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) proportional to L-0.15) in MPCs can be reproduced well in the models with Z(gc) similar to L-0.5 at z = z(trun) when z(trun) similar to 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 (sigma) and their host galaxy masses (M-h) are found to be correlated with one another such that R-e proportional to M-h(0.57) and sigma proportional to 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.