The natural emergence of the correlation between H2 and star formation rate surface densities in galaxy simulations

In this study, we present a suite of high-resolution numerical simulations of an isolated galaxy to test a sub-grid framework to consistently follow the formation and dissociation of H${}_2$ with non-equilibrium chemistry. The latter is solved via the package KROME, coupled to the mesh-less hydrodynamic code GIZMO. We include the effect of star formation (SF), modelled with a physically motivated prescription independent of H${}_2$, supernova feedback and mass losses from low-mass stars, extragalactic and local stellar radiation, and dust and H${}_2$ shielding, to investigate the emergence of the observed correlation between H${}_2$ and SF rate surface densities. We present two different sub-grid models and compare them with on-the-fly radiative transfer (RT) calculations, to assess the main differences and limits of the different approaches. We also discuss a sub-grid clumping factor model to enhance the H${}_2$ formation, consistent with our SF prescription, which is crucial, at the achieved resolution, to reproduce the correlation with H${}_2$. We find that both sub-grid models perform very well relative to the RT simulation, giving comparable results, with moderate differences, but at much lower computational cost. We also find that, while the Kennicutt-Schmidt relation for the total gas is not strongly affected by the different ingredients included in the simulations, the H${}_2$-based counterpart is much more sensitive, because of the crucial role played by the dissociating radiative flux and the gas shielding.