2023ApJ...957..105M

The population of metastable levels is key to high-precision density diagnostics of astrophysical plasmas. In photoionized plasmas, density is used to infer the distance from the ionizing source, which is otherwise difficult to obtain. Perfecting models that compute these populations is thus crucial. The present paper presents a semianalytic hydrogenic approximation for assessing the relative importance of different processes in populating atomic levels. This approximation shows that in the presence of a radiation source, photoexcitations and collisional excitations are both important over a wide range of plasma temperatures and ionizing spectra, while radiative recombination is orders of magnitude weaker. The interesting case of Fe⁺²¹ with a collisional radiative model with photoexcitation demonstrates this effect. The population of the first excited metastable level in Fe⁺²¹ is sensitive to the electron number density in the critical range of n_e = 10¹²-10¹⁵ cm^–3; it was observed to be significantly populated in the X-ray spectrum of the 2005 outburst of the X-ray binary GRO J1655-40. The present model shows that photoexcitation is the predominant process indirectly populating the metastable level. For the photoionized plasma in the GRO J1655-40 outflow, the model indicates a measured value of n_e = (2.6 ± 0.5) × 10¹³ cm^–3, implying a distance from the source of r = (4.4 ± 0.4) × 10¹⁰ cm. Finally, we show how the computed critical density and distance of Fe⁺²¹ yield the correct ionization parameter of the ion, independent of ionization balance calculations.