Globular cluster ( GC ) systems around galaxies of a vast mass range show remarkably simple scaling relations .
The combined mass of all GCs is a constant fraction of the total galaxy mass and the mean metallicity and metallicity dispersion of the GC system scale up weakly with galaxy mass .
The metallicity of massive , metal-poor ( ‘ ‘ blue '' ) clusters increases with cluster mass , while that of metal-rich ( ‘ ‘ red '' ) clusters does not .
A significant age-metallicity relation emerges from analysis of resolved stellar populations in Galactic GCs and unresolved populations in nearby galaxies .
Remarkably , all these trends can be explained by a simple merger-based model developed in previous work and updated here using recent observations of galaxy scaling relations at high redshift .
We show that the increasing dispersion of GC metallicity distributions with galaxy mass is a robust prediction of the model .
It arises from more massive galaxies having more mergers that combine satellite GC systems .
The average metallicity also increases by 0.6 dex over 3 dex in halo mass .
The models show a non-linear trend between the GC system mass and host galaxy mass which is consistent with the data .
The model does not consider GC self-enrichment , yet predicts a correlation between cluster mass and metallicity for massive blue clusters .
The age-metallicity relation is another robust prediction of the model .
Half of all clusters are predicted to form within the redshift range 5 < z < 2.3 , corresponding to ages of 10.8 - 12.5 Gyr , in halos of masses 10 ^ { 11 } -10 ^ { 12.5 } M _ { \odot } .