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.