Astrophysics ★★☆ Moderate

🌌 Galactic Rotation Curve

Stars far from a galaxy's centre orbit faster than Kepler's law predicts. Vera Rubin's discovery of flat rotation curves — V(r) = constant — is the most direct evidence for dark matter halos. Adjust the dark matter fraction and watch the predicted curve change.

V_max: — km/s V_flat: — km/s Dark matter: 75% R_halo: — kpc

🌌 The Dark Matter Mystery

If only luminous matter existed, orbital velocity would fall off as V ∝ 1/√r (Keplerian) beyond the visible disk. Instead, observations show V ≈ constant out to 200+ kpc — the flat rotation curve. This demands a large invisible mass component: the dark matter halo.

V_total(r) = √[ V_disk²(r) + V_halo²(r) ]

The NFW (Navarro-Frenk-White, 1996) profile describes DM density as ρ(r) = ρ₀ / (r/rs)(1 + r/rs)², giving a halo velocity contribution that stays nearly flat at large r. Dark matter makes up ~85% of all matter in the Universe.

About this simulation

This simulation reproduces the observation that made Vera Rubin famous: stars far from a galaxy's centre orbit much faster than visible matter alone can explain. It computes V_total(r) = √[V_disk²(r) + V_halo²(r)], combining a Freeman-1970 disk model with an NFW (Navarro-Frenk-White) dark matter halo profile, and lets you compare the resulting flat rotation curve against the falling Keplerian curve that pure visible mass would predict.

🔬 What it shows

Without dark matter, orbital velocity should fall off as V ∝ 1/√r (Keplerian) beyond the visible disk edge — the same way planets slow down further from the Sun. Real galaxies instead show flat or slowly rising rotation curves at large radii, which requires an additional, invisible mass component distributed in an NFW halo with density ρ(r) = ρ₀/[(r/rs)(1+r/rs)²].

🎮 How to use

Choose a galaxy preset (Milky Way, Andromeda, dwarf galaxy) from the dropdown, or adjust Dark matter fraction, Galaxy mass, and Halo scale directly. The dashed Keplerian curve shows what velocities would look like with visible mass alone, the DM halo (NFW) curve shows dark matter's contribution, and the solid total curve is what's actually observed — V_max and V_flat readouts update live.

💡 Did you know?

Vera Rubin's rotation curve measurements in the 1970s were one of the first strong pieces of observational evidence for dark matter — decades before particle physicists had any direct detection candidate. The mismatch between visible mass and orbital speed is still unexplained by ordinary matter alone, which is why the dark matter halo remains the leading explanation.

Frequently asked questions

Why would rotation velocity fall off with radius if only visible matter existed?

Beyond a galaxy's visible disk, essentially all the mass is enclosed within any given radius, so orbital mechanics behaves like planets around the Sun: V ∝ 1/√r, the same Keplerian falloff you'd get orbiting any point mass. This is exactly what's plotted as the dashed curve, and it's not what real galaxies show.

What does a "flat" rotation curve actually mean?

Instead of falling off, orbital velocity stays roughly constant (or even rises slightly) at large radii in real galaxies. This can only happen if the enclosed mass keeps growing proportionally with radius even far outside the visible disk — implying a huge, extended, invisible mass distribution rather than a fixed total mass.

What is the NFW profile and why is it shaped that way?

The Navarro-Frenk-White profile ρ(r) = ρ₀/[(r/rs)(1+r/rs)²] is a density shape derived from cosmological simulations of how dark matter halos form under gravity. It's steep near the centre and falls off more gradually at large radii, and integrating it gives a velocity contribution that stays close to flat over a wide range of radii — matching observations.

How does the halo scale (rs) parameter change the curve?

The halo scale radius rs sets where the NFW density profile transitions from its steep inner slope to its shallower outer slope. A larger rs spreads the dark matter mass over a bigger volume, which changes where the rotation curve flattens out and how quickly V_max is reached.

Do dwarf galaxies need more or less dark matter than large spirals?

Dwarf galaxies typically show an even higher dark matter fraction than large spirals like the Milky Way or Andromeda, because their visible (luminous) mass is small while their measured rotation speeds are still relatively fast for their size — you can see this by switching between galaxy presets and comparing the dark matter percentage each one implies.