The importance of tides for the Local Group dwarf spheroidals
  There are two main tidal effects which can act on the Local Group dwarf spheroidals (dSphs): tidal stripping and tidal shocking. Using N-body simulations, we show that tidal stripping always leads to flat or rising projected velocity dispersions beyond a critical radius; it is $\sim 5$ times more likely, when averaging over all possible projection angles, that the cylindrically averaged projected dispersion will rise, rather than be flat. In contrast, the Local Group dSphs, as a class, show flat or falling projected velocity dispersions interior to $\sim 1$ kpc. This argues for tidal stripping being unimportant interior to $\sim 1$ kpc for most of the Local Group dSphs observed so far.   These results have important implications for the formation of the dSphs and for cosmology. A tidal origin for the formation of these Local Group dSphs (in which they contain no dark matter) is strongly disfavoured. In the cosmological context, a naive solution to the missing satellites problem is to allow only the most massive substructure dark matter halos around the Milky Way to form stars. It is possible for dSphs to reside within these halos ($\sim 10^{10}$M$_\odot$) and have their velocity dispersions lowered through the action of tidal shocks, but only if they have a central density core in their dark matter, rather than a cusp. dSphs can reside within cuspy dark matter halos if their halos are less massive ($\sim 10^{9}$M$_\odot$) and therefore have smaller central velocity dispersions initially (abridged). 
J. I. Read, M. I. Wilkinson, N. Wyn Evans, G. Gilmore & Jan T. Kleyna