Galaxy Rotation Curve & Dark Matter

Keplerian prediction vs observed flat rotation · NFW halo · baryonic decomposition
Total (observed)
Stellar disk
Gas disk
NFW dark halo
Keplerian (no DM)
Stellar mass (10¹⁰ M☉) 6.0
Gas mass (10¹⁰ M☉) 2.0
DM halo mass (10¹¹ M☉) 12
NFW concentration c 10
Galaxy preset
Galaxy rotation curves measure stellar/gas orbital velocities v(r) = √(GM(r)/r). For a centrally-concentrated baryonic disk alone, v should fall as ∝ 1/√r (Keplerian) at large radii. Instead, observations show flat rotation curves extending to 10× the optical radius, demanding an extended dark matter halo. The NFW profile ρ(r) = ρ_s/[(r/r_s)(1+r/r_s)²] (Navarro-Frenk-White 1996) from N-body simulations provides an excellent fit. Dark matter constitutes ~85% of total matter in the universe.