 Navarro–Frenk–White profile

The Navarro--Frenk--White profile is an empirical model for the spherically averaged mass density of collisionless dark matter halos. Julio F. Navarro, Carlos S. Frenk and Simon D. M. White found that the same two-parameter shape fitted halos in their hierarchical-clustering N-body simulations over a broad resolved radial interval.^[ref]

Writing $x=r/r_s$, the profile iswith positive scale radius $r_s$ and characteristic density ${\rho }_s$. Its inner density cusp scales as $r^{-1}$ and its outer tail as $r^{-3}$. Integrating $4\pi r^2\rho$ gives the enclosed massAlthough the central density diverges, the enclosed mass tends to zero as $r^2$. At large radius the total mass diverges logarithmically, so a quoted halo mass requires a finite boundary convention, such as a specified mean enclosed overdensity. The halo concentration compares that boundary radius with $r_s$. The simulation fit is useful for consistent halo descriptions and gravitational lensing calculations; its empirical success does not require every halo or baryon-modified inner region to follow it exactly.

The Navarro–Frenk–White (NFW) profile is a mathematical model that describes the density distribution of dark matter in galaxies and galaxy clusters. It was introduced by the astrophysicists Julio Navarro, Carlos Frenk, and Simon White in their 1996 paper. The NFW profile is significant in cosmology and astrophysical studies because it provides insights into how dark matter is structured in the universe.