# Early growth of typical high redshift black holes seeded by direct collapse

Muhammad A. Latif, Marta Volonteri, John H. Wise

► To cite this version:

Muhammad A. Latif, Marta Volonteri, John H. Wise. Early growth of typical high redshift black holes seeded by direct collapse. Monthly Notices of the Royal Astronomical Society, 2018, 476 (4), pp.5016-5025. 10.1093/mnras/sty622. hal-01703553

HAL Id: hal-01703553

https://hal.science/hal-01703553v1

Submitted on 9 Jan 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Early growth of typical high-redshift black holes seeded by direct collapse

Muhammad A. Latif,<fnref n="1" />,<fnref n="2" />* Marta Volonteri<fnref n="2" /> and John H. Wise<fnref n="3" />

Accepted 2018 March 3. Received 2018 February 26; in original form 2018 January 23

## ABSTRACT

Understanding the growth of high-redshift massive black holes (MBHs) is a problem of great astrophysical interest. The most luminous quasars at $z > 6$ are frequently observed but they represent only the tip of the iceberg as the majority of the low-luminosity active galactic nuclei (AGN) population remains undetected. In this study, we perform a radiation hydrodynamics cosmological simulation to study the growth of ‘normal’ black holes in the high-redshift universe. In our simulation, we model the formation of Pop III and Pop II stars along with their chemical, mechanical, and radiative feedback. We consider both UV and X-ray emission from an accreting BH to simulate its radiative feedback. The selected halo has a mass of $3 \times 10^{10} M_{\odot}$ at $z = 7.5$ and we turn on radiative feedback from a MBH seed of $10^5 M_{\odot}$ along with *in situ* star formation at $z = 12$ when the halo mass reaches well above the atomic cooling limit. We find that the MBH accretes only about $2200 M_{\odot}$ during 320 Myr and the average mass accretion on to the MBH is a few times $10^{-6} M_{\odot} \text{yr}^{-1}$. Our results suggest that the stunted growth of MBH is a consequence of supernovae in tandem with MBH feedback which drive large outflows and evacuate the gas from MBH vicinity. This may explain why a population of low-luminosity AGN has not been detected so-far at $z > 6$; the large contrast between the star formation rate and the MBH accretion rate may make then hard to detect even in upcoming deep surveys.

**Key words:** black hole physics – methods: numerical – galaxies: formation – early Universe – cosmology: theory.

## 1 INTRODUCTION

Supermassive black holes (SMBHs) of millions to billions of solar masses are common at the centres of present-day galaxies and may have co-evolved with their hosts (see Kormendy & Ho 2013 and references therein). On the other hand, high-redshift surveys have detected dozens of quasars at $z \ge 6$ powered by the accretion on to SMBHs of a few billion solar masses within the first Gyr after the big bang (Fan et al. 2003; Willott et al. 2007; Jiang et al. 2009; Mortlock et al. 2011; Bañados et al. 2014; Venemans et al. 2015; Wu et al. 2015; Bañados et al. 2017). These quasars represent the tip of the iceberg as many low-luminosity active galactic nuclei (AGN) may have gone undetected in present surveys due to current observational constraints. Therefore, the population and growth of BHs remain elusive at earlier cosmic epochs. Understanding their formation and growth mechanisms are questions of a prime astrophysical interest.

Seeds of SMBHs may have formed at high redshift and evolved via accretion or merging to reach a billion solar masses for the most extreme cases. The main pathways for SMBH formation are

a collapse of a massive star, run-away collisions in stellar clusters and a direct collapse of gas cloud into a massive BH, see a recent review on this topic by Latif & Ferrara (2016). The mass of seed BH depends on the formation channel and varies from 10 to $10^5 M_{\odot}$ (Volonteri 2010; Haiman 2013). Large-scale cosmological simulations exploring the growth of BHs commonly employ thermal feedback without proper radiation transfer calculations and use Bondi prescription with a resolution of about a kpc (Booth & Schaye 2009; Sijacki et al. 2015; Di Matteo et al. 2017) except Dubois et al. (2012) with a resolution of about 10 pc. They may overestimate the mass accretion on to a MBH by not resolving the Bondi radius (Gaspari, Ruszkowski & Oh 2013; Johnson & Haardt 2016; Gaspari & Sadowski 2017; Negri & Volonteri 2017). Numerical experiments exploring the growth of a stellar mass BH including a detailed treatment for its feedback show that gas in the surrounding gets photoevaporated and leads to its stunted growth shortly after its formation (Johnson & Bromm 2007; Alvarez, Wise & Abel 2009; Milosavljević et al. 2009; Park & Ricotti 2011). Similarly, Jeon et al. (2012) and Jeon et al. (2014) found that BH feedback strongly suppresses its growth in minihaloes and also influences the star formation in the host galaxies. These studies either employed idealized initial conditions or focused on the growth of low-mass BHs

<footnote n="1">¹Department of Physics, COMSATS Institute of Information Technology, Park Road, 44000 Islamabad, Pakistan</footnote>

<footnote n="2">²Institut d'Astrophysique de Paris, Sorbonne Universités, UPMC Univ Paris 06 et CNRS, UMR 7095, F-75014 Paris, France</footnote>

<footnote n="3">³Center for Relativistic Astrophysics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332, USA</footnote>

<footnote>* E-mail: malatif@comsats.edu.pk</footnote>
in the first minihaloes forming at $z = 10-30$, using cosmological simulations.

Johnson et al. (2011) performed a 3D smoothed particle hydrodynamical simulation with a ray tracing algorithm to model radiative feedback from a MBH in an atomic cooling halo. They found that accretion rate on to the BH drops down to $10^{-5} M_{\odot}yr^{-1}$ in about 1 Myr due to the photoheating and radiation pressure. However, these simulations were performed for primordial gas composition collapsing isothermally with no *in situ* star formation. The impact of X-ray feedback from a MBH seed on its growth was explored via cosmological radiation transfer simulations by employing the adaptive mesh refinement (AMR) technique in a halo of $\sim 10^8 M_{\odot}$ (Aykutalp et al. 2013, 2014). They found that X-ray feedback from BH self-regulates its growth and also induces star formation. Recently, Smidt et al. (2017) performed radiative transfer cosmological simulations to explore the role of X-ray feedback on its growth assuming a single frequency bin at 1 keV in the context of the most luminous high-redshift quasars. They found that dense cold accretion flows feed MBH which grows up to billion solar masses by $z = 7$ and may explain the existence of $z > 6$ quasars.

In this study, we focus on the growth of 'normal' BHs, not the extreme population such as the brightest quasars at $z > 6$ in the early universe. To accomplish this goal, we perform an AMR cosmological simulation coupled with radiative transfer algorithm MORAY (Wise & Abel 2011). We model feedback from a MBH by including both UV and X-ray (11.2 eV–1.1 keV) emission from an accreting BH of $10^5 M_{\odot}$. We also follow the formation of Population III (Pop III) and Population II (Pop II) stars along with their radiative, chemical, and mechanical feedback. For star formation, we employ recipes for Pop III and Pop II from Wise et al. (2012b) which allows transition to second generation of stars for $Z/Z_{\odot} > 10^{-4}$. Pushing the state of the art in this field, this work provides better insight about the growth of normal black holes at high redshift ($z > 6$).

This article is organized in the following way. In Section 2, we describe in detail the simulation setup and prescriptions for feedback from MBH/stars as well as recipes for star formation. We present our main results in Section 3 and confer our conclusions in Section 4.

## 2 NUMERICAL METHODS

We conduct the simulation using the public version of cosmological hydrodynamical code ENZO (Bryan et al. 2014). It is an AMR grid-based code which makes use of the message passing interface to run on parallel systems. The equations for hydrodynamics are solved with the piece-wise parabolic method and we employed the HLLC Riemann solver to capture strong shock and rarefaction waves. The code makes use of a particle-mesh based N-body solver to compute dark matter (DM) dynamics. A multigrid Poisson solver is used for self-gravity calculations.

We start our simulation at $z = 150$ with cosmological initial conditions generated from the MUSIC package (Hahn & Abel 2011) and use the latest Planck data with $\Omega_m = 0.3089$, $\Omega_\Lambda = 0.6911$, $H_0 = 0.6774$ to generate initial conditions (Planck Collaboration XIII 2016). Our periodic box has a size of comoving 8 Mpc h$^{-1}$ on each side, we select the most massive halo forming in our computational volume and place it at the centre of the simulation box. We employ nested grid initial conditions with a root grid resolution of $256^3$ cells, an equal number of DM particles and two additional nested grids with $256^3$ cells, resulting in an effective resolution of $1024^3$. This setup provides us an effective DM resolution of $\sim 53 000 M_{\odot}$. We further employ eight additional dynamic

refinement levels during the course of simulation which yields a maximal physical resolution of 3.6 pc at $z = 11$. Our resolution criteria is based on the baryonic overdensity of 4, the particle mass resolution of $\rho_{DM}\Delta x^3r^{\ell\alpha}$ where $\rho_{DM}$ is the DM density, $\Delta x$ is the root grid cell size, $r = 2$ is the refinement factor, $\ell$ is the refinement level, and $\alpha = -0.3$ makes the refinement super-Lagrangian and a fixed Jeans resolution of at least four cells, similar to Latif, Schleicher & Hartwig (2016). The simulated halo has a mass of $3 \times 10^{10} M_{\odot}$ and $6.2 \times 10^{10} M_{\odot}$ at $z = 7.5$ and $z = 6$, respectively. The virial radius of the halo at $z = 7.5$ is 21.5 kpc. We follow its formation from $z = 14$ down to $z = 7.5$, turn on star formation and feedback from the MBH at $z = 12$ when the halo mass is $\sim 10^9 M_{\odot}$ and it is resolved by 20 000 DM particles. We did not allow star formation in the halo before $z = 12$ assuming that one of its progenitors formed a MBH of $10^5 M_{\odot}$ via direct collapse (Latif et al. 2013; Johnson et al. 2013). We mention the consequences of such delayed star formation in the discussion section.

We employ a non-equilibrium time-dependent chemical model which solves rate equations of nine primordial species $H, H^+, H^-, He, He^+, He^{++}, H_2, H_2^+, e^-$. Our chemical model is mainly based on Anninos et al. (1997) and Abel et al. (1997). It includes cooling due to the collisional excitation, collisional ionization, radiative recombination, bremsstrahlung radiation, $H_2$ cooling, and Compton heating/cooling. In addition to primordial cooling, we also include metallicity-dependent metal lines (C, N, O, Si etc.) cooling from Glover & Jappsen (2007) which operates in the regime $100-10^4$ K, above $10^4$ K, the cooling function of Sutherland & Dopita (1993) is employed. We only consider metal line cooling from metals produced by Pop III stars and ignore the effect of cooling by metals produced by Pop II stars, doing so we may underestimate the stellar mass by a factor of 2, for further details see Wise et al. (2012a). We assume a constant $H_2$ dissociating flux of strength $J_{21} = 500$, where $J_{21}$ is in units of $10^{-21} \text{ erg s}^{-1} \text{ cm}^{-2} \text{ Hz}^{-1}$. Our chemistry solver is coupled with the radiative transfer module MORAY to take into account heating from photoionization and secondary ionization heating (Shull & van Steenberg 1985) from X-rays emitted by a MBH.

### 2.1 Star formation

Our star formation criteria are primarily based on Wise & Abel (2008) and Wise et al. (2012b) for Pop III and Pop II stars, respectively, which we briefly summarize here. We model the formation of both Pop III and Pop II stars and distinguish them based on the metallicity of gas cloud. Pop II stars in our simulation are formed for $Z/Z_{\odot} > 10^{-4}$, otherwise Pop III stars form. A Pop III star particle is allowed to form when a cell has an overdensity of $5 \times 10^5 (10^3 \text{ cm}^{-3}$ at $z = 10$), a molecular hydrogen ($H_2$) fraction of $\ge 5 \times 10^{-4}$ and the flow is convergent ($\nabla \cdot v_{\text{gas}} < 0$). Each Pop III star particle represents a single star and its mass is randomly sampled from the initial mass function (IMF) with mass range between 1 and $300 M_{\odot}$ with the following shape,

$$f(\log M)dM = M^{-1.3} \exp \left[ - \left( \frac{M_{\text{char}}}{M} \right)^{1.6} \right] dM, \quad (1)$$

where $M_{\text{char}}$ is the characteristic mass and is set to $100 M_{\odot}$. The chosen IMF behaves as a Salpeter IMF above $M_{\text{char}}$ and has an exponential cutoff below it. The Pop II star formation criterion is similar to Pop III but the requirement for minimum $H_2$ is removed as gas in the presence of metals can cool down even in the presence of a UV background. Pop III star particles are restricted to form in
cells with temperature <1000 K. Contrary to a Pop III star particle, a Pop II star particle represents a star cluster with a minimum mass of 1000 M☉ with a Salpeter IMF. Pop II star particles that are born with <1000 M☉ continue to accrete gas until they cross this threshold. For cells meeting this criteria, 7 per cent of the cold gas (T < 1000 K) within a sphere over a dynamical time-scale of about 3 Myr ($\rho_{av} \sim 1000 \mu \text{ cm}^{-3}$) is converted into stars. Both newly forming Pop III and Pop II star particles are merged within a radius of 10 pc in a single time-step.

## 2.2 Stellar feedback

Star particles are treated as point sources of radiation, and the radiative feedback from stars is modelled using the adaptive ray tracing scheme based on HEALPIX framework (Abel & Wandelt 2002; Wise & Abel 2011) which is self-consistently coupled with the hydrodynamics. Moreover, star particles emit ionizing radiation with a monochromatic spectrum. The H₂ dissociating radiation (LW) from radiation sources is modelled with an inverse-square profile around them, optically thin limit. The mass-dependent hydrogen ionizing and LW luminosities of Pop III stars are taken from Schaerer (2002). For Pop III stars, we take a monochromatic spectrum with an energy of 29.6 eV suitable for stars with surface temperatures of $10^5$ K, while for Pop II stars, we take a fixed spectrum of 21.6 eV appropriate for low-metallicity stars (Schaerer 2003). Pop II stars emit 6000 hydrogen ionizing photons per stellar baryon for 20 Myr, or equivalently $2.4 \times 10^{47}$ photons s$^{-1}$ M☉$^{-1}$.

Depending upon their mass, Pop III stars end their lives either as a supernovae (SNe) or collapse into a BH. We model SN energy and also X-ray feedback from a stellar mass black holes via ray tracing module mentioned above. Pop III stars with masses between 11–40 and 140–260 M☉ die as Type II SNe and pair-instability SNe (PISNe), respectively (Heger et al. 2003). While Pop III stars with mass between 40–140 and above 260 M☉ are expected to directly collapse into a BH (Heger & Woosley 2002; Heger et al. 2003). The typical energy for Type II SNe from 11 to 20 M☉ stars is $10^{51}$ erg s$^{-1}$ and for 20–40 M☉ stars energy is taken from Nomoto et al. (2006) while for PISNe is $10^{51}-10^{53}$ erg s$^{-1}$ (Heger & Woosley 2002). Pop II star clusters generate $6.8 \times 10^{48}$ erg s$^{-1}$ M☉$^{-1}$ from SNe 4 Myr after their formation, which is distributed in a sphere of radius 10 pc.

## 2.3 Massive black hole feedback

We insert a massive black hole (MBH) seed of $10^5$ M☉ at the halo centre at $z = 12$ possibly formed via direct collapse (Latif et al. 2013) and treat it as collisionless sink particle that can grow via accretion. For the spectral energy distribution (SED) of a MBH, we compute multicomponent spectrum which includes both the multicolour blackbody and a power-law component $\propto E^{-\alpha}$ with $\alpha = 1$ (Shakura & Sunyaev 1973; Sazonov, Ostriker & Sunyaev 2004). We model both UV and X-ray feedback from an accreting MBH by considering the energy range from 11.2 to 1100 eV. Four energy bins at 13.6, 24.6, 54.4, and 1 keV are used when generating the photons. We treat the MBH particle as a radiation source and perform 3D radiative transfer calculations to model its radiative feedback by making use of radiative transfer module MORAY that couples it with hydrodynamics. We have extended the implementation of a radiative feedback from a MBH by adding more energy bins, originally from Kim et al. (2011). The luminosity of an accreting black hole can be estimated as

$$L_{BH} = \epsilon_{r} \dot{M}_{BHC} c^{2}, \qquad (2)$$

where $\epsilon_{r}$ is the radiative efficiency, assumed to be 0.1, $\dot{M}_{BH}$ is the MBH accretion rate, and c is the speed of light. We estimate the total number of ionizing photons from MBH as $L_{BH} \times dt_{ph}/E_{av}$, where $dt_{ph}$ is the radiation transport time-step and $E_{av}$ is the average energy in the given frequency bin. These photons interact with the surrounding gas by photoionizing hydrogen and helium atoms, even causing secondary ionizations via suprathermal electrons, and photoheating the gas. For a detailed description about these processes, we refer the reader to Kim et al. (2011). We model the gas accretion on to the MBH following the prescription of Kim et al. (2011) and estimate $\dot{M}_{BH}$ using the Eddington limited Bondi–Hoyle equation as follows:

$$ \begin{aligned} \dot{M}_{BH} &= \min(\dot{M}_{B}, \dot{M}_{Edd}) \\ &= \min\left(\frac{4\pi G^2 M_{BH}^2 \rho_{B}}{c_s^3}, \frac{4\pi G M_{BH} m_{p}}{\epsilon_{r} \sigma_{T} c}\right), \end{aligned} \qquad (3) $$

where G is the gravitational constant, $M_{BH}$ the black hole mass, $\rho_{B}$ is the density at the Bondi radius, $c_s$ is the sound speed, $m_p$ is the proton mass, $\sigma_T$ is the Thomson scattering cross-section. The Bondi accretion radius is given by

$$R_B = \frac{2GM_{BH}}{c_s^2}. \qquad (4)$$

A portion of gas with mass $\dot{M}_{BH} \Delta t$ inside the Bondi radius is accreted on to a MBH and is uniformly subtracted from grid cells within the Bondi sphere. The maximum resolution in our simulation is 3.6 pc, which is close to the Bondi radius for $10^5$ M☉ black holes sitting in T ~ 8000 K gas (i.e. 8.6 pc). Therefore, the Bondi radius is resolved at most times, when the gas temperature is allowing us to probe the gas dynamics on to accreting MBH.

# 3 RESULTS

In this section, we present results from a 3D cosmological radiation hydrodynamical simulation performed to explore the growth of ‘normal’ BHs within the first Gyr after the big bang. The simulated halo has a mass of $3 \times 10^{10}$ M☉ at $z = 7.5$ and we follow its formation from $z = 14$ down to $z = 7.5$. We insert a MBH particle of $10^5$ M☉ at $z = 12$ when halo mass reaches ~$10^9$ M☉, well above the atomic cooling limit, and turn on radiation feedback from the MBH. The merger history of the simulated halo shows that it has gone through three major mergers (mass ratio greater than 1:2) at cosmic times of 425, 586, and 645 Myr, respectively, and many minor mergers. Our simulation does not resolve star formation in haloes below ~$10^9$ M☉ at $z > 12$ and we discuss its implications in the caveats section.

## 3.1 Star formation

In our simulation Pop III stars begin to form in pristine H₂ clouds self-shielded from the MBH radiation, 2–3 Myr after turning on the star formation which is restricted to the main halo. They explode as supernovae within a few Myr after their formation due to high masses and enrich the interstellar medium with metals. The first Pop II star cluster forms 3 Myr after the birth of Pop III stars, immediately after SNe. Both Pop III and Pop II stars continue to form but Pop II stellar mass overtakes the Pop III stellar mass after 5 Myr. The decline in Pop III stellar mass by a factor of a few after 13 Myr is due to the death of massive stars, and it later on increases up to $10^5$ M☉. Pop III stars keep forming in metal free minihaloes and at the same time they continue to explode as
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Time evolution of stellar and BH masses. The green line shows mass in Pop III stars, orange line represent Pop II stellar mass and blue line shows the MBH mass. Time is measured in Myr after the big bang.</figcaption></figure>

SNe. Fig. 1 shows that the average Pop III stellar mass over the simulated time is ~$10^4 M_{\odot}$ while wiggles on the Pop III stellar mass plot indicate the epochs of starburst and massive SNe going off. Peaks in the Pop III stellar mass correspond to the mergers of minihaloes occurring at those epochs. Star formation mainly occurs in the primary halo and remains inhibited in the surrounding haloes due to the feedback from primary halo.

A large number of SNe generate massive galaxy-wide outflows and particularly these outflows are observed at 450, 497, 560, and 640 Myr, where time is the age of the universe, as shown in Fig. 2. SNe along with AGN feedback heat the gas above $10^4$ K already at $z = 10$. Highly anisotropic H II regions are formed at these epochs which propagate through the interstellar medium and heat the surrounding gas. By $z = 7.5$, the H II region extends out to 20 kpc. These SNe keep enriching the halo with metals, and the Pop II stellar mass increases over time due to the efficient metal cooling, culminating in ~$10^9 M_{\odot}$ of Pop II stars by $z = 7.5$. As soon as first Pop III star goes SNe, it enriches the medium with metallicity of $10^{-2} Z_{\odot}$ well above the critical metallicity and a Pop III star cluster forms, see the top left panel of Fig. 3. The average metallicity enhancement from Pop III stars alone is about $10^{-2} Z_{\odot}$ and our estimates for the metallicity from Pop III stars are shown in Fig. 3. Metal enrichment is very inhomogeneous and extends beyond the virial radius. Also, pockets of metal poor ($Z/Z_{\odot} \le 10^{-4}$) gas exist down to $z = 7.5$ in filaments.

The density structure inside the halo is quite clumpy and turbulent which leads to chaotic accretion, also see Gaspari et al. (2017). The state of gas density at various epochs is shown in Fig. 4 which depicts the occurrence of major merger between $z = 8.8$ and $z = 7.5$. The peak density is about $10^4 \text{ cm}^{-3}$ while the typical gas density is about $10-100 \text{ cm}^{-3}$. The overall density structure in the halo

becomes filamentary by the end of the simulation, shown in Fig. 4. The average star formation rate (SFR) in our simulations for Pop III stars is $10^{-3} M_{\odot} \text{ yr}^{-1}$ while the average SFR for Pop II stars is a few $M_{\odot} \text{ yr}^{-1}$ and peaks around $10 M_{\odot} \text{ yr}^{-1}$. The Pop II SFR falls below $1 M_{\odot} \text{ yr}^{-1}$ during the strong outflows as they evacuate gas from the halo. Overall, the average SFR is ~$2 M_{\odot} \text{ yr}^{-1}$ and peaks in SFR correspond to the mergers occurring at those epochs. Most of the SF occurs inside the primary halo. These results are comparable to the SFR main sequence at $z = 6.5$ from the CANDELS survey (Salmon et al. 2015, see Fig. 2). The typical SFRs observed in the CANDELS survey are between 1 and $100 M_{\odot} \text{ yr}^{-1}$, with stellar masses of a few times $10^8-10^{10} M_{\odot}$ and $z$ between 3.5 and 6.5. Although, the simulated galaxy is at $z = 7.5$, at slightly higher redshift, but its stellar mass and the SFR are close to the observed range at $z = 6.5$. Such a comparison confirms that the simulated galaxy is a typical, not completely off the main sequence observed at $z > 6$ and agree with predictions from theoretical models (Somerville et al. 2012; Behroozi, Wechsler & Conroy 2013; Davé et al. 2013).

## 3.2 Black hole growth

The initial mass accretion rate on to the MBH is ~$10^{-5} M_{\odot} \text{ yr}^{-1}$ and continues to increase for about first 3 Myr. The X-ray and UV feedback from the MBH photodissociate molecular hydrogen and photoionize hydrogen and helium atoms in its surrounding. Such energy deposition photoevaporates the clumpy gas and forces it away from the MBH. The luminosity from young stars exceeds the MBH luminosity within the central kpc region which further heats and expels the gas from the central potential. As a result the temperature of gas rises to $\ge 10^4$ K, and the expanding H II region leaves behind a low-density medium. In the meantime the first Pop III SN occurs
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Projections of density-weighted temperature along the y-axis at various redshifts for the central 14 kpc region. The top left panel shows the moment when first SN goes off while other panels depict the epochs when large outflows are produced by the SNe in tandem with MBH feedback.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Projections of density-weighted metallicity originating from Pop III SNe along the y-axis at the same redshifts as Fig. 2 for the central 14 kpc region.</figcaption></figure>

that further pushes the gas away from the MBH and generates an outflow. Consequently, mass accretion on to the MBH drops below $10^{-6} M_{\odot} yr^{-1}$ as shown in Fig. 5. In the aftermath of SN, metal cooling brings the gas temperature down to $\le 10^4$ K and increased accretion on to the MBH starts again after a few Myr. Accretion on to the MBH continues until many SNe explode. They in tandem with MBH feedback expel the gas from MBH neighbourhood and drive large outflows. On a few occasions the MBH gets trapped inside SN remnants. Subsequently, the accretion rate drops significantly and the growth of the MBH is halted for a few Myr. As mentioned

above, large outflows observed at about 400, 450, 480, 560, and 640 Myr strongly influence the MBH growth and particularly their impact is severe when the stellar mass is less than $10^8 M_{\odot}$.

The mass accretion on to the MBH reaches brief maxima of $10^{-4} M_{\odot} yr^{-1}$, but starbursts generate large kpc-wide outflows and regulate the growth of MBH. This trend has been observed particularly for the first 150 Myr of simulation similar to previous works (Dubois et al. 2012; Habouzit, Volonteri & Dubois 2016; Prieto et al. 2017). The ratio of the MBH mass accretion rate to the Eddington accretion rate, so-called the Eddington ratio, increases up
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Projections of density-weighted gas density along the y-axis at the same redshifts as Fig. 2 for the central 14 kpc region.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** The black hole mass evolution (top panel) and the mass accretion rate on to the MBH (bottom panel) over the cosmic time in Myr after the big bang, showing the lack of the growth of ‘normal’ BHs in the early universe.</figcaption></figure>
to a ~0.03 in the first 20 Myr and declines during the massive outflows generated by SNe. The average Eddington ratio during the simulation is ~$10^{-3}$. In our simulation the MBH never accretes at the Eddington limit.

The average accretion rate on to the MBH is a few times $10^{-6} M_{\odot} yr^{-1}$ and remains highly intermittent throughout the simulation. In total about 2200 $M_{\odot}$ are accreted on to the MBH during 320 Myr out of which about 1000 $M_{\odot}$ is accreted during the first 40 Myr. Over time, the halo and stellar mass increase as the potential well gets deeper. Therefore, the average density in the halo increases as well as the average temperature due to the continuous heating of gas by SNe and AGN feedback. Consequently, the growth of the MBH tends to be faster during the last 50 Myr. In Fig. 6, we plot the accretion rate on to the MBH against the SFR. The ratio between MBH accretion rate and SFR is ~$10^{-3}$ for Pop III stars and ~$10^{-6}$ for Pop II stars; this confirms that the MBH grows much more slowly than its host galaxy, since SFR and therefore stellar mass are dominated by Pop II stars. Unless MBH accretion becomes more consistent, the MBH-galaxy system will drift towards a smaller ratio between MBH and stellar mass, creating a MBH ‘undermassive’ with respect to its galaxy. The large ratio between SFR and MBH accretion rate would also make it difficult to detect the AGN, it’s luminosity likely swamped by that of the stellar population (see Volonteri et al. 2017).

Overall, the stunted growth of MBH is a consequence of SNe in tandem with BH feedback which expel gas from the MBH surroundings and quench its growth. These findings are consistent with previous works exploring the growth of BHs at early cosmic times (Dubois et al. 2012, 2015; Habouzit, Volonteri & Dubois 2016; Angles-Alcazar et al. 2017; Biernacki, Teyssier & Bleuler 2017; Di Matteo et al. 2017; Prieto et al. 2017; Smidt et al. 2017). They also found that MBH does not grow efficiently in high-redshift galaxies when stellar mass is below $10^9 M_{\odot}$. These studies ignored the formation and feedback from Pop III stars which can be important during the early stages of galaxy formation. By following the formation and feedback from Pop III stars, we found that it makes the growth of MBH even more difficult as massive Pop III stars could produce PISNe which are more effective in ejecting the gas from central potential, being 10–100 times more energetic than Type II SNe. Consequently, in comparison with earlier findings, the mean accretion rate on to the MBH is about two orders of magnitude smaller. These differences arise from modelling the feedback from Pop III stars and inclusion of both UV and X-ray feedback from the MBH. Our results are more robust than previous estimates as we perform radiative transfer calculations to model the radiative feedback from both stars and the central MBH.

Recently, it was found from BLUETIDES simulations that MBH can grow up to a few times $10^8 M_{\odot}$ already at $z=8$ in haloes sitting in low tidal fields (Di Matteo et al. 2017). It should be noted that the halo mass in our simulation is factor of 10 lower compared to Di Matteo et al. (2017) but the spatial resolution is about 50 times higher. Moreover, they employed thermal feedback to model feedback from MBHs while we performed radiative transfer calculations. MBH does not grow much in our case, most likely the differences arise from the environment of the halo, its merger history and the sub-grid physics. The other works exploring the growth of MBH had a spatial resolution of about few hundred pc (Costa et al. 2014; Feng et al. 2014; Schaye et al. 2015; Feng et al. 2016) and used thermal feedback from MBH. Doing so, they may have overestimated the mass accretion on to MBH, see Negri & Volonteri (2017) for a comparison of different resolutions and consequences of variations in the implementation of thermal feedback recipes.

# 4 DISCUSSION AND CONCLUSIONS

We have performed a cosmological radiation hydrodynamical simulation to explore the growth of ‘normal’ BHs in the first Gyr after the big bang. To accomplish this goal, we selected a halo of $3 \times 10^{10} M_{\odot}$ at $z=7.5$. Our simulation includes both UV and X-ray feedback from an accreting BH and *in situ* star formation along with their chemical, mechanical and radiative feedback. Our recipes for Pop III and Pop II star formation are based on Wise et al. (2012b) and we insert a MBH of $10^5 M_{\odot}$ at $z=12$ by turning on its feedback when halo mass reaches well above the atomic cooling limit.

(i) Our results show that the MBH has accreted only about 2200 $M_{\odot}$ over the course of 320 Myr and the average mass accretion rate on to the MBH is a few times $10^{-6} M_{\odot} yr^{-1}$.

(ii) The stunted growth of the MBH is a consequence of large outflows driven by SNe in tandem with AGN feedback which expel the gas out of its surroundings.

(iii) Pop III SNe quickly enrich the ISM with metals in about a few Myr.

(iv) The average SFR during the simulation is ~$1 M_{\odot} yr^{-1}$ and SFR mainly occurs in the primary halo.

The mass accretion rate on to MBH is highly intermittent and peaks around $10^{-4} M_{\odot} yr^{-1}$. Interestingly, our results are comparable to the delayed cooling case of high-resolution cosmological simulation of Dubois et al. (2015, hereafter called S15) where strong SN feedback halts the growth of MBH down to $z=3.5$. Their simulations have effective resolution of 8.7 pc and halo mass of $10^{12} M_{\odot}$ at $z=2$. They employed simple thermal feedback prescription for MBH accretion (for a detailed description see S15). In our case energetic SNe from massive stars along with AGN feedback effectively heat the gas to high temperatures and yield results similar to the delayed cooling case of S15.

Pop III stars quickly enrich the medium with metals and the first Pop II star cluster formed 3 Myr after the birth of Pop III stars in our simulation. The latter have a top heavy IMF and thus shorter lives and are initially more effective in removing the gas from the central potential and regulating the growth of a MBH. The maximum total Pop III stellar mass in our simulation is ~$10^5 M_{\odot}$ and the average Pop III stellar mass at any given time is ~$10^4 M_{\odot}$. The Pop II stellar mass becomes greater than Pop III mass after first 5 Myr and reaches up to ~$10^9 M_{\odot}$ by the end of our simulation. The average SFR is about ~$1 M_{\odot} yr^{-1}$ and peaks around $10 M_{\odot} yr^{-1}$. The MBH to stellar mass ratio is ~$10^{-3}$ for the first 50 Myr and approaches ~$10^{-4}$ in about 100 Myr after the beginning of simulation which is roughly consistent with the observed BH-stellar mass relation in low-mass galaxies in the local universe by Reines & Volonteri (2015).

The peak bolometric luminosity from the MBH is about $4 \times 10^{41} erg s^{-1}$ while the corresponding X-ray luminosity is ~$10^{40} erg s^{-1}$. This is about two orders of magnitude lower than the Chandra Deep Field South detection limits for an exposure of 4 Ms. The Eddington ratio is $10^{-3}$ much lower compared to the luminous quasars. This may explain why such faint sources have not been detected so far. The local analogues of these sources are low-luminosity AGNs provided that the stellar mass–BH relation holds at high redshift (Overzier et al. 2009; Jia et al. 2011; Alexandroff et al. 2012). These findings are consistent with current observations of high redshift AGN (Willott 2011; Giallongo et al. 2015; Weigel et al. 2015). We have estimated the flux from the AGN in the near-infrared (NIR) band (1–2.2 micron) assuming a bolometric correction of ~7 per cent in the NIR. The estimated flux is
<figure><img src="image_8.png" /><figcaption>**Figure 6.** The MBH accretion rate against SFR is shown here. The green squares represent Pop III SFRs while orange triangles correspond to Pop II SFRs. They are plotted for all halo progenitors at all redshifts. The grey-shaded region shows the range of SFR found in Salmon et al. (2015).</figcaption></figure>

~10⁻²¹ erg s⁻¹ cm⁻² which is about three orders of magnitude lower than the observational limit for the *James Webb Space Telescope* with NIRCAM for S/N = 10 and integration time of 10 ks. However, SFR is about six orders of magnitude higher than mass accretion rate on to the MBH. Therefore, it will be difficult to distinguish the AGN from the stellar population (Volonteri et al. 2017). Depending upon the line of the sight, the average column density is 10²⁰ cm⁻² which is below the Compton thick limit for obscured AGN. Therefore, the simulated AGN is not Compton thick but too faint to be detected with current surveys. This may explain the paucity of AGN in high-redshift Lyman Break galaxies.

In our simulation, we activated star formation and their feedback at $z = 12$ when halo mass is 10⁹ M☉. Doing so, star formation was delayed as Pop III stars are expected to form in ~10⁸ M☉ haloes under moderate LW flux which is a shortcoming of our simulation. We expect that if Pop III stars were formed in the progenitor haloes they would have enriched their hosts and neighbouring haloes with metals and led to earlier transition from Pop III to Pop II stars. Also MBH could not have formed via direct collapse due to early metal enrichment. Such prior star formation may have lowered the gas content in the halo, preheated the gas and consequently the impact of starburst may have been lower. However, we expect that role of such prior Pop III star formation to be only important during the early phases of galaxy formation.

The direct collapse BHs are expected to form in metal free haloes of ~10⁸ M☉ at ~$z > 10$ but in our simulation we inserted MBH in 10⁹ M☉ halo due to the high computational demand of the radiative transfer calculation. If we had to insert MBH into ~10⁸ M☉ halo, we had to refine even larger region to resolve the progenitors of the haloes. We also assumed here that the MBH formed in one of the progenitor haloes via direct collapse which mandates that the host

halo of ~10⁸ M☉ was metal free and irradiated with a strong LW flux. These conditions should be assessed in future studies to explore their feasibility. In such a scenario, the impact of prior star formation would be less important as it naturally suppresses the star formation in the host halo. If the MBH was formed via accretion/merging of stellar mass black holes then the feedback from such a BH would have expelled gas from the halo and regulated the star formation in the host galaxy. Future simulations should self-consistently model the formation of MBH along with star formation to better understand their role in galaxy assembly and BH growth in the early universe.

One of the shortcomings of this work is that cooling is considered only from metals produced by Pop III stars. Consequently, the galaxy stellar mass is expected to be lower by a factor of 2 compared to the metal cooling both from Pop III and Pop II stars (see Wise et al. 2012a for a detailed discussion). Furthermore, we employed the Bondi–Hoyle formalism for accretion on to the MBH which assumes spherical symmetry and is only an approximation for low-resolution simulations. In reality, gas around the MBH settles in a rotationally supported disc which cannot be resolved in the present-day numerical simulations. The maximum resolution in our simulation is a few pc which is far from resolving the accretion disc and flow around the event horizon of a MBH. Recently Sugimura et al. (2017) performed 2D radiation hydrodynamical simulations to explore the impact of an-isotropic radiation feedback on BH growth. They found that radiation feedback is mainly confined to the bi-polar region while accretion still continues from the equatorial plane. This results in higher accretion rate on to the BH compared to the an isotropic case and even exceeds the Eddington value. However, other studies found that as the disc wind opening angle increases, winds kinematically get coupled with the surrounding gas and lead to an isotropic flow, see Novak, Ostriker &
Ciotti (2011) and Ciotti et al. (2017) for a detailed discussion. It is expected that radiative feedback may become already isotropic by the time it reaches the resolution limit (a few parsecs) of our simulation.

Due to the resolution constraints, we employed a Bondi–Hoyle prescription for MBH accretion which does not take into account the angular momentum of the gas (Debuhr et al. 2010; Power, Baugh & Lacey 2010; Hopkins & Quataert 2011), and provides only an approximate solution to the real accretion inflow, which can at times be underestimated or overestimated. When the accretion radius is close to the Bondi radius, however, the Bondi formalism provides a good estimate of the mass flux (Negri & Volonteri 2017). In future studies, alternative approaches considering the angular momentum transport should be explored. In this study, we only considered the coupling of X-rays with primordial gas chemistry and ignored the interaction of X-rays with metals. The presence of metals can attenuate X-rays and may impact the formation of H II region as well as the growth of MBH (see Aykutalp et al. 2013).

ACKNOWLEDGEMENTS

This work was granted access to the HPC resources of TGCC under the allocation x2016046955 made by GENCI. The research leading to these results has also received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 614199, project 'BLACK'). This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 656428. JHW is supported by National Science Foundation grants AST-1333360 and AST-1614333, NASA grant NNX17AG23G, and Hubble theory grants HST-AR-13895 and HST-AR-14326. The simulation results are analysed using the visualization toolkit for astrophysical data YT (Turk et al. 2011).

REFERENCES

Abel T., Wandelt B. D., 2002, MNRAS, 330, L53

Abel T., Anninos P., Zhang Y., Norman M. L., 1997, New Astron., 2, 181

Alexandroff R. et al., 2012, MNRAS, 423, 1325

Alvarez M. A., Wise J. H., Abel T., 2009, ApJ, 701, L133

Angles-Alcazar D., Faucher-Giguere C.-A., Quataert E., Hopkins P. F., Feldmann R., Torrey P., Wetzel A., Kereš D., 2017, MNRAS, 472, L109

Anninos P., Zhang Y., Abel T., Norman M. L., 1997, New Astron., 2, 209

Aykutalp A., Wise J. H., Meijerink R., Spaans M., 2013, ApJ, 771, 50

Aykutalp A., Wise J. H., Spaans M., Meijerink R., 2014, ApJ, 797, 139

Bañados E. et al., 2014, AJ, 148, 14

Bañados E. et al., 2018, Nature, 553, 473

Behroozi P. S., Wechsler R. H., Conroy C., 2013, ApJ, 770, 57

Biernacki P., Teyssier R., Bleuler A., 2017, MNRAS, 469, 295

Booth C. M., Schaye J., 2009, MNRAS, 398, 53

Bryan G. L. et al., 2014, ApJS, 211, 19

Ciotti L., Pellegrini S., Negri A., Ostriker J. P., 2017, ApJ, 835, 15

Costa T., Sijacki D., Trenti M., Haehnelt M. G., 2014, MNRAS, 439, 2146

Davé R., Katz N., Oppenheimer B. D., Kollmeier J. A., Weinberg D. H., 2013, MNRAS, 434, 2645

Debuhr J., Quataert E., Ma C.-P., Hopkins P., 2010, MNRAS, 406, L55

Di Matteo T., Croft R. A. C., Feng Y., Waters D., Wilkins S., 2017, MNRAS, 467, 4243

Dubois Y., Pichon C., Haehnelt M., Kimm T., Slyz A., Devriendt J., Pogosyan D., 2012, MNRAS, 423, 3616

Dubois Y., Volonteri M., Silk J., Devriendt J., Slyz A., Teyssier R., 2015, MNRAS, 452, 1502 (S15)

Fan X., Strauss M. A., Schneider D. P., Becker R. H., White R. L., Haiman Z., Gregg M., 2003, AJ, 125, 1649

Feng Y., Di Matteo T., Croft R., Khandai N., 2014, MNRAS, 440, 1865

Feng Y., Di-Matteo T., Croft R. A., Bird S., Battaglia N., Wilkins S., 2016, MNRAS, 455, 2778

Gaspari M., Sadowski A., 2017, ApJ, 837, 149

Gaspari M., Ruszkowski M., Oh S. P., 2013, MNRAS, 432, 3401

Gaspari M. et al., 2018, ApJ, 854, 167

Giallongo E. et al., 2015, A&A, 578, A83

Glover S. C. O., Jappsen A.-K., 2007, ApJ, 666, 1

Habouzit M., Volonteri M., Dubois Y., 2017, MNRAS, 468, 3935

Hahn O., Abel T., 2011, MNRAS, 415, 2101

Haiman Z., 2013, in Wiklind T., Mobasher B., Bromm V., eds, Astrophysics and Space Science Library, Vol. 396, The First Galaxies. Springer-Verlag, Berlin. p. 293

Heger A., Woosley S. E., 2002, ApJ, 567, 532

Heger A., Fryer C. L., Woosley S. E., Langer N., Hartmann D. H., 2003, ApJ, 591, 288

Hopkins P. F., Quataert E., 2011, MNRAS, 415, 1027

Jeon M., Pawlik A. H., Greif T. H., Glover S. C. O., Bromm V., Milosavljević M., Klessen R. S., 2012, ApJ, 754, 34

Jeon M., Pawlik A. H., Bromm V., Milosavljević M., 2014, MNRAS, 440, 3778

Jia J., Ptak A., Heckman T. M., Overzier R. A., Hornschemeier A., LaMassa S. M., 2011, ApJ, 731, 55

Jiang L. et al., 2009, AJ, 138, 305

Johnson J. L., Bromm V., 2007, MNRAS, 374, 1557

Johnson J. L., Haardt F., 2016, PASA, 33, e007

Johnson J. L., Khochfar S., Greif T. H., Durier F., 2011, MNRAS, 410, 919

Johnson J. L., Whalen D. J., Li H., Holz D. E., 2013, ApJ, 771, 116

Kim J.-h., Wise J. H., Alvarez M. A., Abel T., 2011, ApJ, 738, 54

Kormendy J., Ho L. C., 2013, ARA&A, 51, 511

Latif M. A., Ferrara A., 2016, PASA, 33, e051

Latif M. A., Schleicher D. R. G., Schmidt W., Niemeyer J. C., 2013, MNRAS, 436, 2989

Latif M. A., Schleicher D. R. G., Hartwig T., 2016, MNRAS, 458, 233

Milosavljević M., Bromm V., Couch S. M., Oh S. P., 2009, ApJ, 698, 766

Mortlock D. J. et al., 2011, Nature, 474, 616

Negri A., Volonteri M., 2017, MNRAS, 467, 3475

Nomoto K., Tominaga N., Umeda H., Kobayashi C., Maeda K., 2006, Nucl. Phys. A, 777, 424

Novak G. S., Ostriker J. P., Ciotti L., 2011, ApJ, 737, 26

Overzier R. A. et al., 2009, ApJ, 706, 203

Park K., Ricotti M., 2011, ApJ, 739, 2

Planck Collaboration XIII, 2016, A&A, 594, A13

Power C., Baugh C. M., Lacey C. G., 2010, MNRAS, 406, 43

Prieto J., Escala A., Volonteri M., Dubois Y., 2017, ApJ, 836, 216

Reines A. E., Volonteri M., 2015, ApJ, 813, 82

Salmon B. et al., 2015, ApJ, 799, 183

Sazonov S. Y., Ostriker J. P., Sunyaev R. A., 2004, MNRAS, 347, 144

Schaerer D., 2002, A&A, 382, 28

Schaerer D., 2003, A&A, 397, 527

Schaye J. et al., 2015, MNRAS, 446, 521

Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337

Shull J. M., van Steenberg M. E., 1985, ApJ, 298, 268

Sijacki D., Vogelsberger M., Genel S., Springel V., Torrey P., Snyder G. F., Nelson D., Hernquist L., 2015, MNRAS, 452, 575

Smidt J., Whalen D. J., Johnson J. L., Li H., 2017, ApJ, preprint (arXiv:1703.00449)

Somerville R. S., Gilmore R. C., Primack J. R., Domínguez A., 2012, MNRAS, 423, 1992

Sugimura K., Hosokawa T., Yajima H., Omukai K., 2017, MNRAS, 469, 62

Sutherland R. S., Dopita M. A., 1993, ApJS, 88, 253

Turk M. J., Smith B. D., Oishi J. S., Skory S., Skillman S. W., Abel T., Norman M. L., 2011, ApJS, 192, 9

Venemans B. P. et al., 2015, MNRAS, 453, 2259

Volonteri M., 2010, A&AR, 18, 279
Volonteri M., Reines A. E., Atek H., Stark D. P., Trebitsch M., 2017, ApJ,
849, 155

Weigel A. K., Schawinski K., Treister E., Urry C. M., Koss M., Trakhtenbrot
B., 2015, MNRAS, 448, 3167

Willott C. J., 2011, ApJ, 742, L8

Willott C. J. et al., 2007, AJ, 134, 2435

Wise J. H., Abel T., 2008, ApJ, 685, 40

Wise J. H., Abel T., 2011, MNRAS, 414, 3458

Wise J. H., Abel T., Turk M. J., Norman M. L., Smith B. D., 2012a, MNRAS,
427, 311

Wise J. H., Turk M. J., Norman M. L., Abel T., 2012b, ApJ, 745, 50

Wu X.-B. et al., 2015, Nature, 518, 512

This paper has been typeset from a TeX/LA TeX file prepared by the author.