Hypervirial Models of Stellar Systems

A family of cusped potential-density pairs is presented for modelling galaxies and dark haloes. The density profile is cusped like 1/r^(2-p) at small radii. The distribution function is simple and takes the form L^(p-2) E^[(3p+1)/2] where E is the binding energy and L is the angular momentum. The models all possess the remarkable property that the virial theorem holds locally, from which they earn their name as the hypervirial family. Famously, this property was first discovered by Eddington to hold for the Plummer model in 1916. In fact, the seductive properties of the Plummer model extend to the whole hypervirial family, including the members possessing the cosmologically important cusps of 1/r or 1/r^1.5 or 1/r^1.33. The intrinsic and projected properties of the family of models are discussed in some detail.