{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5b6b322d0e40ccdb1775f3e62927212ffcae9bccfddd5e176f64817e953a2d99","created":"2026-10-03T07:17:55Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ba9f9b2b81daeb93b69efc901f5acafa74cdb99152eae8d1ccfbb84abdf2048b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"astro.smbh-binaries.final-parsec","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"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.","posed_since":"1980","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.","problem_ref":null,"references":"","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.","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.","title":"How fast do black hole binaries shrink from parsec to 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