🕳️ Accretion Disk Temperature Gradient

About this simulation

Gas falling toward a black hole rarely falls straight in — leftover angular momentum flattens it into a spinning accretion disk. Friction between neighboring rings orbiting at different speeds (viscous heating) converts orbital energy into heat, and that heat is radiated away as light whose color depends on local temperature. This simulation reproduces that process with real inverse-square gravity and the classical Shakura-Sunyaev disk temperature law.

How it works

• Thousands of particles orbit under Newtonian gravity F ∝ M / r² and drift slowly inward due to viscous torque, exactly like real accreting gas.
• Each particle's color encodes local temperature: T(r) ∝ (Rin/r)^0.75 · √(1 − √(Rin/r)), the Shakura-Sunyaev profile, running from dull red (cool, outer disk) through orange-yellow to blue-white (hot, inner disk).
• Inside the innermost stable circular orbit (ISCO), no stable orbit exists — particles plunge rapidly toward the horizon instead of spiraling gently, matching general relativity's prediction.
• When Doppler beaming is on, the side of the disk sweeping toward the camera brightens and the receding side dims, mimicking relativistic beaming of the fast-orbiting inner gas.

Controls

• Black hole mass — sets the Schwarzschild radius and the depth of the gravity well; heavier holes pull harder but have a proportionally larger, cooler inner disk.
• Accretion rate — how fast gas is being fed in; higher rates raise the whole disk's temperature and brightness.
• Spin (a/M) — a spinning black hole drags the ISCO closer to the horizon, letting the hottest gas orbit deeper in the well.
• Relativistic Doppler beaming — toggle the brightness asymmetry caused by the fast orbital motion of the inner disk.
• ↺ Reset disk — respawns the particle field. Drag to rotate, scroll to zoom.

Did you know?

A black hole itself emits no light — every photon associated with an "image" of a black hole, including the Event Horizon Telescope's pictures of M87* and Sagittarius A*, actually comes from glowing gas in the accretion disk (or jets) outside the event horizon.