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Title: Long-term evolution of supercritical black hole accretion with outflows: a subgrid feedback model for cosmological simulations
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 more » 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. « less
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The astrophysical journal
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National Science Foundation
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  1. Abstract

    It is one of the biggest issues in black hole (BH) astrophysics how to evaluate BH feedback to its environments precisely. Aiming at studying the unique gas dynamics of super-Eddington flow around supermassive black hole (SMBH) seeds at high redshift, we carried out axisymmetric two-dimensional radiation hydrodynamic simulations using a nested simulation-box method. Here we divide the simulation box into an inner zone at (2–3 × 103)rSch (with rSch being the Schwarzschild radius) and an outer zone at (2 × 103–3 × 106)rSch, with smooth connection of the physical quantities, such as gas density, velocity, and radiation energy. We start the calculation by injecting mass through the outer boundary of the inner zone at a constant rate of $\dot{M}_{\rm {inj}}=10^3L_{\rm {Edd}}/c^2$, where LEdd is the Eddington luminosity and c is the speed of light. A powerful outflow is generated in the innermost region and it propagates from the inner zone to the outer zone. The outflows are characterized by a velocity of 0.02c (0.7c) and density of 10−17 (10−19) g cm−3 for near the edge-on (face-on) direction. The outflow is gradually accelerated as it travels by accepting radiation-pressure force. The final mass outflow rate at the outermost boundary is $\dot{M}_{\rm {out}}\simmore »0.3 \times \dot{M}_{\rm {inj}}$. By extrapolating the outflow structure to a further larger scale, we find that the momentum and energy fluxes at r ∼ 0.1 pc are ∼10–100 LEdd/c and ∼0.1–10 LEdd, respectively. Moreover, we find that the impacts are highly anisotropic, in the sense that larger impacts occur towards the face-on direction than in the edge-on direction. These results indicate that the BH feedback will work more efficiently on the interstellar medium than assumed in the cosmological simulations.

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    We present two general relativistic radiation magnetohydrodynamics (GRRMHD) simulations of magnetically arrested discs (MADs) around non-spinning (a* = 0) and spinning (a* = 0.9) supermassive black holes (BHs). In each simulation, the mass accretion rate is decreased with time such that we sample Eddington-scaled rates over the range $3 \gtrsim \dot{M}/\dot{M}_{\rm {Edd}}\gtrsim 0.3$. For the non-spinning BH model, the total and radiative efficiencies increase as the accretion rate decreases, varying over the range $\eta _{\rm {tot}}\sim 9\!-\!16{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 6{-}12{{\ \rm per\ cent}}$, respectively. This model shows very little jet activity. In contrast, the spinning BH model has a strong relativistic jet powered by spin energy extracted from the BH. The jet power declines with accretion rate such that $\eta _{\rm {jet}}\sim 18{-}39{{\ \rm per\ cent}}$ while the total and radiative efficiencies are $\eta _{\rm {tot}}\sim 64{-}100{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 45{-}79{{\ \rm per\ cent}}$, respectively. We confirm that mildly sub-Eddington discs can extract substantial power from a spinning BH, provided they are in the MAD state. The jet profile out to $100\, GM/c^2$ is roughly parabolic with a power-law index of k ≈ 0.43−0.53 during the sub-Eddington evolution. Both models show significantmore »variability in the outgoing radiation which is likely associated with episodes of magnetic flux eruptions. The a* = 0.9 model shows semiregular variations with a period of $\sim 2000\, GM/c^3$ over the final $\sim 10\, 000\, GM/c^3$ of the simulation, which suggests that magnetic flux eruptions may be an important source of quasi-periodic variability. For the simulated accretion rates, the a* = 0 model is spinning up while the a* = 0.9 model is spinning down. Spinup–spindown equilibrium of the BH will likely be achieved at 0.5 < a*, eq < 0.6, assuming continuous accretion in the MAD state.

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    The early growth of black holes (BHs) in high-redshift galaxies is likely feedback regulated. While radiative feedback has been extensively studied, the role of mechanical feedback has received less scrutiny to date. Here, we use high-resolution parsec-scale hydrodynamical simulations to study jet propagation and its effect on 100 M⊙ BH accretion in the dense, low-metallicity gas expected in early protogalaxies. As the jet propagates, it shocks the surrounding gas forming a jet cocoon. The cocoon consists of a rapidly cooling cold phase at the interface with the background gas and an overpressured subsonic phase of reverse shock-heated gas filling the interior. We vary the background gas density and temperature, BH feedback efficiency, and the jet model. We found that the width of the jet cocoon roughly follows a scaling derived by assuming momentum conservation in the jet-propagation direction and energy conservation in the lateral directions. Depending on the assumed gas and jet properties, the cocoon either stays elongated to large radii or isotropizes before reaching the Bondi radius, forming a nearly spherical bubble. Lower jet velocities and higher background gas densities result in self-regulation to higher momentum fluxes and elongated cocoons. In all cases, the outward cocoon momentum flux balancesmore »the inward inflowing gas momentum flux near the Bondi radius, which ultimately regulates BH accretion. The time-averaged accretion rate always remains below the Bondi rate, and exceeds the Eddington rate only if the ambient medium is dense and cold, and/or the jet is weak (low velocity and mass loading).

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    We explore implications of a range of black hole (BH) seeding prescriptions on the formation of the brightest $z$ ≳ 6 quasars in cosmological hydrodynamic simulations. The underlying galaxy formation model is the same as in the IllustrisTNG simulations. Using constrained initial conditions, we study the growth of BHs in rare overdense regions (forming $\gtrsim 10^{12}\, {\rm M}_{\odot }\,h^{-1}$ haloes by $z$ = 7) using a  (9 Mpc h−1)3 simulated volume. BH growth is maximal within haloes that are compact and have a low tidal field. For these haloes, we consider an array of gas-based seeding prescriptions wherein $M_{\mathrm{seed}}=10^4\!-\!10^6\, {\rm M}_{\odot }\,h^{-1}$ seeds are inserted in haloes above critical thresholds for halo mass and dense, metal-poor gas mass (defined as $\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, in units of Mseed). We find that a seed model with $\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfully produces a $z$ ∼ 6 quasar with $\sim 10^9\, {\rm M}_{\odot }$ mass and ∼1047 erg s−1 luminosity. BH mergers play a crucial role at $z$ ≳ 9, causing an early boost in BH mass at a time when accretion-driven BH growth is negligible. With more stringent seeding conditions (e.g. $\tilde{M}_{\mathrm{sf,mp}}=1000$), the relative paucity of BH seeds results in a much lower merger rate. In this case, $z$more »≳ 6 quasars can only be formed if we enhance the maximum allowed BH accretion rates (by factors ≳10) compared to the accretion model used in IllustrisTNG. This can be achieved either by allowing for super-Eddington accretion, or by reducing the radiative efficiency. Our results demonstrate that progenitors of $z$ ∼ 6 quasars have distinct BH merger histories for different seeding models, which will be distinguishable with Laser Interferometer Space Antenna observations.

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    Direct collapse black holes (BHs) are promising candidates for producing massive z ≳ 6 quasars, but their formation requires fine-tuned conditions. In this work, we use cosmological zoom simulations to study systematically the impact of requiring: (1) low gas angular momentum (spin), and (2) a minimum incident Lyman–Werner (LW) flux in order to form BH seeds. We probe the formation of seeds (with initial masses of $M_{\rm seed} \sim 10^4\!-\!10^6\, \mathrm{M}_{\odot }\, h^{-1})$ in haloes with a total mass >3000 × Mseed and a dense, metal-poor gas mass >5 × Mseed. Within this framework, we find that the seed-forming haloes have a prior history of star formation and metal enrichment, but they also contain pockets of dense, metal-poor gas. When seeding is further restricted to haloes with low gas spins, the number of seeds formed is suppressed by factors of ∼6 compared to the baseline model, regardless of the seed mass. Seed formation is much more strongly impacted if the dense, metal-poor gas is required to have a critical LW flux (Jcrit). Even for Jcrit values as low as 50J21, no $8\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$ seeds are formed. While lower mass ($1.25\times 10^{4},1\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$) seeds do form, they are strongly suppressed (by factors of ∼10–100) comparedmore »to the baseline model at gas mass resolutions of $\sim 10^4~\mathrm{M}_{\odot }\, h^{-1}$ (with even stronger suppression at higher resolutions). As a result, BH merger rates are also similarly suppressed. Since early BH growth is dominated by mergers in our models, none of the seeds are able to grow to the supermassive regime ($\gtrsim 10^6~\mathrm{M}_{\odot }\, h^{-1}$) by z = 7. Our results hint that producing the bulk of the z ≳ 6 supermassive BH population may require alternate seeding scenarios that do not depend on the LW flux, early BH growth dominated by rapid or super-Eddington accretion, or a combination of these possibilities.

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