= Dynamical surface density from vertical stellar motions
{title2=$\Sigma_{\rm dyn}(<|z|)$}
The <vertical Jeans equation> determines $K_z=\partial_z\Phi$ from a tracer's density and <velocity dispersion>, with a correction for the tilted <velocity ellipsoid>. Integrating the axisymmetric <Poisson equation for Newtonian gravity> gives
$$
2\pi G\Sigma_{\rm dyn}(<|z|)=K_z(z)+\int_0^z\frac1R\partial_R(R\partial_R\Phi)\,dz'
$$
for $z>0$ and reflection symmetry. Subtracting independently estimated stellar and gas <surface densities> constrains any additional gravitating component; a <dark matter halo> also contributes, so an excess is not automatically a dark disk.
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