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During post-Newtonian evolution of a compact binary, a mass ratio differentfrom 1 provides a second small parameter, which can lead to unexpected results.We present a statistics of supermassive black hole candidates, which enables usfirst to derive their mass distribution, then to establish a logarithmicallyeven probability of the mass ratios at their encounter. In the mass ratio range(1/30,1/3) of supermassive black hole mergers representing 40% of all possiblecases, the combined effect of spin-orbit precession and gravitational radiationleads to a spin-flip of the dominant spin during the inspiral phase of themerger. This provides a mechanism for explaining a large set of observations onX-shaped radio galaxies. In another 40%, with mass ratios (1/30,1/1000) aspin-flip never occurs, while in the remaining 20% of mergers with mass ratios(1/3,1) it may occur during the plunge. We analyze the magnitude of thespin-flip angle occurring during the inspiral as function of the mass ratio andoriginal relative orientation of the spin and orbital angular momentum. We alsoderive a formula for the final spin at the end of the inspiral in this massratio range.

Supermassive black hole spin-flip during the inspiral