Scouring by supermassive black hole (SMBH) binaries is the most accepted mechanism for

the formation of the cores seen in giant elliptical galaxies. However, an additional mecha-

nism is required to explain the largest observed cores. A likely mechanism is gravitational

wave (GW) recoil, which is expected to naturally occur following SMBH mergers.

We model core formation by both scouring and recoil, performing N-body simulations

of galactic mergers of multicomponent galaxies, based on the observed parameters of

massive elliptical galaxies with cores > 0.5 kpc. After scouring is complete, the SMBHs

are merged and given a GW recoil kick of between 0.1 and 0.9 of the escape speed (v_esc ) of

the remnant galaxies. We confirm that binary scouring forms cores < 1.3 kpc in size, but

find that recoil kicks with < 0.5 v_esc are necessary to form the largest cores. Furthermore,

we find that large kicks leave a unique signature of a flat core in the 3D stellar density,

and that stars bound to the SMBH remnant after smaller kicks can be dragged back to

the centre, forming a cusp in the density profile within the flattened core. This new ‘black

hole dragging’ mechanism may explain the apparent nuclear star clusters observed at the

centres of some galaxies with large cores.

Finally, as a first step towards predicting whether GW recoil has occurred in observed

giant elliptical galaxies, we refit the surface brightness profiles of 24 galaxies with cores >

0.5 kpc using a single (core-Sérsic) model. This self-consistent dataset lays the foundation

for harnessing the presence of flat cores and/or apparent nuclear star clusters to empirically

constrain the black hole recoil velocity distribution function. This, in turn, will provide

constraints on the distribution function of black hole spin in the most massive black holes.