Dark Matter Halos: Flat Rotation Curves & the NFW Density Profile

Rotation curves that refuse to fall off

In the 1970s Vera Rubin and Kent Ford measured how fast stars orbit at different distances from the centres of spiral galaxies. If all the mass were in visible stars and gas, Keplerian orbital velocity should fall off as v ∝ 1/√r at large radius — the same reason outer planets orbit the Sun more slowly than inner ones. Instead, stars in the outer disk orbit at roughly constant velocity no matter how far out they are: a flat rotation curve. That requires an extended halo of unseen mass whose density falls as 1/r², keeping the enclosed mass growing with radius so that v = √(GM/r) stays constant.

Keplerian (visible matter only):  v ∝ 1/√r  for large r
Observed (with dark matter halo): v ≈ constant  (flat rotation curve)
Halo density (isothermal): ρ(r) ∝ 1/r²  → M(r) ∝ r  → v = √(GM/r) = constant

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The NFW profile and the evidence beyond rotation curves

N-body simulations of cold dark matter collapse predict a specific density shape, the Navarro-Frenk-White (NFW) profile, characterised by a halo mass (often quoted as M₂₀₀, the mass within the radius where average density is 200× the critical density) and a concentration parameter c describing how centrally peaked the halo is. Rotation curves are only one of several independent lines of evidence for dark matter: gravitational lensing shows galaxies and clusters bending light more than their visible mass allows, galaxy cluster dynamics — first noted by Fritz Zwicky in 1933 — show galaxies moving far too fast to be gravitationally bound by visible mass alone, and the relative heights of the CMB's acoustic peaks require roughly five times more dark matter than ordinary (baryonic) matter.

The Bullet Cluster: dark matter caught in the act

The clearest single piece of evidence is the Bullet Cluster (1E 0657-558), where two galaxy clusters collided roughly 150 million years ago. The stars in each cluster passed through largely unimpeded, but the hot X-ray-emitting gas — which makes up about 90% of the baryonic mass — was slowed by electromagnetic drag and now lags behind. Gravitational lensing maps show the bulk of the mass staying co-located with the collisionless stars, not the gas, directly demonstrating that most of the cluster's mass is a weakly self-interacting component that passed straight through the collision: dark matter. Modified-gravity theories struggle to explain this separation.

What could dark matter actually be?

The leading candidates are WIMPs (weakly interacting massive particles, ~10–1000 GeV/c², predicted by supersymmetry), axions (ultra-light particles around 10⁻⁵–1 eV/c² proposed to solve the strong CP problem), sterile neutrinos, and primordial black holes. Direct-detection experiments like LUX-ZEPLIN and XENONnT search for nuclei recoiling off WIMPs, while ADMX searches for axion-photon conversion in a magnetic field. After roughly 30 years of searching, no dark matter particle has been confirmed, and the field is increasingly shifting toward lighter and more exotic candidates.

Frequently asked questions

Why do flat galaxy rotation curves imply dark matter?

If a galaxy's mass were all in its visible stars and gas, orbital velocity should fall off as 1/√r at large radius, following Kepler's laws. Instead, stars in the outer disk orbit at roughly constant velocity no matter how far out they are, which requires an extended halo of unseen mass whose density falls as 1/r², keeping enclosed mass growing with radius.

What does the Bullet Cluster prove about dark matter?

When two galaxy clusters collided, their hot X-ray-emitting gas — 90% of the baryonic mass — was slowed by electromagnetic drag and lagged behind, while gravitational lensing showed the bulk of the mass staying co-located with the collisionless stars. That separation between where the normal matter is and where the gravitating mass is directly demonstrates a weakly self-interacting, non-baryonic component: dark matter.

What are the leading candidates for what dark matter actually is?

The main candidates are WIMPs (weakly interacting massive particles, 10-1000 GeV/c², predicted by supersymmetry), axions (ultra-light particles around 10⁻⁵–1 eV/c² proposed to solve the strong CP problem), sterile neutrinos, and primordial black holes. After roughly 30 years of direct-detection searches, no dark matter particle has been confirmed.

Try it live

Everything above runs in your browser — open Dark Matter Halo, drag the halo mass, concentration and stellar fraction sliders, or pick a preset from Milky Way to Dwarf Galaxy, and watch the rotation curve respond in real time. Nothing is installed, nothing is uploaded.

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