The old question whether models of stellar atmospheres are wrong, adequate, or even overelaborated, is discussed with a number of examples from contemporary research as a background. A simple quality classification scheme for models of different types is presented. It is concluded that, in spite of rapid recent progress, we are far from having fully satisfactory theoretical representations of stellar atmospheres. Reasons for continuing the efforts to reach a higher degree of physical consistency in model atmosphere work are discussed.

We briefly describe the current version of the PHOENIX code. We then present some illustrative results from the modeling of Type Ia and Type II supernovae, hot stars, and irradiated giant planets. Good fits to observations can be obtained, when account is taken for spherically symmetric, line-blanketed, static or expanding atmospheres.

In most stellar atmosphere models, a homogeneous chemical composition is assumed, which is a good approximation for many stars. With the absence of convection and mass–loss, however, gravitational settling can produce a chemical stratification gradient. Typical examples are white dwarfs. In hot stars this diffusion process is modified by the radiative acceleration, resulting in levitation of ions with large radiative cross sections. The status of our program for self-consistent stratified non-LTE model atmospheres is presented.

A similar presentation has been published in the volume New Quests in Stellar Astrophysics: The Link between Stars and Cosmology Astrophysics and Space Science Library, vol. 274 (eds. M. Chavez, A. Bressan, A. Buzzoni, and D. Mayya) Dordrecht: Kluwer, pp. 1-10, 2002. Here I quote the abstract and list only the section headings.

The aim of the Round Table (RT) ”Problems in modelling stellar atmospheres“ was that of giving a panoramic view of the state of art on the atmospheric models used to predict observations of stars from T to A spectral type, the Sun included.

The current status and future prospects for methods of 3D NLTE radiative transfer are reviewed. Scaling properties and parallelization issues are discussed. Codes of today are capable of solving the diagnostic problem (given model atmosphere) with atomic models of 20-100 levels making possible detailed 3D NLTE determinations of abundances employing 3D LTE model atmospheres. Calculating consistent 3D NLTE radiation hydrodynamic models is orders of magnitude more demanding computationally but methods exist that give a reasonably correct description of the radiation interactions in a statistical sense.

We briefly review the assumptions and methods required to construct NLTE line-blanketed model atmospheres of hot stars. We describe our new grid of NLTE model atmospheres covering the parameter range of O stars at various metallicities. We have applied these new models to the analysis of HST/STIS and FUSE UV spectra of O stars in the SMC. This analysis leads us to revise down the effective temperature scale of O-type stars.

We describe our method to construct line blanketed NLTE model atmospheres for hot stars. We employ the Accelerated Lambda Iteration and use statistical methods to deal with metal line blanketing.

The mechanism responsible for driving the ubiquitous winds of cool giant and supergiant stars remains to be established. To this end, we are constructing semi-empirical models of the extended outer atmospheres (‘chromospheres’) and winds of selected red supergiants. These models are constrained by analyses of the UV line spectra of single stars, and of red supergiants in binaries that eclipse their main-sequence companions: the ζ Aur and VV Cep stars. These detached binaries are well-separated, with no evidence of mass transfer. The C II] 2325 Å line profiles of the binaries are similar to those of comparable single stars, suggesting that the chromospheres remain relatively unperturbed by binarity. However, it is unclear how much binarity disturbs the wind: binary observations suggest a gradual acceleration (β ∼ 3), but line profile analyses of single red supergiants imply a rapid acceleration (β < 1). To date, we have obtained extensive series of HST/GHRS and STIS observations of three eclipsing red supergiant binaries: ζ Aur, HR 2554 and VV Cep. In this paper, we focus on ζ Aur, and present observations and modelling results for this eclipsing binary.

This Round Table addresses various problems related to the radiative energy transport calculations and the challenges related to the introduction of 3D hydrodynamic models, models with pulsations, connecting stellar atmospheres to the circumstellar medium etc. We have discussed several examples of environment not properly treated by radiative transfer calculations and outlined future development directions in this field.

We constructed hydrodynamical model atmospheres for mid M-type main-, as well as pre-main-sequence objects. Despite the complex chemistry encountered in such cool atmospheres a reasonably accurate representation of the radiative transfer is possible. The detailed treatment of the interplay between radiation and convection in the hydrodynamical models allows to study processes usually not accessible within the framework of conventional model atmospheres. In particular, we determined the efficiency of the convective energy transport, and the efficiency of mixing by convective overshoot. The convective transport efficiency expressed in terms of an equivalent mixing-length parameter amounts to values around ≈ 2 in the optically thick, and ≈ 2.8 in the optically thin regime. The thermal structure of the formally convectively stable layers is little affected by convective overshoot and wave heating, i.e. stays close to radiative equilibrium. Mixing by convective overshoot shows an exponential decline with geometrical distance from the Schwarzschild stability boundary. The scale height of the decline varies with gravitational acceleration roughly as g–1/2, with 0.5 pressure scale heights at log g=5.0.

This review focuses on different patterns of magnetoconvection and on aspects of flux expulsion, flux separation and flux pumping. The transition between magnetoconvection and small-scale dynamo action will be described and the rôle of rotation in leading to large-scale dynamo action will be emphasized. An attempt will be made to relate the results of numerical experiments to magnetic features that can be observed on the Sun, and must also be present in other late-type stars.

We present an overview of the concepts underlying advanced non-local Reynolds stress models of turbulent convection and review a comparison of this approach with a series of numerical simulations of fully compressible convection. We then discuss results from applications of the model to complete envelopes of A-type main sequence stars. The non-local model reproduces surface velocities in agreement with the lower limit of observed macro- and microturbulence velocities of A-star photospheres, the asymmetry of the surface velocity field as inferred from spectral line profiles, and the overall structure of the photospheric and subphotospheric convection zones, as predicted by the most recent numerical simulations available for these stars. Traditionally, local models of convection are unable to do so. We conclude with a brief survey of extensions of the model which are interesting for other applications such as atmospheres of solar type stars and overshooting below deep convective envelopes or above the core in massive stars.

We present a new 3D MHD code for the simulation of solar magnetoconvection. The code is designed for use on parallel computers and in the choice of methods emphasis has been laid on efficient parallelization. We give a description of the numerical methods and discuss the non-local and non-grey treatment of the radiative transfer. Test calculations underlining the importance of non-grey effects and first results of the simulation of a solar plage region are shown.

Magnetoconvection simulations on meso-granule and granule scales near the solar surface are used to study small scale dynamo activity, the emergence and disappearance of magnetic flux tubes, and the formation and evolution of micropores.

From weak seed fields, convective motions produce highly intermittent magnetic fields in the intergranular lanes which collect over the boundaries of the underlying meso-granular scale cells. Instances of both emerging magnetic flux loops and magnetic flux disappearing from the surface occur in the simulations. We show an example of a flux tube collapsing to kG field strength and discuss how the nature of flux disappearance can be investigated. Observed Stokes profiles of small magnetic structures are severely distorted by telescope diffraction and seeing.

Because of the strong stratification, there is little recycling of plasma and field in the surface layers. Recycling instead occurs by exchange with the deep layers of the convection zone. Plasma and field from the surface descend through the convection zone and rise again toward the surface. Because only a tiny fraction of plasma rising up from deep in the convection zone reaches the surface due to mass conservation, little of the magnetic energy resides in the near surface layers. Thus the dynamo acting on weak incoherent fields is global, rather than a local surface dynamo.

The main results of stellar structure, evolution and oscillations given by our non-local statistical theory of convection are summarized in this paper. A main difficulty of convection theories, i.e. supersonic convection, is also discussed.

Developments in instrumentation, numerical simulations, and theory are rapidly changing our view of solar magnetism. There are now observations that show magnetic field emerging on all convective scales. The emergence rate replaces the quiet Sun flux in less than 12 hours and even active region and sunspot fields are replaced in less than a month. There is evidence for local dynamo action suggesting that a bottom to a convection zone is not required for stellar magnetic activity. It is now recognized that 3D magnetic reconnection is fundamentally different from 2D. Time sequences of the one arc second spatial resolution TRACE images show that the temperature and density structure of the corona changes as fast as radiation and conduction allow. Because adjacent loops are observed in a range of temperatures that span at least 30 000 to 2 500 000 K, there is a inter mixture of temperatures regimes throughout the corona. Consequently, there is no line of sight through the corona that can be characterized by a single temperature and density. It would be surprising if other stars or other astrophysical systems with magnetic fields were simpler than the solar atmosphere.