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Supermassive stars with masses of M* ≃ 104–105 M⊙ are invoked as possible seeds of high-redshift supermassive black holes, but it remains under debate whether their protostar indeed acquires sufficient mass via gas accretion overcoming radiative feedback. We investigate protostellar growth in dynamically heated atomic cooling haloes (ACHs) found in recent cosmological simulations, performing three-dimensional radiation hydrodynamical simulations that consider stellar evolution under variable mass accretion. We find that one of the ACHs feeds the central protostar at rates exceeding a critical value, above which the star evolves in a cool bloating phase and hardly produces ionizing photons. Consequently, the stellar mass reaches M* ≳ 104 M⊙ unimpeded by radiative feedback. In the other ACH, where the mass supply rate is lower, the star evolves almost as a hot main-sequence star, emitting intense ionizing radiation. Then, the stellar mass growth is terminated around 500 M⊙ by photoevaporation of the circumstellar disc. Our simulations provide a formula of the final stellar mass determined either by stellar feedback or their lifetime as a function of the mass supply rate from the parent cloud. Combining the results with the statistical properties of star-forming clouds in high-redshift quasar progenitor haloes, we construct a top-heavy mass distribution of primordial stars over M* ≃ 100–105 M⊙, approximately following a power-law spectrum of ${\propto} M_\ast ^{-1.3}$. Their black hole remnants would be further fed via the dense debris disc, powering ‘milliquasars’ with a bolometric luminosity of Lbol ≳ 1043 erg s−1.

 

Supermassive stars (SMSs) with masses of 𝑀∗ ≃ 104–105 M⊙ are invoked as possible seeds of high-redshift supermassive black holes, but it remains under debate whether their protostar indeed acquires sufficient mass via gas accretion overcoming radiative feedback. We investigate protostellar growth in dynamically heated atomic-cooling haloes (ACHs) found in recent cosmological simulations, performing three-dimensional radiation hydrodynamical (RHD) simulations that consider stellar evolution under variable mass accretion. We find that one of the ACHs feeds the central protostar at rates exceeding a critical value, above which the star evolves in a cool bloating phase and hardly produces ionizing photons. Consequently, the stellar mass reaches 𝑀∗ 􏰁 104 M⊙ unimpeded by radiative feedback. In the other ACH, where the mass supply rate is lower, the star spends most of its life as a hot main-sequence star, emitting intense ionizing radiation. Then, the stellar mass growth is terminated around 500 M⊙ by photoevaporation of the circumstellar disk. A series of our RHD simulations provide a formula of the final stellar mass determined either by stellar feedback or their lifetime as a function of the mass supply rate from the parent cloud in the absence of stellar radiation. Combining the results with the statistical properties of SMS-forming clouds in high-redshift quasar progenitor haloes, we construct a top-heavy mass distribution of primordial stars over 𝑀∗ ≃ 100–105 M⊙, approximately following a power-law spectrum of ∝ 𝑀−1.3 with a steeper decline at 𝑀 􏰁 2 × 104 M . Their massive BH remnants would be ∗∗⊙ further fed via the dense debris disk, powering “milli-quasars" with a bolometric luminosity of 𝐿bol 􏰁 1043 erg s−1. 

Observations of the most luminous quasars at high redshifts (z > 6) have revealed that the largest supermassive black holes (SMBHs) at those epochs tend to be substantially overmassive relative to their host galaxies compared to the local relations, suggesting they experienced rapid early growth phases. We propose an assembly model for the SMBHs that end up in rare massive ∼ 1012 M⊙ host halos at z ∼ 6−7, applying a kinetic feedback prescription for BHs accreting above the Eddington rate, provided by radiation hydrodynamic simulations for the long-term evolution of the accretion-flow structure. The large inflow rates into these halos during their assembly enable the formation of > 109 M⊙ SMBHs by z ∼ 6, even starting from stellar-mass seeds at z ∼ 30, and even in the presence of outflows that reduce the BH feeding rate, especially at early times. This mechanism also naturally yields a high BH-to-galaxy mass ratio of > 0.01 before the SMBH mass reaches MBH > 109 M⊙ by z ∼ 6. These fast-growing SMBH progenitors are bright enough to be detected by upcoming observations with the James Webb Space Telescope over a wide range of redshift (7 < z < 15), regardless of how they were seeded. 

We study the long-term evolution of the global structure of axisymmetric accretion flows onto a black hole (BH) at rates substantially higher than the Eddington value (Mdot,Edd)performing two-dimensional hydrodynamical simulations with and without radiative diffusion. In the high-accretion optically-thick limit, where the radiation energy is efficiently trapped within the inflow, the accretion flow becomes adiabatic and comprises of turbulent gas in the equatorial region and strong bipolar outflows. As a result, the mass inflow rate decreases toward the center as Mdot,in∝r_p with p∼0.5−0.7 and a small fraction of the inflowing gas feeds the nuclear BH. Thus, super-Eddington accretion is sustained only when a larger amount of gas is supplied from larger radii at >100−1000 Mdot, Edd. The global structure of the flow settles down to a quasi-steady state in millions of the orbital timescale at the BH event horizon, which is >10−100 times longer than that addressed in previous (magneto-)RHD simulation studies. Energy transport via radiative diffusion accelerates the outflow near the poles in the inner region but does not change the overall properties of the accretion flow compared to the cases without diffusion. Based on our simulation results, we provide a mechanical feedback model for super-Eddington accreting BHs. This can be applied as a sub-grid model in large-scale cosmological simulations that do not sufficiently resolve galactic nuclei, and to the formation of the heaviest gravitational-wave sources via accretion in dense environments. 

The detection of starlight from the host galaxies of quasars during the reionization epoch (z > 6) has been elusive, even with deep HST observations1,2. The current highest redshift quasar host detected3, at z = 4.5, required the magnifying effect of a foreground lensing galaxy. Low-luminosity quasars4,5,6 from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP)7 mitigate the challenge of detecting their underlying, previously-undetected host galaxies. Here we report rest-frame optical images and spectroscopy of two HSC-SSP quasars at z > 6 with JWST. Using NIRCam imaging at 3.6μm and 1.5μm and subtracting the light from the unresolved quasars, we find that the host galaxies are massive (stellar masses of 13 × and 3.4 × 1010 M⊙, respectively), compact, and disk-like. NIRSpec medium-resolution spectroscopy shows stellar absorption lines in the more massive quasar, confirming the detection of the host. Velocity-broadened gas in the vicinity of these quasars enables measurements of their black hole masses (1.4 × 109 and 2.0 × 108 M⊙, respectively). Their location in the black hole mass - stellar mass plane is consistent with the distribution at low redshift, suggesting that the relation between black holes and their host galaxies was already in place less than a billion years after the Big Bang. 

ABSTRACT Recent three-dimensional cosmological simulations of protogalaxy formation have suggested that supermassive stars (SMSs) can form in gas clouds in which H2 cooling is suppressed by dynamical heating prior to the activation of atomic cooling, but they stopped short of the following growth of a central protostar. Here, we examine whether accretion on the protostellar core in this cloud is sufficiently rapid, in the face of the radiation feedback, to produce an SMS. We perform one-dimensional radiation-hydrodynamical simulations of the hot collapsing cloud with non-equilibrium chemical reactions directly adopting the cloud properties from Wise et al. as an initial condition. We find that the stellar Lyman–Werner (LW) radiation from the SMS dissociates H2 in the inner regions of the gas flow, increasing gas temperature and thermal pressure, and temporarily stopping the accretion. However, this negative feedback ceases when the self-gravity and inward ram pressure force on larger scales push the gas inwards. The central protostar is unable to expand an H ii region due to the high density, and grows to a mass of ${\gtrsim}10^5\, {\rm M}_{\odot }$. Our results suggests the successful formation of SMSs, and resulting massive (${\sim}10^5\, {\rm M}_{\odot }$) remnant black holes in the clouds, but need to be confirmed in two- or three-dimensional simulations. 

The existence of ∼10 9 M ⊙ supermassive black holes (SMBHs) within the first billion years of the Universe has stimulated numerous ideas for the prompt formation and rapid growth of black holes (BHs) in the early Universe. Here, we review ways in which the seeds of massive BHs may have first assembled, how they may have subsequently grown as massive as ∼10 9 M ⊙ , and how multimessenger observations could distinguish between different SMBH assembly scenarios. We conclude the following: ▪  The ultrarare ∼10 9 M ⊙ SMBHs represent only the tip of the iceberg. Early BHs likely fill a continuum from the stellar-mass (∼10M ⊙ ) to the supermassive (∼10 9 ) regimes, reflecting a range of initial masses and growth histories. ▪  Stellar-mass BHs were likely left behind by the first generation of stars at redshifts as high as ∼30, but their initial growth typically was stunted due to the shallow potential wells of their host galaxies. ▪  Conditions in some larger, metal-poor galaxies soon became conducive to the rapid formation and growth of massive seed holes, via gas accretion and by mergers in dense stellar clusters. ▪  BH masses depend on the environment (such as the number and properties of nearby radiation sources and the local baryonic streaming velocity) and on the metal enrichment and assembly history of the host galaxy. ▪  Distinguishing between assembly mechanisms will be difficult, but a combination of observations by the Laser Interferometer Space Antenna (probing massive BH growth via mergers) and by deep multiwavelength electromagnetic observations (probing growth via gas accretion) is particularly promising.