The typical mass ratio and typical final spin in supermassive black hole
  mergers
  We prove that merging supermassive black holes (SMBHs) typically have neither
equal masses, nor is their mass ratio too extreme. The majority of such mergers
fall into the mass ratio range of 1:30 to 1:3, implying a spin flip during the
inspiral. We also present a simple expression for the final spin $\chi_{f}$ of
the emerging SMBH, as function of the mass ratio, initial spin magnitudes, and
orientation of the spins with respect to the orbital plane and each other. This
formula approximates well more cumbersome expressions obtained from the fit
with numerical simulations. By integrating over all equally likely orientations
for precessing mergers we determine a lower approximant to the final spin
distribution as function of the mass ratio alone. By folding this with the
derived mass ratio dependent merger rate we derive a lower bound to the typical
final spin value after mergers. We repeat the procedure deriving an upper bound
for the typical spin in the case when the spins are aligned to the orbital
angular momentum, such that there is no precession in the system. Both slopes
of $\chi_{f}$ as function of the initial spins being smaller than one lead to
two attractors at $\chi_{f}^{prec}=0.2$ and $\chi_{f}^{align}=0.45$,
respectively. Real mergers, biased toward partial alignment by interactions
with the environment (accretion, host galaxy, etc.) would generate a typical
final spin lying between these two limiting values. These are the typical
values of the spin after the merger, starting from which the spin can built up
by further gaseous accretion.
