Does the Fornax dwarf spheroidal have a central cusp or core?
Abstract
The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at several hundred parsecs from its centre. In a cuspy CDM halo the globulars would sink to the centre from their current positions within half a billion years. We show that this timing problem is even more severe when interactions between the globular clusters are taken into account. Even when two globulars start at initially very similar radii (within ~100pc of each other), but quite different orientations, the globulars arrive at one certain radius at very different times (separated by ~1Gyr). We show that a solution to these timing problems 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 defined 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 with mass ~0.5keV, consistent with that required to significantly alleviate the substructure problem.Keywords
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