Escape probability methods versus "exact" transfer for modelling the X-ray spectrum of Active Galactic Nuclei and X-ray binaries

In the era of XMM-Newton and Chandra missions, it is crucial to use codes able to compute correctly the line spectrum of X-ray irradiated thick media (Thomson thickness of the order of unity) to build models for the structure and the emission of the central regions of AGN or X-ray binaries. In all photoionized codes except in our code Titan, the line intensities are computed with the "escape probability approximation". In its last version, Titan solves the transfer of a thousand lines and of the continuum with the ``Accelerated Lambda Iteration" method, which is one of the most efficient and most secure for line transfer. We find that for conditions typical of the AGN or X-ray binary emission medium, all escape approximations commonly used lead to an overestimation of the soft X-ray lines which can reach one order of magnitude for intense lines.