Planar virial trace
= Planar virial trace
{title2=$\Pi_\perp=\Pi_{xx}+\Pi_{yy}$}
The planar trace of the <stellar pressure-energy tensor> is the sum of its two Cartesian in-plane components. For an axisymmetric nonstreaming population it equals $\int\rho(\langle v_R^2\rangle+\langle v_\phi^2\rangle)d^3x$, not merely the cylindrical radial second moment. A spherical isotropic population has $\Pi_\perp=2\Pi_{zz}$.