Galactic Rotation Curve (2D) — Dark Matter Evidence

Galaxy Presets

Halo Parameters

Dark matter fraction 75%

Galaxy mass 6.5 ×10¹⁰ M☉

Halo scale radius r_s 20 kpc

Orbit speed (visual) 1.0×

Live Readout

V at 20 kpc

— km/s

V_flat (asymptotic)

— km/s

Keplerian excess

—×

Halo mass fraction

—%

How it works

Total circular velocity combines a Freeman-1970 visible disk term with an NFW (Navarro–Frenk–White) dark-matter halo term, added in quadrature:

V_total(r) = sqrt( V_disk(r)^2 + V_halo(r)^2 )
V_halo(r)^2 = G*M_halo * [ln(1+x) - x/(1+x)] / (Mnorm * r),  x = r/r_s

With no dark matter, V_disk alone falls off as roughly 1/√r beyond the visible disk — the dashed Keplerian curve. Real galaxies stay flat instead, which is exactly what the NFW halo term reproduces once the dark-matter fraction is turned up. Star colour on the left encodes orbital speed (blue → red = slow → fast); the "Keplerian excess" stat is the ratio of the actual V_flat to the no-halo Keplerian prediction at the same radius.

Keplerian (no DM) Disk stars Total (observed)