The Failure of Self-Interacting Dark Matter to solve the Overabundance   of Dark Satellites and the Soft Core Question
  Self-interacting dark matter was proposed by Spergel & Steinhardt (2000) to alleviate two conflicts between Cold Dark Matter (CDM) models and observations. Firstly, CDM N-body simulations predict dark matter halo density profiles that diverge at the centre in disagreement with the constant density cores observed in late-type dwarf and Low Surface Brightness (LSB) galaxies. Secondly, N-body simulations predict an overabundance of subhalos in the Galactic halo. Using a simple semi-analytical argument we show that weakly self-interacting dark matter models, which can produce halo cores of the sizes observed in dark matter dominated galaxies, are unable to reconcile the number of satellites in the Galactic halo with the observed number of dwarf galaxies in the Local Group. 
Elena D'Onghia (1), Andreas Burkert (1) ((1)Max-Planck-Institute for   Astronomie (Heidelberg))