Abstract
Uniquely among the dwarf spheroidal (dSph) satellite galaxies of the Milky Way, Fornax hosts globular clusters. It remains a puzzle as to why dynamical friction has not yet dragged any of Fornax's five globular clusters to the centre, and also why there is no evidence that any similar star cluster has been in the past (for Fornax or any other dSph). We set up a suite of 2800 N-body simulations that sample the full range of globular-cluster orbits and mass models consistent with all existing observational constraints for Fornax. In agreement with previous work, we find that if Fornax has a large dark-matter core then its globular clusters remain close to their currently observed locations for long times. Furthermore, we find previously unreported behaviour for clusters that start inside the core region. These are pushed out of the core and gain orbital energy, a process we call 'dynamical buoyancy'. Thus a cored mass distribution in Fornax will naturally lead to a shell-like globular cluster distribution near the core radius, independent of the initial conditions. By contrast, CDM-type cusped mass distributions lead to the rapid infall of at least one cluster within \Delta t = 1-2Gyr, except when picking unlikely initial conditions for the cluster orbits (\sim 2% probability), and almost all clusters within \Delta t = 10Gyr. Alternatively, if Fornax has only a weakly cusped mass distribution, dynamical friction is much reduced. While over \Delta t = 10Gyr this still leads to the infall of 1-4 clusters from their present orbits, the infall of any cluster within \Delta t = 1-2Gyr is much less likely (with probability 0-70%, depending on \Delta t and the strength of the cusp). Such a solution to the timing problem requires that in the past the globular clusters were somewhat further from Fornax than today; they most likely did not form within Fornax, but were accreted.
Highlights
The Fornax dwarf spheroidal galaxy is the most massive undisrupted dSph satellite of the Milky Way (Walker et al 2009)
(iii) For all except model large core (LC), cluster GC3 always reaches the core of Fornax within 10 Gyr, constituting the long-term timing problem
The Fornax galaxy is unique among the Milky Way dSphs in having five surviving globular clusters (GCs)
Summary
The Fornax dwarf spheroidal (dSph) galaxy is the most massive undisrupted dSph satellite of the Milky Way (Walker et al 2009). Using numerical simulations and analytic arguments Goerdt et al (2006) proposed that the current distribution of the Fornax clusters can be explained by the diminution of dynamical friction on the edge of a cored matter distribution which causes the clusters to remain outside the dark matter core radius Dynamical reasons for this ‘core-stalling’ effect have been explored in Read et al (2006b), Inoue (2009) and Cole, Dehnen & Wilkinson (2011). The Milky Way dSphs have been observed intensively in recent years, primarily because these systems are the most dark matter dominated known They contain mostly intermediate or old stellar populations which are likely to be well mixed in the dark matter potential because star formation ceased many dynamical times ago.
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