Density positivity for an axisymmetric logarithmic potential
= Density positivity for an axisymmetric logarithmic potential
{title2=$q^2\geq1/2$}
The <Poisson equation for Newtonian gravity> gives
$$
\rho=\frac{V^2}{4\pi Gq^2}\frac{R^2+(2-q^{-2})z^2}{(R^2+q^{-2}z^2)^2}.
$$
For $V>0$, nonnegative <mass density> away from the origin is equivalent to $q^2\geq1/2$. Strict positivity requires $q^2>1/2$. This condition does not by itself guarantee a nonnegative <galactic distribution function>.