Computational Simulations of the Solar Atmosphere

The following pages show selected examples of computer simulations of magnetoconvection in the solar atmosphere. Results of numerical simulations are needed for the interpretation and physical understanding of high resolution observations of solar surface magnetism that are recorded with large solar telescopes, such as the German Vacuum Tower Telescope (VTT) on Tenerife or the upcoming GREGOR telescope (still under construction). The numerical simulations are carried out at the Kiepenheuer-Institut, using various computational platforms in house and at the High-Performance Computing-Center Stuttgart. Selected publications, posters, and other material are listed further below.

• Magnetohydrodynamic simulation from the convection zone to the chromosphere

• Canopies and current sheets in the lower chromosphere

• Dynamical interaction of magnetic flux sheets with convective flow

• Formation of a magnetic flux concentration

• Time-slice movie of solar granulation

• Selected, recent publications

• Less easily accessible publications

• Posters

• Reports

For acquiring a deeper understanding of the different atmospheric layers of the Sun and the magnetohydrodynamic coupling and interaction between them, we carry out three-dimensional simulations encompassing the top layers of the convection zone up to the middle chromosphere. The computational domain extends from 1400 km below the mean surface of optical depth unity (the "solar surface") to 1400 km above it and 4800 km x 4800 km in the horizontal directions. The spatial resolution of the computation in the horizontal direction is 40 km; in the vertical it increases from 20 km throughout the photosphere and chromosphere to 50 km in the convection zone. The lateral boundary conditions are periodic, whereas the lower boundary is ``open'' in the sense that the fluid can freely flow in and out of the computational domain under the condition of vanishing total mass flux. The specific entropy of the inflowing mass is fixed to a value so as to yield solar radiative flux at the upper boundary.

The simulation starts with a homogeneous, vertical, unipolar magnetic field superposed on a previously computed, relaxed model of thermal convection. The flux density of 0.001 T mimics a magnetically very quiet (inter-network) region of the Sun. The magnetic field is constrained to have vanishing horizontal components at the top and bottom boundary but lines of force can freely move in the horizontal direction, allowing for flux concentrations to extend right to the boundaries. The magnetic field is free to expand with height through the photospheric layers into the more or less homogeneous chromospheric field.

   Fig. 1

Download a vector graphics of a vertical and of horizontal sections and the corresponding captions. Watch a QuickTime movie of the horizontal (4.5 MB) and of the verticall (2.8 MB) sections.

Following can be seen from the simulation:

• The magnetic field concentrates in narrow sheets and small knots near the surface of optical depth unity (tau = 1) with field strengths up to approximately 0.1 T.
• Occasionally, these magnetic flux concentrations extend down to the bottom boundary but more often, they live in a narrow layer around the surface of tau = 1, only.
• In the chromospheric layer (horizontal section at a height of 1300 km) the magnetic field is highly dynamic undergoing continuous rearrangement on a time scale of less than 1 min, much shorter than in the photospheric or convection-zone layers.
• The chromospheric field has a strength between 0.0002 and 0.004 T. Different from the surface magnetic field, it is more homogeneous and fills practically the entire space.
• Seemingly detached from but clearly excited by the processes that take place in the photosphere, transient filaments of stronger than average magnetic field form in the chromospheric layers. Two examples are visible around x = 1.0 and x = 2.7 Mm near the contour of beta = 1 in the the snapshot of Fig. 1 (top). They form in the compression zone downstream and along propagating shock fronts.
• Very commonly forms a ``small-scale magnetic canopy field'' extending in a more or less horizontal direction over expanding granules. The formation proceeds by action of the horizontally expanding flow above granule centers. An example can be seen near the center of the top panel of Fig. 1.

A very common phenomenon that can be observed in the simulation run of the previous section is the formation of a small-scale magnetic "canopy" field that extends in a more or less horizontal direction over expanding granules and in between photospheric flux concentrations (also visible in Fig. 1, top). The formation of such canopy fields proceeds by the action of the expanding flow above granule centers. This flow transports "shells" of horizontal magnetic field to the upper photosphere and lower chromosphere, where layers of different field directions may be pushed together. This leads to a complicated meshwork of current sheets in a height range from approximately 400 to 900 km.

   Fig. 2

Get a vector graphics of this figure.

Notice

• the direction reversal of the magnetic field in subsequent layers of enhanced electric current density in a height of around 0.5 Mm in the top panel,
• the conspicuous double layers of current sheets in the horizontal section at z = 90 km framing the photospheric magnetic flux sheets,
• the vertically extending current sheet visible at x = 1.5 Mm in the lower left corner of the horizontal section at z = 1310 km that is caused by a corresponding chromospheric shock wave.

The interaction of magnetic fields with convective flows and their influence on the radiation transfer in the photosphere and the uppermost layers of the convection zone of the Sun is crucial for a number of key processes in the solar and in stellar atmospheres, namely:

• concentration of magnetic flux into structures of high field strength;
• modification or suppression of the convective energy transport by strong magnetic fields;
• global luminosity variations due to local energy flux deficit (sunspots) or flux excess (plages and network faculae);
• transport of mechanical energy from convective layers into the chromosphere and the corona.

   Fig. 3

Download a compressed vector graphics of Fig. 3. Watch an mpeg or QuickTime movie of the temperature and magnetic field, or watch an mpeg or QuickTime movie of the temperature and magnetic field together with tracer particles.

Fig. 1 is a snapshot of the simulation shown in the accompanying movies. Magnetic field lines are shown in black, the velocity field (se the vector graphics) is indicated by white arrows. The temperature field is rendered in colors with the corresponding scaling given in Kelvin in the top bar. The horizontal black curve indicates the optical depth unity surface for vertically incident lines of sight (roughly speaking, the solar surface). Two shock waves can be seen, one just above the downflow at approximately x = 2000 km travelling to the left and one within the magnetic flux sheet at a hight of around y = 500 km propagating vertically upwards. The flux sheet is framed by two strong and narrow ``downflow jets''.

Dynamical phenomena, which may contribute to chromospheric and coronal heating, like the bending and horizontal displacement of a flux sheet caused by pressure forces of the convective flow, as well as the excitation and propagation of shock waves, both within and outside the magnetic structure, are routinely observed in the simulation. The observational signatures of the shocks and transverse displacements leave imprints upon the computed synthetic Stokes profiles (spectral lines in the polarized Sun light), and should be detectable with high time-cadence (time steps of 10 sec) observing runs.

   Fig. 4

Fig. 4 shows a time sequence of Stokes-I (left) and Stokes-V (right) profiles of the spectral line FeI 525.02 nm, centered in time around a shock event within the flux sheet (cf, t = 16 min in the movie). Time increases from bottom to top and consecutive profiles are separated by 10 seconds each. Tick marks on the vertical axes indicate 10 % for Stokes-I and 2.5 % for Stokes-V, relative to the continuum intensity. The superposition of a redshifted pre-shock profile and a blueshifted post-shock profile leads to the complex V-profiles h-o during the transit of the shock front through the height interval where the spectral line is formed. Stokes-I originates mainly in the field-free region outside the flux sheet so that the shock only weakly affects the I-profile in the far blue wing.

Watch an mpeg or QuickTime movie of synthetic Stokes profiles.

In an attempt to understand the formation of small scale magnetic flux concentrations in the solar photosphere we have also followed the evolution of a homogeneous and dispersed vertical magnetic field that is initially superimposed on an evolved state of non-stationary convection. The magnetic field becomes quickly concentrated in the "intergranular lanes" of the convecting plasma and a flux sheet forms with a maximum field strength of 1600 Gauss at the solar surface, a value well above the kinetic equipartition value of about 700 Gauss. The simulations show that the field is concentrated by a combined action of kinematic flux gathering (as a consequence of the `frozen in' condition of the magnetic field) and intensification by the downflow.

     Fig. 5

Fig. 5 shows magnetic field lines after the formation process has taken place. The magnetic field is concentrated in a flux sheet at the location of a convective downflow. Also shown is the optical depth unity surface which is depressed at the position of the flux sheet due to the partial evacuation of the sheet. The plasma beta (ratio of gas pressure to magnetic pressure) along the "axis" of the flux sheet is almost constant from the photosphere down to a depth of 400 km and has a value between 0.1 and 0.2.

In the present simulation the intense field flux sheet is rather shallow and the formation process takes place in a surface layer of only about 500 km thickness. Shortly after the formation, a "rebound" of the downflowing gas takes place, leading to an upflow of gas that subsequently develops into a strong upward travelling shock and to the dispersal of the flux concentration. A figure showing a time series of the formation process can be obtained by downloading the corresponding compressed (Gzip) PS-file (785kB).

Time-slice diagrams of solar granulation show the intensity of the granular pattern along a thin slice as a function of time. They are useful to determine evolution properties for a large number of granules. The movie shows in the top panel the granular evolution within a narrow strip of the solar surface of 60 arcsec length and 2.5 arcsec width. Centred within this strip is a slice of 0.5 arcsec width, which was used to construct the time-slice image shown in the bottom panel. The intergranular lane position, determined with help of a thinning algorithm, is indicated in the top panel by the vertical white lines. Their height and vertical position is identical to that of the slice. The bottom panel shows the corresponding time-slice diagram (time increases in vertical direction), where the horizontal white line indicates the time level corresponding to the time instant shown in the top panel. Also indicated in the bottom image is the skeleton of integranular lanes. It can be followed what kind of granular evolution produces what kind of structure (branching) in the skeleton plot of the integranular lanes.

    MPEG, 2.8 MB

See the article by D.A.N. Müller, O. Steiner, R. Schlichenmaier, and P.N. Brandt: 2001, Solar Physics, for more information on time-slice diagrams of solar granulation.

		Recent advances in the exploration of the small-scale structure of the quiet solar atmosphere: vortex flows, the horizontal magnetic field, and the Stokes-V line ratio method O. Steiner and R. Rezaei: 2012, in The Fifth Hinode Science Meeting: Exploring the Active Sun, L. Golub, I. de Moortel, and T. Shimizu (eds.), ASP Conference Series
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		Revealing the nature of magnetic shadows with numerical 3D-MHD simulations C. Nutto, O. Steiner, and M. Roth: 2012, Astronomy & Astrophysics Letters, 542, L30
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		Stokes diagnostics of wave propagation in the magnetic network of the Sun G. Vigeesh, O. Steiner, and S.S. Hasan: 2011, Solar Physics, 273, 15
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		Excitation of slow modes in network magnetic elements through magnetic pumping Y. Kato, O. Steiner, M. Steffen, and Y. Suematsu: 2011, ApJ Letters, 730, L24-L88
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		Detection of vortex tubes in solar granulation from observations with SUNRISE O. Steiner, M. Franz, N. Bello González, Ch. Nutto, R. Rezaei, V. Martínez Pillet, J. A. Bonet Navarro, J. C. del Toro Iniesta, V. Domingo, S. K. Solanki, M. Knölker, W. Schmidt, P. Barthol, and A. Gandorfer: 2010, ApJ Letters, 680, L85-L88
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		Magnetic Coupling in the Quiet Solar Atmosphere O. Steiner: 2010, in Magnetic Coupling between the Interior and the Atmosphere of the Sun, S. S. Hasan and R. J. Rutten (eds.), Astrophysics and Space Science Proceedings, Springer-Verlag, p.~166-185
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		The horizontal internetwork magnetic field: numerical simulations in comparison to observations with Hinode O. Steiner, R. Rezaei, W. Schaffenberger, and S. Wedemeyer-Bühm: 2008, ApJ Letters, 680, L85-L88
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		Hinode observations reveal boundary layers of magnetic elements in the solar photosphere R. Rezaei, O.Steiner, S. Wedemeyer-Böhm, R. Schlichenmaier, W. Schmidt, and B.W. Lites: 2007, Astronomy & Astrophysics Letters, 476, L33-L36
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		Opposite magnetic polarity of two photospheric lines in single spectrum of the quiet Sun R. Rezaei, R. Schlichenmaier, W. Schmidt, and O. Steiner: 2007, Astronomy & Astrophysics Letters, 469, L9-L12
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		Photospheric processes and magnetic flux tubes O. Steiner: 2007, Lecture Notes of the 2006 Kodai School on Solar Physics held at Kodaikanal Solar Observatory (India) from Dec 10-22, 2006. S.S. Hasan and D. Banerjee (eds.), American Institute of Physics (AIP) Press. p. 74-121
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		Recent progresses in the simulation of small-scale magnetic fields O. Steiner: 2007, in Modern Solar Facilities - Advanced Solar Science, F. Kneer K.G. Puschmann, A.D. Wittmann (eds.), Universitätsverlag Göttingen, p. 321-337
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		First local helioseismic experiments with CO5BOLD O. Steiner, G. Vigeesh, L. Krieger, S. Wedemeyer-Böhm, & B. Freytag: 2007, Astronomische Nachrichten/Astronomical Notes, AN 328, 323 - 328
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		What is heating the quiet-Sun chromosphere? S. Wedemeyer-Böhm, O. Steiner, J.~Bruls, & W. Rammacher: 2007, in Coimbra Solar Physics Meeting on the Physics of Chromospheric Plasmas, P.~Heinzel, I.~Dorotovic, & R. J. Rutten (eds.), ASP-Conference Series 368, p. 93-102
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		Holistic MHD-Simulation from the Convection Zone to the Chromosphere W. Schaffenberger, S. Wedemeyer-Böhm, O. Steiner & B. Freytag: 2005, in Solar MHD: Theory and Observations -- a High Spatial Resolution Perspective, J. Leibacher, H. Uitenbroek, & R. F. Stein (eds.), Proceedings of the 23rd NSO Sacramento Peak Summer Workshop in honor of Bob Stein, ASP-Conference Series 354, p. 345-350
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		Recent progresses in the physics of small-scale magnetic fields O. Steiner: 2006, in The Dynamic Sun: Challenges for Theory and Observations, Proceedings of the 11th European Solar Physics Meeting held in Leuven (2005), D. Danesy, S. Poedts, A. De Groof, & J. Andries (eds.), ESA Publication SP-600 (CD-ROM)
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		Magnetohydrodynamic simulation from the convection zone to the chromosphere W. Schaffenberger, S. Wedemeyer-Böhm, O. Steiner & B. Freytag: 2006, in Chromospheric and Coronal Magnetic Fields, D. Innes, A. Lagg, S. Solanki, & D. Danesy (eds.), ESA Publication SP-596 (CD-ROM)
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		Simulations of magnetohydrodynamics and CO formation from the convection zone to the chromosphere S. Wedemeyer-Böhm, W. Schaffenberger, O. Steiner, M. Steffen, B. Freytag, and I. Kamp: 2005, in Chromospheric and Coronal Magnetic Fields, D. Innes, A. Lagg, S. Solanki, & D. Danesy (eds.), ESA Publication SP-596 (CD-ROM)
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		The deep roots of solar radiance variability O. Steiner & A. Ferriz-Mas: 2005, Memorie della Società Astronomica Italiana, 75, 282
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		Connecting solar radiance variability to the solar dynamo with the virial theorem O. Steiner & A. Ferriz-Mas: 2004, Astronomische Nachrichten/Astronomical Notes, AN, 326, 190
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		Connecting solar radiance variability to the solar dynamo with the virial theorem O. Steiner: 2004, A.V. Stepanov, E.E Benevolenskaya, and A.G. Kosovichev (eds.), IAU Symp. 223, p. 77-80
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		Understanding facular granules and lanes O. Steiner: 2004, A.V. Stepanov, E.E Benevolenskaya, and A.G. Kosovichev (eds.), IAU Symp. 223, p. 299-300
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		Radiative properties of magnetic elements: II. Center to limb variation of the appearance of photospheric faculae O. Steiner: 2004, Astronomy & Astrophysics, 430, 691-700
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		Indications of shock waves in the solar photosphere J. Rybák, H. Wöhl, A. Kucera, A. Hanselmeier, and O. Steiner: 2004, Astronomy & Astrophysics, 420, 1141
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		Distribution of magnetic flux density at the solar surface. Formulation and results from simulations O. Steiner: 2003, Astronomy & Astrophysics, 406, 1088
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		Photospheric magnetic field at small scales O. Steiner: 2003, in Turbulence, Waves, and Instabilities in the Solar Plasma, R. Erdélyi, K. Petrovay, B. Roberts, & M. Aschwanden (eds.), NATO Advanced Research Workshop, Kluwer, p. 117
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		Large-Scale Flow in Two-Dimensional Simulation of Solar Convection O. Steiner: 2003, in Modelling of Stellar Atmospheres, N. E. Piskunov, W. W. Weiss, D. F. Gray (eds.), IAU Symp. 210
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		Multi-Grid Radiative Transfer Revisited O. Steiner: 2003, Stellar Atmosphere Modeling, I. Hubeny, D. Mihalas, and K. Werner, (eds.), ASP Ser. 288, p. 83
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		Time-slice diagrams of solar granulation D.A.N. Müller, O. Steiner, R. Schlichenmaier, and P.N. Brandt: 2001, Solar Physics, 203, 211
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		The formation of asymmetric Stokes-V profiles in the presence of a magnetopause Steiner, O.: 2000, Solar Physics, 196, p. 245
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		Flux Tube Dynamics Steiner, O.: 1999, in Magnetic Fields and Oscillations, Proc. of the 3rd Advances in Solar Physics Euroconference, (B. Schmieder, A. Hofmann, and J. Staude, eds.), ASP Conference Series 184, p. 38
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		Chromosphere: magnetic canopy Steiner, O.: 1999, in Encyclopedia of Astronomy and Astrophysics, Paul Murdin (Editor-in-Chief) Nature Publishing Group, Macmillian Publishers Ltd., UK, www.ency-astro.com
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		Numerical Simulations of Magnetic Flux Sheets Steiner, O., Knölker, M., & Schüssler, M.: 1997, in Proceedings of the MINI-Workshop on Solar Magnetic Fields, ed. V. Hansteen, Institute of Theoretical Astrophysics, University of Oslo, Oslo
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		Convective intensification of magnetic fields on the solar surface O. Steiner: 1996 in: Solar and Galactic Magnetic Fields, D. Schmitt and H.-H. Voigt (eds.), Nachrichten der Akademie der Wissenschaften in Göttingen, II. Mathematisch-Physikalische Klasse, Vol. 4, Vandenhoeck & Rupprecht, Göttingen, p. 15
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		Dynamical Interaction of Solar Magnetic Elements and Granular Convection: Results of a Numerical Simulation O. Steiner, M. Knölker and M. Schüssler 1994 in: Solar Surface Magnetism, Robert J. Rutten and Carol R. Schrijver (eds.), NATO ASI Series C-433, Kluwer, Dordrecht
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		Numerical simulations in solar physics - comparing synthetic with real observations O. Steiner, H. Peter, R. Rezaei, R. Schlichenmaier, Kiepenheuer-Institut für Sonnenphysik & S. Wedemeyer-Böhm, Institute of Theoretical Astrophysics, University of Oslo
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		Holistic magnetohydrodynamic simulation from the convection zone to the chromosphere W. Schaffenberger, S. Wedemeyer-Böhm, O. Steiner, Kiepenheuer-Institut and B. Freytag, Los Alamos National Laboratory
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		Understanding facular granules and facular lanes O. Steiner, Kiepenheuer-Institut
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		Solar Radiance Variability as a Direct Consequence of the Flux-tube Dynamo O. Steiner, Kiepenheuer-Institut
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		Multi-Grid Radiative Transfer Revisited O. Steiner, Kiepenheuer-Institut
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		Formation of asymmetric Stokes-V profiles in the presence of a magnetopause O. Steiner, U. Grossmann-Doerth, and M. Schüssler, Kiepenheuer-Institut
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		Multi-Grid Radiation Transfer Revisited O. Steiner
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		Large-scale flow in two-dimensional simulation of solar convection O. Steiner, Kiepenheuer-Institut
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		Formation of the G-band in Magnetic Elements of the Solar Atmosphere O. Steiner and J. Bruls, Kiepenheuer-Institut, and P. Hauschildt, University of Georgia, Athens
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		Contrast of Magnetic Elements in the G-band and Across the Solar Spectrum O. Steiner and J. Bruls, Kiepenheuer-Institut, and P. Hauschildt, Hamburger Sternwarte, Hamburg
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		From the polytropic atmosphere to numerical simulation of thermal convection O. Steiner, Kiepenheuer-Institut, 1998
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		Divergenzfreie diskrete Formulierung der Induktionsgleichung bei adaptiver Gitterverfeinerung O. Steiner, Kiepenheuer-Institut, 1994
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		A short description of CYL2D, a radiative transfer code O. Steiner, Kiepenheuer-Institut, 1993
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		Notes on a Novel 2D-NLTE Radiation Transfer Code O. Steiner, Kiepenheuer-Institut, 1991
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-Written by O. Steiner. (Please, find my e-mail address on the KIS homepage under Kontakte/contacts.