Galactic Halo Cusp versus Core: Tidal Effects in Mergers

We show how the buildup of halos by merging satellites forces an inner cusp, with a density profile \rho \propto r^{-\alpha} where \alpha \to \alpha_a \gsim 1$. Our analysis is based on a new prescription for tidal stripping as a function of \alpha(r), using a simple toy model which matches N-body simulations. In a core of \alpha < 1 there is tidal compression rather than stripping and the satellites sink towards the halo center, causing a rapid steepening of the profile to \alpha > 1. Where \alpha > 1, the stripping of each satellite shell is preceded by gradual puffing up, which makes the stripping more efficient at larger \alpha, causing flattening where \alpha is large enough. Therefore, we can show using linear perturbation analysis that a sequence of mergers slowly leads to a fixed point \alpha(r)=\alpha_a. This result implies that a cusp is enforced as long as enough satellite material makes it into the inner halo and is deposited there. We conclude that in order to maintain a flat core, as indicated by observations, satellites must be disrupted outside the core, e.g., because of puffing up due to baryonic feedback effects.