Supermassive black hole spin-flip during the inspiral

During post-Newtonian evolution of a compact binary, a mass ratio ν 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, and then to establish a logarithmically even probability in ν of the mass ratios at their encounter. In the mass ratio range ν in (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 ν in (1/30, 1/1000) a spin-flip never occurs, while in the remaining 20% of mergers with mass ratios ν in (1/3, 1) it may occur during the plunge. We analyze the magnitude of the spin-flip angle occurring during the inspiral as a 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.