{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"79cbd839dbe5fb3bf1d152412b9a7c72d732621e710c46cba8c7215567246c4d","created":"2026-10-03T07:17:55Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"699486a873c1145e301cdedb13ccf1500775560dfca8b50fb7d9ad621be26899","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"astro.first-smbh.super-eddington-growth","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"A black hole normally cannot swallow gas faster than a limit set by the outward push of the light the infalling gas emits (the Eddington limit). Growing a billion-solar-mass black hole within 700 million years from a small seed seems to need this limit to be exceeded for a long time.","posed_since":"","precise":"Determine whether seeds of $10^{2}-10^{5}\\,M_{\\mathrm{sun}}$ formed at $z \\sim 20-30$ can sustain a duty-cycle-averaged Eddington ratio $\\mathrm{mdot}/\\mathrm{mdot}_{\\mathrm{Edd}} \\ge 1$, with $\\mathrm{mdot}_{\\mathrm{Edd}} = L_{\\mathrm{Edd}}/(\\eta c^2)$, $L_{\\mathrm{Edd}} = 4 \\pi G M m_p c / \\sigma_T = 1.26x10^{38} (M/M_{\\mathrm{sun}})\\,\\mathrm{erg/s}$ and $\\eta$ the radiative efficiency, over the $\\sim 5x10^{8}\\,\\mathrm{yr}$ available before $z \\sim 7.5$ (e-folding time $\\sim 4.5x10^{7} (\\eta/0.1)\\,\\mathrm{yr}$), or must grow through super-Eddington episodes, despite radiative feedback, angular-momentum barriers and supernova-driven gas removal. The answer is yes or no with the required duty cycle, Eddington ratio and $\\eta$, or the Eddington-ratio distribution that reproduces the $z > 6$ black hole mass function.","problem_ref":null,"references":"","settled_by":"Radiation-hydrodynamic simulations resolving scales from inside the Bondi radius to the host galaxy, checked against measured Eddington-ratio distributions of $z > 6$ AGN.","status_note":"","title":"Can early black holes sustain accretion above the Eddington 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