= Hernquist model
{c}
{title2=$\psi=GM/(r+a)$}
The <Hernquist model> has <relative potential> $\psi=GM/(r+a)$ and density $\rho=Ma/[2\pi r(r+a)^3]$. It has enclosed <mass> $Mr^2/(r+a)^2$, a central $r^{-1}$ cusp and an outer $r^{-4}$ tail. Since $r\rho=a\psi^3/(2\pi G^3M^2)$, the <half-anisotropic distribution function> is $f(E,L)=3aE^2/(4\pi^3G^3M^2L)$ for $0<E<GM/a$. Its moments are $\langle v_r^2\rangle=\psi/4$ and each tangential moment $\psi/8$. Isotropic and other admissible anisotropic distributions can also support this same density; the <gravitational potential> does not select a unique <velocity> anisotropy.
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