{"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 limit?","topic_ref":"b31645054af13e29c5201707761f4cbb39ef8dced934561a5f80d1a755665bcf"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"94780311e94b80e046d44f41c38819ece486a5283d489bc557754a42b1556407","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"92b0846aeb38c684527b6b0eb8900dd32c3d8e17d994477a764325a75447451c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sjhU5FVR45LSzXJrmGMFMJPC_ZUKEYLaCBGnOZxC_frOd8ug3_Nk-z9dlvRuPU-ZwuW33m5MUw_tnHUsiA6xBg"},"schema":"pubphys.envelope/1"},"record_hash":"94780311e94b80e046d44f41c38819ece486a5283d489bc557754a42b1556407","leaf_index":533}