= Astrophysical volume filling factor
{title2=$f_V=V_{\rm emitting}/V$}
The fraction $f_V$ of a geometric volume occupied by a specified emitting gas phase is its volume filling factor. For approximately uniform <density> within that phase, a density-squared <luminosity> scales as $n_e^2f_VV$. Without knowledge of $f_V$, emission gives an rms-density combination rather than a unique mean gas <density>. This filling factor is distinct from the fraction of a <telescope> beam occupied on the sky.
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