Cusped logarithmic spherical galaxy model
= Cusped logarithmic spherical galaxy model
{title2=$\Phi=v_0^2\log(1+r/a)$}
This spherical <gravitational potential>, with $a,v_0>0$, has density $\rho=v_0^2(2a+r)/(4\pi Gr(a+r)^2)$ and <circular speed> $v_c=v_0\sqrt{r/(a+r)}$. It combines a central $1/r$ density cusp with an outer <flat galaxy rotation curve>, but its total mass is infinite. It differs from a logarithmic potential with a constant-density core.