= Maximally prograde stellar distribution
{title2=$F_+(E,L_z)=2F(E,L_z)\Theta(L_z)$}
For a nonrotating axisymmetric <galactic distribution function> even in $L_z$, reverse every retrograde azimuthal <velocity>. The resulting distribution is $F_+(E,L_z)=2F(E,L_z)\Theta(L_z)$: it preserves density and even <velocity> moments but makes the <streaming velocity> $\langle|v_\phi|\rangle$. Dependence on conserved $E,L_z$ preserves stationarity. A centered <Gaussian distribution> of width $\sigma$ becomes a <half-normal distribution>, with mean $\sqrt{2/\pi}\sigma$.
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