Properties of spherical galaxies and clusters with an NFW density profile

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters with isotropic velocity tensors whose density profiles obey the universal form first obtained in high resolution cosmological N -body simulations by Navarro, Frenk & White. Analytical solutions 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. 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 Sérsic R 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 outwards at all radii. Hence, the NFW model seems inconsistent with the observations of elliptical galaxies.