The spatial distribution of globular clusters in dwarf spheroidal galaxies and the timing problem

The dynamical friction time-scale of massive globular clusters (GCs) in the inner regions of cuspy dark haloes in dwarf spheroidal (dSph) galaxies can be much shorter than the Hubble time. This implies that a small fraction of the GCs is expected to be caught close to the centre of these galaxies. We compare the radial distribution of GCs predicted in simple Monte Carlo models with that of a sample of 38 spectroscopically confirmed GCs plus 17 GC candidates associated mainly with low-luminosity dSph galaxies. If dark matter haloes follow an NFW profile, the observed number of off-centre GCs at projected distances less than one-half the galaxy effective radius is significantly higher than the models predict. This timing problem can be viewed as a fine-tuning of the starting GC distances. As a result of the short sinking time-scale for GCs in the central regions, the radial distribution of GCs is expected to evolve significantly during the next 1-2 Gyr. However, dark matter haloes with cores of size comparable to the galaxy effective radii can lead to a slow orbital inspiral of GCs in the central regions of these galaxies, providing a simple solution to the timing problem. We also examine any indication of mass segregation in the summed distribution of our sample of GCs.