2015ApJ...806...36H

An increasing body of data reveals a one-to-one linear correlation between galaxy halo mass and the total mass in its globular cluster (GC) population,, valid over five orders of magnitude. In this paper we explore the nature of this correlation for galaxies of different morphological types and for the subpopulations of metal-poor (blue) and metal-rich (red) GCs. For the subpopulations of different metallicity, we find and with similar scatter. The numerical values of these exponents can be derived from the detailed behavior of the red and blue GC fractions with galaxy mass and provide a self-consistent set of relations. In addition, all morphological types (E, S0, S/Irr) follow the same relation, but with a second-order trend for spiral galaxies to have a slightly higher fraction of metal-rich GCs for a given mass. These results suggest that the amount of gas available for GC formation at high redshift was in nearly direct proportion to the dark matter halo potential, in strong contrast to the markedly nonlinear behavior of total stellar mass versus halo mass. Of the few available theoretical treatments that directly discuss the formation of GCs in a hierarchical-merging framework, we find that the model of Kravtsov & Gnedin best matches these observations. They find that the blue, metal-poor GCs formed in small halos at and did so in nearly direct proportion to halo mass. Similar models addressing the formation rate of the red, more metal-rich GCs in the same detail and continuing to lower redshift are still needed for a comprehensive picture.