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In this work, we study the stellar-dynamical hardening of unequal masssupermassive black hole (SMBH) binaries in the central regions of merginggalactic nuclei. We present a comprehensive set of direct $N$-body simulationsof the problem, varying both the total mass and the mass ratio of the SMBHbinary (SMBHB). Simulations were carried out with the $\varphi-$GPU $N$-bodycode, which enabled us to fully exploit supercomputers equipped with graphicprocessing units (GPUs). As a model for the galactic nuclei, we adopted initialaxisymmetric, rotating models, aimed at reproducing the properties of agalactic nucleus emerging from a galaxy merger event, containing two SMBHswhich were unbound initially. We found no 'final-parsec problem', as our SMBHstend to pair and shrink without showing significant signs of stalling. Thisconfirms earlier results and extends them to large particle numbers androtating systems. We find that the SMBHB hardening depends on thebinary-reduced mass ratio via a single parameter function. Our results suggestthat, at a fixed value for the SMBHB primary mass, the merger time of highlyasymmetric binaries is up to four order of magnitudes smaller than theequal-mass binaries. This can significantly affect the population of SMBHspotentially detectable as gravitational wave sources.

Merging of unequal mass binary black holes in non-axisymmetric galactic nuclei