New strong constraints on the central behaviour of spherical galactic models -- No NFW cusp

TL;DR

This paper establishes constraints on spherical galactic models near the center, showing that common models like NFW, Jaffe, and Hernquist cannot accurately describe the central regions of galaxies or dark matter halos, especially lacking a cusp.

Contribution

It provides new theoretical constraints on the central behavior of spherical galactic models, challenging the validity of popular models like NFW, Jaffe, and Hernquist at small radii.

Findings

NFW model cannot describe central cusps in dark matter halos.

Jaffe and Hernquist models are reliable only beyond 0.2 R_e.

Models with zero mass at the center require velocity and gravitational field to vanish.

Abstract

We first stress that any spherically symmetric galactic model whose integrated mass profile $M (r) \to 0$ as $r \to 0$ is physically consistent close to the centre only provided that the circular velocity $v_c (r) \to 0$ and the gravitational field $g (r) \to 0$ as $r \to 0$. Next, we apply such a statement to a broad class of five-parameter spherical galactic models, which includes most of those used in astrophysics and cosmology. In particular, we discover that the Jaffe and Hernquist models can only be trusted for $r \gtrsim 0.2 \, R_e$, while the NFW model cannot describe the central region either of regular galaxy clusters or of pure dark matter halos, thereby failing to predict any central cusp.