Using archival VLBI data for 3114 radio-luminous active galactic nuclei, we
searched for binary supermassive black holes using a radio spectral index
mapping technique which targets spatially resolved, double radio-emitting
nuclei. Only one source was detected as a double nucleus. This result is
compared with a cosmological merger rate model and interpreted in terms of (1)
implications for post-merger timescales for centralisation of the two black
holes, (2) implications for the possibility of "stalled" systems, and (3) the
relationship of radio activity in nuclei to mergers. Our analysis suggests that
the binary evolution of paired supermassive black holes (both of masses >= 1e8
Msun) spends less than 500 Myr in progression from the merging of galactic
stellar cores to within the purported stalling radius for supermassive black
hole pairs. The data show no evidence for an excess of stalled binary systems
at small separations. We see circumstantial evidence that the relative state of
radio emission between paired supermassive black holes is correlated within
orbital separations of 2.5 kpc.Comment: 11 Pages, 7 figures, accepted for publication in MNRA