  Fornax is the most massive of the Milky Way dwarf spheroidal galaxies and has
five globular clusters orbiting in a dense background of dark matter.
Observational analyses suggest that globular clusters were initially much more
massive and lost most of their stars to the Fornax field. We re-investigate the
Fornax cusp-core problem, to clarify tensions between simulations and
observations concerning the dark matter halo density profile. N-body
simulations predict a centrally steep power-law density profile, while
observations of the globular clusters seem to prefer that the dark matter halo
density is constant at the center. For the first time, we ran pure N-body
simulations with entirely live systems, i.e. self-gravitating systems composed
of particles (including stars and dark matter). Only this numerical approach
accounts correctly for dynamical friction and tidal effects between Fornax and
the globular clusters. We show that a weak cusp ($r_{s}=$ 1.5 kpc) or a large
core ($r_{c}=$ 848 pc) are not compatible with the current observed positions
and masses of Fornax clusters. In contrast, a small dark matter core ($r_{c}=$
282 pc) for Fornax naturally reproduces the cluster spatial and mass
distributions over a wide range of initial globular cluster masses. We derive
an upper limit of $r_{c}\lesssim$ 282 pc. This core size range favors only warm
dark datter (WDM). It is also possible to obtain a compatible core size range
from cold dark matter (CDM) theories, if the initial halo's central cusp is
heated by gas to form a small core.
