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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 unique solution of the structure of the irradiated medium is obtained only if electron conduction is considered. The subject of our study is to estimate how the effect of thermal conduction affects the structure and transmitted spectrum of the warm absorber computed by solving radiative transfer with the code TITAN. We developed a new computational mode for the code TITAN to obtain several solutions for a given external conditions and we test a posteriori which solution is the closest one to the required integral condition based on conduction. We demonstrate that the automatic mode of the code TITAN provides the solution to the radiative transfer which is generally consistent with the estimated exact solution within a few per cent accuracy, with larger errors for some line intensities (up to 20 per cent) for iron lines at intermediate ionization state., Comment: Astronomy and Astrophysics (in press)

New high-resolution spectropolarimetric observations of solar prominences require improved radiative modelling capabilities in order to take into account both multi-dimensional - at least 2D - geometry and complex atomic models. This makes necessary the use of very fast numerical schemes for the resolution of 2D non-LTE radiative transfer problems considering freestanding and illuminated slabs. The implementation of Gauss-Seidel and successive over-relaxation iterative schemes in 2D, together with a multi-grid algorithm, is thoroughly described in the frame of the short characteristics method for the computation of the formal solution of the radiative transfer equation in cartesian geometry. We propose a new test for multidimensional radiative transfer codes and we also provide original benchmark results for simple 2D multilevel atom cases which should be helpful for the further development of such radiative transfer codes, in general., Comment: 10 pages, 8 figures, accepted to A&A

Recent modeling of the warm absorber in active galactic nuclei has proved the usefulness of constant total (gas plus radiation) pressure models, which are highly stratified in temperature and density. We explore the consistency of those models when the typical variation of the flux from the central source is taken into account. We perform a variability study of the warm absorber response, based on timescales and our photoionization code TITAN. We show that the ionization and recombination timescales are much shorter than the dynamical timescale. Clouds very close to the central black hole will maintain their equilibrium since the characteristic variability timescales of the nuclear source are longer than cloud timescales. For more distant clouds, the density structure has no time to vary, in response to the variations of the temperature or ionization structure, and such clouds will show the departure from the constant pressure equilibrium. We explore the impact of this departure on the observed properties of the transmitted spectrum and soft X-ray variability: (i) non uniform velocities, of the order of sound speed, appear due to pressure gradients, up to typical values of 100 km/s. These velocities lead to the broadening of lines. This broadening is usually observed and very difficult to explain otherwise. (ii) Energy-dependent fractional variability amplitude in soft X-ray range has a broader hump around ~ 1-2 keV, and (iv) the plot of the equivalent hydrogen column density vs. ionization parameter is steeper than for equilibrium clouds. The results have the character of a preliminary study and should be supplemented in the future with full time-dependent radiation transfer and dynamical computations., Comment: 9 pages, 7 figures, accepted for publication by Astronomy & Astrophysics

A photoionized gas in thermal equilibrium can display a thermal instability, with 3 or more solutions in the multi-branch region of the S-shape curve giving 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. The purpose of our study is the thermal instability in optically thick, stratified media, in total pressure equilibrium. We have developped a new algorithm to select the hot/cold stable solution, and thereof to compute a fully consistent photoionization model. We have 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. We have demonstrated that the thermal instability problem is quite different in thin or thick media. In thick media the spectral distribution changes as the radiation progresses inside the ionized gas. This has observational implications in the emitted/absorbed spectra, ionization states, and variability. However impossible to know what solution the plasma will adopt when attaining the multi-solutions regime, we expect the emitted/absorbed spectrum to be intermediate between those resulting from pure cold and hot models. Large spectral fluctuations corresponding to the onset of a cold/hot solution could be observed in timescales of 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., Comment: LaTeX file: 18 pages, including 14 figures. Accepted for publication in Astronomy & Astrophysics

(Abridged) Many active galactic nuclei exhibit X-ray features typical of the highly ionized gas called "Warm Absorber" (WA). Such a material appears to be stratified, displaying zones of different density, temperature, and ionization. In this paper, we investigate the possibility of modelling the WA gas in NGC 3783 as a single medium in total pressure equilibrium, in contrast to the current descriptions that are based on the presence of multiple regions, each in constant density. The assumption of total pressure equilibrium yields a more physical description of the WA, resulting in the natural stratification of the ionized gas, and providing an explanation for the presence of lines from different ionization states, as observed in WA spectra. We have used the photoionization code TITAN to compute a grid of constant total pressure models with the purpose of fitting the WA in NGC 3783. We have compared our models to the 900 ks Chandra spectrum of NGC 3783 and to previous studies where the WA was described by multiple zones of constant density. Our results show that the WA features in NGC 3783 can be well reproduced by a clumpy, ionized gas with cosmic abondances, ionization parameter = 2500 erg cm s^-1, column density = 4 10^22 cm^-2, and constant total pressure. We have shown that the WA in NGC3783 can be modelled by a single medium in total pressure equilibrium; this is probably the case for other WAs currently described by multi-zone, constant density models., Comment: Accepted for publication in Astronomy & Astrophysics Letters

Although published in 1995, the Gauss-Seidel method for solving the non-LTE radiative transfer problem has deserved too little attention in the astrophysical community yet. Further tests of the performances and of the accuracy of the numerical scheme are provided., Comment: 3 pages, 2 figures, poster SF2A-2004, published by EDP-Sciences Conference Series

We test the accuracy of the ALI method, widely used in stellar atmosphere modelling, by solving exactly a standard radiative transfer problem in plane-parallel geometry. Some recommendations are given for a practical use of this method., Comment: 4 pages, 4 figures, abstracts SF2A-2003, published in EDP-Sciences Conference Series

The 2-10 keV continuum of AGN is generally well represented by a single power law. However, at smaller energies the continuum displays an excess with respect to the extrapolation of this power law, called the ''soft X-ray excess''. Until now this soft X-ray excess was attributed, either to reflection of the hard X-ray source by the accretion disk, or to the presence of an additional comptonizing medium, giving a steep spectrum. An alternative solution proposed by Gierlinski and Done (2004) is that a single power law well represents both the soft and the hard X-ray emission and the impression of the soft X-ray excess is due to absorption of a primary power law by a relativistic wind. We examine the advantages and drawbacks of reflection versus absorption models, and we conclude that the observed spectra can be well modeled, either by absorption (for a strong excess), or by reflection (for a weak excess). However the physical conditions required by the absorption models do not seem very realistic: we would prefer an ''hybrid model''., Comment: 4 pages, 3 figures, abstracts SF2A-2005, published by EDP-Sciences Conference Series

We are interested in electrons kinetics in a stellar atmosphere to validate or invalidate the usually accepted hypothesis of thermalisation of electrons. For this purpose, we calculate the velocity distribution function of electrons by solving the kinetic equation of these particles together with the equations of radiative transfer and statistical equilibrium. We note that this distribution can deviate strongly from a Maxwell-Boltzmann distribution if non-LTE effects are important. Some results and astrophysical consequences are examined., Comment: 4 pages, 1 figure, conference, journal-ref updated

(Shortened version): The mass loss rates, expansion velocities and dust-to-gas density ratios from millimetric observations of 119 carbon-rich giants are compared, as functions of stellar parameters, to the predictions of recent hydrodynamical models. Distances and luminosities previously estimated from HIPPARCOS data, masses from pulsations and C/O abundance ratios from spectroscopy, and effective temperatures from a new homogeneous scale, are used. Predicted and observed mass loss rates agree fairly well, as functions of effective temperature.(shortened). Four stars with detached shells, i.e. episodic strong mass loss, and five cool infrared carbon-rich stars with optically-thick dust shells, have mass loss rates much larger than predicted values.(shortened). Recent drift models can contribute to minimize the discrepancy since they include more dust. Simple approximate formulae are proposed., Comment: 12 pages, 2 figures, electronic table 3 (2 files included in the archive), A&A, accepted 23 July 2004

We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical scheme where a Cauchy integral equation is reduced to a couple of Fredholm integral equations. It is expressed in terms of two auxiliary functions $\zeta_+$ and $\zeta_-$ we introduce in this paper. These functions show remarkable analytical properties in the complex plane. They satisfy a simple algebraic relation which generalizes the factorization relation of semi-infinite media. They are regular in the domain of the Fredholm integral equations they satisfy, and thus can be computed accurately. As an illustration, the X- and Y-functions are calculated in the whole complex plane, together with the extension in this plane of the so-called Sobouti's functions., Comment: 26 pages, Transport Theory and Statistical Physics, submitted January 2003

We come back to a non linear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab., Comment: 20 pages, JQSRT, accepted 9 July 2003

In the central part of this paper, we revisit the classical study of the H-function defined as the unique solution, regular in the right complex half-plane, of a Cauchy integral equation. We take advantage of our work on the N-function published in the first article of this series. The H-function is then used to solve a class of Cauchy integral equations occurring in transfer problems posed in plane-parallel media. We obtain a concise expression of the unique solution analytic in the right complex half-plane, then modified with the help of the residue theorem for numerical calculations., Comment: 19 pages, Transport Theory and Statistical Processes, submitted January 2003

We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the second kind with regular kernels. This classical scheme is used to clarify the emergence of the auxiliary functions expressing the solution of the problem. There are four such functions, two of them being classical ones. This problem is encountered while studying the propagation of light in strongly scattering media such as stellar atmospheres., Comment: 17 pages, 5 figures, Journal of Integral Equations and Applications, accepted 19 December 2004

We solve the integral equation describing the propagation of light in an isothermal plane-parallel atmosphere of optical thickness $\tau^*$, adopting a uniform thermalization parameter $\epsilon$. The solution given by the ALI method, widely used in the field of stellar atmospheres modelling, is compared to the exact solution. Graphs are given that illustrate the accuracy of the ALI solution as a function of the parameters $\epsilon$, $\tau^*$ and optical depth variable $\tau$., Comment: 7 pages, 11 figures, A&A, accepted 30 July 2003, minor corrections

We come back to the analytical solution of the standard transfer problem in a stellar atmosphere. It consists in solving the radiative transfer equation in a homogeneous and isothermal plane-parallel atmosphere, with light scattering taken as isotropic and monochromatic. The literature on the subject is reviewed and the existing solution in a finite slab is improved thanks to the introduction of non classical auxiliary functions. Eleven-figure tables of the solution are given for typical values of the input parameters currently met in stellar atmospheres., Comment: 23 pages, 1 figure