Simulating the Spatial Distribution and Kinematics of Globular Clusters within Galaxy Clusters in Illustris
We study the assembly of globular clusters (GCs) in 9 galaxy clusters using the cosmological simulation Illustris. GCs are tagged to individual galaxies at infall time and their tidal removal and distribution within the cluster is followed later self-consistently by the simulation. The method relies on the simple assumption of a single power-law relation between halo mass (M_vir) and mass in GCs (M_GC) as found in observations. We find that the GCs specific frequency $S_N$ as a function of V-band magnitude naturally reproduces the observed "U"-shape, due to the combination of a power law M_GC-M_vir relation and the non-linear M_*-M_vir relation from the simulation. Additional scatter in the $S_N$ values are traced back to galaxies with early infall times due to the evolution in the M_*-M_vir relation with redshift. GCs that have been tidally removed from their galaxies form today the intra-cluster component from which about ~60% were brought in by galaxies that orbit today within the cluster potential. The remaining "orphan" GCs are contributed by satellite galaxies with a wide range of stellar masses that are fully tidally disrupted at z=0. This intra-cluster component is a good dynamical tracer of the dark matter potential providing an estimate of the velocity dispersion of the dark matter with 25% accuracy. As a consequence of the accreted nature of most intra-cluster GCs, their orbits are fairly radial with a predicted orbital anisotropy \beta ~ 0.5. However, local tangential motions may appear as a consequence of localized substructure, providing a possible interpretation to the \beta<0 values suggested in observations of M87 or NGC 1407.