  We use measurements of the stellar velocity dispersion profile of the Fornax
dwarf spheroidal galaxy to derive constraints on its dark matter distribution.
Though the data are unable to distinguish between models with small cores and
those with cusps, we show that a large > 1 kpc dark matter core in Fornax is
highly implausible. Irrespective of the origin of the core, reasonable
dynamical limits on the mass of the Fornax halo constrain its core radius to be
no larger than 700 pc. We derive an upper limit core radius of 300 pc by
demanding that the central phase space density of Fornax not exceed that
directly inferred from the rotation curves of low-mass spiral galaxies.
Further, if the halo is composed of warm dark matter then phase-space
constraints force the core to be quite small in order to avoid conservative
limits from the Ly alpha forest power spectrum, implying a core radius < 85 pc.
We discuss our results in the context of the idea that the extended globular
cluster distribution in Fornax can be explained by the presence of a large 1.5
kpc core. A self-consistent core of this size would be drastically inconsistent
with the expectations of standard warm or cold dark matter models, and would
also require an unreasonably massive dark matter halo, with a maximum circular
velocity of 200 km/s.
