Globular clusters as tracers of the host galaxy mass distribution: the
  Fornax dSph test case
  The Fornax dwarf spheroidal galaxy is the most massive satellites of the
Milky Way, claimed to be embedded in a huge dark matter halo, and the only
among the Milky Way satellites hosting five globular clusters. Interestingly,
their estimated masses, ages and positions seem hardly compatible with the
presence of a significant dark matter component, as expected in the $\Lambda$
CDM scheme. Indeed, if Fornax would have a CDM halo with a standard density
profile, all its globular clusters should have sunk to the galactic centre many
Gyr ago due to dynamical friction. Due to this, some authors proposed that the
most massive clusters may have formed out of Fornax and later tidally captured.
In this paper we investigate the past evolution of the Fornax GC system by
using both a recently developed, semi-analytical treatment of dynamical
friction and direct $N$-body simulations of the orbital evolution of the
globular clusters within Fornax and of Fornax galaxy around the Milky Way. Our
results suggest that an "in-situ" origin for all the clusters is likely if
their observed positions are close to their spatial ones and their orbits are
almost circular. Moreover, the Milky Way seems to accelerate the GC decay
reducing the decay time of $15\%$. Nevertheless, our results indicate that the
GCs survival probability exceeds $50\%$, even in the case of cuspy density
profiles. We conclude that more detailed data are required to shed light on the
Fornax dark matter content, to distinguish between a cuspy or a cored profile.
