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.
