Velocity moments of an isotropic Mestel disk
= Velocity moments of an isotropic Mestel disk
{title2=$\sigma_R^2=\sigma_\phi^2=v_0^2$}
The planar <Mestel disk> has $F(E)\propto e^{-E/v_0^2}$, giving independent centered <Gaussian distributions> for $v_R,v_\phi$ with <velocity dispersions> $\sigma_R=\sigma_\phi=v_0$. Its <streaming velocity> is zero. A <maximally prograde stellar distribution> instead has mean $\sqrt{2/\pi}v_0$ and azimuthal <variance> $v_0^2(1-2/\pi)$, while all second raw moments remain unchanged.