On the origin of mass–metallicity relations, blue tilts and scaling relations for metal‐poor globular cluster systems

We investigate formation processes and physical properties of globular cluster systems (GCSs) in galaxies based on high‐resolution cosmological simulations with globular clusters. We focus on metal‐poor clusters (MPCs) and correlations with their host galaxies by assuming that MPC formation is truncated at a high redshift ( z trun ≥ 6) . We find that the correlation between mean metallicities ( Z gc ) of MPCs and their host galaxy luminosities ( L ) flattens from z = z trun to 0. We also find that the observed relation ( Z gc ∝ L 0.15 ) in MPCs can be reproduced well in the models with Z gc ∼ L 0.5 at z = z trun when z trun ∼ 10 , if mass‐to‐light ratios are assumed to be constant at z = z trun . A flatter L – Z gc at z = z trun is found to be required to explain the observed relation for constant mass‐to‐light ratio models with lower z = z trun . However, better agreement with the observed relation is found for models with different mass‐to‐light ratios between z = z trun and 0. It is also found that the observed colour–magnitude relation of luminous MPCs (i.e. ‘blue tilts’) may only have a small contribution from the stripped stellar nuclei of dwarf galaxies, which have nuclei masses that correlate with their total mass at z = z trun . The simulated blue tilts are found to be seen more clearly in more massive galaxies, which reflects the fact that more massive galaxies at z = 0 are formed from a larger number of dwarfs with stellar nuclei formed at z > z trun . The half‐number radii ( R e ) of GCSs, velocity dispersions of GCSs (σ) and their host galaxy masses ( M h ) are found to be correlated with one another such that R e ∝ M h 0.57 and σ∝ M h 0.32 . Based on these results, we discuss the link between hierarchical merging histories of galaxies and the physical properties of MPCs, the origin of the L – Z gc relation and non‐homology of GCSs.