= Jaffe model
{c}
{title2=$\rho(r)=\frac{Ma}{4\pi r^2(r+a)^2}$}
= Jaffe profile
{c}
{synonym}
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 $r\to0$ and does not imply a central point mass.
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