Supermassive black hole spin-flip during the inspiral
  During post-Newtonian evolution of a compact binary, a mass ratio different
from 1 provides a second small parameter, which can lead to unexpected results.
We present a statistics of supermassive black hole candidates, which enables us
first to derive their mass distribution, then to establish a logarithmically
even 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 possible
cases, the combined effect of spin-orbit precession and gravitational radiation
leads to a spin-flip of the dominant spin during the inspiral phase of the
merger. This provides a mechanism for explaining a large set of observations on
X-shaped radio galaxies. In another 40%, with mass ratios (1/30,1/1000) a
spin-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 the
spin-flip angle occurring during the inspiral as function of the mass ratio and
original relative orientation of the spin and orbital angular momentum. We also
derive a formula for the final spin at the end of the inspiral in this mass
ratio range.
