The Navarro-Frenk-White (NFW) profile is a widely used model for describing the <a href="https://www.wikiwhat.page/kavramlar/dark%20matter%20halos">dark matter halos</a> that surround galaxies and galaxy clusters. It's named after Julio Navarro, Carlos Frenk, and Simon White, who proposed the profile based on N-body simulations of structure formation in a cold dark matter universe.
The NFW profile is a <a href="https://www.wikiwhat.page/kavramlar/density%20profile">density profile</a>, meaning it describes how the density of dark matter varies as a function of distance from the center of the halo. The key feature of the NFW profile is that it predicts a <a href="https://www.wikiwhat.page/kavramlar/cuspy%20core">cuspy core</a>, where the density increases steeply towards the center. Specifically, the density follows a power-law relationship with radius (r), with ρ(r) ∝ 1/r at small radii.
The NFW profile is characterized by two parameters:
Scale Radius (r<sub>s</sub>): This is the radius at which the logarithmic slope of the density profile is -2. It marks the transition between the inner and outer regions of the halo.
Characteristic Density (ρ<sub>s</sub>): This is the density at the scale radius. Often, the profile is instead parameterized by the <a href="https://www.wikiwhat.page/kavramlar/concentration%20parameter">concentration parameter</a> (c), which is defined as the ratio of the virial radius (r<sub>vir</sub>) to the scale radius (r<sub>s</sub>): c = r<sub>vir</sub>/r<sub>s</sub>. The virial radius is the radius within which the average density is a certain multiple of the critical density of the universe.
The mathematical expression for the NFW density profile is:
ρ(r) = ρ<sub>s</sub> / [(r/r<sub>s</sub>)(1 + r/r<sub>s</sub>)<sup>2</sup>]
While the NFW profile provides a good fit to the average density profiles of dark matter halos in simulations, observations of some galaxies, particularly dwarf galaxies, have revealed discrepancies. These discrepancies, often referred to as the "core-cusp problem", suggest that the actual density profiles of dark matter halos may be less cuspy than predicted by the NFW profile. Other models, such as the Einasto profile, have been proposed as alternatives to the NFW profile. The NFW profile is a cornerstone of modern <a href="https://www.wikiwhat.page/kavramlar/cosmology">cosmology</a>.
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