Globular cluster numbers in dark matter haloes: an empirical model within EMERGE
We present an empirical model for the number of globular clusters (GCs) in galaxies based on recent data showing a tight relationship between dark matter halo virial masses and GC numbers. Based on these relations, our model forms GCs in haloes with masses between $M_\mathrm{seedGC} = 3.2 \times 10^8\,\mathrm{M}_\odot$ and $4.7 \times 10^8\,\mathrm{M}_\odot$, depending on the observations used for calibration. We confirm previous works that reported the observed linear correlation as being a consequence of hierarchical merging and its insensitivity to the exact GC formation processes at higher virial masses. We find that the scatter of the linear relation is strongly correlated with the relative amount of smooth accretion: the more dark matter is smoothly accreted, the fewer GCs a halo has compared to other haloes of the same mass. This scatter is smaller than that introduced by halo mass measurements, indicating that the number of GCs in a galaxy is a good tracer for its dark matter mass. Smooth accretion is also the reason for a lower average dark matter mass per GC in low-mass haloes. The resulting linear relation and its scatter are independent of redshift up to $z = 6$, as well as the average amount of smooth accretion. Finally, we successfully reproduce the observed general trend of GCs being old and the tendency of more massive haloes hosting older GC systems, while failing to obtain the younger GC populations found in some galaxies, clearly indicating the need for an additional GC formation mechanism.