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A photoionized gas under constant pressure can display a thermal instability,with three or more solutions for possible thermal equilibrium. A uniquesolution of the structure of the irradiated medium is obtained only if electronconduction is considered. The subject of our study is to estimate how theeffect of thermal conduction affects the structure and transmitted spectrum ofthe warm absorber computed by solving radiative transfer with the code TITAN.We developed a new computational mode for the code TITAN to obtain severalsolutions for a given external conditions and we test a posteriori whichsolution is the closest one to the required integral condition based onconduction. We demonstrate that the automatic mode of the code TITAN providesthe solution to the radiative transfer which is generally consistent with theestimated exact solution within a few per cent accuracy, with larger errors forsome line intensities (up to 20 per cent) for iron lines at intermediateionization state.

Thermal instability in X-ray photoionized media in Active Galactic Nuclei: II. Role of the thermal conduction in warm absorber