= Gaussian line-of-sight velocity distribution
{c}
{title2=$p(v_{\rm los})=(\sqrt{2\pi}\sigma_0)^{-1}e^{-v_{\rm los}^2/(2\sigma_0^2)}$}
For an <isothermal collisionless tracer> without streaming or an escape cutoff, integrate its three-dimensional <Maxwell-Boltzmann velocity distribution> over the two transverse <velocities>. The remaining marginal is the displayed <normal distribution>. Its width and mean do not depend on position. Integrating along the <line of sight> therefore only multiplies the marginal by the projected <surface density>; the normalized observed velocity distribution remains the same Gaussian at every projected radius.
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