The survival of globular clusters in a cuspy Fornax

It has long been argued that the radial distribution of globular clusters (GCs) in the Fornax dwarf galaxy requires its dark matter halo to have a core of size $\sim 1$ kpc. We revisit this argument by investigating analogues of Fornax formed in E-MOSAICS, a cosmological hydrodynamical simulation that self-consistently follows the formation and evolution of GCs in the 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 $M_{\rm GC}\geq4\times10^4 {~\rm M_\odot}$ to sink to the centre of their host where they are tidally disrupted. 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 survival probability of a GC increases rapidly with the radial distance at which it formed ($r_{\rm init}$): it is 37 per cent for GCs with $r_{\rm init} \leq 1$ kpc and 92 per cent for GCs with $r_{\rm init} \geq 1$ kpc. The present-day radial distribution of GCs in E-MOSAICS turns out to be indistinguishable from that in Fornax, demonstrating that, contrary to claims in the literature, the presence of five GCs in the central kiloparsec of Fornax does not exclude a cuspy DM halo.