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Title: How fast do black hole binaries shrink from parsec to merger?
Plain: 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: 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.
Settled by: 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.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: 1980