Navarro-Frenk-White profile

The Navarro-Frenk-White profile (NFW profile) is a spatial mass distribution function (not "mass function" in the sense of a PMF) for the internals of dark matter halos, developed from cosmological N-body simulations run by Navarro, Frenk, and White. The distribution has been adopted for use within other models.

            ρ0
ρ(r) = ———————————————
       (r/Rs)(1+r/Rs)2

• r - distance from a center of the halo.
• ρ(r) - density at r.
• ρ₀ - a density parameter for the halo.
• R_s - a scale parameter for the halo.

The latter two (parameters) must be chosen to fit the halo. Generalized NFW profiles (GNFW profiles) generalize this model: example using a form attributed to Zhao (Zhao profile):

            ρ0
ρ(r) = ——————————————————
       (r/Rs)β(1+r/Rs)3-β

• β - free parameter.