The Pulse of a Black Hole: How Brightness Trembles at the Horizon ✛ ✎

Original: "Probing the details of relativistic electrons with multifrequency observations of M87 black hole"
· J. G. J. Keuper, M. Moscibrodzka
arXiv:2609.11609v1 · 2026-09-10 · arXiv non-exclusive · independent analysis · 2 min
Scientists have calculated how the brightness of a black hole changes across different frequencies and found a way to tell hot electrons from cold ones.

The black hole at the center of the Virgo galaxy has a pulse. It is not a sound but a trembling of brightness: the light strengthens, then weakens, and does so differently at different radio frequencies. Astronomers call this difference the spectral index. If the light is much brighter at a high frequency than at a low one, the index is large. If the brightness is nearly the same, the index is small.

Scientists built a computer model of this black hole. They ran it five times at different rotation speeds and generated 500 snapshots for each run. Then they calculated what each snapshot would look like at six frequencies. The result was 240 000 images. For each one, they measured the spectral index and watched how it trembled from snapshot to snapshot.

The spectral index is like the slope of a roof. A steep roof: brightness drops quickly with frequency. A gentle slope: the light barely changes.

It turned out that the trembling depends on the temperature of the electrons, the particles that swirl around the hole and glow. If the electrons are cold, the index jumps wildly: the roof now stands on end, now lies flat. If they are hot, the trembling is weaker. And if the electrons have a "tail" of very fast particles, the trembling nearly stops. That tail holds the roof's slope steady, the way a guy wire holds a mast.

Actual observations from 2018 have already ruled out several models. For example, a rapidly spinning black hole with cold electrons did not fit: its image came out too small. In 2026, the Event Horizon Telescope will shoot the first "movie" of a black hole at several frequencies. From how strongly the spectral index trembles, we will be able to tell what the electrons there are really like: cold, hot, or with a fast tail. That is how a black hole's pulse will tell us about its heart.

The photon ring of M87* has a spectral index near zero, while the outer regions can reach -3, which means a sharp change in the emission properties on a scale of just a few gravitational radii.

\alpha_{I,\nu_1-\nu_2} = \frac{\ln(F_{\nu_1}/F_{\nu_2})}{\ln(\nu_1/\nu_2)}
The slope of the spectrum, calculated from the ratio of fluxes at two frequencies
R(\beta) = R_{\text{high}}\frac{\beta^2}{1+\beta^2} + R_{\text{low}}\frac{1}{1+\beta^2}
A parameterization of how the temperature ratio depends on the plasma beta parameter
\nu_{\text{crit}} \propto \Theta_e^2 B
The frequency at which the spectrum transitions from optically thick to optically thin
Concepts
EHT m87 event horizon black hole variability horizon area h alpha