In this paper we explore collisional ionization and time-evolving photoionization in the X-ray-discovered, ionized absorbers in Seyfert galaxies. These absorbers show temporal changes inconsistent with simple equilibrium models. We develop a simple code to follow the temporal evolution of nonequilibrium photoionized gas. As a result several effects appear that are easily observable and that, in fact, may explain otherwise paradoxical behavior. Specifically, we find the following: 1. In many important astrophysical conditions (O VII, O VIII dominant and high [1022.5 cm-2] column density) pure collisional and photoionization equilibria can be distinguished with moderate spectral resolution observations, because of a strong absorption structure between 1 and 3 keV. This feature is due mainly to iron L XVII-XIX and neon K IX-X absorption, which is much stronger in collisional models. This absorption structure may be misinterpreted as a flattening of the intrinsic emission spectrum above ~1 keV in low-resolution data. 2. In time-evolving nonequilibrium photoionization models the response of the ionization state of the gas to sudden changes of the ionizing continuum is smoothed and delayed at low gas densities (usually up to 108 cm-3), even when the luminosity increases. The recombination time can be much longer (up to orders of magnitude) than the photoionization timescale. Hence, a photoionized absorber subject to frequent, quick, and consistent changes of ionizing luminosity is likely to be overionized with respect to the equilibrium ionization state. 3. If the changes of the ionizing luminosity are not instantaneous, and the electron density is low enough (the limit depends on the average ionization state of the gas but is usually ~107 to ~108 cm-3), the ionization state of the gas can continue to increase while the source luminosity decreases, so a maximum in the ionization state of a given element may occur during a minimum of the ionizing intensity (the opposite of the prediction of equilibrium models). 4. Different ions of different elements reach their equilibrium configuration on different timescales, so models in which all ions of all elements are in photoionization equilibrium so often fail to describe active galactic nucleus (AGN) spectral evolution. These properties are similar to those seen in several ionized absorbers in AGNs, properties that had hitherto been puzzling. We applied these models to a high signal-to-noise ratio ROSAT PSPC observation of the Seyfert 1 galaxy NGC 4051. The compressed dynamical range of variation of the ionization parameter U and the ionization delays seen in the ROSAT observations of NGC 4051 may be simply explained by a nonequilibrium photoionization model, giving well-constrained parameters: n=(1.0)×108 cm-3 and R=(0.74)×1016 cm (~3 light-days).
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