If the activity of active galactic nuclei ( AGNs ) is predominantly induced by major galaxy mergers , then a significant fraction of AGNs should harbor binary massive black holes in their centers .
We study the mass function of binary massive black holes in nearby AGNs based on the observed AGN black-hole mass function and theory of evolution of binary massive black holes interacting with a massive circumbinary disk in the framework of coevolution of massive black holes and their host galaxies .
The circumbinary disk is assumed to be steady , axisymmetric , geometrically thin , self-regulated , self-gravitating but non-fragmenting with a fraction of Eddington accretion rate , which is typically one tenth of Eddington value .
The timescale of orbital decay is then estimated as \sim 10 ^ { 8 } yr for equal mass black-hole , being independent of the black hole mass , semi-major axis , and viscosity parameter but dependent on the black-hole mass ratio , Eddington ratio , and mass-to-energy conversion efficiency .
This makes it possible for any binary massive black holes to merge within a Hubble time by the binary-disk interaction .
We find that ( 1.8 \pm 0.6 \% ) for the equal mass ratio and ( 1.6 \pm 0.4 \% ) for the one-tenth mass ratio of the total number of nearby AGNs have close binary massive black holes with orbital period less than ten years in their centers , detectable with on-going highly sensitive X-ray monitors such as Monitor of All-sky X-ray Image and/or Swift /Burst Alert Telescope .
Assuming that all binary massive black holes have the equal mass ratio , about 20 \% of AGNs with black hole masses of 10 ^ { 6.5 - 7 } M _ { \odot } has the close binaries and thus provides the best chance to detect them .