The equation of transfer is a two-faced equation, easy to solve at times, and difficult to solve at other times, depending on the values assumed by its coefficients. It is rather tractable when applied to the deep layers of atmospheres and for frequencies from their continuum spectrum, but this solvability is in stark contrast to the difficulty in solving it close to the surface of atmospheres or within spectral lines. It follows that the photons most rich in information that reach our telescopes are also the most difficult to interpret. The purpose of this note is to stress this point and to illustrate it with some examples taken from the solar atmosphere.

The development of fast numerical methods for multilevel radiative transfer (RT) applications often leads to important breakthroughs in astrophysics, becausethey allow the investigation of problems that could not be properly tackled using the methods previously available. Probably, themost familiar example is the so-called Multilevel Accelerated Λ-Iteration (MALI) technique of Rybicki & Hummerfor the case of a local approximate operator,which is based on Jacobi iteration. However, there are superior operator-splitting methods, based on Gauss-Seidel (GS) and Successive Overrelaxation (SOR) iteration, which provide a dramatic increase in the speed with which non-LTE multilevel transfer problems can be solved in one, two and three-dimensional geometries. Such RT methods, which were introduced by Trujillo Bueno & Fabiani Bendicho ten years ago, are the main subject ofthe first part of this paper. We show in some detail how they can be applied for solving multilevel RT problems in spherical geometry, for both atomic and molecular line transitions. The second part of the article addresses the issue of the calculation of the molecular number densities when the approximation of instantaneous chemical equilibrium turns out to be inadequate, which happens to be the case wheneverthe dynamical time scales of the astrophysical plasma under considerationare much shorter than the time needed by the molecules to form.

This is a review of methods for the solution of non-LTE radiativetransfer equations in long cylinders. The principal goal of thesemethods is the modelling of elongated structuresimbedded in the solar corona, such as loops or prominence threads.These objects are submitted to the solar radiation, which determinesthe boundary conditions of the problem. Different cases areexamined. Concerning the geometry, one-dimension and two-dimensioncases are treated. The two-dimension case itself is subdivided into(radius, altitude) and (radius, azimuth) problems, which are treated byquite different methods. Another distinction concerns the method ofresolution: semi-analytical, Monte-Carlo and finite-differencemethods are examined. Some methods are restricted to a two-levelatom, others allow the treatment of realistic multilevel cases. Somerecent results, obtained with finite-difference, acceleratedΛ-iteration methods, are presented.

We present a method for solving the radiative transferequation in axial symmetry both in static case and in moving media.A usage of this method is shown here for stellar atmospheres, stellar winds, and accretion discs. The effects of limb darkening and stellar rotation are discussed, too.

The Finite Rank Approximation (FRA) based methodis well known in operator approximation theory but it is also useful for suggesting numerical methods for solvingintegral equations. In this document we describe two FRA methods for the numerical resolution of the integral formulation of the 1D RadiativeTransfer Equation (RTE) posed in a static slab; we browse some advantages of them (especially the possibility to control the error) and we give some reduction of computation technics (iterative refinement schemes)which can be used with these methods. Numerical results obtained for a realistic Sun atmosphere model are given. In the last section we give an example of an inverse problem associated to the RTE:we show the iterative recovering of the albedo from the measurement of the outgoing specific intensityat a surface of the considered domain.

Solving the radiative transfer problem is a common problematic to may fields in astrophysics. With the increasing angular resolution of spatial or ground-based telescopes (VLTI, HST) but also with the next decade instruments (NGST, ALMA, ...), astrophysical objects reveal and will certainly reveal complex spatial structures.Consequently, it is necessary to develop numerical tools being able to solve the radiative transfer equation in three dimensions in order to model and interpret these observations. I present a 3D radiative transfer program, using a new method for the construction of an adaptive spatial grid, based on the Monte Claro method. With the help of this tools, one can solve the continuum radiative transfer problem (e.g. a dusty medium), computes the temperature structure of the considered medium and obtain the flux of the object (SED and images).

HERACLES is a new code that solve the radiative transfer coupled tothe hydrodynamics. The radiation is describe by a moment model usingthe M1 closure relation which allow to preserve large angularanisotropy in the radiation field. We present here the model, itsnumerical implementation and some test cases. The tests and thecomparison with other methods show the good accuracy of our model invarious situations. The results show that HERACLES is accurate inboth the diffusion and the transport limit and could therefor be usedin various astrophysical fields such as radiative shocks,fragmentation and formation of dense cores in the interstellar medium,protoplanetary discs, jets...

We present a progress report on including all the lines in the linelists,including all the lines in the opacities, including all the lines inthe model atmosphere and spectrum synthesis calculations, producinghigh-resolution, high-signal-to-noise atlases that show (not quite) allthe lines, so that finally we can determine the properties of stars froma few of the lines.

We present a new 3D continuum radiative transfer code, MCFOST, based on a Monte-Carlo method. The reliability and efficiencyof the code is tested by comparison with five different radiative transfer codespreviously tested by Pascucci et al. (2004), using a 2D diskconfiguration. When tested against the same disk configuration,no significant difference is found between the temperature and SEDcalculated with MCFOST and with the other codes. Thecomputed values are well within the range of values computed by theother codes. The code-to-code differences are small, they rarelyexceed 10% and are usually much smaller.

Red Supergiant (RSG) represent a key-phase in the evolution of massive stars. These stars are characterized by strong mass loss of unknown origin. Observations show strong line profile fluctuations in depth, width and velocity, suggesting giant convective cells which could explain mass loss.Recently, radiative hydrodynamics (RHD) simulations of these stars show a peculiar convection pattern with giant cells. We performed 3D pure LTE radiative transfer calculations in snapshots of 3D hydrodynamical simulations taking into account the Doppler shifts caused by the convective motions. Computed spectra from RHD models qualitatively reproduce observations.


Nonlinear modeling of pulsating stars has two features. Firstly, a self-consistent time-dependent model must includenot only the optically thin atmospheric region, but also the sub-photospheric envelope, where the instability regions are located.The physical conditions and spatial scales of these regions are verydifferent, while the accuracy of calculations should be as high as possible,especially for the radiative shock waves.As show numerical experiments, the loss of accuracy in the description of theatmospheric dynamics may seriously affect the calculatedmotions in the inner region,and vice versa, to say nothing of the synthetic line spectrum which is one ofthe main goals of the atmosphere modelling. Secondly, to obtain the limit cycle we must run the hydromodel forabout 103 to 104 pulsational cycles. It isthus clear that we have to simplify the problem of the radiativehydrodynamics in order to obtain reliable resultin a reasonable CPU time. In the presenttalk we describe one of possible approaches which gives good results at least in a semi-quantitative way.

With the advent of the present and future spatial X-ray missions, it becomes crucial to model correctly the line spectrum of X-ray emitting/absorbing media.We have built a photoionization code, TITAN, solving the transfer of a thousand lines and of the continuum with the “Accelerated Lambda Iteration” method (ALI), which is most reliable for line transfer.We give some details about this method and a justification for its use as a complement to usual approximations (e.g., escape probability or two-stream) made at present in other codes.We show that the escape probability approximation leads to a wrong estimation of the emitted X-ray line intensities, especially in the soft X-ray range.The errors can exceed one order of magnitude in the case of thick media (Thomson thickness of the order of unity).It also happens, but for different reasons, in the case of moderately thin media (Thomson thickness of 0.001 to 0.1), characteristic of the Warm Absorber in Seyfert 1 or of the X-ray emitting medium in Seyfert 2.Using TITAN, new diagnostics based on He-like ion lines of the n=2 complex are proposed and some examples are presented here, concerning in particular the influence of the transfer method on the G ratio. We show an example of the influence of the direction on the emission/absorption spectrum.We also give insights about the influence of numerical methods for the computation of radiative transfer, and how to handle the ALI method in such problems where important gradients occur.


Miras and Semi-Regular variables are, among Red Giants, cool objects which are difficult to understand. This paper presents an adaptation of the spectral synthesis code SYNSPEC to cool objects. Some examples of application of this code to static and dynamical structures are presented.



Emission line spectra of planetary nebulae are computed and compared to theobservations. This allows for a derivation of the kinematical data concerningspecific nebulae as well as for general conclusions concerning stellarevolution.


The aim of this work is to help for choosing the optimal configuration of the VLTI for the observation of dust shell inner boundary of the S star π1 Gru. We show that this depends on the choice of the used geometrical model. The visibility curves produced by different models are compared to that predicted by the DUSTY spherical transfer radiative numerical code fitting real wide-band spectrophotometric data. The JMMC-ASPRO software is used to calculate the visibility points from the DUSTY code. The optimal configuration of the VLTI with 2 and 3 auxiliary telescopes, depending on the used geometrical model, minimizes the error on the inner shell radius.

We present recent results on active hot stars using the first VLTI/MIDI and VLTI/AMBER observations, and the SIMECA code developed by Stee (1994). α Arae was the first classical Be star observed with MIDI (June 2003) and AMBER (February 2005). The size of its circumstellar envelope was measured and thanks to the spectrally-resolved interferometric AMBER observations, we were able, for the first time to evidence the Keplerian rotation of the circumstellar disc. MWC 297 is one of the brightest Herbig Be star, and it was then observed during the first commissioning run of AMBER in May 2004. The data obtained were good enough to allow us to infer the accretion disc extension, as well as to put strong constraints on the stellar wind geometry and kinematics.


I present a survey of recent discoveries concerning circumstellar envelopes around evolved stars: asymptotic giant branch stars and (proto-) planetary nebulae, and radiative techniques used to infer their properties.

ASAP is a project initiated at the MPIfR which aims at providing a new generation of scientific analysis tools to extract the physical information from the high dynamical range data of current and future instruments. It was motivated by the ALMA project but the concepts and their implementations are applicable to all wavelengths. This presentation is focused on DALIA (Direct Aproach to spectral Line Analysis), a prototype software for forward modeling. It consists of a JAVA graphical user interface through which the user can fit models to observations. The models are stored as binaries and are described by XML files according to a schema. New models developed in any language can thus be easily added to the model database by the user. The different steps of the fit (simulation, evaluation, parameter change) can be executed manually or automatically through an optimization engine. The interface allows the user to have a direct control on the model parameters which can be fixed or constrained. The data to be modeled can be of any type (1D, 2D, 3D, specral, spatial, temporal...) and associations of datasets of different types are supported as long as the axes are identical to those of the model output. In this prototype the FITS format is supported. For spectral synthesis, the spectroscopic data from the molecular databases (Cologne, JPL) are used. This approach is very generic and uses concepts similar to those of the Virtual Observatory. Its integration into the VO would allow astronomers to use the data archives to constrain a model and would permit to store model solutions for each source. These model solutions could thus be easily shared and be improved with the aquisition of new data.