New Strong Constraints on the Central Behaviour of Spherical Galactic Models

Abstract

First of all, we show that any spherically symmetric galactic model with integrated mass profile M(r)→0 as r→0 is physically correct close to the centre only provided that the circular velocity vc(r)→0 and the gravitational field g(r)→0 as r→0. Next, we apply this statement to a broad class of five-parameter spherical galactic models, including most of those used in astrophysics and cosmology. Specifically, we show that the Jaffe and Hernquist models can be trusted only for r≳0.2Re (Re being the effective radius), while the Navarro–Frank–White (NFW) model cannot describe galaxies in the central region of regular clusters. We also briefly discuss the relevance of our result for the NFW profile of pure dark matter halos. However, we are unable to tell at which central distance the NFW model breaks down in either case, and this is a challenge for future investigations.