Origins of scaling relations of globular cluster systems

Globular cluster (GC) systems demonstrate tight scaling relations with the properties of their host galaxies. In previous work, we developed an analytic model for GC formation in a cosmological context that matches nearly all of these observed scaling relations. Here, we apply our model to investigate in detail the physical origins and evolution of these scaling relations. The ratio of the combined mass in GCs M_GC to the host dark matter halo mass M_h is nearly constant at all redshifts, but its normalization evolves by a factor of ∼10 from birth to z = 0. The relation is steeper than linear at halo masses M_h≲ 10^{11.5} M_{⊙ }, primarily due to non-linearity in the stellar mass-halo mass relation. The near constancy of the ratio M_GC/M_h, combined with the shape of the stellar mass-halo mass relation, sets the characteristic U shape of the GC specific frequency as a function of host galaxy mass. The contribution of accreted satellite galaxies to the buildup of GC systems is a strong function of the host galaxy mass, ranging from ≈0 per cent at M_h≈ 10^{11} M_{⊙ } to 80 per cent at M_h≈ 10^{15} M_{⊙ }. The metal-poor clusters are significantly more likely to form ex situ relative to the metal-rich clusters, but a substantial fraction of metal-poor clusters still form in situ in lower mass galaxies. Cluster formation occurs essentially continuously at high redshift, while at low redshift galactic mergers become increasingly important for cluster formation. Consequently, although major mergers form clusters efficiently, they are too rare to form most clusters.