Core creation in galaxies and haloes via sinking massive objects: application to binary nuclei

Massive objects sinking within galaxies or dark matter haloes via dynamical friction will exchange momentum with central particles, ejecting them from the cusp and reducing the density of the inner region. We explore parameter space using numerical simulations and give empirical relations for the size of the resulting core within structures that have different initial cusp slopes. We show that simple energetic arguments can be used to predict these scaling laws. As an application we consider the dwarf spheroidal galaxy VCC 128 which has a double nucleus separated by less than a hundred parsecs. If this galaxy has a surrounding cold dark matter halo with central density proportional to r then these objects should sink to the centre of the cusp and coalesce in a few million years. We show that the sinking nuclei naturally create a core equal to their current separation if the initial dark matter cusp is slightly shallower than a log slope of -0.75 at ∼ 0.1% of the virial radius. The sinking objects naturally stall at this radius for many Gyrs. This may be indirect observational evidence for central dark matter cusps shallower than r at the very centres of dark matter haloes.