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Galaxy Rotation Curves

Why do galaxies spin faster than Newtonian gravity predicts? — Dark matter evidence

Dark Matter Cosmology Galaxy Dynamics NFW Profile

Stars (disk)

Bulge

Newtonian v(r)

+Dark Matter (observed)

Dark Matter halo

Stellar Mass 1.0 ×10¹⁰ M☉ Dark Matter Fraction 0.85 Halo Scale r_s 8 kpc Disk Scale Length 3 kpc

V_max = — km/s V_flat = — km/s R_opt = — kpc M_DM/M_total = —

The Dark Matter Mystery

For stars far from the galactic centre, Newtonian gravity predicts v(r) ∝ 1/√r (Keplerian decline), just like planets in a solar system. But Vera Rubin (1970s) discovered that real galaxies show flat rotation curves: v(r) ≈ const at large r.

This requires an invisible mass component — the dark matter halo — with density profile described by the NFW (Navarro–Frenk–White) formula: ρ(r) = ρ₀ / [(r/rₛ)(1 + r/rₛ)²]. Dark matter makes up ~85% of total matter in the Universe yet emits no light.

Adjust sliders to see how each component contributes to the total rotation curve.