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# Formation of massive black holes in rapidly growing pre-galactic gas clouds

## Abstract

The origin of the supermassive black holes that inhabit the centres of massive galaxies remains unclear1,2. Direct-collapse black holes—remnants of supermassive stars, with masses around 10,000 times that of the Sun—are ideal seed candidates3,4,5,6. However, their very existence and their formation environment in the early Universe are still under debate, and their supposed rarity makes modelling their formation difficult7,8. Models have shown that rapid collapse of pre-galactic gas (with a mass infall rate above some critical value) in metal-free haloes is a requirement for the formation of a protostellar core that will then form a supermassive star9,10. Here we report a radiation hydrodynamics simulation of early galaxy formation11,12 that produces metal-free haloes massive enough and with sufficiently high mass infall rates to form supermassive stars. We find that pre-galactic haloes and their associated gas clouds that are exposed to a Lyman–Werner intensity roughly three times the intensity of the background radiation and that undergo at least one period of rapid mass growth early in their evolution are ideal environments for the formation of supermassive stars. The rapid growth induces substantial dynamical heating13,14, amplifying the Lyman–Werner suppression that originates from a group of young galaxies 20 kiloparsecs away. Our results strongly indicate that the dynamics of structure formation, rather than a critical Lyman–Werner flux, is the main driver of the formation of massive black holes in the early Universe. We find that the seeds of massive black holes may be much more common than previously considered in overdense regions of the early Universe, with a co-moving number density up to 10−3 per cubic megaparsec.

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## Data availability

The numerical experiments presented here were run with a hybrid OpenMP+MPI fork of the Enzo code, which is available from https://bitbucket.org/jwise77/openmp, using the changeset bcb436949d16. The data are publicly available from the Renaissance Simulation Laboratory at http://girder.rensimlab.xyz.

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## Acknowledgements

J.H.W. thanks A. Benson for assistance with the code Galacticus. J.H.W. was supported by NSF awards AST-1614333 and OAC-1835213, NASA grant NNX17AG23G, and Hubble theory grant HST-AR-14326. J.A.R. acknowledges support from the EU commission via the Marie Skłodowska-Curie Grant ‘SMARTSTARS’ (grant number 699941). B.W.O. was supported in part by NSF awards PHY-1430152, AST-1514700 and OAC-1835213, by NASA grants NNX12AC98G and NNX15AP39G, and by Hubble theory grants HST-AR-13261.01-A and HST-AR-14315.001-A. M.L.N. was supported by NSF grants AST-1109243, AST-1615858 and OAC-1835213. The simulation was performed on Blue Waters operated by the National Center for Supercomputing Applications (NCSA) with PRAC allocation support by the NSF (awards ACI-0832662, ACI-1238993 and ACI-1514580). The subsequent analysis and the re-simulations were performed with NSF’s XSEDE allocation AST-120046 on the Stampede2 resource. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the NSF (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its NCSA. The freely available astrophysical analysis code yt29 and plotting library matplotlib were used to construct numerous plots within this paper. Computations described in this work were performed using the publicly available Enzo code, which is the product of a collaborative effort of many independent scientists from numerous institutions.

### Reviewer information

Nature thanks N. Yoshida and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

J.H.W. and J.A.R. conceived the idea, performed the analysis and drafted the paper. The Renaissance simulations were conducted by H.X. and J.H.W., and the re-simulations of the target haloes were conducted by J.H.W. B.W.O. performed the Monte Carlo analysis for the number density estimate. All authors contributed to the interpretation of the results and to the text of the final manuscript.

### Corresponding author

Correspondence to John H. Wise.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Simulated and critical halo mass growth rates for SMS formation.

A halo conducive for SMS formation must grow to the atomic-cooling limit (2.2 × 107Mʘ at z = 15; orange dotted line) without hosting star formation or being chemically enriched from nearby galaxies. Haloes with masses below minimum mass Mmin,LW (dashed green line) are suppressed by an external LW radiation field. Above this mass, haloes with sufficient dynamical heating to suppress radiative cooling grow above a critical rate (equation (1)), shown for H2 number fractions fH2 of 10−4 (blue solid line), 10−5 (orange solid line) and 10−6 (green solid line). The simulated growth rates of the MMH (circles) and LWH (triangles) are above the 10−6 rate once the halo masses pass Mmin,LW. Above a halo mass of 8 × 106Mʘ (a virial temperature of 8,000 K at z = 15), dynamical heating will not suppress cooling because the atomic-radiative cooling rates are several orders of magnitude higher than the molecular ones. Both haloes grow rapidly to Mmin,LW, causing dynamical heating and preventing collapse for a sound-crossing time. The LWH grows from 8 × 106Mʘ to the atomic-cooling limit within a dynamical time of the central core. Both conditions set a critical growth rate (thick solid grey lines). All other atomic-cooling haloes (grey points) have similar growth rates between halo masses of Mmin,LW and 8 × 106Mʘ but far short of the critical growth rate. Nearly all of these haloes cool and form stars before reaching the atomic-cooling limit.

### Extended Data Fig. 2 Gravitational instability of the growing core.

The ratio of the enclosed gas mass Menc and the Jeans mass MJeans as a function enclosed gas mass is shown for the MMH (solid lines) and the LWH (dashed lines) when each halo first becomes gravitationally unstable (thick black lines), that is, when Menc/MJeans ≥ 1 (shaded region), and in the final simulation state (thin blue lines). The orange circles and red squares indicate the mass scale of the collapsing gas cloud that is co-located with the centre of the host halo.

### Extended Data Fig. 3 Thermal and turbulent support of the collapsing core.

a, b, Gravitational forces dominate over thermal and turbulent internal pressures within the collapsing core in the MMH (a) and the LWH (b). The thermal sound speed (blue dotted lines) and turbulent root-mean-square velocity (orange dash-dotted line) both contribute to the effective sound speed (black solid line) that provides partial resistance to a catastrophic collapse. The radial infall speed (green dashed line) shows that the flow becomes supersonic at the Jeans mass scale and then transitions to a subsonic flow at smaller mass scales. In the LWH, the radial inflow becomes transonic at a mass scale of 103Mʘ.

### Extended Data Fig. 4 Rotational properties of the target haloes.

a, Radially averaged profiles of circular velocity $${v}_{{\rm{Kep}}}=\sqrt{GM/r}$$ (red lines) and rotational velocity vrot (blue lines) around the largest principal axis of the MMH (dashed lines) and the LWH (solid lines) at the end of the simulation. b, Radially averaged profiles of the fractional rotational support; a ratio greater than one indicates that rotational velocities are sufficient to prevent gravitational collapse. The shaded regions show where the systems are rotationally supported: 2 × 103Mʘ–3.3 × 105Mʘ for the MMH (light shading) and 7 × 103Mʘ–6 × 104Mʘ for the LWH (dark shading). Rotation works in tandem with thermal and turbulent pressures to marginally slow the collapse, seen in the lower infall speeds at these mass scales in Extended Data Fig. 3. Inside 100Mʘ, this rotational measure becomes ill-defined because the rotation centre and centre-of-mass are not co-located; thus, we do not conclude that the inner portions are rotationally supported even though vrot/vKep > 1.

### Extended Data Fig. 5 Distribution of fragmentation-prone regions.

ad, Density-weighted projections of a local estimate of the Toomre Q parameter (equation (2)) for the MMH (a, b) and the LWH (c, d) in a field of view of 20 pc (left) and 4 pc (right), centred on the densest point and aligned to be perpendicular with the angular momentum vector of the disk. A value greater than one indicates that rotation and internal pressure stabilizes regions against fragmentation into smaller self-gravitating objects. In the MMH, this analysis highlights the clump fragments with the filaments being only marginally stable at Q ≈ 1. The sheet in the LWH that formed from a preceding major halo merger is apparent in this measure. The bulk of the sheet is only marginally stable, with the edge and collapsing centre containing an environment that is conducive to fragmentation.

### Extended Data Fig. 6 Growth rates for fragmentation.

A rotating system will fragment into self-gravitating clumps only when the growth rates of the density perturbations are faster than the collapse timescale. a, Cylindrical radial profiles of Q when considering only thermal support (red) and with thermal and turbulent support (blue), for the MMH (dashed) and the LWH (solid). The shaded region indicates where the system is unstable to fragmentation. b, The unstable regions have a characteristic growth rate, defining a growth timescale tgrow, which exhibits an increasing trend with radius for the MMH (orange) and the LWH (green). c, If the ratio of tgrow and the free-fall time tff is less than one, the region can fragment before it gravitationally collapses. In the MMH, this condition is true at radii less than 0.03 pc, indicating that small-scale fragmentation might occur but will subsequently be suppressed by a rapid monolithic collapse. The LWH exhibits this feature inside 0.1 pc but is surrounded by gas that is stable against fragmentation.

### Extended Data Fig. 7 Clump infall rates and timescales.

Similar to the results presented in Fig. 4d, the self-gravitating clumps are growing through radial infall. a, The infall rates are computed as the mass flux through spherical shells and steadily increase with enclosed mass. The rate in the single clump of the LWH (dotted purple line) is more than a factor three greater than the three major clumps in the MMH. The circles mark the infall rate at the clump mass. b, The infall time, the ratio of the mass enclosed and infall rate, is an informative scale that can be used to compare against star-formation timescales. This timescale is constant and approximately 10 kyr within 100Mʘ for all clumps and rises to about 100 kyr for the entire clump, marked by the circles. This rapid infall suggests that sufficient mass will collapse into the supermassive protostar before it reaches main-sequence.

### Extended Data Fig. 8 Thermal and turbulent support of collapsing clumps.

ad, Same as Extended Data Fig. 3, but for the clumps in the LWH (a) and the MMH (bd). The vertical dotted lines mark the clump mass. The radial inflows are subsonic for all four clumps, but the clump in LWH contains transonic flows between 100Mʘ and 1,000Mʘ. Thermal support is dominant inside the clumps, unlike the larger parent Jeans-unstable system, where turbulent effective pressures are comparable to their thermal counterparts (see Extended Data Fig. 3).

### Extended Data Fig. 9 Abundance estimate of DCBHs.

The cumulative probability of the co-moving number density of haloes that potentially host supermassive star formation is shown for the rare-peak (red solid line), normal (blue dashed line) and void (black dash-dotted line) regions of the Renaissance simulations. Their respective median number densities are 1.1 × 10−3, about 10−7 and 0 haloes per co-moving Mpc3. Subsequent DCBH formation is most likely to occur in overdense regions of the early Universe, whereas few or no haloes will form in average and underdense regions.

## Supplementary information

### Video 1

Rotation and zoom of the most massive halo (MMHalo). Projections of gas density (left) and temperature (right), zooming from cosmological scales to the supermassive star candidate

### Video 2

Rotation and zoom of the most irradiated halo (LWHalo). Projections of gas density (left) and temperature (right), zooming from cosmological scales to the supermassive star candidate

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Wise, J.H., Regan, J.A., O’Shea, B.W. et al. Formation of massive black holes in rapidly growing pre-galactic gas clouds. Nature 566, 85–88 (2019). https://doi.org/10.1038/s41586-019-0873-4

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• DOI: https://doi.org/10.1038/s41586-019-0873-4

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