Intertwined Formation of $\rm{H_2}$, Dust, and Stars in Cosmological Simulations

Context: Molecular hydrogen ( H2 ) is crucial in galaxy formation and evolution, serving as the main fuel for star formation (SF). In metal-enriched environments, H2 primarily forms on interstellar dust grain surfaces. However, due to the complexities of modelling this process, SF in cosmological simulations often relies on empirical or theoretical frameworks validated only in the Local Universe to estimate the abundance of H2 . Aims: This study aims to model the connection between star, dust, and H2 formation processes in cosmological simulations. Methods: We include H2 formation on dust grain surfaces and account for molecule destruction and radiation shielding into the SF and feedback model MUPPI. Results: The model reproduces key properties of observed galaxies for stellar, dust, and H2 components. The cosmic density of H2 ( ρH2 ) peaks around z=1.5 , then decreases by half towards z=0 , showing milder evolution than observed. The H2 mass function since z=2 also shows gentler evolution. Our model successfully recovers the integrated molecular Kennicutt-Schmidt (mKS) law between surface star formation rate ( ΣSFR ) and surface H2 density ( ΣH2 ) at z=0 , already evident at z=2 with a higher normalization. We find hints of a broken power law with a steeper slope at higher ΣH2 , aligning with some observational findings. Additionally, the H2 -to-dust mass ratio in galaxies shows a decreasing trend with gas metallicity and stellar mass. The H2 -to-dust mass fraction for the global galaxy population is higher at higher redshifts. The analysis of the atomic-to-molecular transition on a particle-by-particle basis suggests that gas metallicity cannot reliably substitute the dust-to-gas ratio in models simulating dust-promoted H2 .