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arxiv: 1906.11243 · v1 · pith:NPC5FCFDnew · submitted 2019-06-26 · 🌌 astro-ph.GA · astro-ph.HE· gr-qc

First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

The Event Horizon Telescope Collaboration This is my paper

Pith reviewed 2026-05-25 15:14 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.HEgr-qc
keywords black hole shadowM87Event Horizon Telescopesupermassive black holegeneral relativity testGRMHD simulationsradio interferometryKerr metric
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The pith

EHT observations of M87 show a bright crescent with a central dark region whose size matches the shadow of a 6.5-billion-solar-mass Kerr black hole.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the properties of the radio source at the center of galaxy M87 using 2017 Event Horizon Telescope data. Geometric crescent models fitted to the visibility data are preferred over other comparably complex shapes, and GRMHD simulations calibrate the observed ring diameter to physical scales. More than half the arcsecond-scale flux originates near the horizon while emission inside that region is suppressed by more than a factor of ten. These results are used to infer an angular gravitational radius and, with an adopted distance, a black-hole mass that is consistent with general relativity. The consistency across independent fitting methods, image reconstructions, and simulation libraries forms the core evidence presented.

Core claim

Across all methods the data show a crescent of diameter 42 plus or minus 3 microarcseconds whose interior is suppressed by more than a factor of ten; associating this feature with lensed emission around the photon ring yields an angular gravitational radius of 3.8 plus or minus 0.4 microarcseconds and a mass of 6.5 plus or minus 0.2 statistical plus or minus 0.7 systematic times 10 to the ninth solar masses, consistent with a central Kerr black hole.

What carries the argument

Asymmetric crescent (ring with interior brightness depression) models fitted directly to visibility data and calibrated against GRMHD simulations of the emission region.

If this is right

  • More than 50 percent of the total flux at arcsecond scales originates from within a few gravitational radii of the horizon.
  • Emission interior to the shadow region is suppressed by a factor greater than 10.
  • The fractional width of the crescent is constrained to be less than 0.5.
  • All analysis pipelines and data sets return statistically consistent values for the ring diameter and inferred mass.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future multi-epoch or multi-frequency EHT observations could test whether the shadow size remains stable as predicted by the Kerr metric.
  • The same crescent-fitting approach could be applied to other nearby low-luminosity AGN once comparable resolution is achieved.
  • The mass value supplies an independent anchor for dynamical models of the M87 stellar cluster and jet.

Load-bearing premise

That the observed crescent is produced by lensed emission immediately outside the black-hole shadow rather than by some unrelated astrophysical structure.

What would settle it

An independent mass measurement from stellar or gas dynamics that lies outside the reported 6.5 plus or minus 0.9 times 10 to the ninth solar-mass range, or a higher-resolution image showing no central brightness depression at the predicted scale.

Figures

Figures reproduced from arXiv: 1906.11243 by The Event Horizon Telescope Collaboration.

Figure 1
Figure 1. Figure 1: (u, v)-coverage (left panel) and visibility amplitudes (right panel) of M87 for the high-band April 11 data. The (u, v)-coverage has two primary orientations, east–west in blue and north–south in red, with two diagonal fillers at large baselines in green and black. Note that the Large Millimeter Telescope (LMT) and the Submillimeter Telescope (SMT) participate in both orientations, and that the LMT amplitu… view at source ↗
Figure 2
Figure 2. Figure 2: , which summarizes the results of fitting a series of increasingly complex geometric models to the M87 data. We [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic diagrams illustrating the crescent components of the xs‐ring (left panel) and xs‐ringauss (right panel) models. Dashed lines outline the inner and outer circular disk components that are differenced to produce the crescent models, and for the xs‐ringauss model the FWHM of the fixed Gaussian component is additionally traced as a dotted line. The red and green curves above and to the right of each … view at source ↗
Figure 4
Figure 4. Figure 4: , with their corresponding image domain representa￾tions shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Image domain representations of a random posterior sample from the xs‐ring (left panel) and xs‐ringauss (right panel) model fits to the April 6 high-band data set; note that these are representative images drawn from the posteriors, and thus do not represent maximum likelihood or other “best-fit” equivalents. The xs‐ring model fit uses only closure quantities, so we have scaled the total flux density to be… view at source ↗
Figure 6
Figure 6. Figure 6: Joint posteriors for the key physical parameters derived from GC model fits to the April 5, high-band data set. Blue contours (upper-right triangle) show xs‐ ring posteriors obtained from the dynesty-based fitting scheme, while red contours (lower-left triangle) show xs‐ringauss posteriors obtained using THEMIS. Contours enclose 68% and 95% of the posterior probability. Note that recovery of the total comp… view at source ↗
Figure 7
Figure 7. Figure 7: Posterior medians and 68% confidence intervals for selected parameters derived from GC model fitting for all observing days and bands. Blue circular points indicate xs‐ring fits using the dynesty-based fitting scheme applied to individual data sets (i.e., a single band on a single day). Red square points indicate xs‐ringauss fits using THEMIS applied to individual data sets, while orange square points show… view at source ↗
Figure 8
Figure 8. Figure 8: shows the θg values obtained as a result of applying our calibrated scaling factor to the crescent diameter values measured for each day and band, and [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: We show in Paper V that these approximations generally hold for flux and mass for rescalings by factors of 2 from their fiducial values. 6.3. Fitting Single Snapshots to EHT Data For both model selection and parameter estimation, the first step is fitting an SSM model to the EHT data set described in detail in Section 2.1. The only difference here is that intra-site baselines are excluded. These probe ang… view at source ↗
Figure 10
Figure 10. Figure 10: Distributions of recovered θg from five representative GRMHD simulations as measured by the THEMIS (left; maroon) and GENA (right; green) pipelines. Only those snapshots for which the likelihood is above the median (THEMIS), or for which the combined χ2 statistic is below the median (GENA) are included. For a wide range of simulations, the recovered θg are consistent with each other. All of the simulation… view at source ↗
Figure 11
Figure 11. Figure 11: Visibility amplitude and closure phase residuals for an SSM fit to the April 5, high-band data for a “good” snapshot image frame from a MAD simulation with a* = 0, i = 167°, and Rhigh = 160. The reduced-χ2 values for the fits are 5.9 (THEMIS) and 7.3 (GENA). All residuals are normalized by their corresponding estimated observational errors [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Three sample SSM fits to April 6 high-band data. All are from models with THEMIS-AIS pAIS > 0.1. In panels (a) and (b), the prominent photon ring places a strong constraint on θg. In panel (c), the extended disk emission results in a smaller θg estimate. 16 The Astrophysical Journal Letters, 875:L6 (44pp), 2019 April 10 The EHT Collaboration et al [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Constraints on θg arising from the GRMHD model fitting procedure, by day and band. The maroon squares and green triangles are the constraints arising form the THEMIS and GENA pipelines. Solid error bars indicate the 68% confidence levels about the median. The maroon colored band indicates the combined constraint across both bands and all days [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: shows the mean diameters of images reconstructed using the low-band data during all four days of M87 observations with three image reconstruction methods (eht￾imaging, SMILI, DIFMAP; see Paper IV). Image samples are reconstructed for each data set and for a wide range of weights of the regularizers (∼2000 images for eht-imaging and SMILI and ∼30 for DIFMAP, see Paper IV). Diameters measured from the full … view at source ↗
Figure 16
Figure 16. Figure 16: shows the shaded region for this model, which follows a similar trend. The measured properties of the images and source models inferred by all methods generally fall within the expected bands. At least part of the systematic differences in our diameter measurements may be attributed to the relatively large uncertainty in width, as a result of their weak anti-correlation. 7.3. From Image Diameter to Angula… view at source ↗
Figure 18
Figure 18. Figure 18: shows the distribution of the fractional spread in diameters for the Top Set images of M87 reconstructed using two image domain methods (eht-imaging and SMILI) for the April 5 low-band data set. The figure also shows the fractional spread in diameters of a subset of ∼300 images among those in the GRMHD image library discussed in Paper V that provide acceptable fits according to AIS. Note that these compar… view at source ↗
Figure 19
Figure 19. Figure 19: Estimates of the mass of the central black hole in M87 for the three different measurement techniques employed in this Letter (see also [PITH_FULL_IMAGE:figures/full_fig_p021_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Spectral energy distribution of a putative photosphere in comparison to EHT and multi-wavelength data. The lower limit for the thermal bump associated with boundary-layer emission in the absence of a horizon is shown for a compact object with the size reported here (dark green band and arrow) and a jet power 1042 erg s−1 . The photospheric component has been added to a jet synchrotron emission model (blu… view at source ↗
Figure 21
Figure 21. Figure 21: shows the posterior on the fractional deviation between the EHT and the dynamical inferences of the mass-to￾distance ratio, when we assume the prior measurements based on stellar and gas dynamics. We find δ = −0.01 ± 0.17 (68% credible intervals) for the stellar and δ = 0.78 ± 0.3 for the gas dynamics priors. The fact that our measurement θg is consistent with one of the prior measurements θdyn allows us … view at source ↗
Figure 22
Figure 22. Figure 22: Reconstructed LMT station gains by THEMIS from GC model fits to the April 5, 6, 10, and 11 low-band data sets. All other station gains are very close to unity, and are consistent with those from image reconstruction. The inferred LMT gains are consistent with those found in Paper IV across all days. 26 The Astrophysical Journal Letters, 875:L6 (44pp), 2019 April 10 The EHT Collaboration et al [PITH_FULL_… view at source ↗
Figure 23
Figure 23. Figure 23: ). We find that two nuisance Gaussians for the xs‐ ringauss GC model (for a total of 26 free parameters), and three for the xs‐ring GC model (for a total of 28 free parameters), are the threshold values that most generally satisfy this criterion. These values are thus used for all GC model fits presented in this Letter. When fit alongside the GC models to the M87 data, we find that the nuisance Gaussian c… view at source ↗
Figure 24
Figure 24. Figure 24: Examples of GRMHD snapshots used for calibration (see Appendix D). The top three panels show the images used to calibrate the “observational uncertainty” associated with changing (u, v)-sampling and systematics across days (Part I). The bottom four panels show example images taken from the pool of 100 that were used to calibrate the “theoretical uncertainty” caused by different physical parameters and tur… view at source ↗
Figure 25
Figure 25. Figure 25: Reconstructed diameters using the GC models from synthetic data generated from GRMHD simulations. Green bands show the one-sided 68-percentile ranges within the Part I reconstructions (left). The red bands show the one-sided 68-percentile range of the combined Part I and II reconstructions (right). These are separated by GRMHD simulation type: MAD models are collected in white panels, while SANE models ar… view at source ↗
Figure 26
Figure 26. Figure 26: Sources and magnitudes of random and systematic uncertainty on the measurement of θg with GC models. These include the average posterior (blue), the impact of different realizations of unmodeled observational systematic errors (e.g., polarization leakage, (u, v)-coverage, etc.; green), and the impact of variations in the assumed underlying GRMHD simulation (red). (The latter two match the appropriately co… view at source ↗
Figure 27
Figure 27. Figure 27: Illustration of “good” (top panels) and two “bad” (middle and bottom panels) models following the THEMIS-AIS procedure. Closure phases are shown for three triangles at 5 UTC for April 5 as proxies for the χ2 . Blue dots indicate the closure phases for the best-fit SSM associated with each simulation snapshot image. The red diamond shows the same for the average snapshot image. The green triangle shows the… view at source ↗
Figure 28
Figure 28. Figure 28: Anticipated cumulative distribution function of reduced χ2 for the SSM for the same three representative models shown in [PITH_FULL_IMAGE:figures/full_fig_p036_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Example joint posterior plots for the SSM parameters from one of the many mock analyses performed as part of the ensemble-based posterior estimation validation. Shown are the distributions for compact flux density, θg, and PA from SSM analyses of simulated data sets using individual frame snapshots. Left panel: the posteriors from fitting only the frame from which the data was generated. Right panel: the … view at source ↗
Figure 30
Figure 30. Figure 30: shows the fractional differences in the measured diameters and fractional widths inferred using these three different variants. The differences in diameter between the three cases have means of 0.4–0.9 μas and comparable standard deviations, whereas the differences in fractional width have a mean of zero and a standard deviation of 0.04. These differences are smaller than the differences in the feature pa… view at source ↗
Figure 31
Figure 31. Figure 31: Assuming Gaussian posteriors P(μ) for the distance modulus measurements with the means and standard deviations given in [PITH_FULL_IMAGE:figures/full_fig_p039_31.png] view at source ↗
read the original abstract

We present measurements of the properties of the central radio source in M87 using Event Horizon Telescope data obtained during the 2017 campaign. We develop and fit geometric crescent models (asymmetric rings with interior brightness depressions) using two independent sampling algorithms that consider distinct representations of the visibility data. We show that the crescent family of models is statistically preferred over other comparably complex geometric models that we explore. We calibrate the geometric model parameters using general relativistic magnetohydrodynamic (GRMHD) models of the emission region and estimate physical properties of the source. We further fit images generated from GRMHD models directly to the data. We compare the derived emission region and black hole parameters from these analyses with those recovered from reconstructed images. There is a remarkable consistency among all methods and data sets. We find that >50% of the total flux at arcsecond scales comes from near the horizon, and that the emission is dramatically suppressed interior to this region by a factor >10, providing direct evidence of the predicted shadow of a black hole. Across all methods, we measure a crescent diameter of 42+/-3 micro-as and constrain its fractional width to be <0.5. Associating the crescent feature with the emission surrounding the black hole shadow, we infer an angular gravitational radius of GM/Dc2 = 3.8+/- 0.4 micro-as. Folding in a distance measurement of 16.8(+0.8,-0.7) Mpc gives a black hole mass of M = 6.5 +/- 0.2(stat) +/-0.7(sys) 10^9 Msun. This measurement from lensed emission near the event horizon is consistent with the presence of a central Kerr black hole, as predicted by the general theory of relativity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript presents 2017 Event Horizon Telescope observations of M87, fitting geometric crescent models (asymmetric rings with interior depressions) to visibility data using two independent sampling algorithms, directly fitting GRMHD images, and comparing to reconstructed images. All methods converge on a crescent diameter of 42±3 μas with fractional width <0.5; >50% of arcsecond-scale flux originates near the horizon with interior emission suppressed by >10, yielding an angular gravitational radius of 3.8±0.4 μas and a black-hole mass of 6.5±0.2(stat)±0.7(sys)×10^9 M⊙ when combined with the 16.8 Mpc distance. The result is presented as direct evidence for the black-hole shadow and consistency with a central Kerr black hole.

Significance. If the crescent-to-shadow association holds, this constitutes the first horizon-scale imaging of a black-hole shadow with mass inferred from lensed emission near the event horizon. The convergence of independent pipelines (two visibility samplers, GRMHD image fits, and image reconstructions) together with explicit inclusion of both statistical and systematic uncertainties is a notable strength; the mass is consistent with stellar-dynamical estimates while remaining independent of them.

minor comments (2)
  1. [Abstract] Abstract and §4: the factor-of->10 interior suppression is stated as a key result; a short quantitative statement on how this factor is extracted from the geometric-model posterior versus the GRMHD fits would improve clarity.
  2. The distance uncertainty is propagated into the final mass error budget, but the text could explicitly note whether the distance prior is treated as Gaussian or asymmetric in the reported ±0.7(sys) term.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, recognition of the convergence across independent analysis methods, and recommendation to accept. No major comments were raised that require response or revision.

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in independent EHT data

full rationale

The paper fits geometric crescent models directly to the 2017 EHT visibility data using two independent samplers, measures a statistically preferred crescent diameter of 42±3 μas with fractional width <0.5, and reports >10× interior flux suppression. GRMHD simulations are used solely to calibrate the conversion factor associating the observed crescent with the angular gravitational radius (yielding 3.8±0.4 μas); mass follows from multiplication by an external distance (16.8 Mpc). Direct GRMHD image fitting and image reconstruction are performed on the same dataset and yield consistent results. No equation or step reduces the reported mass or shadow identification to a fitted input by construction, and no load-bearing premise rests on an unverified self-citation chain. The central claims remain externally falsifiable against the raw visibility data and independent distance measurement.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard general-relativity assumptions plus one key interpretive step; no new particles or forces are introduced.

free parameters (1)
  • distance to M87
    External prior measurement used to convert angular gravitational radius to physical mass; value 16.8(+0.8,-0.7) Mpc stated in abstract.
axioms (2)
  • domain assumption Spacetime around the central object is described by the Kerr metric of general relativity
    Invoked when stating consistency with a central Kerr black hole (abstract final sentence).
  • domain assumption The fitted crescent corresponds to emission surrounding the black hole shadow
    Explicitly stated as the interpretive step linking geometric model to physical shadow (abstract).

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Works this paper leans on

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