Galactic Halo Cusp/Core: Steepening by Tidal Compression

We explain in simple terms how the buildup of dark halos by merging satellites inevitably leads to an inner cusp of density profile $\rho \propto r^{-\alpha}$ with $\alpha \gsim 1$, as seen in cosmological N-body simulations. A flatter core with $\alpha <1$ exerts on each satellite tidal compression in all directions, which prevents deposit of stripped satellite material in this region. This makes the satellite orbits decay from the radius where $\alpha \sim 1$ to the halo center with no tidal mass transfer in the core and thus causes a rapid steepening of the inner profile. The transition at $\alpha \sim 1$ is addressed qualitatively in the extreme limits of impulse and adiabatic approximations and using tidal radii for satellites on radial and circular orbits. These tidal effects and the resulting steepening of the profile are then demonstrated using merger N-body simulations. In an associated paper we address the subsequent slow convergence to an asymptotic stable cusp with $\alpha \gsim 1$. Our result implies that an inner cusp is enforced as long as enough satellite material makes it intact into the inner halo and is deposited there. We conclude that in order to maintain a flat core as indicated by observations, CDM satellites must be disrupted outside the core. This could be the result of puffing up of small halos due to baryonic feedback processes, which could actually be stimulated by the same effect of tidal compression in the halo core.