The importance of tides for the Local Group dwarf spheroidals

There are two main tidal effects that 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 ∼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 ∼1 kpc. This argues for tidal stripping being unimportant interior to ∼1 kpc for most of the Local Group dSphs observed so far. We show that tidal shocking may still be important, however, even when tidal stripping is not. This could explain the observed correlation for the Local Group dSphs between central surface brightness and distance from the nearest large galaxy. These results have important implications for the formation of the dSphs and for cosmology. As a result of the existence of cold stars at large radii in several dSphs, 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 haloes around the Milky Way to form stars. It is possible for dSphs to reside within these haloes (∼10 10 M� ) 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. A central density cusp persists even after unrealistically extreme tidal shocking and leads to central velocity dispersions which are too high to be consistent with data from the Local Group dSphs. dSphs can reside within cuspy dark matter haloes if their haloes are less massive (∼10 9 M� ) and therefore have smaller