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The fundamental plane of star formation in galaxies revealed by the EAGLE hydrodynamical simulations

We investigate correlations between different physical properties of star-forming galaxies in the "Evolution and Assembly of GaLaxies and their Environments" (EAGLE) cosmological hydrodynamical simulation suite over the redshift range $0\le z\le 4.5$. A principal component analysis reveals that neutral gas fraction ($f_{\rm gas, neutral}$), stellar mass ($M_{\rm stellar}$) and star formation rate (SFR) account for most of the variance seen in the population, with galaxies tracing a two-dimensional, nearly flat, surface in the three-dimensional space of $f_{\rm gas, neutral}-M_{\rm stellar}-\rm SFR$ with little scatter. The location of this plane varies little with redshift, whereas galaxies themselves move along the plane as their $f_{\rm gas, neutral}$ and SFR drop with redshift. The positions of galaxies along the plane are highly correlated with gas metallicity. The metallicity can therefore be robustly predicted from $f_{\rm gas, neutral}$, or from the $M_{\rm stellar}$ and SFR. We argue that the appearance of this "fundamental plane of star formation" is a consequence of self-regulation, with the plane's curvature set by the dependence of the SFR on gas density and metallicity. We analyse a large compilation of observations spanning the redshift range $0\lesssim \rm z\lesssim 2.5$, and find that such a plane is also present in the data. The properties of the observed fundamental plane of star formation are in good agreement with EAGLE's predictions.