NFW Dark Matter Halo Concentration

N-Body Simulation · Galactic Rotation Curve Analysis · Three Concentration Parameters
c = 6
Low Concentration
Diffuse Halo
Peak V_circ
165 km/s
Flat Radius
12 kpc
Core Type
Diffuse
Low concentration spreads dark matter too broadly. Diffuse core produces a shallow potential well — the rotation curve rises slowly and peaks weakly at 165 km/s before flattening far out at 12 kpc. The galaxy lacks central density; inner stellar orbits are underpowered.
c = 10
Optimal Concentration
Goldilocks
Peak V_circ
210 km/s
Flat Radius
8 kpc
Core Type
Ideal
The Goldilocks concentration. NFW profile at c=10 matches observed Milky Way–type galaxies perfectly. The halo provides the right potential depth — rotation curve rises smoothly to 210 km/s, flattens naturally at 8 kpc, and sustains a realistic spiral structure with well-defined arms and central bulge.
c = 18
High Concentration
Over-Steep
Peak V_circ
255 km/s
Flat Radius
4 kpc
Core Type
Cuspy
Over-concentrated dark matter creates a cuspy inner rise — the rotation curve spikes sharply to 255 km/s then drops, flattening too early at just 4 kpc. The excessive central density disrupts disk formation, compressing gas violently and distorting stellar orbits in the inner region.
Circular Velocity Curves — Vcirc(r) vs Galactocentric Radius
c = 6 · Diffuse
c = 10 · Optimal
c = 18 · Cuspy
t = 0.00 Gyr