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 (ztrun ≥ 6). We find that the correlation between mean metallicities (Zgc) of MPCs and their host galaxy luminosities (L) flattens from z = ztrun to z = 0. We also find that the observed relation (Zgc ∝ L ) in MPCs can be reproduced well in the models with Zgc ∼ L 0.5 at z = ztrun when ztrun ∼ 10, if mass-to-light-ratios are assumed to be constant at z = ztrun. A flatter L − Zgc at z = ztrun is found to be required to explain the observed relation for constant mass-to-light-ratio models with lower z = ztrun. However, better agreement with the observed relation is found for models with different mass-to-light-ratios between z = ztrun and z = 0. It is also found that the observed color-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 = ztrun. 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 > ztrun. The half-number radii (Re) of GCSs, velocity dispersions of GCSs (σ), and their host galaxy masses (Mh) are found to be correlated with one another such that Re ∝ Mh 0.57 and σ ∝ Mh . 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− Zgc relation, and non-homology of GCSs.