Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature volume 566, pages 85–88 (2019)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Thermal and chemical evolution of the immediate pre-galactic environment.
Fig. 2: Mass growth histories of the target haloes.
Fig. 3: Morphology of the collapsing objects.
Fig. 4: Gravitational collapse of the target haloes.

Similar content being viewed by others

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.

References

  1. Volonteri, M. The formation and evolution of massive black holes. Science 337, 544–547 (2012).

    Article  ADS  CAS  Google Scholar 

  2. Greif, T. H. The numerical frontier of the high-redshift Universe. Comput. Astrophys. Cosmol. 2, 3 (2015).

    Article  ADS  Google Scholar 

  3. Omukai, K. Primordial star formation under far-ultraviolet radiation. Astrophys. J. 546, 635–651 (2001).

    Article  ADS  CAS  Google Scholar 

  4. Begelman, M. C., Volonteri, M. & Rees, M. J. Formation of supermassive black holes by direct collapse in pre-galactic haloes. Mon. Not. R. Astron. Soc. 370, 289–298 (2006).

    Article  ADS  CAS  Google Scholar 

  5. Hosokawa, T., Omukai, K. & Yorke, H. W. Rapidly accreting supergiant protostars: embryos of supermassive black holes? Astrophys. J. 756, 93 (2012).

    Article  ADS  Google Scholar 

  6. Ardaneh, K. et al. Direct collapse to supermassive black hole seeds with radiation transfer: cosmological haloes. Mon. Not. R. Astron. Soc. 479, 2277–2293 (2018).

    Article  ADS  Google Scholar 

  7. Habouzit, M., Volonteri, M., Latif, M., Dubois, Y. & Peirani, S. On the number density of ‘direct collapse’ black hole seeds. Mon. Not. R. Astron. Soc. 463, 529–540 (2016).

    Article  ADS  CAS  Google Scholar 

  8. Chon, S., Hosokawa, T. & Yoshida, N. Radiation hydrodynamics simulations of the formation of direct-collapse supermassive stellar systems. Mon. Not. R. Astron. Soc. 475, 4104–4121 (2018).

    Article  ADS  Google Scholar 

  9. Hosokawa, T., Yorke, H. W., Inayoshi, K., Omukai, K. & Yoshida, N. Formation of primordial supermassive stars by rapid mass accretion. Astrophys. J. 778, 178 (2013).

    Article  ADS  Google Scholar 

  10. Umeda, H., Hosokawa, T., Omukai, K. & Yoshida, N. The final fates of accreting supermassive stars. Astrophys. J. 830, L34 (2016).

    Article  ADS  Google Scholar 

  11. O’Shea, B. W., Wise, J. H., Xu, H. & Norman, M. L. Probing the ultraviolet luminosity function of the earliest galaxies with the renaissance simulations. Astrophys. J. 807, L12 (2015).

    Article  ADS  Google Scholar 

  12. Xu, H., Wise, J. H., Norman, M. L., Ahn, K. & O’Shea, B. W. Galaxy properties and UV escape fractions during the epoch of reionization: results from the Renaissance simulations. Astrophys. J. 833, 84 (2016).

    Article  ADS  Google Scholar 

  13. Yoshida, N., Abel, T., Hernquist, L. & Sugiyama, N. Simulations of early structure formation: primordial gas clouds. Astrophys. J. 592, 645–663 (2003).

    Article  ADS  CAS  Google Scholar 

  14. Fernandez, R., Bryan, G. L., Haiman, Z. & Li, M. H2 suppression with shocking inflows: testing a pathway for supermassive black hole formation. Mon. Not. R. Astron. Soc. 439, 3798–3807 (2014).

    Article  ADS  CAS  Google Scholar 

  15. Mortlock, D. J. et al. A luminous quasar at a redshift of z = 7.085. Nature 474, 616–619 (2011).

    Article  ADS  CAS  Google Scholar 

  16. Bañados, E. et al. An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5. Nature 553, 473–476 (2018).

    Article  ADS  Google Scholar 

  17. Bryan, G. L. et al. ENZO: an adaptive mesh refinement code for astrophysics. Astrophys. J. Suppl. Ser. 211, 19 (2014).

    Article  ADS  Google Scholar 

  18. Wise, J. H. & Abel, T. ENZO+MORAY: radiation hydrodynamics adaptive mesh refinement simulations with adaptive ray tracing. Mon. Not. R. Astron. Soc. 414, 3458–3491 (2011).

    Article  ADS  Google Scholar 

  19. Shang, C., Bryan, G. L. & Haiman, Z. Supermassive black hole formation by direct collapse: keeping protogalactic gas H2 free in dark matter haloes with virial temperatures T vir ≳ 104 K. Mon. Not. R. Astron. Soc. 402, 1249–1262 (2010).

    Article  ADS  CAS  Google Scholar 

  20. Agarwal, B., Smith, B., Glover, S., Natarajan, P. & Khochfar, S. New constraints on direct collapse black hole formation in the early Universe. Mon. Not. R. Astron. Soc. 459, 4209–4217 (2016).

    Article  ADS  CAS  Google Scholar 

  21. Glover, S. C. O. Simulating the formation of massive seed black holes in the early Universe – I. An improved chemical model. Mon. Not. R. Astron. Soc. 451, 2082–2096 (2015).

    Article  ADS  CAS  Google Scholar 

  22. Machacek, M. E., Bryan, G. L. & Abel, T. Simulations of pregalactic structure formation with radiative feedback. Astrophys. J. 548, 509–521 (2001).

    Article  ADS  CAS  Google Scholar 

  23. Schleicher, D. R. G., Palla, F., Ferrara, A., Galli, D. & Latif, M. Massive black hole factories: supermassive and quasi-star formation in primordial halos. Astron. Astrophys. 558, A59 (2013).

    Article  ADS  Google Scholar 

  24. Hosokawa, T. et al. Formation of massive primordial stars: intermittent UV feedback with episodic mass accretion. Astrophys. J. 824, 119 (2016).

    Article  ADS  Google Scholar 

  25. Sakurai, Y., Hosokawa, T., Yoshida, N. & Yorke, H. W. Formation of primordial supermassive stars by burst accretion. Mon. Not. R. Astron. Soc. 452, 755–764 (2015).

    Article  ADS  CAS  Google Scholar 

  26. Hirano, S., Hosokawa, T., Yoshida, N. & Kuiper, R. Supersonic gas streams enhance the formation of massive black holes in the early universe. Science 357, 1375–1378 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  27. Onoue, M. et al. Minor contribution of quasars to ionizing photon budget at z ∼ 6: update on quasar luminosity function at the faint end with Subaru/Suprime-Cam. Astrophys. J. 847, L15 (2017).

    Article  ADS  Google Scholar 

  28. Kim, Y. et al. The Infrared Medium-deep Survey. IV. The low Eddington ratio of a faint quasar at z ∼ 6: not every supermassive black hole is growing fast in the early Universe. Astrophys. J. 855, 138 (2018).

    Article  ADS  Google Scholar 

  29. Turk, M. J. et al. yt: a multi-code analysis toolkit for astrophysical simulation data. Astrophys. J. Suppl. Ser. 192, 9 (2011).

    Article  ADS  Google Scholar 

  30. Abel, T., Bryan, G. L. & Norman, M. L. The formation of the first star in the Universe. Science 295, 93–98 (2002).

    Article  ADS  CAS  Google Scholar 

  31. O’Shea, B. W. & Norman, M. L. Population III star formation in a ΛCDM Universe. I. The effect of formation redshift and environment on protostellar accretion rate. Astrophys. J. 654, 66–92 (2007).

    Article  ADS  Google Scholar 

  32. Turk, M. J., Abel, T. & O’Shea, B. The formation of population III binaries from cosmological initial conditions. Science 325, 601–605 (2009).

    Article  ADS  CAS  Google Scholar 

  33. Xu, H., Wise, J. H. & Norman, M. L. Population III stars and remnants in high-redshift galaxies. Astrophys. J. 773, 83 (2013).

    Article  ADS  Google Scholar 

  34. Xu, H., Ahn, K., Wise, J. H., Norman, M. L. & O’Shea, B. W. Heating the intergalactic medium by X-Rays from population III binaries in high-redshift galaxies. Astrophys. J. 791, 110 (2014).

    Article  ADS  Google Scholar 

  35. Chen, P., Wise, J. H., Norman, M. L., Xu, H. & O’Shea, B. W. Scaling relations for galaxies prior to reionization. Astrophys. J. 795, 144 (2014).

    Article  ADS  Google Scholar 

  36. Ahn, K., Xu, H., Norman, M. L., Alvarez, M. A. & Wise, J. H. Spatially extended 21 cm signal from strongly clustered UV and X-ray sources in the early Universe. Astrophys. J. 802, 8 (2015).

    Article  ADS  Google Scholar 

  37. Xu, H., Norman, M. L., O’Shea, B. W. & Wise, J. H. Late pop III star formation during the epoch of reionization: results from the Renaissance simulations. Astrophys. J. 823, 140 (2016).

    Article  ADS  Google Scholar 

  38. Komatsu, E. et al. Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. Ser. 192, 18 (2011).

    Article  ADS  Google Scholar 

  39. Hahn, O. & Abel, T. Multi-scale initial conditions for cosmological simulations. Mon. Not. R. Astron. Soc. 415, 2101–2121 (2011).

    Article  ADS  CAS  Google Scholar 

  40. Abel, T., Anninos, P., Zhang, Y. & Norman, M. L. Modeling primordial gas in numerical cosmology. New Astron. 2, 181–207 (1997).

    Article  ADS  CAS  Google Scholar 

  41. Smith, B. D., Turk, M. J., Sigurdsson, S., O’Shea, B. W. & Norman, M. L. Three modes of metal-enriched star formation in the early Universe. Astrophys. J. 691, 441–451 (2009).

    Article  ADS  CAS  Google Scholar 

  42. Behroozi, P. S., Wechsler, R. H. & Wu, H.-Y. The ROCKSTAR phase-space temporal halo finder and the velocity offsets of cluster cores. Astrophys. J. 762, 109 (2013).

    Article  ADS  Google Scholar 

  43. Behroozi, P. S. et al. Gravitationally consistent halo catalogs and merger trees for precision cosmology. Astrophys. J. 763, 18 (2013).

    Article  ADS  Google Scholar 

  44. Wise, J. H., Turk, M. J., Norman, M. L. & Abel, T. The birth of a galaxy: primordial metal enrichment and stellar populations. Astrophys. J. 745, 50 (2012).

    Article  ADS  Google Scholar 

  45. Regan, J. A., Johansson, P. H. & Wise, J. H. Forming super-massive black hole seeds under the influence of a nearby anisotropic multi-frequency source. Mon. Not. R. Astron. Soc. 459, 3377–3394 (2016).

    Article  ADS  CAS  Google Scholar 

  46. Wise, J. H. & Abel, T. Suppression of H2 cooling in the ultraviolet background. Astrophys. J. 671, 1559–1567 (2007).

    Article  ADS  CAS  Google Scholar 

  47. O’Shea, B. W. & Norman, M. L. Population III star formation in a Λ CDM Universe. II. Effects of a photodissociating background. Astrophys. J. 673, 14–33 (2008).

    Article  ADS  Google Scholar 

  48. Naoz, S., Yoshida, N. & Gnedin, N. Y. Simulations of early baryonic structure formation with stream velocity. II. The gas fraction. Astrophys. J. 763, 27 (2013).

    Article  ADS  Google Scholar 

  49. Regan, J. A., Johansson, P. H. & Wise, J. H. The effect of dark matter resolution on the collapse of baryons in high-redshift numerical simulations. Mon. Not. R. Astron. Soc. 449, 3766–3779 (2015).

    Article  ADS  CAS  Google Scholar 

  50. Kitsionas, S. & Whitworth, A. P. Smoothed particle hydrodynamics with particle splitting, applied to self-gravitating collapse. Mon. Not. R. Astron. Soc. 330, 129–136 (2002).

    Article  ADS  Google Scholar 

  51. Bromm, V. & Loeb, A. Formation of the first supermassive black holes. Astrophys. J. 596, 34–46 (2003).

    Article  ADS  Google Scholar 

  52. Dotti, M., Colpi, M., Haardt, F. & Mayer, L. Supermassive black hole binaries in gaseous and stellar circumnuclear discs: orbital dynamics and gas accretion. Mon. Not. R. Astron. Soc. 379, 956–962 (2007).

    Article  ADS  Google Scholar 

  53. Hirano, S. et al. One hundred first stars: protostellar evolution and the final masses. Astrophys. J. 781, 60 (2014).

    Article  ADS  Google Scholar 

  54. Chiaki, G. & Yoshida, N. Particle splitting in smoothed particle hydrodynamics based on Voronoi diagram. Mon. Not. R. Astron. Soc. 451, 3955–3963 (2015).

    Article  ADS  CAS  Google Scholar 

  55. Wolcott-Green, J., Haiman, Z. & Bryan, G. L. Photodissociation of H2 in protogalaxies: modelling self-shielding in three-dimensional simulations. Mon. Not. R. Astron. Soc. 418, 838–852 (2011).

    Article  ADS  CAS  Google Scholar 

  56. Smith, B. D. et al. GRACKLE: a chemistry and cooling library for astrophysics. Mon. Not. R. Astron. Soc. 466, 2217–2234 (2017).

    Article  ADS  CAS  Google Scholar 

  57. Barkana, R. & Loeb, A. In the beginning: the first sources of light and the reionization of the Universe. Phys. Rep. 349, 125–238 (2001).

    Article  ADS  CAS  Google Scholar 

  58. Wise, J. H. & Abel, T. Resolving the formation of protogalaxies. I. Virialization. Astrophys. J. 665, 899–910 (2007).

    Article  ADS  CAS  Google Scholar 

  59. Wechsler, R. H., Bullock, J. S., Primack, J. R., Kravtsov, A. V. & Dekel, A. Concentrations of dark halos from their assembly histories. Astrophys. J. 568, 52–70 (2002).

    Article  ADS  CAS  Google Scholar 

  60. Regan, J. A. & Haehnelt, M. G. The formation of compact massive self-gravitating discs in metal-free haloes with virial temperatures of 13000-30000K. Mon. Not. R. Astron. Soc. 393, 858–871 (2009).

    Article  ADS  CAS  Google Scholar 

  61. Wang, B. & Silk, J. Gravitational instability and disk star formation. Astrophys. J. 427, 759–769 (1994).

    Article  ADS  Google Scholar 

  62. Hartwig, T., Agarwal, B. & Regan, J. A. Gravitational wave signals from the first massive black hole seeds. Mon. Not. R. Astron. Soc. 479, L23–L27 (2018).

    Article  ADS  Google Scholar 

  63. Shu, F. H. Self-similar collapse of isothermal spheres and star formation. Astrophys. J. 214, 488–497 (1977).

    Article  ADS  Google Scholar 

  64. Bonnell, I. A., Bate, M. R. & Zinnecker, H. On the formation of massive stars. Mon. Not. R. Astron. Soc. 298, 93–102 (1998).

    Article  ADS  Google Scholar 

  65. Hosokawa, T., Yorke, H. W. & Omukai, K. Evolution of massive protostars via disk accretion. Astrophys. J. 721, 478–492 (2010).

    Article  ADS  Google Scholar 

  66. Woods, T. E., Heger, A., Whalen, D. J., Haemmerlé, L. & Klessen, R. S. On the maximum mass of accreting primordial supermassive stars. Astrophys. J. 842, L6 (2017).

    Article  ADS  Google Scholar 

  67. Chen, K.-J., Heger, A., Woosley, S., Almgren, A. & Whalen, D. J. Pair instability supernovae of very massive population III stars. Astrophys. J. 792, 44 (2014).

    Article  ADS  Google Scholar 

  68. Ota, K. et al. Large-scale environment of a z = 6.61 luminous quasar probed by Lyα emitters and Lyman break galaxies. Astrophys. J. 856, 109 (2018).

    Article  ADS  Google Scholar 

  69. Shankar, F. The demography of supermassive black holes: growing monsters at the heart of galaxies. New Astron. Rev. 53, 57–77 (2009).

    Article  ADS  CAS  Google Scholar 

  70. Terrazas, B. A. et al. Quiescence correlates strongly with directly measured black hole mass in central galaxies. Astrophys. J. 830, L12 (2016).

    Article  ADS  Google Scholar 

  71. Benson, A. J. GALACTICUS: a semi-analytic model of galaxy formation. New Astron. 17, 175–197 (2012).

    Article  ADS  Google Scholar 

  72. Heger, A., Fryer, C. L., Woosley, S. E., Langer, N. & Hartmann, D. H. How massive single stars end their life. Astrophys. J. 591, 288–300 (2003).

    Article  ADS  Google Scholar 

  73. Chatzopoulos, E. & Wheeler, J. C. Effects of rotation on the minimum mass of primordial progenitors of pair-instability supernovae. Astrophys. J. 748, 42 (2012).

    Article  ADS  Google Scholar 

  74. Visbal, E., Haiman, Z. & Bryan, G. L. A no-go theorem for direct collapse black holes without a strong ultraviolet background. Mon. Not. R. Astron. Soc. 442, L100–L104 (2014).

    Article  ADS  CAS  Google Scholar 

Download references

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 and Affiliations

  1. Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Atlanta, GA, USA

    John H. Wise

  2. Centre for Astrophysics and Relativity, School of Mathematical Sciences, Dublin City University, Dublin, Ireland

    John A. Regan & Turlough P. Downes

  3. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, USA

    Brian W. O’Shea

  4. Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA

    Brian W. O’Shea

  5. Center for Astrophysics and Space Sciences, University of California, San Diego, CA, USA

    Michael L. Norman & Hao Xu

  6. San Diego Supercomputer Center, San Diego, CA, USA

    Michael L. Norman & Hao Xu

  7. IBM, Poughkeepsie, NY, USA

    Hao Xu

Authors
  1. John H. Wise
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John A. Regan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Brian W. O’Shea
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael L. Norman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Turlough P. Downes
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

a–d, 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.

a–d, Same as Extended Data Fig. 3, but for the clumps in the LWH (a) and the MMH (b–d). 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.

Extended Data Table 1 Properties of halo candidates hosting supermassive star formation
Full size table

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing