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.

  • Perspective
  • Published:

Black holes up close

Nature volume 615, pages 597–604 (2023)Cite this article

Subjects

Abstract

Recent developments have ushered in a new era in the field of black-hole astrophysics, providing a direct view of the remarkable environment near black-hole event horizons. These observations have enabled astronomers to confirm long-standing ideas on the physics of gas flowing into black holes with temperatures that are hundreds of times greater than at the centre of the Sun. At the same time, the observations have conclusively shown that light rays near a black hole experience large deflections that cause a dark shadow in the centre of the image, an effect predicted by Einstein’s theory of general relativity. With further investment, this field is poised to deliver decades of advances in our understanding of gravity and black holes through stringent tests of general relativity, as well as insights into the role of black holes as the central engines powering a wide range of astronomical phenomena.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Event Horizon Telescope images of two supermassive BHs.
Fig. 2: Numerical simulation of BH accretion and the resulting theoretically predicted image.
Fig. 3: The origin of photon subrings.
Fig. 4: Radio and millimetre images of the relativistic jet in M87*.

Similar content being viewed by others

Data availability

EHT data for Fig. 1 are available at https://github.com/eventhorizontelescope.

Code availability

Figure 1 and the right panel of Fig. 2 were created using the ehtim (eht-imaging) software package90 which is available at https://github.com/achael/eht-imaging.

References

  1. Schwarzschild, K. On the gravitational field of a mass point according to Einstein’s theory. Abh. Konigl. Preuss. Akad. Wiss. Berlin 1916, 189–196 (1916).

    MathSciNet  ADS  Google Scholar 

  2. Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237–238 (1963). An exact analytical solution of general relativity describing the most general spinning uncharged black hole.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Princeton Univ. Press, 2018).

  4. Michell, J. On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose. By the Rev. John Michell, B. D. F. R. S. in a letter to Henry Cavendish, Esq. F. R. S. and A. S. Phil. Trans. R. Soc. Lond. 74, 35–57 (1784).

    Google Scholar 

  5. Laplace, P. S. Beweis des Satzes, dass die anziehende Kraft bey einem Weltkörper so groß seyn könne, dass das Licht davon nicht ausströmen kann. Allg. Geogr. Ephemer. 4, 1–6 (1799).

  6. Thorne, K. S. Black Holes and Time Warps: Einstein’s Outrageous Legacy (W. W. Norton, 1994).

  7. Begelman, M. & Rees, M. Gravity’s Fatal Attraction (Cambridge Univ. Press, 2020).

  8. Penrose, R. Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57–59 (1965). Mathematical proof that black-hole formation is inevitable in general relativity from certain generic initial conditions.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Schmidt, M. 3C 273 : a star-like object with large red-shift. Nature 197, 1040 (1963). Discovery that the quasar 3C 273, later identified as an accreting supermassive black hole, is at a redshift of 0.158 and therefore very distant from our Galaxy and highly luminous.

    Article  ADS  Google Scholar 

  11. Salpeter, E. E. Accretion of interstellar matter by massive objects. Astrophys. J. 140, 796–800 (1964).

    Article  ADS  Google Scholar 

  12. Luminet, J.-P. Image of a spherical black hole with thin accretion disk. Astron. Astrophys. 75, 228–235 (1979).

    ADS  Google Scholar 

  13. Falcke, H., Melia, F. & Agol, E. Viewing the shadow of the black hole at the Galactic Center. Astrophys. J. Lett. 528, 13–16 (2000).

    Article  ADS  Google Scholar 

  14. Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole. Astrophys. J. Lett. 875, 1 (2019). Landmark experiment with the Event Horizon Telescope that obtained the image of the supermassive black hole M87* and confirmed the predicted black-hole shadow.

    Article  ADS  Google Scholar 

  15. Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way. Astrophys. J. Lett. 930, 12 (2022).

    Article  ADS  Google Scholar 

  16. Eckart, A. & Genzel, R. Observations of stellar proper motions near the Galactic Centre. Nature 383, 415–417 (1996).

    Article  CAS  ADS  Google Scholar 

  17. Ghez, A. M., Klein, B. L., Morris, M. & Becklin, E. E. High proper-motion stars in the vicinity of Sagittarius A*: evidence for a supermassive black hole at the center of our Galaxy. Astrophys. J. 509, 678–686 (1998).

    Article  ADS  Google Scholar 

  18. Ghez, A. M., Morris, M., Becklin, E. E., Tanner, A. & Kremenek, T. The accelerations of stars orbiting the Milky Way’s central black hole. Nature 407, 349–351 (2000). Measurement of the accelerations of stars orbiting the object Sagittarius A* at the centre of the Galaxy.

    Article  CAS  PubMed  ADS  Google Scholar 

  19. Schödel, R. et al. A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way. Nature 419, 694–696 (2002). Landmark study that reported a nearly complete orbit of a star at the centre of our Galaxy and proved beyond reasonable doubt that Sagittarius A* is a four-million-solar-mass black hole.

    Article  PubMed  ADS  Google Scholar 

  20. Ghez, A. M. et al. Stellar orbits around the Galactic Center black hole. Astrophys. J. 620, 744–757 (2005).

    Article  ADS  Google Scholar 

  21. Gebhardt, K. et al. The Black Hole mass in M87 from Gemini/NIFS adaptive optics observations. Astrophys. J. 729, 119 (2011).

  22. Hees, A. et al. Testing general relativity with stellar orbits around the supermassive black hole in our Galactic Center. Phys. Rev. Lett. 118, 211101 (2017).

    Article  CAS  PubMed  ADS  Google Scholar 

  23. GRAVITY Collaboration Detection of the gravitational redshift in the orbit of the star S2 near the Galactic Centre massive black hole. Astron. Astrophys. 615, 15 (2018).

    Article  Google Scholar 

  24. Do, T. et al. Relativistic redshift of the star S0-2 orbiting the Galactic Center supermassive black hole. Science 365, 664–668 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  25. GRAVITY Collaboration Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic Centre massive black hole. Astron. Astrophys. 636, 5 (2020).

    Article  Google Scholar 

  26. Di Matteo, T., Springel, V. & Hernquist, L. Energy input from quasars regulates the growth and activity of black holes and their host galaxies. Nature 433, 604–607 (2005).

    Article  PubMed  ADS  Google Scholar 

  27. Brüggen, M. & Kaiser, C. R. Hot bubbles from active galactic nuclei as a heat source in cooling-flow clusters. Nature 418, 301–303 (2002).

    Article  PubMed  ADS  Google Scholar 

  28. Cattaneo, A. et al. The role of black holes in galaxy formation and evolution. Nature 460, 213–219 (2009).

    Article  CAS  PubMed  ADS  Google Scholar 

  29. Fabian, A. C. Observational evidence of active galactic nuclei feedback. Annu. Rev. Astron. Astrophys. 50, 455–489 (2012).

    Article  CAS  ADS  Google Scholar 

  30. Balbus, S. A. & Hawley, J. F. A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214–222 (1991).

    Article  ADS  Google Scholar 

  31. Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973).

    ADS  Google Scholar 

  32. Novikov, I. D. & Thorne, K. S. in Black Holes (Les Astres Occlus) (eds DeWitt, C. & DeWitt, B.) 343–450 (Gordon & Breach, 1973).

  33. Esin, A. A., McClintock, J. E. & Narayan, R. Advection-dominated accretion and the spectral states of black hole X-ray binaries: application to Nova Muscae 1991. Astrophys. J. 489, 865–889 (1997).

    Article  ADS  Google Scholar 

  34. Fabian, A. C. & Canizares, C. R. Do massive black holes reside in elliptical galaxies? Nature 333, 829–831 (1988).

    Article  ADS  Google Scholar 

  35. Ho, L. C. Nuclear activity in nearby galaxies. Ann. Rev. Astron. Astrophys. 46, 475–539 (2008).

    Article  CAS  ADS  Google Scholar 

  36. Goldwurm, A. et al. Possible evidence against a massive black hole at the Galactic Centre. Nature 371, 589–591 (1994).

    Article  CAS  ADS  Google Scholar 

  37. Grindlay, J. E. Black holes take centre stage? Nature 371, 561–562 (1994).

    Article  CAS  ADS  Google Scholar 

  38. Krichbaum, T. P. et al. VLBI observations of the Galactic Center source SGR A* at 86 GHz and 215 GHz. Astron. Astrophys. 335, 106–110 (1998).

    Google Scholar 

  39. Shen, Z.-Q., Lo, K. Y., Liang, M. C., Ho, P. T. P. & Zhao, J.-H. A size of ~1 au for the radio source Sgr A* at the centre of the Milky Way. Nature 438, 62–64 (2005).

    Article  CAS  PubMed  ADS  Google Scholar 

  40. Yuan, F. & Narayan, R. Hot accretion flows around black holes. Ann. Rev. Astron. Astrophys. 52, 529–588 (2014).

    Article  ADS  Google Scholar 

  41. Shapiro, S. L., Lightman, A. P. & Eardley, D. M. A two-temperature accretion disk model for Cygnus X-1: structure and spectrum. Astrophys. J. 204, 187–199 (1976).

    Article  ADS  Google Scholar 

  42. Pringle, J. E. Thermal instabilities in accretion discs. Mon. Not. R. Astron. Soc. 177, 65–71 (1976).

    Article  ADS  Google Scholar 

  43. Piran, T. The role of viscosity and cooling mechanisms in the stability of accretion disks. Astrophys. J. 221, 652–660 (1978).

    Article  ADS  Google Scholar 

  44. Ichimaru, S. Bimodal behavior of accretion disks: theory and application to Cygnus X-1 transitions. Astrophys. J. 214, 840–855 (1977).

    Article  ADS  Google Scholar 

  45. Rees, M. J., Begelman, M. C., Blandford, R. D. & Phinney, E. S. Ion-supported tori and the origin of radio jets. Nature 295, 17–21 (1982).

    Article  CAS  ADS  Google Scholar 

  46. Narayan, R. & Yi, I. Advection-dominated accretion: a self-similar solution. Astrophys. J. Lett. 428, 13–16 (1994).

    Article  ADS  Google Scholar 

  47. Narayan, R. & Yi, I. Advection-dominated accretion: underfed black holes and neutron stars. Astrophys. J. 452, 710–735 (1995).

    Article  ADS  Google Scholar 

  48. Abramowicz, M. A., Chen, X., Kato, S., Lasota, J.-P. & Regev, O. Thermal equilibria of accretion disks. Astrophys. J. Lett. 438, 37–39 (1995).

    Article  ADS  Google Scholar 

  49. Narayan, R., Mahadevan, R. & Quataert, E. in Theory of Black Hole Accretion Disks (eds Abramowicz, M. A. et al.) 148–182 (Cambridge Univ. Press, 1998).

  50. Narayan, R., Yi, I. & Mahadevan, R. Explaining the spectrum of Sagittarius A* with a model of an accreting black hole. Nature 374, 623–625 (1995). Application of the hot-accretion-flow model to an astrophysical black hole, Sagittarius A* at our Galactic Centre.

    Article  CAS  ADS  Google Scholar 

  51. Reynolds, C. S., Di Matteo, T., Fabian, A. C., Hwang, U. & Canizares, C. R. The ‘quiescent’ black hole in M87. Mon. Not. R. Astron. Soc. 283, 111–116 (1996).

    Article  Google Scholar 

  52. Thompson, A. R., Moran, J. M. & Swenson, G. W. Interferometry and Synthesis in Radio Astronomy 3rd edn (Springer, 2017).

  53. Eisenhauer, F. et al. GRAVITY: getting to the event horizon of Sgr A*. In Optical and Infrared Interferometry Society of Photo-Optical Instrumentation Engineers Conference Series Vol. 7013 (eds Schöller, M. et al.) 70132 (SPIE, 2008).

  54. Walker, R. C., Hardee, P. E., Davies, F. B., Ly, C. & Junor, W. The structure and dynamics of the subparsec jet in M87 based on 50 VLBA observations over 17 Years at 43 GHz. Astrophys. J. 855, 128 (2018).

  55. Baganoff, F. K. et al. Rapid X-ray flaring from the direction of the supermassive black hole at the Galactic Centre. Nature 413, 45–48 (2001).

    Article  CAS  PubMed  ADS  Google Scholar 

  56. Genzel, R. et al. Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre. Nature 425, 934–937 (2003).

    Article  CAS  PubMed  ADS  Google Scholar 

  57. Ghez, A. M. et al. Variable infrared emission from the supermassive black hole at the center of the Milky Way. Astrophys. J. Lett. 601, 159–162 (2004).

    Article  ADS  Google Scholar 

  58. GRAVITY Collaboration Detection of orbital motions near the last stable circular orbit of the massive black hole SgrA*. Astron. Astrophys. 618, 10 (2018). Detection of looped clockwise motion of infrared-emitting gas around the Galactic Centre black hole Sagittarius A*.

    Article  Google Scholar 

  59. Gammie, C. F., McKinney, J. C. & Tóth, G. HARM: a numerical scheme for general relativistic magnetohydrodynamics. Astrophys. J. 589, 444–457 (2003).

    Article  ADS  Google Scholar 

  60. De Villiers, J.-P. & Hawley, J. F. A numerical method for general relativistic magnetohydrodynamics. Astrophys. J. 589, 458–480 (2003).

    Article  ADS  Google Scholar 

  61. Mościbrodzka, M., Gammie, C. F., Dolence, J. C., Shiokawa, H. & Leung, P. K. Radiative models of SGR A* from GRMHD simulations. Astrophys. J. 706, 497–507 (2009).

    Article  ADS  Google Scholar 

  62. Dexter, J., Agol, E., Fragile, P. C. & McKinney, J. C. The submillimeter bump in Sgr A* from relativistic MHD simulations. Astrophys. J. 717, 1092–1104 (2010).

    Article  ADS  Google Scholar 

  63. Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. V. Testing astrophysical models of the Galactic Center black hole. Astrophys. J. Lett. 930, 16 (2022).

    Article  ADS  Google Scholar 

  64. Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. VIII. Magnetic field structure near the event horizon. Astrophys. J. Lett. 910, 13 (2021).

    Article  ADS  Google Scholar 

  65. Agol, E. Sagittarius A* polarization: no advection-dominated accretion flow, low accretion rate, and nonthermal synchrotron emission. Astrophys. J. Lett. 538, 121–124 (2000).

    Article  ADS  Google Scholar 

  66. Quataert, E. & Gruzinov, A. Constraining the accretion rate onto Sagittarius A* using linear polarization. Astrophys. J. 545, 842–846 (2000).

    Article  ADS  Google Scholar 

  67. Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. VI. Testing the black hole metric. Astrophys. J. Lett. 930, 17 (2022).

    Article  ADS  Google Scholar 

  68. Newman, E. T. et al. Metric of a rotating, charged mass. J. Math. Phys. 6, 918–919 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  69. Blandford, R. D. & Znajek, R. L. Electromagnetic extraction of energy from Kerr black holes. Mon. Not. R. Astron. Soc. 179, 433–456 (1977). Demonstration that magnetic fields threading the black-hole horizon can extract rotational energy of the black hole, powering relativistic jets.

    Article  ADS  Google Scholar 

  70. Darwin, C. The gravity field of a particle. Proc. R. Soc. Lond. Ser. A 249, 180–194 (1959).

  71. Bardeen, J. M. in Black Holes (Les Astres Occlus) (eds DeWitt, C. & DeWitt, B.) 241–289 (Gordon & Breach, 1973).

  72. Johnson, M. D. & Lupsasca, A. et al. Universal interferometric signatures of a black hole’s photon ring. Sci. Adv. 6, 1310 (2020). Description of the formation of a set of nested self-similar subrings by black-hole lensing, and discussion of how the subrings could be disentangled in the image via interferometry.

    Article  ADS  Google Scholar 

  73. Broderick, A. E., Johannsen, T., Loeb, A. & Psaltis, D. Testing the no-hair theorem with Event Horizon Telescope observations of Sagittarius A*. Astrophys. J. 784, 7 (2014).

    Article  ADS  Google Scholar 

  74. Psaltis, D. et al. Gravitational test beyond the first post-Newtonian order with the shadow of the M87 black hole. Phys. Rev. Lett. 125, 141104 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  75. Chael, A., Johnson, M. D. & Lupsasca, A. Observing the inner shadow of a black hole: a direct view of the event horizon. Astrophys. J. 918, 6 (2021).

    Article  CAS  ADS  Google Scholar 

  76. Johannsen, T. & Psaltis, D. Testing the no-hair theorem with observations in the electromagnetic spectrum. II. Black hole images. Astrophys. J. 718, 446–454 (2010).

    Article  ADS  Google Scholar 

  77. Gralla, S. E., Lupsasca, A. & Marrone, D. P. The shape of the black hole photon ring: a precise test of strong-field general relativity. Phys. Rev. D 102, 124004 (2020).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  78. Penrose, R. Gravitational collapse: the role of general relativity. Nuovo Cimento Rivista Serie 1, 252 (1969).

    ADS  Google Scholar 

  79. Bardeen, J. M., Press, W. H. & Teukolsky, S. A. Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972).

    Article  ADS  Google Scholar 

  80. Semenov, V., Dyadechkin, S. & Punsly, B. Simulations of jets driven by black hole rotation. Science 305, 978–980 (2004).

    Article  CAS  PubMed  ADS  Google Scholar 

  81. Tchekhovskoy, A., Narayan, R. & McKinney, J. C. Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole. Mon. Not. R. Astron. Soc. 418, 79–83 (2011).

    Article  ADS  Google Scholar 

  82. Ricarte, A., Palumbo, D. C. M., Narayan, R., Roelofs, F. & Emami, R. Observational signatures of frame dragging in strong gravity. Astrophys. J. Lett. 941, L12 (2022).

  83. Falcke, H. & Markoff, S. The jet model for Sgr A*: radio and X-ray spectrum. Astron. Astrophys. 362, 113–118 (2000).

    ADS  Google Scholar 

  84. Yusef-Zadeh, F., Roberts, D., Wardle, M., Heinke, C. O. & Bower, G. C. Flaring activity of Sagittarius A* at 43 and 22 GHz: evidence for expanding hot plasma. Astrophys. J. 650, 189–194 (2006).

    Article  CAS  ADS  Google Scholar 

  85. Brinkerink, C. D., Falcke, H., Law, C. J., Barkats, D. & Bower, G. C. et al. ALMA and VLA measurements of frequency-dependent time lags in Sagittarius A*: evidence for a relativistic outflow. Astron. Astrophys. 576, 41 (2015).

    Article  Google Scholar 

  86. Psaltis, D., Wex, N. & Kramer, M. A quantitative test of the no-hair theorem with Sgr A* using stars, pulsars, and the Event Horizon Telescope. Astrophys. J. 818, 121 (2016).

    Article  ADS  Google Scholar 

  87. Arzoumanian, Z. et al. The NANOGrav 12.5 yr data set: search for an isotropic stochastic gravitational-wave background. Astrophys. J. Lett. 905, 34 (2020).

    Article  ADS  Google Scholar 

  88. Kalogera, V. et al. The next generation global gravitational wave observatory: the science book. Preprint at https://arxiv.org/abs/2111.06990 (2021).

  89. Amaro-Seoane, P. et al. Laser Interferometer Space Antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).

  90. Chael, A. A. et al. Interferometric imaging directly with closure phases and closure amplitudes. Astrophys. J. 857, 23 (2018).

    Article  ADS  Google Scholar 

  91. Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. IV. Imaging the central supermassive black hole. Astrophys. J. Lett. 875, 4 (2019).

    Article  ADS  Google Scholar 

  92. Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. VII. Polarization of the ring. Astrophys. J. Lett. 910, 12 (2021).

    Article  ADS  Google Scholar 

  93. Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. III. Imaging of the Galactic Center supermassive black hole. Astrophys. J. Lett. 930, 14 (2022).

    Article  ADS  Google Scholar 

  94. Goddi, C. et al. Polarimetric properties of Event Horizon Telescope targets from ALMA. Astrophys. J. Lett. 910, 14 (2021).

    Article  ADS  Google Scholar 

  95. Kravchenko, E. et al. Linear polarization in the nucleus of M87 at 7 mm and 1.3 cm. Astron. Astrophys. 637, 6 (2020).

    Article  Google Scholar 

  96. Owen, F. N., Eilek, J. A. & Kassim, N. E. M87 at 90 centimeters: a different picture. Astrophys. J. 543, 611–619 (2000).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank A. Chael, D. Palumbo and G. Wong for their help making Figs. 1–3.

Author information

Authors and Affiliations

  1. Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

    Ramesh Narayan

  2. Black Hole Initiative, Harvard University, Cambridge, MA, USA

    Ramesh Narayan

  3. Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA

    Eliot Quataert

Authors
  1. Ramesh Narayan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eliot Quataert
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

R.N. and E.Q. contributed equally to all aspects of the paper.

Corresponding author

Correspondence to Ramesh Narayan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narayan, R., Quataert, E. Black holes up close. Nature 615, 597–604 (2023). https://doi.org/10.1038/s41586-023-05768-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-023-05768-4

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