Could the Event Horizon Telescope resolve the shadow of the ω Cen IMBH? Calculate the angular shadow size, compare to instrument resolution, and see why the answer is no — and by how much.
M87* shadow: ~42 μas (first EHT image, 2019)
EHT angular resolution: ~25 μas at 230 GHz
ngEHT (planned): ~5–15 μas
Space VLBI (concept): ~1–3 μas
Shadow formula (Bardeen 1973): θ ≈ 5.2 GM / (c² d) where d is the distance to the black hole. The factor 5.2 comes from the photon capture cross-section of a Schwarzschild black hole (≈ 3√3 ≈ 5.196).
| Telescope / Array | Resolution (μas) | Shadow / Resolution | Can resolve? |
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The angular radius of the photon capture shadow for a Schwarzschild black hole is: θ_shadow = 3√3 · GM/(c²d) ≈ 5.196 GM/(c²d) (Bardeen 1973). This is commonly approximated as 5.2 GM/(c²d). Note this gives the radius; the diameter quoted here is 2× this value — consistent with EHT convention where the "shadow" is the dark central region bounded by the photon ring.
Event Horizon Telescope Collaboration 2019 (M87*): shadow diameter ~42 μas at distance ~16.8 Mpc. Akiyama et al. 2022 (Sgr A*): ~52 μas at ~8.18 kpc. Angular resolution of EHT at 230 GHz, longest baseline (Earth diameter ~12,742 km): θ_res = λ/B ≈ 1.3mm/12742km ≈ 21 μas.
For M = 7,100 M☉ at d = 5.2 kpc: θ ≈ 5.2 × 6.674×10⁻¹¹ × 7100 × 1.989×10³⁰ / ((2.998×10⁸)² × 5.2 × 3.086×10¹⁹) ≈ 0.17 μas diameter. EHT resolution ≈ 25 μas → factor ~150 too small. No existing radio telescope can resolve this shadow.