The Very Large Telescope Interferometer on Cerro Paranal in Northern Chileis one of the largest optical facilities used in astronomy.It can combine two or three of the four 8.2 m and four movable 1.8 m telescopes,which span baselines between 8 and 202 m.Observations are carried out in the near- and mid-infrared, covering thewavelength range from 1 to 13 μm.


Sophisticated radiative transfer methods have been used for decadesto model one-dimensional static stellar atmospheres.They predict an outward decrease of the atmospheric temperature that is now observable with simple one-baseline interferometers viameasurements of limb darkening.However, the surface layers of many stars are affected by convectionwhich requires a treatment bytime-dependent multi-dimensional radiation hydrodynamics simulations.Solar granulation is directly observable with “ordinary” telescopes.The simulated granule pattern and evolution compares well with the observed ones.The upcoming radio interferometer ALMA could be used to probe the convectioninduced shock-pattern in the chromosphere that is predicted by simulationsand that is not easily observable otherwise.The typical granular scale on other near main-sequence stars is too smallto be accessible by interferometers.However, scaling argumentsand recent numerical simulationspredict very large structures on cool supergiantsand AGB stars.These stars were and are candidates for optical/near-infrared interferometry.The complexity of the predicted surface phenomenarequires good (or at least some) spatial resolution in conjunction withtemporal and frequency resolution.To fully exploit and interpret these data the simulations have to be improvedin terms of treatment of microphysics (especially opacities in the radiative transfer step)and spatial resolution.

Interferometry with large telescopes such as the VLTI is at present not a realistic option in solar physics, nor will it be feasible in the near future. Its proximity, however, allows us to view the Sun in far more detail than we can reasonably expect for other stars even with the next generations of interferometric instruments. For that reason the Sun imposes extremely high requirements on the radiative transfer computations that serve to explain the observations. In the last few decades we have seen the picture of the solar photosphere evolve to a point where we think that we have “understood” most of the basic structures and their physics. The chromosphere, however, still presents a challenge for (magneto)hydrodynamic and radiative transfer modeling. Time-independent gray or multiband radiative transfer assuming local thermodynamic equilibrium (LTE), which for obvious reasons work well in the photosphere, are not valid in the chromosphere. In principle all equilibrium assumptions and time independence should be dropped. The theoretical formulation of that problem is straightforward, but it leads to a numerical problem whose solution requires far more computational resources than currently available.For that reason modelers will have no other option but to continue reducing the full problem to a number of tractable simpler problems with different assumptions and trying to figure out which assumptions are valid.


A short overview about radiative transfer models of Be stars ispresented. Main model requirements for studying Be stars are discussed indetail. Applicability of these models to interferometry is briefly mentioned.



We developed a 3D pure LTE radiative transfer code to derive observables expected for RSGs, with emphasis on small scale structures, from radiative-hydrodynamic (RHD) simulations of red supergiant stars (RSGs) carried out with CO5BOLD (Freytag et al. 2002). We show that the convection-related surface structures are observable with today's interferometers. Moreover, the RHD simulations are a great improvement over parametric models for the interpretation of interferometric observations.


The brightest and unstable stars occupying the upper right part of HRdiagram are briefly introduced. Some examples of interferometricanalysis are given together with derived conclusions.

We present here some issues for the radiation hydrodynamics simulations in the context of young stellar jets and laboratory radiative shocks. We first briefly present some different techniques used to dynamically couple the radiation with the hydrodynamics. Then, we discuss the actual simulations and the improvements that interferometry will bring in a near future. Finally, we present a radiation-hydrodynamics public code which have been developed recently and have already been applied to these two domains.

In the last years, some issues concerning Cepheids have beenresolved, based on observations and modeling. However, as usual, newdifficulties arise. The link between the dynamical structure ofCepheid atmosphere and the distance scale calibration in theuniverse is now clearly established. To support observations, wecurrently need fully consistent hydrodynamical models, includingpulsating and evolutionary theories, convective energy transport,adaptive numerical meshes, and a refined calculation of theradiative transfer within the pulsating atmosphere, and also in theexpected circumstellar envelope (hereafter CSE). Confronting suchmodels with observations (spectral line profiles, spatial- andspectral- visibility curves), will permit to resolve and/orstrengthen subtle questions concerning (1) the limb-darkening, (2)the dynamical structure of Cepheids' atmosphere, (3) the expectedinteraction between the atmosphere and the CSE, and (4) it willbring new insights in determining the fundamental parameters ofCepheids. All these physical quantities are supposed furthermore tobe linked to the pulsation period of Cepheids. From these studies,it will be possible to paint a glowing picture of all Cepheidswithin the instability strip, allowing an unprecedent calibration ofthe period-luminosity relation (hereafter PL relation),leading to new insights in the fields of extragalactic distancescales and cosmology.

Cepheids have been used to determined distance throughout the lastcentury, thanks to the Period-Luminosity (P-L) relation. However, thisrelation has to be observationally calibrated in order to accuratelydetermined distances. One of the most promising technique to directlymeasure distances to Cepheids, hence calibrate the P-L relation, isthe quasi geometric interferometric parallax pulsation, orBaade-Wesselink (Baade 1926; Wesselink 1946) method hereafter IBWM. Wewill present here some of the known interferometric biases to themethod: the uncertainty related to the knowledge of the center-to-limbdarkening of the pulsating Cepheid, and the possible presence of faintcircumstellar envelopes (CSE). These two aspects have been or will bestudied using observational techniques, but still lack comprehensivemodeling, which is mandatory to fully understand and correct for thisbiases in case of sparse observational material.


Recent years have seen a major contribution of infrared interferometry to studies on the circumstellar environment of cool evolved stars. Particularly, two interferometric instruments at ESO's Very Large Telescope Interferometer (VLTI) – AMBER and MIDI – offer the community a novel opportunity to carry out high-angular resolution observations. In the mid-infrared, where thermal emission from the circumstellar gas and/or dust is remarkable, MIDI has proven to be a powerful tool to derive the physical properties of the molecule and dust formation zone close to the star, particularly when combined with radiative transfer modeling. AMBER is also expected to shed more light on the circumstellar material closer to the star and the photosphere itself. In this paper, we present recent results on cool evolved stars obtained with VLTI as well as future prospects for interferometric observations and radiative transfer modeling for cool evolved stars. 


We discuss models of AGB star atmospheres. Special emphasis is put onthe question of opacities, treatment of radiative transfer andsimulation of interferometric results.

New 2D dynamical models for carbon-rich and oxygen-rich AGB stars, and red supergiants are presented which include hydrodynamics with gravity and radiation pressure on dust, equilibrium chemistry, time-dependent dust formation, and coupled frequency-dependent Monte Carlo radiative transfer. The simulations reveal a much more complicated picture of the dust formation and wind acceleration of red giants as compared to 1D spherical models. Triggered by non-spherical pulsations or large-scale convective motions, dust forms event-like in the cooler regions above the stellar surface which temporarily receive less radiation from the star, followed by the radial ejection of dust arcs and clumps. These simulations can possible explain recent high angular resolution interferometric IR observations of red giants, which show an often non-symmetric and highly time-variable innermost dust formation and wind acceleration zone. The new wind models are intended to harvest the results of future interferometric mission like Chara, AMBER on the Vlti, and Alma, aiming to provide the physical answers of the scientific questions arising from these new instruments.

The radiative transfer equation can be solved analytically for optically thin shells. The solution leads to a semi-analytical expression of the visibility function, which can be compared to the numerical solution given by the DUSTY code. Best-fit model parameters are given using real measurements of ISO fluxes, ISI and VLTI-MIDI visibilities for 3 late-type stars.

We present high spatial resolution observations of the mid-infrared core of the dusty symbiotic system HM Sge. The MIDI interferometer was used with the VLT Unit Telescopes and Auxiliary Telescopes providing baselines oriented from PA=42° to 105°. The MIDI visibilities are compared with the ones predicted in the frame of various spherical dust shells published in the literature involving single or double dusty shells intended to account for the influence of the hot White Dwarf. The mid-IR environment is unresolved by a 8m telescope and the MIDI spectrum exhibits a level similar to the ISO spectra recorded 10 yr ago. The discrepancies between the HWHM at different angle orientations suggest an increasing level of asymmetry from 13 to 8 μm. The observations are surprisingly well fitted by the densest (optically thick in the N band) and smallest spherical model published in the literature based on the ISO data, although such a model does not account for the variations of near-IR photometry due to the Mira pulsation cycle suggesting a much smaller optical thickness. These observations also discard the two shells models, developed in an attempt to take into account the effect of the White Dwarf illumination onto the dusty wind of the Mira. These models are too extended, and lead to a level of asymmetry of the dusty environment tightly constrained by the MIDI visibilities. These observations show that a high rate of dust formation is occurring in the vicinity of the Mira which seems to be not highly perturbed by the hot companion.

Near-infrared and mid-infrared broad band interferometric observations of young stellar objectstrace the inner part of the warm dusty circumstellar environment(smaller than a few AUs) and canbe used to constrain its physical properties, in particular tocharacterize the size, location and composition of the emitting region. Because the spatial frequency coverage of current instruments remain sparse,modeling, including detailed radiative transfer (RT), is necessary to geta precise estimate of these properties.


Thanks to the development of long baseline facilities, near infraredinterferometry is becoming an important tool to study the innermostregions of circumstellar proto-planetary disks around close-by pre-mainsequence stars. Providing a milli arcsecond spatial resolution and spectroscopic capabilities, the existing interferometers can, for thefirst time, spatially resolve and separate the gas and dust emissionarising form the disk regions where planets are supposed to form,namely inside few Astronomical Units from the central star. Theobservational limitations and the complexity of the resulting datarequire however to perform the data analysis in the Fourier space bythe comparison with theoretical disk models. To this purpose a numberof self consistent radiative transfer models have been recentlydeveloped. In this chapter I will first review some of the most recentobservational and theoretical results and then, discuss some importantfuture challenges. 


The presence of dust tori in active galactic nuclei (AGN) lies at the heart of AGN unification schemes. The dominating inner part of the tori can only be resolved by infrared interferometry. Here we discuss the present state of torus models and the radiative transfer methods to simulate the infrared SEDs and visibilities for comparison with actual observations. We highlight the differences between smooth and clumpy tori and present a model for the Seyfert 2 nucleus NGC 1068.

Finite Difference and Finite Element algorithms for the solution of the radiative transfer equationas required for the modeling of modern high quality observations are briefly describedand discussed. It is emphasized that in the Finite Element approach there is the possibility to obtain an a-posteriori error estimator, which allows to locally refine the grid and in this way to obtain numerical solutions that do not differfrom the (unknown) analytical solutions by more than a prescribed tolerance.

Active hot stars are hot stars (Teff ≥ 8000 K) exhibiting emission lines (namely hydrogen lines) and IR excess which both originate in a circumstellar environment. In this paper we present in details the SIMECA (SImulation pour Etoiles Chaudes Actives) code which is the only code freely available to model the gaseous environment of active hot stars. It computes line profiles, Spectral Energy Distributions (SED) and intensity maps, which can be directly compared to high angular resolution observations.