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  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. 
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  2. 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. 
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