Linking the fate of massive black hole binaries to the active galactic
  nuclei luminosity function
  Massive black hole binaries are naturally predicted in the context of the
hierarchical model of structure formation. The binaries that manage to lose
most of their angular momentum can coalesce to form a single remnant. In the
last stages of this process, the holes undergo an extremely loud phase of
gravitational wave emission, possibly detectable by current and future probes.
The theoretical effort towards obtaining a coherent physical picture of the
binary path down to coalescence is still underway. In this paper, for the first
time, we take advantage of observational studies of active galactic nuclei
evolution to constrain the efficiency of gas-driven binary decay. Under
conservative assumptions we find that gas accretion toward the nuclear black
holes can efficiently lead binaries of any mass forming at high redshift (> 2)
to coalescence within the current time. The observed "downsizing" trend of the
accreting black hole luminosity function further implies that the gas inflow is
sufficient to drive light black holes down to coalescence, even if they bind in
binaries at lower redshifts, down to z~0.5 for binaries of ~10 million solar
masses, and z~0.2 for binaries of ~1 million solar masses. This has strong
implications for the detection rates of coalescing black hole binaries of
future space-based gravitational wave experiments.
