Correlations of Simulated Black-Hole Movies Reveal Extreme-Lensing Signatures

A black hole’s gravitational pull can deflect light rays to an arbitrary degree. As a result, any source fluctuation near the black hole creates multiple lagged images on an observer’s screen. For optically thin stochastic emission, these light echoes give rise to correlations of brightness fluctuations across time-dependent images (movies). The correlation pattern disentangles source-specific characteristics from universal features dictated by general relativity. This picture has motivated a proposal to use the two-point image correlation function as a probe of extreme gravitational lensing in upcoming black-hole imaging campaigns. In this work, we test the feasibility of this method by computing the two-point correlation function of brightness fluctuations in a black-hole movie of state-of-the-art realism. The movie is generated by ray tracing a general relativistic magnetohydrodynamic simulation, which can then be blurred to any angular resolution. At an effective resolution expected to be achieved by next-generation terrestrial very-long-baseline interferometric arrays, the lensing signatures appear in neither time-averaged images nor light-curve autocorrelations. However, we demonstrate that they are clearly visible in the more fine-grained two-point image correlation function. Our positive findings motivate a more comprehensive investigation into the instrument specifications and inference techniques needed to resolve extreme lensing effects through correlations.

💡 Research Summary

The authors investigate whether extreme‑gravitational‑lensing signatures—specifically the photon‑ring and its higher‑order images—can be detected not by direct imaging but through statistical correlations in time‑dependent black‑hole movies. They start from a high‑resolution GRMHD simulation of a M87*‑like accretion flow (M = 6.5 × 10⁹ M⊙, spin a* = 0.9375, inclination 163°, ion‑electron temperature ratios Rhigh = 40, Rlow = 1). The simulation spans 4000 GM/c³ with a cadence of 0.5 GM/c³. Using general‑relativistic ray tracing they generate three kinds of movies: (1) a realistic “slow‑light” movie where the fluid evolves while photons propagate, preserving true light‑travel‑time effects; (2) a “fast‑light” movie that treats each snapshot as static, thereby erasing temporal lensing correlations; and (3) an n = 0‑only movie that suppresses all indirect photons, eliminating lensing altogether.

To emulate the finite resolution of upcoming VLBI arrays, the images are convolved with Gaussian kernels of FWHM = 5, 10, and 15 µas, corresponding roughly to the expected performance of the next‑generation Event Horizon Telescope (ngEHT) and the space‑based Black‑Hole Explorer (BHEX). Time‑averaged images at all blur levels show no discernible photon‑ring structure, confirming that direct imaging at these resolutions cannot resolve the ring.

The central observable is the normalized two‑point image correlation function

C(T, x, y, x′, y′) = ⟨ΔI(t, x, y) ΔI(t − T, x′, y′)⟩ /