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We follow trajectories of recoiling supermassive black holes (SMBHs) inanalytical and numerical models of galaxy merger remnants with masses of$10^{11} \rm{M_{sun}}$ and $10^{12} \rm{M_{sun}}$. We construct various mergerremnant galaxies in order to investigate how the central SMBH mass and the massratio of progenitor galaxies influence escape velocities of recoiling SMBHs.Our results show that static analytical models of major merger remnant galaxiesoverestimate the SMBHs escape velocities. During major mergers violentrelaxation leads to the decrease of galaxy mass and lower potential at largeremnant radii. This process is not depicted in static analytical potential butclearly seen in our numerical models. Thus, the evolving numerical model is amore realistic description of dynamical processes in galaxies with mergingSMBHs. We find that SMBH escape velocities in numerical major merger remnantgalaxies can be up to 25 per cent lower compared to those in analytical models.Consequently, SMBHs in numerical models generally reach greater galactocentricdistances and spend more time on bound orbits outside of the galactic nuclei.Thus, numerical models predict a greater number of spatially-offset activegalactic nuclei (AGNs).

Recoiling supermassive black holes in analytical and numerical galaxy potential