Galaxy Rotation Curve: The Dark Matter Problem

Dark Matter Halo

Halo mass 2.0× visible

Simulation speed 1.0×

Edge velocity (actual)

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Edge velocity (expected)

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Halo / visible mass ratio

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Rotation curve

Actual (with halo) Expected (visible mass only)

How it works

For a star orbiting at radius r in a circular orbit, gravity supplies the centripetal force, which gives the orbital speed in terms of the mass M(r) enclosed inside that radius:

v(r) = sqrt( G · M(r) / r )

If a galaxy's mass were just its visible stars and gas (concentrated in the disk), M(r) stops growing far from the center, so v(r) should fall off — the dashed "expected" curve. Real galaxies don't do this: their rotation curves stay flat (or even climb) all the way to the edge. That only works if M(r) keeps growing linearly with r out there — an invisible, roughly spherical halo of mass with no light of its own. That's the dark matter halo (the translucent sphere around the disk).

Halo mass — how much extra invisible mass the halo adds, in units of the galaxy's visible (baryonic) mass. At 0, stars follow the naive falling curve and the animation visibly winds up over time; increase it and the outer stars keep pace, flattening the curve.
Halo: visible — toggle the translucent halo sphere so you can see its extent versus the flat disk of stars.
Expected curve — toggle the dashed baryonic-only prediction on the chart, for direct comparison against the actual (solid) curve the simulated stars are obeying.
Simulation speed — how fast orbital time advances, so you don't have to wait to see the outer stars complete a lap.

This mismatch — first measured precisely by Vera Rubin in the 1970s — is one of the strongest pieces of evidence for dark matter, alongside gravitational lensing and the Bullet Cluster. Nobody has directly detected a dark matter particle yet; experiments like LUX-ZEPLIN and XENONnT are trying.

Core / bulge Disk stars Dark matter halo

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