Does the Fornax dwarf spheroidal have a central cusp or core

ABSTRACT The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbitingat ∼ 1kpc from its centre. In a cuspy CDM halo the globulars would sink to thecentre from their current positions within a few Gyrs, presenting a puzzle as to whythey survive undigested at the present epoch. We show that a solution to this timingproblem is to adopt a cored dark matter halo. We use numerical simulations andanalytic calculations to show that, under these conditions, the sinking time becomesmany Hubble times; the globulars effectively stall at the dark matter core radius. Weconclude that the Fornax dwarf spheroidal has a shallow inner density profile with acore radius constrained by the observed positions of its globular clusters. If the phasespace density of the core is primordial then it implies a warm dark matter particleand gives an upper limit to its mass of ∼ 0.5keV, consistent with that required tosignificantly alleviate the substructure problem.Keywords: galaxies:starclusters — galaxies:dwarfs— galaxies:individual (Fornax)methods: N-body simulations