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We investigate the abundance of galactic molecular hydrogen (H$_2$) in the"Evolution and Assembly of GaLaxies and their Environments" (EAGLE)cosmological hydrodynamic simulations. We assign H$_2$ masses to gas particlesin the simulations in post-processing using two different prescriptions thatdepend on the local dust-to-gas ratio and the interstellar radiation field.Both result in H$_2$ galaxy mass functions that agree well with observations inthe local and high-redshift Universe. The simulations reproduce the observedscaling relations between the mass of H$_2$ and the stellar mass, starformation rate and stellar surface density. Towards high edshifts, galaxies inthe simulations display larger H$_2$ mass fractions, and correspondingly lowerH$_2$ depletion timescales, also in good agreement with observations. Thecomoving mass density of H$_2$ in units of the critical density, $\Omega_{\rmH_2}$, peaks at $z\approx 1.2-1.5$, later than the predicted peak of the cosmicstar formation rate activity, at $z\approx 2$. This difference stems from thedecrease in gas metallicity and increase in interstellar radiation field withredshift, both of which hamper H$_2$ formation. We find that the cosmic H$_2$budget is dominated by galaxies with $M_{\rm H_2}>10^9\,\rm M_{\odot}$, starformation rates $>10\,\rm M_{\odot}\,\rm yr^{-1}$ and stellar masses $M_{\rmstellar}>10^{10}\,\rm M_{\odot}$, which are readily observable in the opticaland near-IR. The match between the H$_2$ properties of galaxies that emerge inthe simulations and observations is remarkable, particularly since H$_2$observations were not used to adjust parameters in EAGLE.

Molecular hydrogen abundances of galaxies in the EAGLE simulations