Context: A photoionized gas in thermal equilibrium can display a thermal instability, with three or more solutions in the multi-branch region of the S-shape curve that gives the temperature versus the radiation-to-gas-pressure ratio. Many studies have been devoted to this curve and to its dependence on different parameters, always in the optically thin case.
Aims: The subject of our study is the thermal instability in optically thick, stratified media in total pressure equilibrium. We are also interested in comparing photoionization models issued from the hot and cold stable solutions with the currently used models, which are computed with an approximate, intermediate solution.
Methods: We developed a new algorithm that selects the hot/cold stable solution and therefrom computes a fully consistent photoionization model. We implemented it in the TITAN code and computed a set of models encompassing the range of conditions valid for the warm absorber in active galactic nuclei.
Results: We demonstrate that the thermal instability problem is quite different in thin and thick media. Models computed with the hot/cold stable solution and with an intermediate solution differ throughout the gas slab, with the spectral distribution changing as the radiation progresses inside the ionized gas. These effects depend on the thickness of the medium and on its ionization.
Conclusions: .This has observational implications for the emitted/absorbed spectra, ionization states, and variability. However impossible it is to know what solution the plasma will adopt when attaining the multi-solution regime, we expect the emitted/absorbed spectrum to be intermediate between those resulting from pure cold and hot models; such a phase-mixed medium can be reproduced well by intermediate solution models. Large spectral fluctuations corresponding to the onset of a cold/hot solution could be observed in timescales on the order of the dynamical time. A strong turbulence implying supersonic velocities should permanently exist in the multi-branch region of thick, stratified, pressure equilibrium media.