Every galaxy here is a test particle orbiting the cluster's shared gravity well while jittering with a velocity dispersion σ — the spread of line-of-sight speeds astronomers actually measure with a spectrograph. For a cluster in equilibrium the virial theorem states 2K + U = 0: twice the kinetic energy of the galaxies exactly balances (minus) their gravitational potential energy. Solving that for an isothermal sphere of radius R gives the mass the cluster must have to hold together:
2K + U = 0
M_virial ≈ 5·R·σ² / G (R fixed at 1 Mpc here)
Add up every star and every kelvin of the hot X-ray-emitting intracluster gas and the result — the "visible mass" slider — falls far short of M_virial for any realistic σ. That gap is the classic cluster-scale evidence for dark matter, first spotted by Fritz Zwicky in the Coma Cluster in 1933, decades before galaxy rotation curves made the same case for individual galaxies.
- Galaxies — how many orbiting members the cluster contains; larger clusters average hundreds to thousands.
- Velocity dispersion σ — the random orbital speed spread; real clusters run roughly 500–1400 km/s, far faster than any single galaxy's internal rotation.
- Visible mass — the combined mass of stars and the hot intracluster medium (the orange haze) — typically only ~10–15% of a cluster's true mass.
- Dark matter toggle — with dark matter included, gravity uses the full virial mass and the cluster stays bound. Switch it off and gravity falls back to visible mass alone: σ now exceeds the escape speed, so galaxies drift outward and the cluster visibly disperses — exactly the instability real clusters would suffer without their dark matter halo.