Does the Fornax dwarf spheroidal have a central cusp or core?

Goerdt, Tobias ; Moore, Ben ; Read, J. I. ; Stadel, Joachim ; Zemp, Marcel

In: Monthly Notices of the Royal Astronomical Society, 2006, vol. 368, no. 3, p. 1073-1077

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    The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ∼1 kpc from its centre. In a cuspy cold dark matter halo the globulars would sink to the centre from their current positions within a few Gyr, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ∼0.5 keV, consistent with that required to significantly alleviate the substructure problem