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State-of-the-art energetic and morphological modelling of the launching site of the M87 jet


M87 has been the target of numerous astronomical observations across the electromagnetic spectrum, and very long baseline interferometry has resolved an edge-brightened jet1,2,3,4. However, the origin and formation of its jets remain unclear. In our current understanding, black holes (BH) are the driving engine of jet formation5, and indeed the recent Event Horizon Telescope observations revealed a ring-like structure in agreement with theoretical models of accretion onto a rotating Kerr BH6. In addition to the spin of the BH being a potential source of energy for the launching mechanism, magnetic fields are believed to play a key role in the formation of relativistic jets7,8. A priori, the spin, a, of the BH in M87 is unknown; however, when accounting for the estimates of the X-ray luminosity and jet power, values of \(\left|{a}_{\star }\right|\gtrsim 0.5\) appear favoured6. Besides the properties of the accretion flow and the BH spin, the radiation microphysics including the particle distribution (thermal6 and non-thermal9,10) as well as the particle acceleration mechanism11 play a crucial role. We show that general relativistic magnetohydrodynamic simulations and general relativistic radiative transfer calculations can reproduce the broadband spectrum from the radio to the near-infrared regime and simultaneously match the observed collimation profile of M87, thus allowing us to set rough constraints on the dimensionless spin of M87* to be 0.5 a 1.0, with higher spins being possibly favoured.

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Fig. 1: Large-scale 3D morphology of the jet and disk from a 3D GRMHD MAD simulation for a BH with a = 0.9375.
Fig. 2: Broadband spectrum of the flux density of M87.
Fig. 3: Morphological comparison between observations and theoretical models.
Fig. 4: Jet diameter comparison between observations and theoretical models.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The publicly released version of the GRMHD code BHAC can be found at The eht-imaging software to convolve the images is available at repository


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This research is supported by the ERC synergy grant ‘BlackHoleCam: Imaging the Event Horizon of Black Holes’ (grant no. 610058). C.M.F. is supported by the Black Hole Initiative at Harvard University, which is supported by a grant from the John Templeton Foundation. A.N. was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the ‘2nd Call for H.F.R.I. Research Projects to support Post-Doctoral Researchers’ (project no. 00634). Z.Y. is supported by a UK Research and Innovation Stephen Hawking Fellowship and acknowledges support from a Leverhulme Trust Early Career Fellowship. J.D. is supported by NASA grant no. NNX17AL82 and a Joint Columbia/Flatiron Postdoctoral Fellowship. Research at the Flatiron Institute is supported by the Simons Foundation. The simulations were performed on Goethe-HLR at the Center for Scientific Computing in Frankfurt, on Iboga at the Institut für Theoretische Physik in Frankfurt, and on Pi2.0 at Shanghai Jiao Tong University.

Author information

Authors and Affiliations



A.C.-O. and C.M.F. performed and analysed the GRRT calculations and wrote the manuscript. Y.M. performed the GRMHD simulations and wrote the manuscript. A.N. wrote the manuscript. Z.Y. authored the GRRT code BHOSS. O.P. authored the GRMHD code BHAC. J.D. helped in the GRRT calculations. H.F. and M.K. wrote the manuscript. L.R. wrote the manuscript and coordinated the various aspects of the research. All authors discussed the results and commented on all versions of the manuscript.

Corresponding authors

Correspondence to Alejandro Cruz-Osorio, Christian M. Fromm or Yosuke Mizuno.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Astronomy thanks Bidisha Bandyopadhyay and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data

Extended Data Fig. 1 Large-scale morphology of the jet from GRMHD simulations of a Kerr BH with spin a = 0.9375 (the BH spin is aligned with the z axis).

a) Shown the magnetisation parameters σ, b) the dimensionless electron temperature Θe, c) the distribution of the power-law index κ, and d) the weighted temperature w. All quantities are averaged in space (over the azimuthal direction) and in time (over a time interval of 2,000 M with a cadence of 10 M). The white dashed line marks the boundary between bounded and unbounded (Be > 1.02) material, while the black lines show the most important contours of the logarithm of the magnetisation, \({{{\mathrm{log}}}\,}_{10}\sigma =-1.0,\,0.0\), and 0.5. Moving out from the polar axis, we report the contours for the ‘jet spine’, the ‘jet sheath’, and the ‘external wall’.

Extended Data Fig. 2 Small-scale morphology of the jet from GRMHD simulations.

Same as in Extended Data Fig. 1, Kerr BH with spin a = 0.9375 but on smaller lengthscales.

Extended Data Fig. 3 Same as in Fig. 2, but considering five different values of the black hole spin.

Solid and dotted lines represent nonthermal and thermal emission models, respectively. While gray vertical lines show the most representative frequencies. For each observational data, the uncertainties indicate the variability during the observations.

Extended Data Fig. 4 GRRT and convolved images.

The top panels shown the GRRT, while bottom shown convolved images for thermal and nonthermal emission models for two BHs with spins a= 0.50 and a= 0.9375. The images refer to a representative time (t = 13, 820 M) and we show as an ellipse in the lower-left corner the convolving beam with axes 116 × 307 μas, as in the observational data. The contours in the flux density correspond to \({S}_{i}={S}_{{{{\rm{m}}}}in}+0.43\ {{{\rm{m}}}}Jy\times {\sqrt{2}}^{i}\), where i = 0, 1, …, n, such that Sn < Smax.

Extended Data Fig. 5 Same as in Extended Data Figure 4, but showing the time average computed between 13,000 M and 15,000 M.

Note that all of the features discussed in Fig. Extended Data Figure 4 are present also when averaging in time.

Extended Data Fig. 6 χ2 for the jet width.

χ2 between the observational data and the jet width measured from the numerical simulations (see Fig. 4).

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Cruz-Osorio, A., Fromm, C.M., Mizuno, Y. et al. State-of-the-art energetic and morphological modelling of the launching site of the M87 jet. Nat Astron 6, 103–108 (2022).

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