Populating H₂ and CO in galaxy simulation with dust evolution

There are two major theoretical issues for the star formation law (the relation between the surface densities of molecular gas and star formation rate on a galaxy scale): (i) At low metallicity, it is not obvious that star-forming regions are rich in H₂ because the H₂ formation rate depends on the dust abundance; and (ii) whether or not CO really traces H₂ is uncertain, especially at low metallicity. To clarify these issues, we use a hydrodynamic simulation of an isolated disc galaxy with a spatial resolution of a few tens parsecs. The evolution of dust abundance and grain size distribution is treated consistently with the metal enrichment and the physical state of the interstellar medium. We compute the H₂ and CO abundances using a subgrid post-processing model based on the dust abundance and the dissociating radiation field calculated in the simulation. We find that when themetallicity is≲0.4 Z_⊙ (t < 1 Gyr), H₂ is not a good tracer of star formation rate because H₂-rich regions are limited to dense compact regions. At Z ≳ 0.8 Z_⊙, a tight star formation law is established for both H₂ and CO. At old (t ~ 10 Gyr) ages, we also find that adopting the so-called MRN grain size distribution with an appropriate dust-to-metal ratio over the entire disc gives reasonable estimates for the H₂ and CO abundances. For CO, improving the spatial resolution of the simulation is important, while the H₂ abundance is not sensitive to subresolution structures at Z ≳ 0.4 Z_⊙.