The survival of globular clusters in a cuspy Fornax

It has long been argued that the globular clusters (GCs) in the Fornax dwarf galaxy indicate that its dark matter halo is likely to have a shallow density profile with a core of size ~1 kpc. We revisit this argument by investigating analogues of Fornax formed in MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE (E-MOSAICS), a cosmological hydrodynamical simulation that follows the formation and evolution of GCs in the Evolution and Assembly of GaLaxies and their Environments (EAGLE) galaxy formation model. In EAGLE, Fornax-mass haloes are cuspy and well described by the Navarro-Frenk-White profile. We post-process the E-MOSAICS to account for GC orbital decay by dynamical friction, which is not included in the original model. Dynamical friction causes 33 per cent of GCs with masses $M_{\rm GC}\ge 4\times 10^4{~\rm M_\odot }$ to sink to the centre of their host with the majority being tidally disrupted before forming a nuclear star cluster. Fornax has a total of five GCs, an exceptionally large number compared to other galaxies of similar stellar mass. In the simulations, we find that only 3 per cent of the Fornax analogues have five or more GCs, while 30 per cent have only one and 35 per cent have none. We find that GC systems in satellites are more centrally concentrated than in field dwarfs, and that those formed in situ (45 per cent) are more concentrated than those that were accreted. The present-day radial distribution of GCs in E-MOSAICS Fornax analogues is indistinguishable from that in Fornax, demonstrating that the presence of five GCs in the central kiloparsec of Fornax is consistent with a cuspy dark matter halo.