★★☆ 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.

Dark matter: 75% Galaxy mass (×10¹⁰M☉): 6.5 Halo scale (kpc): 20

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.