Part IV

Event Horizon Telescope

The Event Horizon Telescope (EHT) is a global VLBI array operating at 1.3 mm and 0.87 mm that resolved the first images of a black-hole shadow: M87* in 2019 and Sgr A* in 2022. This module covers the technique, the physics of the shadow, and the polarimetric imaging that has followed.

VLBI at Millimetre Wavelengths

VLBI (very-long-baseline interferometry) correlates signals from geographically-distant antennas to synthesise an aperture of the diameter of the Earth. Angular resolution:

\[ \theta \;\sim\; \lambda / B \;\sim\; 20\ \mu\text{as at}\ \lambda = 1.3\ \text{mm},\ B = 10^4\ \text{km} \]

Matches the ~42 μas Sgr A* shadow and ~51 μas M87* shadow. 1.3 mm is the shortest transmission-window EHT can use globally. Sparse u-v coverage is reconstructed into images via the CLEAN algorithm + Bayesian imaging (eht-imaging, SMILI).

The Shadow Geometry

In Schwarzschild geometry, photons within impact parameter b < 3√3 r_g (where r_g = GM/c²) fall into the hole; b = 3√3 r_g marks the photon sphere. An observer at infinity sees a dark circle of angular radius ~5.2 r_g/D for a non-rotating BH; for Kerr the shadow is slightly asymmetric depending on spin and observer angle. Bardeen 1973 derived the light-bending geometry; current observations strongly constrain GR over Newtonian alternatives.

Simulation: Shadow Image & VLBI Resolution

Python

script.py51 lines

import numpy as np, matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Black-hole shadow model: dark disk of angular size ~5.2 r_g
# surrounded by asymmetric photon ring
import numpy.random as rnd
rnd.seed(0)
N = 400
x, y = np.meshgrid(np.linspace(-3, 3, N), np.linspace(-3, 3, N))
r = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)

# Shadow (dark) inside r=2.6, photon ring at 2.6-2.8, asymmetric Doppler
ring = np.exp(-((r - 2.7)/0.15)**2) * (1 + 0.6*np.sin(phi))
shadow = 1 - np.exp(-(r/2.6)**12)
noise = 0.1 * rnd.normal(size=x.shape)
image = ring * (1 - shadow*0.8) + noise * np.exp(-r/3)
image = np.clip(image, 0, None)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6), facecolor='#0a0a1a')
ax1.imshow(image, cmap='afmhot', extent=[-3, 3, -3, 3])
ax1.set_xlabel('delta x (r_g)', color='#cbd5e1')
ax1.set_ylabel('delta y (r_g)', color='#cbd5e1')
ax1.set_title('Simulated M87* shadow image',
              color='#fde68a', fontweight='bold')
ax1.tick_params(colors='#cbd5e1')
for s in ax1.spines.values(): s.set_color('#334155')

# Angular resolution vs baseline
baseline = np.logspace(0, 7, 200)   # meters
lamb = 1.3e-3                        # 1.3 mm EHT observing wavelength
theta_rad = lamb / baseline
theta_uas = theta_rad * 206265e6     # microarcsec
ax2.set_facecolor('#111827')
ax2.loglog(baseline/1e3, theta_uas, color='#fbbf24', lw=2.5)
ax2.axhline(25, color='#dc2626', ls='--', label='Sgr A* / M87 shadow 42/51 uas')
ax2.axvline(1e4, color='#34d399', ls='--', label='Earth-size baseline ~10^4 km')
ax2.set_xlabel('Baseline (km)', color='#cbd5e1')
ax2.set_ylabel('Angular resolution (uas)', color='#cbd5e1')
ax2.set_title('VLBI theta ~ lambda/B at 1.3 mm',
              color='#fde68a', fontweight='bold')
ax2.grid(True, color='#334155', alpha=0.3, which='both')
ax2.tick_params(colors='#cbd5e1')
for s in ax2.spines.values(): s.set_color('#334155')
ax2.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print('EHT first image M87* 2019, Sgr A* 2022')
print('Baseline ~ Earth diameter gives ~20 uas resolution at 1.3 mm')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Polarimetric Imaging

EHT Collaboration 2021 released linearly-polarised images of M87* showing a spiral magnetic-field structure consistent with magnetically-arrested accretion (MAD). Linear polarisation fraction ~15%, rotation-measure structure tracks the magnetic-field topology. Polarimetric imaging of Sgr A* (2024) confirms similar MAD structure — probably powering the associated jet at Sgr A* (not visible in M87 but consistent).

Key References

• Event Horizon Telescope Collaboration (2019). “First M87 event horizon telescope results. I. The shadow of the supermassive black hole.” Astrophys. J. Lett., 875, L1.

• Event Horizon Telescope Collaboration (2022). “First Sagittarius A* event horizon telescope results.” Astrophys. J. Lett., 930, L12.

• EHTC (2021). “First M87 event horizon telescope results. VIII. Magnetic field structure near the event horizon.” Astrophys. J. Lett., 910, L13.

• Bardeen, J. M. (1973). “Timelike and null geodesics in the Kerr metric.” In Black Holes, Gordon & Breach.

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