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Soft X-ray spectra of some low-mass X-ray binaries and active galactic nuclei show strong emission line features which can be identified as complexes of 3s to 2p transitions in the lowest few iron-L shell ions. We have modeled a line-emitting X-ray binary accretion flow as a photoionized gas. Our results show that the gas is thermally unstable at those temperatures where the iron-L shell ions peak in abundance. A close examination of the thermal and ionization structures of the emission line regions, the mechanisms which control instability, and details of the photoionization model was undertaken in order to reconcile the model predictions with the observations. The possibility of producing the observed iron-L features in a stable conduction front bounding the hot and cold stable gas phases was explored. While a thin conduction front qualitatively reproduces the observed spectral features, it yields insufficient emission measure to account for the observations. For reasonable ionizing spectrum energies and elemental abundances, a photoionized gas is thermally unstable over some temperature range in the vicinity of the iron-L abundance peak. The onset of instability is extremely sensitive to elemental abundances and appears to be controlled by the heating and cooling behavior of iron-L itself, with some contributions due to intermediate-Z L-shell ions. In order for the gas to become stable, the iron abundance must be reduced. Because of the importance of iron-L observationally and as the primary mechanism for controlling instability, the model was modified to include the effects of more detailed calculations of low-temperature dielectronic recombination rates in iron-L shell ions. We discuss the effects of these modifications upon the stability properties of a model gas and comment upon the sensitivity of our conclusions to the accuracy of atomic rates calculations.
