A black hole up close: an interactive model

Light that passes close to a black hole is bent by its gravity. For every point of the screen this model follows a ray of light back from your eye, past the black hole, and finds where it started: on a thin disk of hot gas circling the black hole, on a star far behind it, or nowhere — if the ray falls in.

What you see

• The shadow — the dark middle, where rays end inside the black hole. It is 2.6 times as wide as the event horizon, the boundary from which nothing gets out.
• The far side of the disk, above and below — light from the part of the disk behind the black hole is bent around it. Over the top you see the upper face of the far side, under the bottom its underside.
• The photon ring — the thin bright ring at the edge of the shadow: light that went around the black hole once or more before it reached you.
• One side brighter — near its inner edge the gas moves at half the speed of light. On the side coming toward you its light is brighter and bluer; on the side going away, dimmer and redder (the Doppler effect).
• A dimmer, redder middle — light climbing out of the black hole’s gravity loses energy (gravitational redshift).
• The inner edge — gas cannot circle closer than three times the radius of the horizon. Inside that, it falls in within a turn and gives almost no light.

How it is computed

Each ray follows the exact path of light around a black hole that does not spin, from Einstein’s general relativity (the Schwarzschild solution). The disk is a thin disk as described by Novikov and Thorne: its temperature at each distance from the center comes from their formula, hottest at about 4.8 horizon radii. The color of every point is the glow of gas at that temperature, shifted by the Doppler effect and by gravity. Each ring of gas circles at its own orbital speed; the clock shows the time of a far-away observer, and the light from different parts of the disk takes different times to reach you.

A black hole looks the same at any mass: a heavier one is just larger and slower. That is why Sagittarius A* and M87* give the same picture — compare the sizes and times in their cards.

What is simplified

• The black hole does not spin. How fast Sagittarius A* and M87* spin is not well measured; a spinning black hole would have a slightly flattened shadow and a disk reaching closer in.
• The temperature is our choice: about 5,000 K at the hottest point, a little cooler than the surface of the Sun, so that the disk glows in visible light — white and yellow where it is hottest, orange and red where it is cooler.
• The real Sagittarius A* and M87* have no bright disk like this one. They take in little gas, and what the Event Horizon Telescope imaged is radio light from thin, hot gas around them; the bright ring in those images comes from the same bending of light. Disks like this glow around black holes that feed fast, such as quasars — and they are hotter.
• The streaks on the disk are made up so that you can see the gas move; every ring of gas turns at its true speed. The disk is shown out to 14 horizon radii; farther out it would go on, cooler and dimmer.
• The stars behind are made up too, but their light is bent in the same way.

Sources

• Sagittarius A*: mass 4.30 million Suns and distance 8,277 parsecs (27,000 light-years) — GRAVITY Collaboration, “Mass distribution in the Galactic Center based on interferometric astrometry of multiple stellar orbits”, A&A 657, L12 (2022). Ring 51.8 ± 2.3 microarcseconds — Event Horizon Telescope Collaboration, ApJL 930, L12 (2022).
• M87*: mass 6.5 ± 0.7 billion Suns, distance 16.8 megaparsecs (55 million light-years), ring 42 ± 3 microarcseconds — Event Horizon Telescope Collaboration, “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole”, ApJL 875, L1 (2019).
• The disk: I. D. Novikov & K. S. Thorne, in Black Holes (Les Houches, 1973); D. N. Page & K. S. Thorne, “Disk-Accretion onto a Black Hole. I. Time-Averaged Structure of Accretion Disk”, ApJ 191, 499 (1974).
• Colors of glowing gas: CIE 1931 color matching functions, as fitted by C. Wyman, P.-P. Sloan & P. Shirley, JCGT 2(2), 1 (2013).