On spectroscopic filling factors and the solar transition region

The concept of spectroscopic filling factors is examined by assuming that observable astrophysical plasmas are inhomogeneous and must therefore be described using functions ζ(n), the emission measure differential in electron density n. Using a formal definition for the spectroscopic filling factor (f_s) and simple distribution functions, it is shown that (1) f_s differs from the geometric filling factor f unless the plasma is truly homogeneous [ζ(n) = ζ_o δ(n - n_o)], (2) f_s depends on the choice of line pairs for the same ζ(n), (3) f_s systematically underestimates f, and (4) f_s departs more from f the broader the distribution ζ(n). Implications for the particular case of the unresolved solar transition region are discussed. A dynamic "classical" transition region model appears to satisfy observed properties, including tiny filling factors (10^-5-10^-2) as well as filamentary models. This work highlights the nonunique interpretation of spectral data in terms of unresolved plasma structure.