Navarro-Frenk-White profile
Encyclopedia
The Navarro–Frenk–White profile or NFW profile is a spatial mass distribution of dark matter
fitted to dark matter haloes identified in N-body simulations by Julio Navarro
, Carlos Frenk
and Simon White
. The NFW profile is one of the most commonly used model profiles for dark matter halos.
where ρ0 and the "scale radius", Rs, are parameters which vary from halo to halo.
The integrated mass inside of some radius Rmax is
The total mass is divergent, but it is often useful to take the edge of the halo to
be the virial radius, Rvir ,
which is related to the "concentration parameter", c, and scale radius via
In this case, the total mass in the halo is
The value of c is roughly 10 or 15 for the Milky Way, and may range from 4 to 40
for halos of various sizes.
The integral of the squared density is
so that the mean squared density inside of Rmax is
which for the virial radius simplifies to
and the mean squared density inside the scale radius is simply
configuration of dark matter produced in simulations of collision
less dark matter particles by numerous groups of scientists. Before the dark matter virializes, the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse
of the halos.
Alternative models, in particular the Einasto profile
, have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile. The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.
and M31
may be compatible with the NFW profile for the dark matter halo.
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
fitted to dark matter haloes identified in N-body simulations by Julio Navarro
Julio Navarro (astrophysicist)
Julio F. Navarro is a professor of Astronomy at the department of Physics and Astronomy in the University of Victoria. Dr...
, Carlos Frenk
Carlos Frenk
Professor Carlos Silvestre Frenk is a Mexican-British cosmologist. His main interests lie in the field of cosmology, galaxy formation and computer simulations of cosmic structure formation....
and Simon White
Simon White
Professor Simon David Manton White, FRS is a British astrophysicist. He is one of four directors at the Max Planck Institute for Astrophysics.- Life :...
. The NFW profile is one of the most commonly used model profiles for dark matter halos.
Density distribution
In the NFW profile, the density of dark matter as a function of radius is given by:where ρ0 and the "scale radius", Rs, are parameters which vary from halo to halo.
The integrated mass inside of some radius Rmax is
The total mass is divergent, but it is often useful to take the edge of the halo to
be the virial radius, Rvir ,
which is related to the "concentration parameter", c, and scale radius via
In this case, the total mass in the halo is
The value of c is roughly 10 or 15 for the Milky Way, and may range from 4 to 40
for halos of various sizes.
The integral of the squared density is
so that the mean squared density inside of Rmax is
which for the virial radius simplifies to
and the mean squared density inside the scale radius is simply
Dark matter simulations
The NFW profile is an approximation to the equilibriumThermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
configuration of dark matter produced in simulations of collision
Collision
A collision is an isolated event which two or more moving bodies exert forces on each other for a relatively short time.Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies...
less dark matter particles by numerous groups of scientists. Before the dark matter virializes, the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse
Collapse
Collapse may refer to:* Collapse, the action a collapsible or telescoping object does* Collapse * Collapse * Collapse ** Cave-in is a kind of structural collapse** Collapse of the World Trade Center, a 2001 event...
of the halos.
Alternative models, in particular the Einasto profile
Einasto profile
The Einasto profile is a mathematical function that describes how the density \rho of a spherical stellar system varies with distance r from its center...
, have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile. The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.
Observations of halos
The observations of both the Milky WayMilky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
and M31
Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...
may be compatible with the NFW profile for the dark matter halo.