Super-Eddington Growth Ceiling: Analytic Constraints on the Rapid Growth of Light-Seed Black Holes in Massive Clumps

Abstract

The existence of $\sim 10^{7-8}{\mathrm{M}}_{\odot }$ supermassive black holes at $z\gtrsim 8$ challenges conventional growth channels. One attractive possibility is that light seeds ($M_{\mathrm{BH}}\lesssim 10^3{\mathrm{M}}_{\odot }$) undergo short, super-Eddington episodes when they cross, and are captured by, dense massive gas clumps. We revisit this ``BH-clump-capture'' model using analytic arguments supported by toy-model simulations that follow Bondi-scale inflow, radiative feedback, gas dynamical friction and the recently discovered forward acceleration effect caused by the ionised bubble. For substantial growth the black hole must remain trapped for many dynamical times, which imposes three simultaneous constraints. The clump must be heavier than the black hole (mass doubling condition); its cooling time must exceed the super-Eddington growth time (lifetime condition); and dynamical friction must dominate shell acceleration (BH-trapping condition). These requirements confine viable clumps to a narrow density-temperature region, $n_{\mathrm{H}}\simeq 10^{7-8}{\mathrm{cm}}^{-3}$ and $T\simeq (2-6)\times 10^3\mathrm{K}$, for a $10^3{\mathrm{M}}_{\odot }$ seed. Even inside this sweet spot a $10^3{\mathrm{M}}_{\odot }$ seed grow up at most $4\times 10^3{\mathrm{M}}_{\odot }$; the maximum growth ratio $M_{\mathrm{BH},\mathrm{fin}}/M_{\mathrm{BH}}$ falls approximately as $M_{\mathrm{BH}}^{-0.4}$ and is negligible once $M_{\mathrm{BH}}\gtrsim 10^4{\mathrm{M}}_{\odot }$. The forward-acceleration effect is essential, expelling the black hole whenever photon trapping fails. We conclude that BH-clump-capture model, and potentially broad super-Eddington models, cannot produce the $>10^4{\mathrm{M}}_{\odot }$ seeds required for subsequent Eddington-limited growth, suggesting that alternative pathways, such as heavy seed formation, remain necessary.

arXiv comment17 pages, 7 figures, submitted to MNRAS

References in corpus (80)

• Theory of Star Formation
• A luminous quasar at a redshift of z = 7.085
• On the Fate of Gas Accreting at a Low Rate onto a Black Hole
• An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5
• The Assembly and Merging History of Supermassive Black Holes in Hierarchical Models of Galaxy Formation
• Formation of the First Supermassive Black Holes
• Black Holes, Galaxy Formation, and the M_BH-sigma Relation
• The runaway growth of intermediate-mass black holes in dense star clusters
• The Assembly of the First Massive Black Holes
• Analytical theory for the initial mass function: CO clumps and prestellar cores
• The Birth of a Galaxy: Primordial Metal Enrichment and Stellar Populations
• A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey IV: Discovery of Seven Additional Quasars
• A Luminous Quasar at Redshift 7.642
• Super-critical Accretion Flows around Black Holes: Two-dimensional, Radiation-pressure-dominated Disks with Photon-trapping
• A CEERS Discovery of an Accreting Supermassive Black Hole 570 Myr after the Big Bang: Identifying a Progenitor of Massive z > 6 Quasars
• Rapid growth of high redshift black holes
• Primordial Star Formation under the Influence of Far Ultraviolet Radiation: 1540 Cosmological Halos and the Stellar Mass Distribution
• Formation of the first nuclear clusters and massive black holes at high redshift
• Supermassive Black Hole Formation by Direct Collapse: Keeping Protogalactic Gas H_2--Free in Dark Matter Halos with Virial Temperatures T_vir >~ 10^4 K
• Formation of Primordial Supermassive Stars by Rapid Mass Accretion
• Primordial Star Formation under Far-ultraviolet radiation
• The Assembly of Supermassive Black Holes at High Redshifts
• What is the Highest Plausible Redshift of Luminous Quasars?
• Fluctuations in the High-Redshift Lyman-Werner Background: Close Halo Pairs as the Origin of Supermassive Black Holes
• Can Supermassive Black Holes Form in Metal-Enriched High-Redshift Protogalaxies ?
• Super-Eddington Accretion Disks around Supermassive black Holes
• Hyper-Eddington accretion flows onto massive black holes
• Formation of massive black holes in rapidly growing pre-galactic gas clouds
• Three-dimensional simulations of super-critical black hole accretion disks --- luminosities, photon trapping and variability
• The case for super-critical accretion onto massive black holes at high redshift
• Rapid growth of seed black holes in the early universe by supra-exponential accretion
• Accretion onto Seed Black Holes in the First Galaxies
• Feedback-regulated Super Massive Black Hole Seed Formation
• Resolving the Formation of Protogalaxies. I. Virialization
• Slim disks around Kerr black holes revisited
• The critical radiation intensity for direct collapse black hole formation: dependence on the radiation spectral shape
• Constraining the high redshift formation of black hole seeds in nuclear star clusters with gas inflows
• Accretion onto Intermediate Mass Black Holes Regulated by Radiative Feedback I. Parametric Study for Spherically Symmetric Accretion
• Accretion onto Intermediate-Mass Black Holes in Dense Protogalactic Clouds
• Connecting the first galaxies with ultra faint dwarfs in the Local Group: chemical signatures of Population~III stars
• The erratic dynamical life of black hole seeds in high-redshift galaxies
• Growing massive black holes through super-critical accretion of stellar-mass seeds
• The First Galaxies: Assembly with Black Hole Feedback
• Formation of Intermediate-Mass Black Holes through Runaway Collisions in the First Star Clusters
• Accretion onto Black Holes from Large Scales Regulated by Radiative Feedback. II. Growth Rate and Duty Cycle
• Formation of the Black Holes in the Highest Redshift Quasars
• Formation of an embryonic supermassive star in the first galaxy
• The Growth of Black Holes from Population III Remnants in the Renaissance Simulations
• The Growth Efficiency of High-Redshift Black Holes
• Supermassive black hole formation by the cold accretion shocks in the first galaxies
• Turbulent Cold Flows Gave Birth to the First Quasars
• Cosmological Simulations of Early Blackhole Formation: Halo Mergers, Tidal Disruption, and the Conditions for Direct Collapse
• Supermassive Star Formation via Super Competitive Accretion in Slightly Metal-enriched Clouds
• Collisions in Primordial Star Clusters: Formation Pathway for intermediate mass black holes
• Energy flows in thick accretion disks and their consequences for black hole feedback
• Accretion onto Black Holes from Large Scales Regulated by Radiative Feedback. III. Enhanced Luminosity of Intermediate Mass Black Holes Moving at Supersonic Speeds
• Seeds Don't Sink: Even Massive Black Hole "Seeds" Cannot Migrate to Galaxy Centers Efficiently
• How the super-Eddington regime regulates black hole growth in high-redshift galaxies
• Forming massive seed black holes in high-redshift quasar host progenitors
• Fluctuations in the High-Redshift Lyman-Werner and Lyman-alpha Radiation Backgrounds
• Rapid growth of seed black holes during early bulge formation
• Sustained super-Eddington accretion in high-redshift quasars
• Intermediate-mass black holes from Population III remnants in the first galactic nuclei
• Growth of intermediate mass black holes by tidal disruption events in the first star clusters
• Long-term evolution of supercritical black hole accretion with outflows: a subgrid feedback model for cosmological simulations
• Gaseous dynamical friction under radiative feedback: do intermediate-mass black holes speed up or down?
• Super-critical accretion of medium-weight seed black holes in gaseous proto-galactic nuclei
• Stellar collisions in flattened and rotating Pop. III star clusters
• Global instability by runaway collisions in nuclear stellar clusters: Numerical tests of a route for massive black hole formation
• The effects of a background potential in star cluster evolution: a delay in the relaxation time-scale and runaway collision processes
• Evolution of high-redshift quasar hosts and promotion of massive black hole seed formation
• Structure and Instability of the Ionization Fronts around Moving Black Holes
• Hyper-Eddington Black Hole Growth in Star-Forming Molecular Clouds and Galactic Nuclei: Can It Happen?
• Direct-collapse black hole formation induced by internal radiation of host halos
• From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairing in Dense Proto-Bulge Environments
• Efficiency of black hole formation via collisions in stellar systems: An analysis of data from simulations and observations
• First emergence of cold accretion and supermassive star formation in the early universe
• Three-dimensional radiation hydrodynamics simulations of wandering intermediate-mass black holes considering the anisotropic radiation and dust sublimation
• Hungry or Not: How Stellar-Mass Black Holes Grow (or Don't) in Dark Matter Mini-Haloes at High-Resolution
• Long timescale numerical simulations of large, super-critical accretion discs