Jaffe model ($\rho (r)=\frac{Ma}{4\pi r^2(r+a{)}^2}$)

A spherical stellar model with total mass $M$, scale radius $a$, inner density proportional to $r^{-2}$ and outer density proportional to $r^{-4}$. Integrating its mass density gives $M(r)=Mr/(r+a)$, hence Newtonian gravitational potential $\Phi =(GM/a)\log [r/(r+a)]$, normalized to zero at infinity. Its circular speed satisfies $v_c^2=GM/(r+a)$: it tends to a constant inside the scale radius and becomes Keplerian outside. The central density cusp has vanishing enclosed mass as $r\to 0$ and does not imply a central point mass.