Hypervirial density-potential family ($\psi =GM/(a^p+r^p{)}^{1/p}$)

For $p>0$, the relative potential $GM/(a^p+r^p{)}^{1/p}$ generates density $(p+1)M{a}^p{r}^{p-2}/[4\pi (a^p+r^p{)}^{2+1/p}]$. 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 $\beta =1-p/2$.