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

TL;DR

The paper reports horizon-scale measurements of the M87 black hole using the 2017 Event Horizon Telescope data. It demonstrates a statistically preferred crescent/m darkness morphology by fitting geometric crescent models and GRMHD simulations, then calibrates the measured diameters to a physical scale via GRMHD images. Across geometric, GRMHD, and image-domain analyses, the angular gravitational radius is constrained to θ_g ≈ 3.8 μas, corresponding to a black hole mass M ≈ 6.5 × 10^9 M⊙ (with systematic uncertainties from GRMHD calibration). The results provide robust evidence for a Kerr black hole with a shadow and horizon and establish powerful, consistent cross-method validation of horizon-scale astrophysical inference relevant to strong-field gravity.

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.

Figures (31)

• 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 amplitudes are subject to significant gain errors. There is evidence for substantial depressions in the visibility amplitudes at $\sim 3.4 \mathrm{G} \lambda$ and $\sim 8.3 \mathrm{G} \lambda$. The various lines in the right panel show the expected behavior of (dotted line) a Gaussian, (dashed line) a filled disk, and (green area) a crescent shape along different orientations. The image of M87 does not appear to be consistent with a filled disk or a Gaussian.
• Figure 2: Relative log-likelihood values for different geometric models fit to the M87 data as a function of nominal model complexity; the number of parameters is given in parenthesis for each model. April 5 is shown here, and all days and bands show the same trend. The models shown in this figure are strict subsets of the "generalized crescent model" (labeled here as model " n "; see Section 5.1), and they have been normalized such that the generalized crescent model has a value of$\mathcal{L}=1$; the reduced- $\chi^{2}$ for the generalized crescent fit is 1.24 (see Table 2). We find that the data overwhelmingly prefer crescent models over, e.g., symmetric disk and ring models, and that additional Gaussian components lead to further substantial improvement. Note that a difference of $\sim 5$ on the vertical axis in this plot is statistically significant.
• 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 panel show cross-sectional plots of the intensity through the corresponding horizontal and vertical slices overlaid on the images. The circular and square markers indicate the centers of the outer and inner disks, respectively. The labeled parameters correspond to those described in Section 5.1. Both crescents are shown at an orientation of$\phi=\hat{\phi}=90^{\circ}$.
• Figure 4: Modeled data (top panels) and residuals (bottom panels) for GC model fits to the April 6 high-band data set, with the data plotted in gray; we show results for the median posterior fit. The panels show visibility amplitude (left panels), closure phase (middle panels), and logarithmic closure amplitude (right panels) data. The xs-ringauss model, shown in red, is fit to the visibility amplitudes and closure phases using THEMIS; the dynesty-based xs-ring model, plotted in blue, comes from a fit to closure phases and logarithmic closure amplitude. Because both models fit to closure phases, the center panel shows two sets of models and residuals. All residuals are normalized by the associated observational noise values.
• 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 equal to the 1.0 Jy flux density of the xs-ringauss model fit.