  Recent detailed observations of the radio-loud quasar 3C 186 indicate the
possibility that a supermassive recoiling black hole is moving away from the
host galaxy at a speed of nearly 2100km/s. If this is the case, we can model
the mass ratio and spins of the progenitor binary black hole using the results
of numerical relativity simulations. We find that the black holes in the
progenitor must have comparable masses with a mass ratio $q=m_1/m_2>1/4$ and
the spin of the primary black hole must be $\alpha_2=S_2/m_2^2>0.4$. The final
remnant of the merger is bounded by $\alpha_f>0.45$ and at least $4\%$ of the
total mass of the binary system is radiated into gravitational waves. We
consider four different pre-merger scenarios that further narrow those values.
Assuming, for instance, a cold accretion driven merger model, we find that the
binary had comparable masses with $q=0.70^{+0.29}_{-0.21}$ and the normalized
spins of the larger and smaller black holes were
$\alpha_2=0.94^{+0.06}_{-0.22}$ and $\alpha_1=0.95^{+0.05}_{-0.09}$. We can
also estimate the final recoiling black hole spin
$\alpha_f=0.93^{+0.02}_{-0.03}$ and that the system radiated
$9.6^{+0.8}_{-1.4}\%$ of its total mass, making the merger of those black holes
the most energetic event ever observed.
