Astrophysical volume filling factor ($f_V=V_{\mathrm{emitting}}/V$)

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 $n_e^2{f}_{V}V$. 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.