How fast do black hole binaries shrink from parsec to merger?
In plain words
Two black holes in a merged galaxy sink toward each other by flinging out nearby stars, but they may run out of stars to fling at a separation of about a parsec, too wide for gravitational waves to finish the job. How quickly real binaries cross this gap is unknown.
Precise statement
For a bound binary of total mass $10^{8}-10^{10} M_{\mathrm{sun}}$ at the hardening radius $a_h \sim 1-10\,\mathrm{pc}$ in a galaxy merger remnant, compute the time from $a_h$ to the gravitational-wave-dominated regime ($a \sim 10^{-2}-10^{-3}\,\mathrm{pc}$), including loss-cone refilling in triaxial or rotating stellar potentials, circumbinary gas and triple-black-hole interactions. The answer is the distribution of coalescence times, in particular the fraction of binaries that merge within 1 Gyr and within a Hubble time.
What would settle it
N-body and hydrodynamic simulations of merger remnants run from galaxy scales to coalescence with realistic stellar and gas content, checked against the measured low-frequency gravitational-wave spectrum.
Status in the literature
N-body work from 2006 to 2017 showed that triaxial or rotating merger remnants refill the loss cone, so binaries need not stall; the realistic coalescence-time distribution remains uncertain.