $\sim 50$ km s$^{-1}$ for the densest and coldest gas, most noticeable during the last major merger event ($1.3 < z < 1.5$). After a merger-dominated phase ($1<z<5$), {\small VINTERGATAN} transitions into evolving secularly, with the cold neutral ISM typically featuring velocity dispersion levels of $\sim 10$ km s$^{-1}$. Despite strongly evolving density and turbulence distributions over cosmic time, $\epsilon_{\rm ff}$ at the resolution limit is found to change by only a factor of a few: from median efficiencies of 0.8\% at $z>1$ to 0.3\% at $z<1$. The mass-weighted average shows a universal $\langle \epsilon_{\rm ff} \rangle \approx 1\%$, caused by an almost invariant virial parameter distribution in star forming clouds. Changes in their density and turbulence levels are coupled so the kinetic-to-gravitational energy ratio remains close to constant. Finally, we show that a \textit{theoretically} motivated instantaneous $\epsilon_{\rm ff}$ is intrinsically different to its \textit{observational} estimates adopting tracers of star formation e.g. H$\alpha$. Since the physics underlying star formation can be lost on short ($\sim$ 10 Myr) timescales, caution must be taken when constraining star formation models from observational estimates of $\epsilon_{\rm ff}$.