= Oblate-rotator flattening proxy
{title2=$(v_p/\sigma_x)^2=(e-\beta)/(1-e)$}
The simplified moment prescription $q=\sigma_z^2/(\sigma_x^2+v_p^2)$, with $e=1-q$ and $\beta=1-\sigma_z^2/\sigma_x^2$, gives the displayed relation by solving for $v_p^2$. The prescription is an approximation, not a consequence of the <tensor virial theorem> for arbitrary oblate density profiles. For constant azimuthal streaming $v_{\rm az}$, the one-component streaming second moment is $v_p^2=v_{\rm az}^2/2$.
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