Abstract
It has long been thought that nuclear star clusters (NSCs) cannot co-exist with the most massive supermassive black holes (SMBHs), since SMBH mergers - unavoidable for the most massive systems - would scatter away NSC stars. However, central concentrations of light have now been reported in up to a third of all massive ellipticals. We present a new mechanism for forming NSCs in giant elliptical galaxies, arising naturally from SMBH mergers, which could explain these observations. We call this ''black hole dragging''. After a major merger of two galaxies and their SMBHs, the newly-merged SMBH can receive a gravitational wave recoil kick. We show that recoiling SMBHs induce two competing effects on the galaxy's background stars. Firstly, some stars become bound to the SMBH and co-move with it, an effect strongest at low recoil velocities. Secondly, background stars are ejected as the recoiling SMBH falls back due to dynamical friction, an effect strongest at high recoil velocities. At intermediate recoil velocities (500-1000 km/s), both effects become important, and the density of bound stars can exceed that of the background stellar core. This yields a central dense NSC that is clearly visible in the galaxy's surface brightness profile. We show that NSCs formed in this way have realistic sizes, masses and velocity dispersions when measured similarly to observed systems. This provides a route for even giant ellipticals containing SMBHs to host an NSC. We predict such NSCs should have indistinguishable colors, ages and chemistry from non-NSC central stars, combined with low ellipticities.