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Properties of spherical galaxies and clusters with an NFW density profile
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Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 1 February 2008 (MN LATEX style file v1.4)
Properties of spherical galaxies and clusters with an NFW
density profile
Ewa L. Lokas1 and Gary A. Mamon2,3
1Copernicus Astronomical Center, Bartycka 18, 00–716 Warsaw, Poland
2Institut d’Astrophysique de Paris (CNRS UPR 341), 98 bis Bd Arago, F–75014 Paris, France
3DAEC (CNRS UMR 8631), Observatoire de Paris, Place Jules Janssen, F–92195 Meudon, France
1 February 2008
ABSTRACT
Using the standard dynamical theory of spherical systems, we calculate the properties
of spherical galaxies and clusters whose density profiles obey the universal form first
obtained in high resolution cosmological N -body simulations by Navarro, Frenk
White. We adopt three models for the internal kinematics: isotropic velocities, con-
stant anisotropy and increasingly radial Osipkov-Merritt anisotropy. Analytical solu-
tions are found for the radial dependence of the mass, gravitational potential, velocity
dispersion, energy and virial ratio and we test their variability with the concentration
parameter describing the density profile and amount of velocity anisotropy. We also
compute structural parameters, such as half-mass radius, effective radius and various
measures of concentration. Finally, we derive projected quantities, the surface mass
density and line-of-sight as well as aperture velocity dispersion, all of which can be
directly applied in observational tests of current scenarios of structure formation.
On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW
surface density profile is found to fit well Hubble-Reynolds laws. It is also well fitted
by Se?rsic R1/m laws, for m ? 3, but in a much narrower range of m and with much
larger effective radii than are observed. Assuming in turn reasonable values of the
effective radius, the mass density profiles imply a mass-to-light ratio that increases
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