Hypervirial density-potential family
= Hypervirial density-potential family
{title2=$\psi=GM/(a^p+r^p)^{1/p}$}
For $p>0$, the relative potential $GM/(a^p+r^p)^{1/p}$ generates density $(p+1)Ma^pr^{p-2}/[4\pi(a^p+r^p)^{2+1/p}]$. In unit scales the separable <augmented density> is $(p+1)r^{p-2}\psi^{2p+1}/(4\pi)$. Its <Jeans moments from an augmented density> give constant anisotropy $\beta=1-p/2$.