Author name code: steiner ADS astronomy entries on 2022-09-14 author:"Steiner, Oskar" ------------------------------------------------------------------------ Title: Observation of a small-scale magnetic vortex associated with a chromospheric swirl: signatures of a small-scale magnetic tornado Authors: Milena Diaz Castillo, Saida; Steiner, Oskar; Fischer, Catherine; Berdyugina, Svetlana; Rezaei, Reza Bibcode: 2022cosp...44.2521M Altcode: \newcommand{\ion}[2]{#1\,{\textsc{#2}}} High-resolution solar observations revealed the existence of small-scale swirling vortices in chromospheric intensity maps and velocity diagnostics. These events are commonly localized in the quiet sun intergranular space and are often related to small-scale magnetic flux concentrations at the solar surface. Frequently, vortices have been observed in the vicinity of magnetic flux concentrations, indicating a link between swirls and the evolution of the small-scale magnetic fields. Vortices were also studied with MHD numerical simulations of the solar atmosphere, revealing their complexity, dynamics, and magnetic nature. In particular, it has been suggested that the chromospheric swirling plasma motion is due to a coherently rotating magnetic field structure, which again is driven by a photospheric vortex flow at its footpoint. In this contribution, we present a comprehensive description of the evolution of an isolated small-scale magnetic element interacting with a vortex flow, which in turn is related to a chromospheric swirl. We study observations taken with the CRisp Imaging SpectroPolarimeter (CRISP) instrument and the CHROMospheric Imaging Spectrometer (CHROMIS) at the 1m Swedish Solar Telescope (SST) in April 2019 as part of a SOLARNET access program. The data were taken at quiet-Sun disk-center, recording full Stokes photospheric maps in the \ion{Fe}{i} line at 617\,nm, full Stokes data in the \ion{Ca}{ii} infrared triplet line at 854\,nm, and spectroscopic maps in the H$\alpha$ 656\,nm, \ion{Ca}{ii} K 393\,nm, and \ion{Ca}{ii} H 396\,nm lines. Utilizing the multi-wavelength data and applying height-dependent Stokes inversion and local correlation tracking methods, we are able to analyse the magnetic field dynamics in the presence of vortex structures at photospheric and chromospheric layers. The temporal evolution of the magnetic element shows an appreciable increase in the magnetic field strength during the interaction with the vortex flow, reaching kG values for a few minutes. We also find a clear evidence of a Rapid Blue-shift Excursion (RBE) associated with the magnetic field intensification event propagating along the chromospheric vortex. In addition, we explore the polarization signatures in the photosphere to reveal the intrinsic structure of the magnetic element. Marginal but consistent detection of linear polarization signals in the surroundings of the magnetic element before intensification suggests a magnetic field torsion. Our analysis indicates that we have observed a rotating magnetic object reaching from the photosphere to the chromosphere, resembling a small-scale magnetic tornado. Title: Acoustic-gravity wave propagation characteristics in 3D radiation hydrodynamic simulations of the solar atmosphere Authors: Fleck, Bernhard; Khomenko, Elena; Carlsson, Mats; Rempel, Matthias; Steiner, Oskar; Riva, Fabio; Vigeesh, Gangadharan Bibcode: 2022cosp...44.2503F Altcode: There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D, and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. Title: Small scale Alfvénic vortices in the solar atmosphere Authors: Canivete Cuissa, José Roberto; Steiner, Oskar; Battaglia, Andrea Bibcode: 2022cosp...44.2551C Altcode: Vortices are one of the fundamental small scale features present in the solar atmosphere. They are ubiquitous at photospheric and chromospheric levels and are often tightly coupled to small scale surface magnetic fields. Therefore, they potentially contribute to the transport of energy towards the upper layers of the solar atmosphere. We study the dynamics and the statistical properties of small scale swirls in realistic radiative magneto-hydrodynamical simulations of the solar atmosphere realized with the CO5BOLD code. To this aim, we employ the swirling strength criterion and its evolution equation to investigate the properties and dynamics of 9 identified swirl events. It is found that the studied photospheric and chromospheric swirls are the plasma response to self-consistently launched torsional Alfvén pulses that propagate vertically in the solar atmosphere. To infer the statistical properties of the swirl population in the numerical simulations, we apply a new algorithm for the automatic identification of vortices. This algorithm is based on a state-of-the-art method that combines the rigor of mathematical criteria and the global perspective of morphological techniques. Compared to previous studies, our analysis reveals more and smaller vortical motions in the simulated solar atmosphere. Moreover, it is found that the large majority of the identified swirls in the photosphere show twists in the magnetic field lines compatible with torsional Alfvén waves. Therefore we confirm that the small scale vortices in the lower solar atmosphere are Alfvénic in nature. Title: Methodology for estimating the magnetic Prandtl number and application to solar surface small-scale dynamo simulations Authors: Riva, F.; Steiner, O. Bibcode: 2022A&A...660A.115R Altcode: 2022arXiv220212115R Context. A crucial step in the numerical investigation of small-scale dynamos in the solar atmosphere consists of an accurate determination of the magnetic Prandtl number, Prm, stemming from radiative magneto-hydrodynamic (MHD) simulations.
Aims: The aims are to provide a reliable methodology for estimating the effective Reynolds and magnetic Reynolds numbers, Re and Rem, and their ratio Prm = Rem/Re (the magnetic Prandlt number), that characterise MHD simulations and to categorise small-scale dynamo simulations in terms of these dimensionless parameters.
Methods: The methodology proposed for computing Re and Rem is based on the method of projection on proper elements and it relies on a post-processing step carried out using higher order accurate numerical operators than the ones in the simulation code. A number of radiative MHD simulations with different effective viscosities and plasma resistivities were carried out with the CO5BOLD code, and the resulting growth rate of the magnetic energy and saturated magnetic field strengths were characterised in terms of Re and Rem.
Results: Overall, the proposed methodology provides a solid estimate of the dissipation coefficients affecting the momentum and induction equations of MHD simulation codes, and consequently also a reliable evaluation of the magnetic Prandtl number characterising the numerical results. Additionally, it is found that small-scale dynamos are active and can amplify a small seed magnetic field up to significant values in CO5BOLD simulations with a grid spacing smaller than h = 12 km, even at Prm ≃ 0.65. However, it is also evident that it is difficult to categorise dynamo simulations in terms of Prm alone, because it is not only important to estimate the amplitude of the dissipation coefficients, but also at which scales energy dissipation takes place. Title: Final Report for SAG 21: The Effect of Stellar Contamination on Space-based Transmission Spectroscopy Authors: Rackham, Benjamin V.; Espinoza, Néstor; Berdyugina, Svetlana V.; Korhonen, Heidi; MacDonald, Ryan J.; Montet, Benjamin T.; Morris, Brett M.; Oshagh, Mahmoudreza; Shapiro, Alexander I.; Unruh, Yvonne C.; Quintana, Elisa V.; Zellem, Robert T.; Apai, Dániel; Barclay, Thomas; Barstow, Joanna K.; Bruno, Giovanni; Carone, Ludmila; Casewell, Sarah L.; Cegla, Heather M.; Criscuoli, Serena; Fischer, Catherine; Fournier, Damien; Giampapa, Mark S.; Giles, Helen; Iyer, Aishwarya; Kopp, Greg; Kostogryz, Nadiia M.; Krivova, Natalie; Mallonn, Matthias; McGruder, Chima; Molaverdikhani, Karan; Newton, Elisabeth R.; Panja, Mayukh; Peacock, Sarah; Reardon, Kevin; Roettenbacher, Rachael M.; Scandariato, Gaetano; Solanki, Sami; Stassun, Keivan G.; Steiner, Oskar; Stevenson, Kevin B.; Tregloan-Reed, Jeremy; Valio, Adriana; Wedemeyer, Sven; Welbanks, Luis; Yu, Jie; Alam, Munazza K.; Davenport, James R. A.; Deming, Drake; Dong, Chuanfei; Ducrot, Elsa; Fisher, Chloe; Gilbert, Emily; Kostov, Veselin; López-Morales, Mercedes; Line, Mike; Močnik, Teo; Mullally, Susan; Paudel, Rishi R.; Ribas, Ignasi; Valenti, Jeff A. Bibcode: 2022arXiv220109905R Altcode: Study Analysis Group 21 (SAG21) of the Exoplanet Exploration Program Analysis Group (ExoPAG) was organized to study the effect of stellar contamination on space-based transmission spectroscopy, a method for studying exoplanetary atmospheres by measuring the wavelength-dependent radius of a planet as it transits its star. Transmission spectroscopy relies on a precise understanding of the spectrum of the star being occulted. However, stars are not homogeneous, constant light sources but have temporally evolving photospheres and chromospheres with inhomogeneities like spots, faculae, and plages. This SAG has brought together an interdisciplinary team of more than 100 scientists, with observers and theorists from the heliophysics, stellar astrophysics, planetary science, and exoplanetary atmosphere research communities, to study the current needs that can be addressed in this context to make the most of transit studies from current NASA facilities like HST and JWST. The analysis produced 14 findings, which fall into three Science Themes encompassing (1) how the Sun is used as our best laboratory to calibrate our understanding of stellar heterogeneities ("The Sun as the Stellar Benchmark"), (2) how stars other than the Sun extend our knowledge of heterogeneities ("Surface Heterogeneities of Other Stars") and (3) how to incorporate information gathered for the Sun and other stars into transit studies ("Mapping Stellar Knowledge to Transit Studies"). Title: A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest; Belluzzi, Luca; Mishra, Siddhartha Bibcode: 2021arXiv211011885J Altcode: Context. Several numerical problems require the interpolation of discrete data that present various types of discontinuities. The radiative transfer is a typical example of such a problem. This calls for high-order well-behaved techniques to interpolate both smooth and discontinuous data. Aims. The final aim is to propose new techniques suitable for applications in the context of numerical radiative transfer. Methods. We have proposed and tested two different techniques. Essentially non-oscillatory (ENO) techniques generate several candidate interpolations based on different substencils. The smoothest candidate interpolation is determined from a measure for the local smoothness, thereby enabling the essential non-oscillatory property. Weighted ENO (WENO) techniques use a convex combination of all candidate substencils to obtain high-order accuracy in smooth regions while keeping the essentially non-oscillatory property. In particular, we have outlined and tested a novel well-performing fourth-order WENO interpolation technique for both uniform and nonuniform grids. Results. Numerical tests prove that the fourth-order WENO interpolation guarantees fourth-order accuracy in smooth regions of the interpolated functions. In the presence of discontinuities, the fourth-order WENO interpolation enables the non-oscillatory property, avoiding oscillations. Unlike Bézier and monotonic high-order Hermite interpolations, it does not degenerate to a linear interpolation near smooth extrema of the interpolated function. Conclusions. The novel fourth-order WENO interpolation guarantees high accuracy in smooth regions, while effectively handling discontinuities. This interpolation technique might be particularly suitable for several problems, including a number of radiative transfer applications such as multidimensional problems, multigrid methods, and formal solutions. Title: The Alfvénic nature of chromospheric swirls Authors: Battaglia, Andrea Francesco; Canivete Cuissa, José Roberto; Calvo, Flavio; Bossart, Aleksi Antoine; Steiner, Oskar Bibcode: 2021A&A...649A.121B Altcode: 2021arXiv210307366B Context. Observations show that small-scale vortical plasma motions are ubiquitous in the quiet solar atmosphere. They have received increasing attention in recent years because they are a viable candidate mechanism for the heating of the outer solar atmospheric layers. However, the true nature and the origin of these swirls, and their effective role in the energy transport, are still unclear.
Aims: We investigate the evolution and origin of chromospheric swirls by analyzing numerical simulations of the quiet solar atmosphere. In particular, we are interested in finding their relation with magnetic field perturbations and in the processes driving their evolution.
Methods: The radiative magnetohydrodynamic code CO5BOLD is used to perform realistic numerical simulations of a small portion of the solar atmosphere, ranging from the top layers of the convection zone to the middle chromosphere. For the analysis, the swirling strength criterion and its evolution equation are applied in order to identify vortical motions and to study their dynamics. As a new criterion, we introduce the magnetic swirling strength, which allows us to recognize torsional perturbations in the magnetic field.
Results: We find a strong correlation between swirling strength and magnetic swirling strength, in particular in intense magnetic flux concentrations, which suggests a tight relation between vortical motions and torsional magnetic field perturbations. Furthermore, we find that swirls propagate upward with the local Alfvén speed as unidirectional swirls driven by magnetic tension forces alone. In the photosphere and low chromosphere, the rotation of the plasma co-occurs with a twist in the upwardly directed magnetic field that is in the opposite direction of the plasma flow. All together, these are clear characteristics of torsional Alfvén waves. Yet, the Alfvén wave is not oscillatory but takes the form of a unidirectional pulse. The novelty of the present work is that these Alfvén pulses naturally emerge from realistic numerical simulations of the solar atmosphere. We also find indications of an imbalance between the hydrodynamic and magnetohydrodynamic baroclinic effects being at the origin of the swirls. At the base of the chromosphere, we find a mean net upwardly directed Poynting flux of 12.8 ± 6.5 kW m−2, which is mainly due to swirling motions. This energy flux is mostly associated with large and complex swirling structures, which we interpret as the superposition of various small-scale vortices.
Conclusions: We conclude that the ubiquitous swirling events observed in numerical simulations are tightly correlated with perturbations of the magnetic field. At photospheric and chromospheric levels, they form Alfvén pulses that propagate upward and may contribute to chromospheric heating.

Movie associated to Fig. C.1 is available at https://www.aanda.org Title: On the effect of oscillatory phenomena on Stokes inversion results Authors: Keys, P. H.; Steiner, O.; Vigeesh, G. Bibcode: 2021RSPTA.37900182K Altcode: 2020arXiv200805539K Stokes inversion codes are crucial in returning properties of the solar atmosphere, such as temperature and magnetic field strength. However, the success of such algorithms to return reliable values can be hindered by the presence of oscillatory phenomena within magnetic wave guides. Returning accurate parameters is crucial to both magnetohydrodynamics (MHD) studies and solar physics in general. Here, we employ a simulation featuring propagating MHD waves within a flux tube with a known driver and atmospheric parameters. We invert the Stokes profiles for the 6301 Å and 6302 Å line pair emergent from the simulations using the well-known Stokes Inversions from Response functions code to see if the atmospheric parameters can be returned for typical spatial resolutions at ground-based observatories. The inversions return synthetic spectra comparable to the original input spectra, even with asymmetries introduced in the spectra from wave propagation in the atmosphere. The output models from the inversions match closely to the simulations in temperature, line-of-sight magnetic field and line-of-sight velocity within typical formation heights of the inverted lines. Deviations from the simulations are seen away from these height regions. The inversions results are less accurate during passage of the waves within the line formation region. The original wave period could be recovered from the atmosphere output by the inversions, with empirical mode decomposition performing better than the wavelet approach in this task.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: Acoustic-gravity wave propagation characteristics in three-dimensional radiation hydrodynamic simulations of the solar atmosphere Authors: Fleck, B.; Carlsson, M.; Khomenko, E.; Rempel, M.; Steiner, O.; Vigeesh, G. Bibcode: 2021RSPTA.37900170F Altcode: 2020arXiv200705847F There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. The height dependence of wave power, in particular of high-frequency waves, varies by up to two orders of magnitude between the models, and the phase difference spectra of several models show unexpected features, including ±180° phase jumps.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: On the influence of magnetic topology on the propagation of internal gravity waves in the solar atmosphere Authors: Vigeesh, G.; Roth, M.; Steiner, O.; Fleck, B. Bibcode: 2021RSPTA.37900177V Altcode: 2020arXiv201006926V The solar surface is a continuous source of internal gravity waves (IGWs). IGWs are believed to supply the bulk of the wave energy for the lower solar atmosphere, but their existence and role for the energy balance of the upper layers is still unclear, largely due to the lack of knowledge about the influence of the Sun's magnetic fields on their propagation. In this work, we look at naturally excited IGWs in realistic models of the solar atmosphere and study the effect of different magnetic field topographies on their propagation. We carry out radiation-magnetohydrodynamic simulations of a magnetic field free and two magnetic models-one with an initial, homogeneous, vertical field of 100 G magnetic flux density and one with an initial horizontal field of 100 G flux density. The propagation properties of IGWs are studied by examining the phase-difference and coherence spectra in the kh - ω diagnostic diagram. We find that IGWs in the upper solar atmosphere show upward propagation in the model with predominantly horizontal field similar to the model without magnetic field. In contrast to that the model with predominantly vertical fields show downward propagation. This crucial difference in the propagation direction is also revealed in the difference in energy transported by waves for heights below 0.8 Mm. Higher up, the propagation properties show a peculiar behaviour, which require further study. Our analysis suggests that IGWs may play a significant role in the heating of the chromospheric layers of the internetwork region where horizontal fields are thought to be prevalent.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: Interaction of Magnetic Fields with a Vortex Tube at Solar Subgranular Scale Authors: Fischer, C. E.; Vigeesh, G.; Lindner, P.; Borrero, J. M.; Calvo, F.; Steiner, O. Bibcode: 2020ApJ...903L..10F Altcode: 2020arXiv201005577F Using high-resolution spectropolarimetric data recorded with the Swedish 1 m Solar Telescope, we have identified several instances of granular lanes traveling into granules. These are believed to be the observational signature of underlying tubes of vortical flow with their axis oriented parallel to the solar surface. Associated with these horizontal vortex tubes, we detect in some cases a significant signal in linear polarization, located at the trailing dark edge of the granular lane. The linear polarization appears at a later stage of the granular lane development, and is flanked by patches of circular polarization. Stokes inversions show that the elongated patch of linear polarization signal arises from the horizontal magnetic field aligned with the granular lane. We analyze snapshots of a magnetohydrodynamic numerical simulation and find cases in which the horizontal vortex tube of the granular lane redistributes and transports the magnetic field to the solar surface causing a polarimetric signature similar to what is observed. We thus witness a mechanism capable of transporting magnetic flux to the solar surface within granules. This mechanism is probably an important component of the small-scale dynamo supposedly acting at the solar surface and generating the quiet-Sun magnetic field. Title: Vortices evolution in the solar atmosphere. A dynamical equation for the swirling strength Authors: Canivete Cuissa, José R.; Steiner, Oskar Bibcode: 2020A&A...639A.118C Altcode: 2020arXiv200512871C
Aims: We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria.
Methods: The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative magneto-hydrodynamical simulations of the solar atmosphere produced with the CO5BOLD code.
Results: We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations.
Conclusions: The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics. Title: Numerical Methods for the Radiative Transfer Equation of Polarized Light Authors: Janett, G.; Steiner, O.; Belluzzi, L. Bibcode: 2019ASPC..526..133J Altcode: The quest of the "best formal solver" available is still open and the lack of a clear comparison between the different numerical methods proposed by the community does not facilitate a conclusion. This work presents a reference paradigm for the characterization of formal solvers, based on the concepts of order of accuracy, stability and computational cost. This overview aims to facilitate the comprehension of the advantages and weaknesses of the already existing formal solvers and of those yet to come. Title: A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest; Belluzzi, Luca; Mishra, Siddhartha Bibcode: 2019A&A...624A.104J Altcode: Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data.
Aims: This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim is to propose new techniques which could be suitable for applications in the context of numerical radiative transfer.
Methods: We have proposed and tested two different techniques. Essentially non-oscillatory (ENO) techniques generate several candidate interpolations based on different substencils. The smoothest candidate interpolation is determined from a measure for the local smoothness, thereby enabling the essentially non-oscillatory property. Weighted ENO (WENO) techniques use a convex combination of all candidate substencils to obtain high-order accuracy in smooth regions while keeping the essentially non-oscillatory property. In particular, we have outlined and tested a novel well-performing fourth-order WENO interpolation technique for both uniform and nonuniform grids.
Results: Numerical tests prove that the fourth-order WENO interpolation guarantees fourth-order accuracy in smooth regions of the interpolated functions. In the presence of discontinuities, the fourth-order WENO interpolation enables the non-oscillatory property, avoiding oscillations. Unlike Bézier and monotonic high-order Hermite interpolations, it does not degenerate to a linear interpolation near smooth extrema of the interpolated function. Conclusion. The novel fourth-order WENO interpolation guarantees high accuracy in smooth regions, while effectively handling discontinuities. This interpolation technique might be particularly suitable for several problems, including a number of radiative transfer applications such as multidimensional problems, multigrid methods, and formal solutions. Title: Internal Gravity Waves in the Magnetized Solar Atmosphere. II. Energy Transport Authors: Vigeesh, G.; Roth, M.; Steiner, O.; Jackiewicz, J. Bibcode: 2019ApJ...872..166V Altcode: 2019arXiv190108871V In this second paper of the series on internal gravity waves (IGWs), we present a study of the generation and propagation of IGWs in a model solar atmosphere with diverse magnetic conditions. A magnetic field-free and three magnetic models that start with an initial, vertical, homogeneous field of 10, 50, and 100 G magnetic flux density, are simulated using the CO5BOLD code. We find that the IGWs are generated in similar manner in all four models in spite of the differences in the magnetic environment. The mechanical energy carried by IGWs is significantly larger than that of the acoustic waves in the lower part of the atmosphere, making them an important component of the total wave energy budget. The mechanical energy flux (106-103 W m-2) is a few orders of magnitude larger than the Poynting flux (103-101 W m-2). The Poynting fluxes show a downward component in the frequency range corresponding to the IGWs, which confirm that these waves do not propagate upward in the atmosphere when the fields are predominantly vertical and strong. We conclude that, in the upper photosphere, the propagation properties of IGWs depend on the average magnetic field strength and therefore these waves can be potential candidates for magnetic field diagnostics of these layers. However, their subsequent coupling to Alfvénic waves is unlikely in a magnetic environment permeated with predominantly vertical fields, and therefore they may not directly or indirectly contribute to the heating of layers above plasma-β less than 1. Title: Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca Bibcode: 2018ApJ...865...16J Altcode: 2018arXiv180906604J The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy requirement is quantitatively described for specific situations. Title: Structure of the Balmer jump. The isolated hydrogen atom Authors: Calvo, F.; Belluzzi, L.; Steiner, O. Bibcode: 2018A&A...613A..55C Altcode: 2019arXiv190110241C Context. The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series.
Aims: We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit.
Methods: We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl'Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem.
Results: We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a "Balmer jump" is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way.
Conclusions: The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms. Title: Simulation of the small-scale magnetism in main-sequence stellar atmospheres Authors: Salhab, R. G.; Steiner, O.; Berdyugina, S. V.; Freytag, B.; Rajaguru, S. P.; Steffen, M. Bibcode: 2018A&A...614A..78S Altcode: Context. Observations of the Sun tell us that its granular and subgranular small-scale magnetism has significant consequences for global quantities such as the total solar irradiance or convective blueshift of spectral lines.
Aims: In this paper, properties of the small-scale magnetism of four cool stellar atmospheres, including the Sun, are investigated, and in particular its effects on the radiative intensity and flux.
Methods: We carried out three-dimensional radiation magnetohydrodynamic simulations with the CO5BOLD code in two different settings: with and without a magnetic field. These are thought to represent states of high and low small-scale magnetic activity of a stellar magnetic cycle.
Results: We find that the presence of small-scale magnetism increases the bolometric intensity and flux in all investigated models. The surplus in radiative flux of the magnetic over the magnetic field-free atmosphere increases with increasing effective temperature, Teff, from 0.47% for spectral type K8V to 1.05% for the solar model, but decreases for higher effective temperatures than solar. The degree of evacuation of the magnetic flux concentrations monotonically increases with Teff as does their depression of the visible optical surface, that is the Wilson depression. Nevertheless, the strength of the field concentrations on this surface stays remarkably unchanged at ≈1560 G throughout the considered range of spectral types. With respect to the surrounding gas pressure, the field strength is close to (thermal) equipartition for the Sun and spectral type F5V but is clearly sub-equipartition for K2V and more so for K8V. The magnetic flux concentrations appear most conspicuous for model K2V owing to their high brightness contrast.
Conclusions: For mean magnetic flux densities of approximately 50 G, we expect the small-scale magnetism of stars in the spectral range from F5V to K8V to produce a positive contribution to their bolometric luminosity. The modulation seems to be most effective for early G-type stars. Title: Formal Solutions for Polarized Radiative Transfer. II. High-order Methods Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca Bibcode: 2017ApJ...845..104J Altcode: 2017arXiv170901280J When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al., emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost. Title: On the effect of vorticity on the propagation of internal gravity waves. Authors: Vigeesh, G.; Steiner, O.; Calvo, F.; Roth, M. Bibcode: 2017MmSAI..88...54V Altcode: We compare different models of solar surface convection to study vorticity and how it can influence the propagation of internal gravity waves. We conclude that simulations performed with higher grid resolution may have a reduced gravity wave flux in the lower part of the atmosphere due to strong vorticity. We also show that the vertical extent of the allowed region of propagation depends on the magnetic field inclination. Title: Formal Solutions for Polarized Radiative Transfer. I. The DELO Family Authors: Janett, Gioele; Carlin, Edgar S.; Steiner, Oskar; Belluzzi, Luca Bibcode: 2017ApJ...840..107J Altcode: 2017arXiv170901274J The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at facilitating the comprehension of the advantages and drawbacks of the different formal solvers, this work presents a reference paradigm for their characterization based on the concepts of order of accuracy, stability, and computational cost. Special attention is paid to understand the numerical methods belonging to the Diagonal Element Lambda Operator family, in an attempt to highlight their specificities. Title: High-frequency Oscillations in Small Magnetic Elements Observed with Sunrise/SuFI Authors: Jafarzadeh, S.; Solanki, S. K.; Stangalini, M.; Steiner, O.; Cameron, R. H.; Danilovic, S. Bibcode: 2017ApJS..229...10J Altcode: 2016arXiv161109302J We characterize waves in small magnetic elements and investigate their propagation in the lower solar atmosphere from observations at high spatial and temporal resolution. We use the wavelet transform to analyze oscillations of both horizontal displacement and intensity in magnetic bright points found in the 300 nm and the Ca II H 396.8 nm passbands of the filter imager on board the Sunrise balloon-borne solar observatory. Phase differences between the oscillations at the two atmospheric layers corresponding to the two passbands reveal upward propagating waves at high frequencies (up to 30 mHz). Weak signatures of standing as well as downward propagating waves are also obtained. Both compressible and incompressible (kink) waves are found in the small-scale magnetic features. The two types of waves have different, though overlapping, period distributions. Two independent estimates give a height difference of approximately 450 ± 100 km between the two atmospheric layers sampled by the employed spectral bands. This value, together with the determined short travel times of the transverse and longitudinal waves provide us with phase speeds of 29 ± 2 km s-1 and 31 ± 2 km s-1, respectively. We speculate that these phase speeds may not reflect the true propagation speeds of the waves. Thus, effects such as the refraction of fast longitudinal waves may contribute to an overestimate of the phase speed. Title: Internal Gravity Waves in the Magnetized Solar Atmosphere. I. Magnetic Field Effects Authors: Vigeesh, G.; Jackiewicz, J.; Steiner, O. Bibcode: 2017ApJ...835..148V Altcode: 2016arXiv161204729V Observations of the solar atmosphere show that internal gravity waves are generated by overshooting convection, but are suppressed at locations of magnetic flux, which is thought to be the result of mode conversion into magnetoacoustic waves. Here, we present a study of the acoustic-gravity wave spectrum emerging from a realistic, self-consistent simulation of solar (magneto)convection. A magnetic field free, hydrodynamic simulation and a magnetohydrodynamic (MHD) simulation with an initial, vertical, homogeneous field of 50 G flux density were carried out and compared with each other to highlight the effect of magnetic fields on the internal gravity wave propagation in the Sun’s atmosphere. We find that the internal gravity waves are absent or partially reflected back into the lower layers in the presence of magnetic fields and argue that the suppression is due to the coupling of internal gravity waves to slow magnetoacoustic waves still within the high-β region of the upper photosphere. The conversion to Alfvén waves is highly unlikely in our model because there is no strongly inclined magnetic field present. We argue that the suppression of internal waves observed within magnetic flux concentrations may also be due to nonlinear breaking of internal waves due to vortex flows that are ubiquitously present in the upper photosphere and the chromosphere. Title: CO5BOLD for MHD: progresses and deficiencies . Authors: Steiner, O.; Calvo, F.; Salhab, R.; Vigeesh, G. Bibcode: 2017MmSAI..88...37S Altcode: The magnetohydrodynamics module of CO5BOLD has been steadily improved over the past decade and has been used for various solar and stellar physical applications. We give an overview of current work with it and of remaining and newly emerged shortcomings. Title: Sub-photosphere to Solar Atmosphere Connection Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis, Stathis; Steiner, Oskar Bibcode: 2017hdsi.book..173K Altcode: No abstract at ADS Title: Non-magnetic photospheric bright points in 3D simulations of the solar atmosphere Authors: Calvo, F.; Steiner, O.; Freytag, B. Bibcode: 2016A&A...596A..43C Altcode: 2016arXiv161204278C Context. Small-scale bright features in the photosphere of the Sun, such as faculae or G-band bright points, appear in connection with small-scale magnetic flux concentrations.
Aims: Here we report on a new class of photospheric bright points that are free of magnetic fields. So far, these are visible in numerical simulations only. We explore conditions required for their observational detection.
Methods: Numerical radiation (magneto-)hydrodynamic simulations of the near-surface layers of the Sun were carried out. The magnetic field-free simulations show tiny bright points, reminiscent of magnetic bright points, only smaller. A simple toy model for these non-magnetic bright points (nMBPs) was established that serves as a base for the development of an algorithm for their automatic detection. Basic physical properties of 357 detected nMBPs were extracted and statistically evaluated. We produced synthetic intensity maps that mimic observations with various solar telescopes to obtain hints on their detectability.
Results: The nMBPs of the simulations show a mean bolometric intensity contrast with respect to their intergranular surroundings of approximately 20%, a size of 60-80 km, and the isosurface of optical depth unity is at their location depressed by 80-100 km. They are caused by swirling downdrafts that provide, by means of the centripetal force, the necessary pressure gradient for the formation of a funnel of reduced mass density that reaches from the subsurface layers into the photosphere. Similar, frequently occurring funnels that do not reach into the photosphere, do not produce bright points.
Conclusions: Non-magnetic bright points are the observable manifestation of vertically extending vortices (vortex tubes) in the photosphere. The resolving power of 4-m-class telescopes, such as the DKIST, is needed for an unambiguous detection of them.

The movie associated to Fig. 1 is available at http://www.aanda.org Title: Chromospheric and Coronal Wave Generation in a Magnetic Flux Sheath Authors: Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen, Boris; Wedemeyer, Sven; Carlsson, Mats Bibcode: 2016ApJ...827....7K Altcode: 2016arXiv160608826K Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab “pump” the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of ν ≈ 4 mHz. We conclude that this process of “magnetic pumping” is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils. Title: Polarized radiative transfer in discontinuous media Authors: Steiner, O.; Züger, F.; Belluzzi, L. Bibcode: 2016A&A...586A..42S Altcode: Context. Observations of the solar atmosphere of ever increasing spatial resolution reveal steep gradients in the magnetic field and in thermal states. Likewise, numerical simulations of the solar atmosphere show contact discontinuities and shock fronts. This asks for the development of robust methods for computing the radiative transfer of polarized light in discontinuous media.
Aims: Here, we propose a new concept for dealing with discontinuities in the radiative transfer of polarized light and carry out a few basic test calculations. While in the past, the focus was on interpolating the source function with ever-increasing accuracy and smoothness, we propose to take the opposite approach by reconstructing it with piecewise continuous functions, taking discontinuities on purpose into account. This concept is known from computational fluid dynamics.
Methods: Test calculations were carried out for (I) a Milne-Eddington atmosphere; (II) an atmosphere featuring a single discontinuity that is shifted across one grid cell; and (III) a two-layered atmosphere with discontinuities in the source function, the velocity, and the magnetic field.
Results: It is shown that the method of piecewise continuous reconstruction is a viable approach to solving the radiative transfer equation for polarized light. In the special case where a discontinuity coincides with a computational cell interface, the method is capable of producing the exact solution. Overall, the assessment of the piecewise continuous reconstruction method turns out to be cautiously positive, but it does not lead to an order-of-magnitude improvement in accuracy over conventional methods for the examples considered here. More realistic model atmospheres need to be considered for judging practical applicability. Title: Sub-photosphere to Solar Atmosphere Connection Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis, Stathis; Steiner, Oskar Bibcode: 2015SSRv..196..167K Altcode: 2013SSRv..tmp...93K Magnetic fields extend from the solar interior through the atmosphere. The formation and evolution of active regions can be studied by measuring subsurface flows with local helioseismology. The emergence of magnetic flux from the solar convection zone is associated with acoustic perturbation signatures. In near-surface layers, the average dynamics can be determined for emerging regions. MHD simulations of the emergence of a twisted flux tube show how magnetic twist and free energy are transported from the interior into the corona and the dynamic signatures associated with such transport in the photospheric and sub-photospheric layers. The subsurface twisted flux tube does not emerge into the corona as a whole in emerging active regions. Shear flows at the polarity inversion line and coherent vortical motions in the subsurface flux tubes are the major means by which twist is transported into the corona, leading to the formation of sigmoid-shaped coronal magnetic fields capable of driving solar eruptions. The transport of twist can be followed from the interior by using the kinetic helicity of subsurface flows as a proxy of magnetic helicity; this quantity holds great promise for improving the understanding of eruptive phenomena. Waves are not only vital for studying the link between the solar interior and the surface but for linking the photosphere with the corona as well. Acoustic waves that propagate from the surface into the magnetically structured, dynamic atmosphere undergo mode conversion and refraction. These effects enable atmospheric seismology to determine the topography of magnetic canopies in the solar atmosphere. Inclined magnetic fields lower the cut-off frequency so that low frequency waves can leak into the outer atmosphere. Recent high resolution, high cadence observations of waves and oscillations in the solar atmosphere, have lead to a renewed interest in the potential role of waves as a heating mechanism. In light of their potential contribution to the heating of the solar atmosphere, some of the recent observations of waves and oscillations and ongoing modelling efforts are reviewed. Title: On the Evolution of Magnetic White Dwarfs Authors: Tremblay, P. -E.; Fontaine, G.; Freytag, B.; Steiner, O.; Ludwig, H. -G.; Steffen, M.; Wedemeyer, S.; Brassard, P. Bibcode: 2015ApJ...812...19T Altcode: 2015arXiv150905398T We present the first radiation magnetohydrodynamic simulations of the atmosphere of white dwarf stars. We demonstrate that convective energy transfer is seriously impeded by magnetic fields when the plasma-β parameter, the thermal-to-magnetic-pressure ratio, becomes smaller than unity. The critical field strength that inhibits convection in the photosphere of white dwarfs is in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG field strengths observed in magnetic white dwarfs, implying that these objects have radiative atmospheres. We have employed evolutionary models to study the cooling process of high-field magnetic white dwarfs, where convection is entirely suppressed during the full evolution (B ≳ 10 MG). We find that the inhibition of convection has no effect on cooling rates until the effective temperature (Teff) reaches a value of around 5500 K. In this regime, the standard convective sequences start to deviate from the ones without convection due to the convective coupling between the outer layers and the degenerate reservoir of thermal energy. Since no magnetic white dwarfs are currently known at the low temperatures where this coupling significantly changes the evolution, the effects of magnetism on cooling rates are not expected to be observed. This result contrasts with a recent suggestion that magnetic white dwarfs with Teff ≲ 10,000 K cool significantly slower than non-magnetic degenerates. Title: The statistical properties of vortex flows in the solar atmosphere Authors: Wedemeyer, Sven; Kato, Yoshiaki; Steiner, Oskar Bibcode: 2015IAUGA..2256852W Altcode: Rotating magnetic field structures associated with vortex flows on the Sun, also known as “magnetic tornadoes”, may serve as waveguides for MHD waves and transport mass and energy upwards through the atmosphere. Magnetic tornadoes may therefore potentially contribute to the heating of the upper atmospheric layers in quiet Sun regions.Magnetic tornadoes are observed over a large range of spatial and temporal scales in different layers in quiet Sun regions. However, their statistical properties such as size, lifetime, and rotation speed are not well understood yet because observations of these small-scale events are technically challenging and limited by the spatial and temporal resolution of current instruments. Better statistics based on a combination of high-resolution observations and state-of-the-art numerical simulations is the key to a reliable estimate of the energy input in the lower layers and of the energy deposition in the upper layers. For this purpose, we have developed a fast and reliable tool for the determination and visualization of the flow field in (observed) image sequences. This technique, which combines local correlation tracking (LCT) and line integral convolution (LIC), facilitates the detection and study of dynamic events on small scales, such as propagating waves. Here, we present statistical properties of vortex flows in different layers of the solar atmosphere and try to give realistic estimates of the energy flux which is potentially available for heating of the upper solar atmosphere Title: Properties of small-scale magnetism of stellar atmospheres Authors: Steiner, Oskar; Salhab, René; Freytag, Bernd; Rajaguru, Paul; Schaffenberger, Werner; Steffen, Matthias Bibcode: 2014PASJ...66S...5S Altcode: 2014PASJ..tmp...95S The magnetic field outside of sunspots is concentrated in the intergranular space, where it forms a delicate filigree of bright ribbons and dots as seen on broad band images of the Sun. We expect this small-scale magnetic field to exhibit a similar behavior in stellar atmospheres. In order to find out more about it, we perform numerical simulations of the surface layers of stellar atmospheres. Here, we report on preliminary results from simulations in the range between 4000 K and 6500 K effective temperature with an initial vertical, homogeneous magnetic field of 50 G strength. We find that the field strength of the strongest magnetic flux concentrations increases with decreasing effective temperature at the height level where the average Rosseland optical depth is one. On the other hand, at the same level, the field is less strong than the thermal equipartition value in the coolest model but assumes superequipartition in the models hotter than 5000 K. While the Wilson depression of the strongest field concentrations is about one pressure scale height in the coolest model, it is more than four times the pressure scale height in the hottest one. We also find that the relative contribution of the bright filigree to the bolometric, vertically directed radiative intensity is most significant for the Teff = 5000 K model (0.6%-0.79%) and least significant for the hottest and coolest models (0.1%-0.46% and 0.14%-0.32%, respectively). This behavior suggests that the effect of the small-scale magnetic field on the photometric variability is more significant for K dwarf stars than for F-type and also M-type stars. Title: On the plasma flow inside magnetic tornadoes on the Sun Authors: Wedemeyer, Sven; Steiner, Oskar Bibcode: 2014PASJ...66S..10W Altcode: 2014PASJ..tmp...98W; 2014arXiv1406.7270W High-resolution observations with the Swedish 1-m Solar Telescope (SST) and the Solar Dynamics Observatory (SDO) reveal rotating magnetic field structures that extend from the solar surface into the chromosphere and the corona. These so-called magnetic tornadoes are primarily detected as rings or spirals of rotating plasma in the Ca II 854.2 nm line core (also known as chromospheric swirls). Detailed numerical simulations show that the observed chromospheric plasma motion is caused by the rotation of magnetic field structures, which again are driven by photospheric vortex flows at their footpoints. Under the right conditions, two vortex flow systems are stacked on top of each other. We refer to the lower vortex, which extends from the low photosphere into the convection zone, as intergranular vortex flow (IVF). Once a magnetic field structure is co-located with an IVF, the rotation is mediated into the upper atmospheric layers and an atmospheric vortex flow (AVF, or magnetic tornado) is generated. In contrast to the recent work by Shelyag et al. (2013, ApJ, 776, L4), we demonstrate that particle trajectories in a simulated magnetic tornado indeed follow spirals and argue that the properties of the trajectories decisively depend on the location in the atmosphere and the strength of the magnetic field. Title: Magnetic tornadoes and chromospheric swirls - Definition and classification Authors: Wedemeyer, Sven; Scullion, Eamon; Steiner, Oskar; de la Cruz Rodriguez, Jaime; Rouppe van der Voort, L. H. M. Bibcode: 2013JPhCS.440a2005W Altcode: 2013arXiv1303.0179W Chromospheric swirls are the observational signatures of rotating magnetic field structures in the solar atmosphere, also known as magnetic tornadoes. Swirls appear as dark rotating features in the core of the spectral line of singly ionized calcium at a wavelength of 854.2 nm. This signature can be very subtle and difficult to detect given the dynamic changes in the solar chromosphere. Important steps towards a systematic and objective detection method are the compilation and characterization of a statistically significant sample of observed and simulated chromospheric swirls. Here, we provide a more exact definition of the chromospheric swirl phenomenon and also present a first morphological classification of swirls with three types: (I) Ring, (II) Split, (III) Spiral. We also discuss the nature of the magnetic field structures connected to tornadoes and the influence of limited spatial resolution on the appearance of their photospheric footpoints. Title: On the Effects of the SDO Orbital Motion on the HMI Vector Magnetic Field Measurements Authors: Fleck, B.; Centeno, R.; Cheung, M.; Couvidat, S.; Hayashi, K.; Rezaei, R.; Steiner, O.; Straus, T. Bibcode: 2013enss.confE.145F Altcode: In a previous study we have investigated the magnetic field diagnostics potential of SDO/HMI. We have used the output of high-resolution 3D, time-dependent, radiative magneto-hydrodynamics simulations to calculate Stokes profiles for the Fe I 6173 Å line. From these we constructed Stokes filtergrams using a representative set of HMI filter response functions. The magnetic field vector (x,y) and line-of-sight Doppler velocities V(x,y) were determined from these filtergrams using a simplified version of the HMI magnetic field processing pipeline, and the reconstructed magnetic field (x,y) and line-of-sight velocity V(x,y) were compared to the actual magnetic field (x,y,z) and vertical velocity V0(x,y,z) in the simulations. The present investigation expands this analysis to include the effects of the significant orbital motions of SDO, which, given the limited wavelength range of the HMI filter profiles, affects the outer wing measurements and therefore might impact the magnetic field measurements. We find that the effects of the orbital movement of SDO are noticeable, in particular for the strongest fields (B > 3 kG) and the maximum wavelength shift of 5.5 km/s (3.5 km/s orbital movement + 2 km/s solar rotation). Saturation effects for strong fields (B > 3 kG) are already visible for wavelength shifts of 3.2 km/s (orbital movement, disk center). The measurements of inclination and vertical velocity are more robust. Compared to other factors of uncertainty in the inversion of HMI Stokes measurements the orbital movement is not a major concern or source of error. Title: Three-dimensional magnetohydrodynamic simulations of M-dwarf chromospheres Authors: Wedemeyer, S.; Ludwig, H. -G.; Steiner, O. Bibcode: 2013AN....334..137W Altcode: 2013csss...17..137W; 2012arXiv1207.2342W We present first results from three-dimensional radiation magnetohydrodynamic simulations of M-type dwarf stars with CO5BOLD. The local models include the top of the convection zone, the photosphere, and the chromosphere. The results are illustrated for models with an effective temperature of 3240 K and a gravitational acceleration of {log g = 4.5}, which represent analogues of AD Leo. The models have different initial magnetic field strengths and field topologies. This first generation of models demonstrates that the atmospheres of M dwarfs are highly dynamic and intermittent. Magnetic fields and propagating shock waves produce a complicated fine-structure, which is clearly visible in synthetic intensity maps in the core of the Ca II K spectral line and also at millimeter wavelengths. The dynamic small-scale pattern cannot be described by means of one-dimensional models, which has important implications for the construction of semi-empirical model atmospheres and thus for the interpretation of observations in general. Detailed three-dimensional numerical simulations are valuable in this respect. Furthermore, such models facilitate the analysis of small-scale processes, which cannot be observed on stars but nevertheless might be essential for understanding M-dwarf atmospheres and their activity. An example are so-called ``magnetic tornadoes'', which have recently been found on the Sun and are presented here in M-dwarf models for the first time. Title: First steps with CO5BOLD using HLLMHD and PP reconstruction . Authors: Steiner, O.; Rajaguru, S. P.; Vigeesh, G.; Steffen, M.; Schaffenberger, W.; Freytag, B. Bibcode: 2013MSAIS..24..100S Altcode: We report on first experiences with real-life applications using the MHD-module of CO5BOLD together with the piecewise parabolic reconstruction scheme and present preliminary results of stellar magnetic models with Teff = 4000 K to Teff = 5770 K. Title: The science challenges for large solar telescopes Authors: Steiner, O. Bibcode: 2012IAUSS...6E.101S Altcode: Looking at numerical simulations of highest spatial resolution and highest resolution observations, we endeavor extrapolating what science questions can be tackled with future large solar telescopes. By means of selected examples we shall try to determine the instrumental requirements for answering these questions. For example, what polarimetric accuracy do we need to make progress regarding the topography of the internetwork magnetic field? What spatial and temporal resolution is needed to track the driving forces of dynamic fibrils, spicules and other jet-like features of the solar chromosphere, what to asses the role of vortical flows in the photosphere and its impact on the chromosphere and corona, or what to shed light on the turbulent dynamo supposedly working in the surface layers of the convection zone. Will large solar telescopes help us resolving the remaining puzzles of the sunspot penumbra and the still largely enigmatic formation process of sunspots? Besides such foreseeable science questions however, we should be aware that the best discoveries come unexpectedly and therefore, it may be worthwhile to wonder about what instrumental capabilities may be best conducive to the unexpected. Title: Revealing the nature of magnetic shadows with numerical 3D-MHD simulations Authors: Nutto, C.; Steiner, O.; Roth, M. Bibcode: 2012A&A...542L..30N Altcode: 2012arXiv1205.5308N
Aims: We investigate the interaction of magneto-acoustic waves with magnetic network elements with the aim of finding possible signatures of the magnetic shadow phenomenon in the vicinity of network elements.
Methods: We carried out three-dimensional numerical simulations of magneto-acoustic wave propagation in a model solar atmosphere that is threaded by a complexly structured magnetic field, resembling that of a typical magnetic network element and of internetwork regions. High-frequency waves of 10 mHz are excited at the bottom of the simulation domain. On their way through the upper convection zone and through the photosphere and the chromosphere they become perturbed, refracted, and converted into different mode types. We applied a standard Fourier analysis to produce oscillatory power-maps of the line-of-sight velocity.
Results: In the power maps of the upper photosphere and the lower chromosphere, we clearly see the magnetic shadow: a seam of suppressed power surrounding the magnetic network elements. We demonstrate that this shadow is linked to the mode conversion process and that power maps at these height levels show the signature of three different magneto-acoustic wave modes. Title: Magnetic tornadoes as energy channels into the solar corona Authors: Wedemeyer-Böhm, Sven; Scullion, Eamon; Steiner, Oskar; Rouppe van der Voort, Luc; de La Cruz Rodriguez, Jaime; Fedun, Viktor; Erdélyi, Robert Bibcode: 2012Natur.486..505W Altcode: Heating the outer layers of the magnetically quiet solar atmosphere to more than one million kelvin and accelerating the solar wind requires an energy flux of approximately 100 to 300 watts per square metre, but how this energy is transferred and dissipated there is a puzzle and several alternative solutions have been proposed. Braiding and twisting of magnetic field structures, which is caused by the convective flows at the solar surface, was suggested as an efficient mechanism for atmospheric heating. Convectively driven vortex flows that harbour magnetic fields are observed to be abundant in the photosphere (the visible surface of the Sun). Recently, corresponding swirling motions have been discovered in the chromosphere, the atmospheric layer sandwiched between the photosphere and the corona. Here we report the imprints of these chromospheric swirls in the transition region and low corona, and identify them as observational signatures of rapidly rotating magnetic structures. These ubiquitous structures, which resemble super-tornadoes under solar conditions, reach from the convection zone into the upper solar atmosphere and provide an alternative mechanism for channelling energy from the lower into the upper solar atmosphere. Title: First Results from the SUNRISE Mission Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.; Gandorfer, A.; Hirzberger, J.; Jafarzadeh, S.; Lagg, A.; Riethmüller, T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; González, M. J. M.; Pillet, V. M.; Khomenko, E.; Yelles Chaouche, L.; Iniesta, J. C. d. T.; Domingo, V.; Palacios, J.; Knölker, M.; González, N. B.; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M. Bibcode: 2012ASPC..455..143S Altcode: The SUNRISE balloon-borne solar observatory consists of a 1m aperture Gregory telescope, a UV filter imager, an imaging vector polarimeter, an image stabilization system, and further infrastructure. The first science flight of SUNRISE yielded high-quality data that reveal the structure, dynamics, and evolution of solar convection, oscillations, and magnetic fields at a resolution of around 100 km in the quiet Sun. Here we describe very briefly the mission and the first results obtained from the SUNRISE data, which include a number of discoveries. Title: Excitation of Slow-Modes in Network Magnetic Elements Authors: Kato, Y.; Steiner, O.; Steffen, M.; Suematsu, Y. Bibcode: 2012ASPC..455..237K Altcode: From radiation magnetohydrodynamic (RMHD) simulations of the solar atmosphere we have found a new mechanism for the excitation of longitudinal slow modes within magnetic flux concentrations. It is found that the convective downdrafts in the immediate surroundings of magnetic elements are responsible for the excitation of slow modes. The coupling between the external downdraft and the plasma motion internal to the flux concentration is mediated by the inertial forces of the downdraft that act on the magnetic flux concentration. These forces pump the internal atmosphere in the downward direction, which entails a fast downflow in the photospheric and chromospheric layers of the magnetic element. Subsequent to the transient pumping phase, the atmosphere rebounds, causing a slow mode traveling along the magnetic flux concentration in the upward direction and developing into a shock wave in chromospheric heights, possibly capable of producing some kind of dynamic fibril. This event occurs recurrently. We compare the power spectra of the temperature and velocity of the flux-sheet atmosphere to the corresponding spectra of the unmagnetized atmosphere. Title: 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 Authors: Steiner, O.; Rezaei, R. Bibcode: 2012ASPC..456....3S Altcode: 2012arXiv1202.4040S We review (i) observations and numerical simulations of vortical flows in the solar atmosphere and (ii) measurements of the horizontal magnetic field in quiet Sun regions. First, we discuss various manifestations of vortical flows and emphasize the role of magnetic fields in mediating swirling motion created near the solar surface to the higher layers of the photosphere and to the chromosphere. We reexamine existing simulation runs of solar surface magnetoconvection with regard to vortical flows and compare to previously obtained results. Second, we reviews contradictory results and problems associated with measuring the angular distribution of the magnetic field in quiet Sun regions. Furthermore, we review the Stokes-V-amplitude ratio method for the lines Fe i λλ 630.15 and 630.25 nm. We come to the conclusion that the recently discovered two distinct populations in scatter plots of this ratio must not bee interpreted in terms of “uncollapsed'' and “collapsed'' fields but stem from weak granular magnetic fields and weak canopy fields located at the boundaries between granules and the intergranular space. Based on new simulation runs, we reaffirm earlier findings of a predominance of the horizontal field components over the vertical one, particularly in the upper photosphere and at the base of the chromosphere. Title: On The Magnetic-Field Diagnostics Potential of SDO/HMI Authors: Fleck, Bernard; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno, R.; Cheung, M.; Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.; Viticchie, B. Bibcode: 2012AAS...22020701F Altcode: The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) is designed to study oscillations and the magnetic field in the solar photosphere. It observes the full solar disk in the Fe I absorption line at 6173 Å. We use the output of three high-resolution 3D, time-dependent, radiative magneto-hydrodynamics simulations (two based on the MURaM code, one on the CO5BOLD code) to calculate Stokes profiles for the Fe I 6173 Å line for snapshots of a sunspot, a plage area and an enhanced network region. Stokes filtergrams are constructed for the 6 nominal HMI wavelengths by multiplying the Stokes profiles with a representative set of HMI filter response functions. The magnetic field vector B(x,y) and line-of-sight Doppler velocities V(x,y) are determined from these filtergrams using a simplified version of the HMI magnetic field processing pipeline. Finally, the reconstructed magnetic field B(x,y) and line-of-sight velocity V(x,y) are compared to the actual magnetic field B0(x,y,z) and vertical velocity V0(x,y,z) in the simulations. Title: Detection of Vortex Tubes in Solar Granulation from Observations SUNRISE Authors: Steiner, O.; Franz, M.; González, N. B.; Nutto, C.; Rezaei, R.; Pillet, V. M.; Bonet, J. A.; Iniesta, J. C. d. T.; Domingo, V.; Solanki, S. K.; Knölker, M.; Schmidt, W.; Barthol, P.; Gandorfer, A. Bibcode: 2012ASPC..455...35S Altcode: We investigated a time series of continuum intensity maps and Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar observatory SUNRISE. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. We conclude that these granular lanes are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. This paper is a summary and update of the results previously presented in Steiner et al. (2010). Title: Small-scale rotating magnetic flux structures as alternative energy channels into the low corona Authors: Wedemeyer-Böhm; , Sven; Scullion; , Eamon; Steiner; , Oskar; Rouppe van der Voort, Luc; de la Cruz Rodriguez, Jaime; Erdelyi, Robertus; Fedun, Viktor Bibcode: 2012decs.confE..67W Altcode: Vortex flows are frequently observed in the downflow areas in the lanes between granules. The magnetic field is advected and trapped by these flows in the low photosphere. Consequently, the rotation of a vortex flow is transferred to the atmospheric layers above by means of the magnetic flux structure. This effect results in so-called swirls, which are observed in the chromosphere. New simultaneous observations with the Swedish Solar Telescope and the Solar Dynamics Observatory reveal that chromospheric swirls can have a coronal counterpart. This finding implies that the rotating flux structure couples the layers of the solar atmosphere from the photosphere to the (low) corona. Three-dimensional numerical simulations confirm this picture and reproduce the swirl signature. A combined analysis of the simulations and observations implies that such small-scale rotating flux structures could provide an alternative mechanism for channeling substantial energy from the photosphere into the upper solar atmosphere. Title: On the Magnetic-Field Diagnostics Potential of SDO/HMI Authors: Fleck, B.; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno, R.; Cheung, M.; Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.; Viticchie, B. Bibcode: 2012decs.confE.104F Altcode: The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) is designed to study oscillations and the magnetic field in the solar photosphere. It observes the full solar disk in the Fe I absorption line at 6173 Å. We use the output of three high-resolution 3D, time-dependent, radiative magneto-hydrodynamics simulations (two based on the MURaM code, one on the CO5BOLD code) to calculate Stokes profiles Fi(λ,x,y; i=I, V, Q, U) for the Fe I 6173 Å line for snapshots of a sunspot, a plage area and an enhanced network region. Stokes filtergrams are constructed for the 6 nominal HMI wavelengths by multiplying the Stokes profiles with a representative set of HMI filter response functions. The magnetic field vector B(x,y) and line-of-sight Doppler velocities V(x,y) are determined from these filtergrams using a simplified version of the HMI magnetic field processing pipeline. Finally, the reconstructed magnetic field B(x,y) and line-of-sight velocity V(x,y) are compared to the actual magnetic field B0(x,y,z) and vertical velocity V0(x,y,z) in the simulations. Title: The generation of shock waves traveling from the photosphere to the transition region within network magnetic elements Authors: Kato, Y.; Hansteen, V.; Steiner, O.; Carlsson, M. Bibcode: 2012decs.confE..54K Altcode: We investigate the generation of shock waves near the photosphere by convective downdrafts in the immediate surroundings of the magnetic flux concentration, using radiation magnetohydrodynamic (RMHD) 2D simulations of the solar atmosphere. The simulations comprise the layers from the upper convection zone to the lower corona. We call this the "magnetic pumping process". We find that the generated slow modes via magnetic pumping travel upward along the magnetic flux concentration, developing into a shock wave in chromospheric heights. The waves continue to propagate further up through the transition region and into the corona. In the course of propagation through the transition layer, a small fraction of the longitudinal slow mode is converted into a transverse wave mode. We report on how much energy is deposited by propagating shock waves through the transition region and we discuss the the dissipation process above the photosphere within the magnetic flux concentration.. Title: Simulations of stellar convection with CO5BOLD Authors: Freytag, B.; Steffen, M.; Ludwig, H. -G.; Wedemeyer-Böhm, S.; Schaffenberger, W.; Steiner, O. Bibcode: 2012JCoPh.231..919F Altcode: 2011arXiv1110.6844F High-resolution images of the solar surface show a granulation pattern of hot rising and cooler downward-sinking material - the top of the deep-reaching solar convection zone. Convection plays a role for the thermal structure of the solar interior and the dynamo acting there, for the stratification of the photosphere, where most of the visible light is emitted, as well as for the energy budget of the spectacular processes in the chromosphere and corona. Convective stellar atmospheres can be modeled by numerically solving the coupled equations of (magneto)hydrodynamics and non-local radiation transport in the presence of a gravity field. The CO5BOLD code described in this article is designed for so-called "realistic" simulations that take into account the detailed microphysics under the conditions in solar or stellar surface layers (equation-of-state and optical properties of the matter). These simulations indeed deserve the label "realistic" because they reproduce the various observables very well - with only minor differences between different implementations. The agreement with observations has improved over time and the simulations are now well-established and have been performed for a number of stars. Still, severe challenges are encountered when it comes to extending these simulations to include ideally the entire star or substellar object: the strong stratification leads to completely different conditions in the interior, the photosphere, and the corona. Simulations have to cover spatial scales from the sub-granular level to the stellar diameter and time scales from photospheric wave travel times to stellar rotation or dynamo cycle periods. Various non-equilibrium processes have to be taken into account. Last but not least, realistic simulations are based on detailed microphysics and depend on the quality of the input data, which can be the actual accuracy limiter. This article provides an overview of the physical problem and the numerical solution and the capabilities of CO5BOLD, illustrated with a number of applications. Title: Modification of wave propagation and wave travel-time by the presence of magnetic fields in the solar network atmosphere Authors: Nutto, C.; Steiner, O.; Schaffenberger, W.; Roth, M. Bibcode: 2012A&A...538A..79N Altcode: Context. Observations of waves at frequencies above the acoustic cut-off frequency have revealed vanishing wave travel-times in the vicinity of strong magnetic fields. This detection of apparently evanescent waves, instead of the expected propagating waves, has remained a riddle.
Aims: We investigate the influence of a strong magnetic field on the propagation of magneto-acoustic waves in the atmosphere of the solar network. We test whether mode conversion effects can account for the shortening in wave travel-times between different heights in the solar atmosphere.
Methods: We carry out numerical simulations of the complex magneto-atmosphere representing the solar magnetic network. In the simulation domain, we artificially excite high frequency waves whose wave travel-times between different height levels we then analyze.
Results: The simulations demonstrate that the wave travel-time in the solar magneto-atmosphere is strongly influenced by mode conversion. In a layer enclosing the surface sheet defined by the set of points where the Alfvén speed and the sound speed are equal, called the equipartition level, energy is partially transferred from the fast acoustic mode to the fast magnetic mode. Above the equipartition level, the fast magnetic mode is refracted due to the large gradient of the Alfvén speed. The refractive wave path and the increasing phase speed of the fast mode inside the magnetic canopy significantly reduce the wave travel-time, provided that both observing levels are above the equipartition level.
Conclusions: Mode conversion and the resulting excitation and propagation of fast magneto-acoustic waves is responsible for the observation of vanishing wave travel-times in the vicinity of strong magnetic fields. In particular, the wave propagation behavior of the fast mode above the equipartition level may mimic evanescent behavior. The present wave propagation experiments provide an explanation of vanishing wave travel-times as observed with multi-line high-cadence instruments.

Movies are available in electronic form at http://www.aanda.org Title: Stokes Diagnostics of Magneto-Acoustic Wave Propagation in the Magnetic Network on the Sun Authors: Vigeesh, G.; Steiner, O.; Hasan, S. S. Bibcode: 2011SoPh..273...15V Altcode: 2011SoPh..tmp..349V; 2011arXiv1104.4069V The solar atmosphere is magnetically structured and highly dynamic. Owing to the dynamic nature of the regions in which the magnetic structures exist, waves can be excited in them. Numerical investigations of wave propagation in small-scale magnetic flux concentrations in the magnetic network on the Sun have shown that the nature of the excited modes depends on the value of plasma β (the ratio of gas to magnetic pressure) where the driving motion occurs. Considering that these waves should give rise to observable characteristic signatures, we have attempted a study of synthesised emergent spectra from numerical simulations of magneto-acoustic wave propagation. We find that the signatures of wave propagation in a magnetic element can be detected when the spatial resolution is sufficiently high to clearly resolve it, enabling observations in different regions within the flux concentration. The possibility to probe various lines of sight around the flux concentration bears the potential to reveal different modes of the magnetohydrodynamic waves and mode conversion. We highlight the feasibility of using the Stokes-V asymmetries as a diagnostic tool to study the wave propagation within magnetic flux concentrations. These quantities can possibly be compared with existing and new observations in order to place constraints on different wave excitation mechanisms. Title: On the Magnetic-Field Diagnostics Potential of SDO/HMI Authors: Fleck, B.; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno, R.; Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.; Viticchie, B. Bibcode: 2011sdmi.confE..74F Altcode: The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) is designed to study oscillations and the magnetic field in the solar photosphere. It observes the full solar disk in the Fe I 6173 absorption line. We use the output of two high-resolution 3D, time-dependent, radiative magneto-hydrodynamics simulations (one based on the MURAM code, the other one on the COBOLD code) to calculate Stokes profiles for the Fe I 6173 line for a snapshot of a plage region and a snapshot of an enhanced network region. After spatially degrading the Stokes profiles to HMI resolution, they are multiplied by a representative set of HMI filter response functions and Stokes filtergrams are constructed for the 6 nominal HMI wavelengths. The magnetic field vector and line-of-sight Doppler velocities are determined from these filtergrams using a simplified version of the HMI magnetic field processing pipeline. Finally, the reconstructed magnetic field is compared to the actual magnetic field in the simulation. Title: The Sun at high resolution: first results from the Sunrise mission Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.; Gandorfer, A.; Hirzberger, J.; Lagg, A.; Riethmüller, T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; Pillet, V. Martínez; Khomenko, E.; del Toro Iniesta, J. C.; Domingo, V.; Palacios, J.; Knölker, M.; González, N. Bello; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M. Bibcode: 2011IAUS..273..226S Altcode: The Sunrise balloon-borne solar observatory consists of a 1m aperture Gregory telescope, a UV filter imager, an imaging vector polarimeter, an image stabilization system and further infrastructure. The first science flight of Sunrise yielded high-quality data that reveal the structure, dynamics and evolution of solar convection, oscillations and magnetic fields at a resolution of around 100 km in the quiet Sun. Here we describe very briefly the mission and the first results obtained from the Sunrise data, which include a number of discoveries. Title: On the Origin of Intergranular Jets Authors: Yurchyshyn, V. B.; Goode, P. R.; Abramenko, V. I.; Steiner, O. Bibcode: 2011ApJ...736L..35Y Altcode: 2011arXiv1106.5535Y We observe that intergranular jets, originating in the intergranular space surrounding individual granules, tend to be associated with granular fragmentation, in particular, with the formation and evolution of a bright granular lane (BGL) within individual granules. The BGLs have recently been identified as vortex tubes by Steiner et al. We further discover the development of a well-defined bright grain located between the BGL and the dark intergranular lane to which it is connected. Signatures of a BGL may reach the lower chromosphere and can be detected in off-band Hα images. Simulations also indicate that vortex tubes are frequently associated with small-scale magnetic fields. We speculate that the intergranular jets detected in the New Solar Telescope (NST) data may result from the interaction between the turbulent small-scale fields associated with the vortex tube and the larger-scale fields existing in the intergranular lanes. The intergranular jets are much smaller and weaker than all previously known jet-like events. At the same time, they appear much more numerous than the larger events, leading us to the speculation that the total energy release and mass transport by these tiny events may not be negligible in the energy and mass-flux balance near the temperature minimum atop the photosphere. The study is based on the photospheric TiO broadband (1.0 nm) filter data acquired with the 1.6 m NST operating at the Big Bear Solar Observatory. The data set also includes NST off-band Hα images collected through a Zeiss Lyot filter with a passband of 0.025 nm. Title: Excitation of magneto-acoustic waves in network magnetic elements Authors: Kato, Yoshiaki; Steiner, Oskar; Steffen, Matthias; Suematsu, Yoshinori Bibcode: 2011IAUS..273..442K Altcode: From radiation magnetohydrodynamic (RMHD) simulations we track the temporal evolution of a vertical magnetic flux sheet embedded in a two-dimensional non-stationary atmosphere that reaches all the way from the upper convection zone to the low chromosphere. Examining its temporal behavior near the interface between the convection zone and the photosphere, we describe the excitation of propagating longitudinal waves within the magnetic element as a result of convective motion in its surroundings. Title: Flux Tube Model Authors: Steiner, O. Bibcode: 2011ascl.soft05008S Altcode: This Fortran code computes magnetohydrostatic flux tubes and sheets according to the method of Steiner, Pneuman, & Stenflo (1986) A&A 170, 126-137. The code has many parameters contained in one input file that are easily modified. Extensive documentation is provided in README files. Title: Excitation of Slow Modes in Network Magnetic Elements Through Magnetic Pumping Authors: Kato, Yoshiaki; Steiner, Oskar; Steffen, Matthias; Suematsu, Yoshinori Bibcode: 2011ApJ...730L..24K Altcode: 2011arXiv1102.5164K From radiation magnetohydrodynamic simulations of the solar atmosphere, we find a new mechanism for the excitation of longitudinal slow modes within magnetic flux concentrations. We find that the convective downdrafts in the immediate surroundings of magnetic elements are responsible for the excitation of slow modes. The coupling between the external downdraft and the plasma motion internal to the flux concentration is mediated by the inertial forces of the downdraft that act on the magnetic flux concentration. These forces, in conjunction with the downward movement, pump the internal atmosphere in the downward direction, which entails a fast downdraft in the photospheric and chromospheric layers of the magnetic element. Subsequent to the transient pumping phase, the atmosphere rebounds, causing a slow mode traveling along the magnetic flux concentration in the upward direction. It develops into a shock wave in chromospheric heights, possibly capable of producing some kind of dynamic fibril. We propose an observational detection of this process. Title: Magneto-acoustic wave propagation and mode conversion in a magnetic solar atmosphere: Comparing results from the CO5BOLD code with ray theory Authors: Nutto, C.; Steiner, O.; Roth, M. Bibcode: 2010AN....331..915N Altcode: 2010arXiv1009.5586N We present simulations of magneto-acoustic wave propagation in a magnetic, plane-parallel stratified solar model atmosphere, employing the CO5BOLD-code. The tests are carried out for two models of the solar atmosphere, which are similar to the ones used by \citet{nutto_cally07} and \citet{nutto_schunker06}. The two models differ only in the orientation of the magnetic field. A qualitative comparison shows good agreement between the numerical results and the results from ray theory. The tests are done in view of the application of the present numerical code for the computation of energy fluxes of propagating acoustic waves into a dynamically evolving magnetic solar atmosphere. For this, we consider waves with frequencies above the acoustic cut-off frequency. Title: Detection of Vortex Tubes in Solar Granulation from Observations with SUNRISE Authors: Steiner, O.; Franz, M.; Bello González, N.; Nutto, Ch.; Rezaei, R.; Martínez Pillet, V.; Bonet Navarro, J. A.; del Toro Iniesta, J. C.; Domingo, V.; Solanki, S. K.; Knölker, M.; Schmidt, W.; Barthol, P.; Gandorfer, A. Bibcode: 2010ApJ...723L.180S Altcode: 2010arXiv1009.4723S We have investigated a time series of continuum intensity maps and corresponding Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar observatory SUNRISE. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. From cross sections through the computational domain of the simulation, we conclude that these granular lanes are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. We propose that the observed vortex tubes may represent only the large-scale end of a hierarchy of vortex tubes existing near the solar surface. Title: CO5BOLD: COnservative COde for the COmputation of COmpressible COnvection in a BOx of L Dimensions with l=2,3 Authors: Freytag, Bernd; Steffen, Matthias; Wedemeyer-Böhm, Sven; Ludwig, Hans-Günter; Leenaarts, Jorrit; Schaffenberger, Werner; Allard, France; Chiavassa, Andrea; Höfner, Susanne; Kamp, Inga; Steiner, Oskar Bibcode: 2010ascl.soft11014F Altcode: CO5BOLD - nickname COBOLD - is the short form of "COnservative COde for the COmputation of COmpressible COnvection in a BOx of L Dimensions with l=2,3".

It is used to model solar and stellar surface convection. For solar-type stars only a small fraction of the stellar surface layers are included in the computational domain. In the case of red supergiants the computational box contains the entire star. Recently, the model range has been extended to sub-stellar objects (brown dwarfs).

CO5BOLD solves the coupled non-linear equations of compressible hydrodynamics in an external gravity field together with non-local frequency-dependent radiation transport. Operator splitting is applied to solve the equations of hydrodynamics (including gravity), the radiative energy transfer (with a long-characteristics or a short-characteristics ray scheme), and possibly additional 3D (turbulent) diffusion in individual sub steps. The 3D hydrodynamics step is further simplified with directional splitting (usually). The 1D sub steps are performed with a Roe solver, accounting for an external gravity field and an arbitrary equation of state from a table.

The radiation transport is computed with either one of three modules:

MSrad module: It uses long characteristics. The lateral boundaries have to be periodic. Top and bottom can be closed or open ("solar module").

LHDrad module: It uses long characteristics and is restricted to an equidistant grid and open boundaries at all surfaces (old "supergiant module").

SHORTrad module: It uses short characteristics and is restricted to an equidistant grid and open boundaries at all surfaces (new "supergiant module").

The code was supplemented with an (optional) MHD version [Schaffenberger et al. (2005)] that can treat magnetic fields. There are also modules for the formation and advection of dust available. The current version now contains the treatment of chemical reaction networks, mostly used for the formation of molecules [Wedemeyer-Böhm et al. (2005)], and hydrogen ionization [Leenaarts & Wedemeyer-Böhm (2005)], too.

CO5BOLD is written in Fortran90. The parallelization is done with OpenMP directives. Title: A Chromospheric Conundrum? Authors: Judge, Philip; Knölker, Michael; Schmidt, Wolfgang; Steiner, Oskar Bibcode: 2010ApJ...720..776J Altcode: 2010arXiv1007.1203J We examine spectra of the Ca II H line, obtained under good seeing conditions with the VTT Echelle Spectrograph in 2007 June, and higher resolution data of the Ca II λ8542 line from Fabry-Pérot instruments. The VTT targets were areas near disk center which included quiet Sun and some dispersed plage. The infrared data included quiet Sun and plage associated with small pores. Bright chromospheric network emission patches expand little with wavelength from line wing to line center, i.e., with increasing line opacity and height. We argue that this simple observation has implications for the force and energy balance of the chromosphere, since bright chromospheric network emission is traditionally associated with enhanced local mechanical heating which increases temperatures and pressures. Simple physical considerations then suggest that the network chromosphere may not be able to reach horizontal force balance with its surroundings, yet the network is a long-lived structure. We speculate on possible reasons for the observed behavior. By drawing attention to a potential conundrum, we hope to contribute to a better understanding of a long-standing unsolved problem: the heating of the chromospheric network. Title: Magnetic Coupling in the Quiet Solar Atmosphere Authors: Steiner, O. Bibcode: 2010ASSP...19..166S Altcode: 2010mcia.conf..166S; 2009arXiv0904.2026S Three kinds of magnetic couplings in the quiet solar atmosphere are highlighted and discussed, all fundamentally connected to the Lorentz force: first, the coupling of the convecting and overshooting fluid in the surface layers of the Sun with the magnetic field. Here, the plasma motion provides the dominant force, which shapes the magnetic field and drives the surface dynamo. Progress in the understanding of the horizontal magnetic field is summarized and discussed. Second, the coupling between acoustic waves and the magnetic field, in particular the phenomenon of wave conversion and wave refraction. It is described how measurements of wave travel times in the atmosphere can provide information about the topography of the wave conversion zone, that is, the surface of equal Alfvéen and sound speed. In quiet regions, this surface separates a highly dynamic magnetic field with fast moving magnetosonic waves and shocks around and above it from the more slowly evolving field of high-beta plasma below it. Third, the magnetic field also couples to the radiation field, which leads to radiative flux channeling and increased anisotropy in the radiation field. It is shown how faculae can be understood in terms of this effect. The article starts with an introduction to the magnetic field of the quiet Sun in the light of new results from the Hinode space observatory and with a brief survey of measurements of the turbulent magnetic field with the help of the Hanle effect. Title: Numerical simulations of wave propagation in the solar chromosphere . Authors: Nutto, C.; Steiner, O.; Roth, M. Bibcode: 2010MmSAI..81..744N Altcode: 2010arXiv1009.5607N We present two-dimensional simulations of wave propagation in a realistic, non-stationary model of the solar atmosphere. This model shows a granular velocity field and magnetic flux concentrations in the intergranular lanes similar to observed velocity and magnetic structures on the Sun and takes radiative transfer into account.

We present three cases of magneto-acoustic wave propagation through the model atmosphere, where we focus on the interaction of different magneto-acoustic wave modes at the layer of similar sound and Alfvén speeds, which we call the equipartition layer. At this layer acoustic and magnetic mode can exchange energy depending on the angle between the wave vector and the magnetic field vector.

Our results show that above the equipartition layer and in all three cases the fast magnetic mode is refracted back into the solar atmosphere. Thus, the magnetic wave shows an evanescent behavior in the chromosphere. The acoustic mode, which travels along the magnetic field in the low plasma-beta regime, can be a direct consequence of an acoustic source within or outside the low-beta regime, or it can result from conversion of the magnetic mode, possibly from several such conversions when the wave travels across a series of equipartition layers. Title: Wave propagation and energy transport in the magnetic network of the Sun Authors: Vigeesh, G.; Hasan, S. S.; Steiner, O. Bibcode: 2009A&A...508..951V Altcode: 2009arXiv0909.2325V Aims. We investigate wave propagation and energy transport in magnetic elements, which are representatives of small scale magnetic flux concentrations in the magnetic network on the Sun. This is a continuation of earlier work by Hasan et al. (2005, ApJ, 631, 1270). The new features in the present investigation include a quantitative evaluation of the energy transport in the various modes and for different field strengths, as well as the effect of the boundary-layer thickness on wave propagation.
Methods: We carry out 2D MHD numerical simulations of magnetic flux concentrations for strong and moderate magnetic fields for which β (the ratio of gas to magnetic pressure) on the tube axis at the photospheric base is 0.4 and 1.7, respectively. Waves are excited in the tube and ambient medium by a transverse impulsive motion of the lower boundary.
Results: The nature of the modes excited depends on the value of β. Mode conversion occurs in the moderate field case when the fast mode crosses the β = 1 contour. In the strong field case the fast mode undergoes conversion from predominantly magnetic to predominantly acoustic when waves are leaking from the interior of the flux concentration to the ambient medium. We also estimate the energy fluxes in the acoustic and magnetic modes and find that in the strong field case, the vertically directed acoustic wave fluxes reach spatially averaged, temporal maximum values of a few times 106 erg cm-2 s-1 at chromospheric height levels.
Conclusions: The main conclusions of our work are twofold: firstly, for transverse, impulsive excitation, flux tubes/sheets with strong fields are more efficient than those with weak fields in providing acoustic flux to the chromosphere. However, there is insufficient energy in the acoustic flux to balance the chromospheric radiative losses in the network, even for the strong field case. Secondly, the acoustic emission from the interface between the flux concentration and the ambient medium decreases with the width of the boundary layer. Title: The Horizontal Magnetic Field of the Quiet Sun: Numerical Simulations in Comparison to Observations with Hinode Authors: Steiner, O.; Rezaei, R.; Schlichenmaier, R.; Schaffenberger, W.; Wedemeyer-Böhm, S. Bibcode: 2009ASPC..415...67S Altcode: 2009arXiv0904.2030S Three-dimensional magnetohydrodynamic simulations of the surface layers of the Sun intrinsically produce a predominantly horizontal magnetic field in the photosphere. This is a robust result in the sense that it arises from simulations with largely different initial and boundary conditions for the magnetic field. While the disk-center synthetic circular and linear polarization signals agree with measurements from Hinode, their center-to-limb variation sensitively depends on the height variation of the horizontal and the vertical field component and they seem to be at variance with the observed behavior. Title: Near-surface stellar magneto-convection: simulations for the Sun and a metal-poor solar analog Authors: Steffen, Matthias; Ludwig, H. -G.; Steiner, O. Bibcode: 2009IAUS..259..233S Altcode: 2009arXiv0902.2753S We present 2D local box simulations of near-surface radiative magneto-convection with prescribed magnetic flux, carried out with the MHD version of the CO5BOLD code for the Sun and a solar-like star with a metal-poor chemical composition (metal abundances reduced by a factor 100, [M/H] = -2). The resulting magneto-hydrodynamical models can be used to study the influence of the metallicity on the properties of magnetized stellar atmospheres. A preliminary analysis indicates that the horizontal magnetic field component tends to be significantly stronger in the optically thin layers of metal-poor stellar atmospheres. Title: Numerical simulation of wave propagation in magnetic network Authors: Vigeesh, G.; Hasan, S. S.; Steiner, O. Bibcode: 2009IAUS..257..185V Altcode: We present 2-D numerical simulations of wave propagation in the magnetic network. The network is modelled as consisting of individual magnetic flux sheets located in intergranular lanes. They have a typical horizontal size of about 150 km at the base of the photosphere and expand upward and become uniform. We consider flux sheets of different field strengths. Waves are excited by means of transverse motions at the lower boundary, to simulate the effect of granular buffeting. We look at the magneto-acoustic waves generated within the flux sheet and the acoustic waves generated in the ambient medium due to the excitation. We calculate the wave energy fluxes separating them into contributions from the acoustic and the Poynting part and study the effect of the different field strengths. Title: Observational Evidence for Shocks in the Solar Photosphere - New TESOS/VTT Results Authors: Rybak, J.; Kucera, A.; Hanslmeier, A.; Woehl, H.; Wedemeyer-Boehm, S.; Steiner, O. Bibcode: 2008ESPM...12.2.36R Altcode: High-resolution spectroscopic observations recently acquired with the TESOS spectrometer at the Vacuum Tower Telescope (VTT, Observatorio del Teide, Tenerife) are used to test predictions regarding strongly dynamic events in the photosphere as obtained from three-dimensional numerical simulations with the CO5BOLD-code.

Time series of two-dimensional maps of the Fe I 543.4 nm spectral line profile at different centre-to-limb positions are investigated in a statistical sense by comparing the distributions of individual spectral parameters derived from observations with the corresponding distributions from synthesized spectra calculated with the LINFOR3D code from the simulations. Appropriate degradation of the synthesized spectra was applied in order to take the limited spatial resolution of the telescope, seeing effects, and the scattered instrumental light into account.

At the actual spatial resolution of 0.5 arc sec, the statistics show that signatures of the photospheric dynamics, including the most dynamical events like occasional supersonic flows of plasma in the nearly horizontal direction, are very similar in both observations and simulations.

Discrepancies are found only for those spectral parameters (residual line intensity, Doppler line core shifts), which are affected by non-LTE effects, since non-LTE effects are not taken into account in the synthesis of the Fe I 543.4nm spectral line. Title: Numerical Experiments with Magnetoacoustic Waves in the Solar Atmosphere Authors: Nutto, C.; Schaffenberger, W.; Steiner, O. Bibcode: 2008ESPM...12.3.23N Altcode: With numerical experiments we explore the feasibility of using high frequency waves for probing the magnetic field in the photosphere and the chromosphere of the Sun. We track monochromatic wave trains that propagates through a magnetically structured, realistic solar atmosphere. When entering the magnetically dominated chromosphere, the waves undergo partial mode conversion and get refracted and reflected. We explore the relationship between wave travel times and the topography of the surface of equal Alfven and sound speeds, viz., the magnetic canopy. Title: Numerical simulation of wave propagation in the presence of a magnetic flux sheet Authors: Vigeesh, G.; Steiner, O.; Hasan, S. S. Bibcode: 2008ESPM...12.3.24V Altcode: We model network magnetic fields as consisting of individual magnetic flux sheets located in intergranular lanes. With a typical horizontal size of about 150 km at the base of the photosphere, they expand upward and merge with their neighbors at a height of about 600 km. Above a height of approximately 1000 km the magnetic field starts to become uniform. Granular buffeting is thought to excite waves in this medium, which is modeled by means of transversal motions at the lower boundary. The transverse driving, generates both fast and slow waves within the flux sheet and acoustic waves in the ambient medium. We consider flux sheets of different field strengths and different boundary-layer widths. Separating the energy flux of the waves into contributions due to the acoustic flux and the Poynting flux, we show the longitudinal and transversal components of both and study their temporal evolution. Title: The Horizontal Internetwork Magnetic Field: Numerical Simulations in Comparison to Observations with Hinode Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm, S. Bibcode: 2008ESPM...12.3.22S Altcode: Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe I 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where, depending on the initial state or the boundary condition, it surpasses the vertical component by a factor of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean horizontal field component that is 1.6 or 4.3 times stronger than the vertical component, depending on the initial state or the boundary condition. This is a consequence of both the intrinsically stronger flux density of and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, whereas it is negative in the convectively unstable layer below it. Title: The Horizontal Internetwork Magnetic Field: Numerical Simulations in Comparison to Observations with Hinode Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm, S. Bibcode: 2008ApJ...680L..85S Altcode: 2008arXiv0801.4915S Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe I 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where, depending on the initial state or the boundary condition, it surpasses the vertical component by a factor of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean horizontal field component that is 1.6 or 4.3 times stronger than the vertical component, depending on the initial state or the boundary condition. This is a consequence of both the intrinsically stronger flux density of and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, whereas the Poynting flux is negative in the convectively unstable layer below it. Title: Wave propagation in multiple flux tubes and chromospheric heating Authors: Hasan, S. S.; van Ballegooijen, A.; Steiner, O. Bibcode: 2008IAUS..247...82H Altcode: 2007IAUS..247...82H This investigation is a continuation of earlier work on the dynamics of the magnetic network. In a previous calculation (Hasan et al. 2005), we examined the response of a single flux tube to transverse motions of its footpoints. We now extend this analysis to a more realistic model of the network consisting of multiple flux tubes. We apply a transverse velocity perturbation uniformly along the lower boundary located at the base of the photosphere. Our 2-D MHD simulations enable us to study the complex wave pattern due to waves generated in the individual tubes as well as their interaction with those emanating from adjacent tubes. Our results show that the dominant heating of the chromosphere occurs due to slow magnetoacoustic waves in a region that is close to the central region of the flux tube. Title: Inferring the chromospheric magnetic topology through waves Authors: Hasan, S. S.; Steiner, O.; van Ballegooijen, A. Bibcode: 2008IAUS..247...78H Altcode: 2007IAUS..247...78H The aim of this work is to examine the hypothesis that the wave propagation time in the solar atmosphere can be used to infer the magnetic topography in the chromosphere as suggested by Finsterle et al. (2004). We do this by using an extension of our earlier 2-D MHD work on the interaction of acoustic waves with a flux sheet. It is well known that these waves undergo mode transformation due to the presence of a magnetic field which is particularly effective at the surface of equipartition between the magnetic and thermal energy density, the β = 1 surface. This transformation depends sensitively on the angle between the wave vector and the local field direction. At the β = 1 interface, the wave that enters the flux sheet, (essentially the fast mode) has a higher phase speed than the incident acoustic wave. A time correlation between wave motions in the non-magnetic and magnetic regions could therefore provide a powerful diagnostic for mapping the magnetic field in the chromospheric network. Title: Hinode observations reveal boundary layers of magnetic elements in the solar photosphere Authors: Rezaei, R.; Steiner, O.; Wedemeyer-Böhm, S.; Schlichenmaier, R.; Schmidt, W.; Lites, B. W. Bibcode: 2007A&A...476L..33R Altcode: 2007arXiv0711.0408R Aims:We study the structure of the magnetic elements in network-cell interiors.
Methods: A quiet Sun area close to the disc centre was observed with the spectro-polarimeter of the Solar Optical Telescope on board the Hinode space mission, which yielded the best spatial resolution ever achieved in polarimetric data of the Fe I 630 nm line pair. For comparison and interpretation, we synthesize a similar data set from a three-dimensional magneto-hydrodynamic simulation.
Results: We find several examples of magnetic elements, either roundish (tube) or elongated (sheet), which show a central area of negative Stokes-V area asymmetry framed or surrounded by a peripheral area with larger positive asymmetry. This pattern was predicted some eight years ago on the basis of numerical simulations. Here, we observationally confirm its existence for the first time.
Conclusions: We gather convincing evidence that this pattern of Stokes-V area asymmetry is caused by the funnel-shaped boundary of magnetic elements that separates the flux concentration from the weak-field environment. On this basis, we conclude that electric current sheets induced by such magnetic boundary layers are common in the photosphere. Title: How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes Authors: Ferriz-Mas, A.; Steiner, O. Bibcode: 2007SoPh..246...31F Altcode: A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 105 G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 105-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the "Ω effect" in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 105-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of "convective collapse" for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed. Title: Variation of the Stokes-V area asymmetry across magnetic elements Authors: Rezaei, R.; Steiner, O.; Wedemeyer-Böhm, S.; Schlichenmaier, R.; Lites, B. W. Bibcode: 2007AN....328..706R Altcode: No abstract at ADS Title: Opposite magnetic polarity of two photospheric lines in single spectrum of the quiet Sun Authors: Rezaei, R.; Schlichenmaier, R.; Schmidt, W.; Steiner, O. Bibcode: 2007A&A...469L...9R Altcode: 2007arXiv0704.3135R Aims:We study the structure of the photospheric magnetic field of the quiet Sun by investigating weak spectro-polarimetric signals.
Methods: We took a sequence of Stokes spectra of the Fe I 630.15 nm and 630.25 nm lines in a region of quiet Sun near the disk center, using the POLIS spectro-polarimeter at the German VTT on Tenerife. The line cores of these two lines form at different heights in the atmosphere. The 3σ noise level of the data is about 1.8 × 10-3 I_c.
Results: We present co-temporal and co-spatial Stokes-V profiles of the Fe I 630 nm line pair, where the two lines show opposite polarities in a single spectrum. We compute synthetic line profiles and reproduce these spectra with a two-component model atmosphere: a non-magnetic component and a magnetic component. The magnetic component consists of two magnetic layers with opposite polarity: the upper one moves upwards while the lower one moves downward. In-between, there is a region of enhanced temperature.
Conclusions: The Stokes-V line pair of opposite polarity in a single spectrum can be understood as a magnetic reconnection event in the solar photosphere. We demonstrate that such a scenario is realistic, but the solution may not be unique. Title: Photospheric processes and magnetic flux tubes Authors: Steiner, Oskar Bibcode: 2007AIPC..919...74S Altcode: 2007arXiv0709.0081S New high-resolution observations reveal that small-scale magnetic flux concentrations have a delicate substructure on a spatial scale of 0.1''. Their basic structure can be interpreted in terms of a magnetic flux sheet or tube that vertically extends through the ambient weak-field or field-free atmosphere with which it is in mechanical equilibrium. A more refined interpretation comes from new three-dimensional magnetohydrodynamic simulations that are capable of reproducing the corrugated shape of magnetic flux concentrations and their signature in the visible continuum. Faculae are another manifestation of small-scale magnetic flux concentrations. It is shown that the characteristic asymmetric shape of the contrast profile of faculae is an effect of radiative transfer across the rarefied atmosphere of the magnetic flux concentration. Also discussed are three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. They show a highly dynamic chromospheric magnetic field, marked by rapidly moving filaments of stronger than average magnetic field that form in the compression zone downstream and along propagating shock fronts. The simulations confirm the picture of flux concentrations that strongly expand through the photosphere into a more homogeneous, space filling chromospheric field. Future directions in the simulation of small-scale magnetic fields are indicated with a few examples from recent reports.

The second part of these lecture notes is devoted to a few basic properties of magnetic flux tubes that can be considered to be an abstraction of the more complicated flux concentrations known from observations and numerical simulations. By analytical means we will find that an electrical current flows in a sheet at the surface of a flux-tube for which location we also derive the mechanical equilibrium condition. The equations for constructing a magnetohydrostatic flux tube embedded in a gravitationally stratified atmosphere are derived. It is shown that the expansion of a flux tube with height sensibly depends on the difference in the thermal structure between the atmosphere of the flux tube and the surrounding atmosphere. Furthermore, we will find that radiative equilibrium produces a smaller temperature gradient within the flux tube compared to that in the surrounding atmosphere. The condition for interchange stability is derived and it is shown that small-scale magnetic flux concentrations are liable to the interchange instability. Title: What is Heating the Quiet-Sun Chromosphere? Authors: Wedemeyer-Böhm, S.; Steiner, O.; Bruls, J.; Rammacher, W. Bibcode: 2007ASPC..368...93W Altcode: 2006astro.ph.12627W It is widely believed that the heating of the chromosphere in quiet-Sun internetwork regions is provided by dissipation of acoustic waves that are excited by the convective motions close to the top of the convection zone and in the photospheric overshoot layer. This view lately became challenged by observations suggesting that the acoustic energy flux into the chromosphere is too low, by a factor of at least ten. Based on a comparison of TRACE data with synthetic image sequences for a three-dimensional simulation extending from the top layers of the convection zone to the middle chromosphere, we come to the contradicting conclusion that the acoustic flux in the model provides sufficient energy for heating the solar chromosphere of internetwork regions. The role of a weak magnetic field and associated electric current sheets is also discussed. Title: First local helioseismic experiments with CO5BOLD Authors: Steiner, O.; Vigeesh, G.; Krieger, L.; Wedemeyer-Böhm, S.; Schaffenberger, W.; Freytag, B. Bibcode: 2007AN....328..323S Altcode: 2007astro.ph..1029S With numerical experiments we explore the feasibility of using high frequency waves for probing the magnetic fields in the photosphere and the chromosphere of the Sun. We track a plane-parallel, monochromatic wave that propagates through a non-stationary, realistic atmosphere, from the convection-zone through the photosphere into the magnetically dominated chromosphere, where it gets refracted and reflected. We compare the wave travel time between two fixed geometrical height levels in the atmosphere (representing the formation height of two spectral lines) with the topography of the surface of equal magnetic and thermal energy density (the magnetic canopy or β=1 contour) and find good correspondence between the two. We conclude that high frequency waves indeed bear information on the topography of the `magnetic canopy'. Title: Recent progresses in the simulation of small-scale magnetic fields Authors: Steiner, O. Bibcode: 2007msfa.conf..321S Altcode: 2007arXiv0705.1848S New high-resolution observations reveal that small-scale magnetic flux concentrations have a delicate substructure on a spatial scale of 0.1". Its basic structure can be interpreted in terms of a magnetic flux sheet or tube that vertically extends through the ambient weak-field or field-free atmosphere with which it is in mechanical equilibrium. A more refined interpretation comes from new three-dimensional magnetohydrodynamic simulations that are capable of reproducing the corrugated shape of magnetic flux concentrations and their signature in the visible continuum. Furthermore it is shown that the characteristic asymmetric shape of the contrast profile of facular granules is an effect of radiative transfer across the rarefied atmosphere of the magnetic flux concentration. I also discuss three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. They show a highly dynamic chromospheric magnetic field, marked by rapidly moving filaments of stronger than average magnetic field that form in the compression zone downstream and along propagating shock fronts. The simulations confirm the picture of flux concentrations that strongly expand through the photosphere into a more homogeneous, space filling chromospheric field. Future directions in the simulation of small-scale magnetic fields are indicated by a few examples of very recent work. Title: A New Method for Comparing Numerical Simulations with Spectroscopic Observations of the Solar Photosphere Authors: Rybák, J.; Kučera, A.; Wöhl, H.; Wedemeyer-Böhm, S.; Steiner, O. Bibcode: 2006ASPC..354...77R Altcode: A method for comparing high-resolution spectroscopic observations of the solar photosphere with numerical simulations of convection in the solar photosphere is presented.

It is based on the comparison of the granular continuum contrast obtained from both the observations and the synthetic spectra, when the latter are calculated from numerical simulations using a particular type of data degradation. This method can be used post facto when a minimum of auxiliary information on characteristics of the telescope/spectrograph and on seeing conditions is available.

Here, the method is applied to results of numerical simulations computed with the CO5BOLD code and high-resolution spectroscopic observations obtained with the VTT on Tenerife. Title: Holistic MHD-Simulation from the Convection Zone to the Chromosphere Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.; Freytag, B. Bibcode: 2006ASPC..354..345S Altcode: A three-dimensional magnetohydrodynamic simulation of the integral layers from the convection zone to the chromosphere has been carried out. The simulation represents magnetoconvection in a quiet network-cell interior. The following preliminary new results are obtained: The chromospheric magnetic field is very dynamic with a continuous rearrangement of magnetic flux on a time scale of less than one~minute. Rapidly moving magnetic filaments (rarely exceeding 40~G) form in the compression zone downstream and along propagating shock fronts that are present throughout the chromosphere. The magnetic filaments rapidly move, form, and dissolve with the shock waves. Flux concentrations strongly expand through the photosphere into a more homogeneous, space filling chromospheric field. ``Canopy fields'' form on a granular scale above largely field-free granule centers leading to a mesh-work of current sheets in a height range between approximately 400 and 900~km. Title: Recent Progresses in the Physics of Small-Scale Magnetic Fields Authors: Steiner, O. Bibcode: 2005ESASP.600E..10S Altcode: 2005ESPM...11...10S; 2005dysu.confE..10S No abstract at ADS Title: Simulations of Magnetohydrodynamics and CO Formation from the Convection Zone to the Chromosphere Authors: Wedemeyer-Böhm, S.; Schaffenberger, W.; Steiner, O.; Steffen, M.; Freytag, B.; Kamp, I. Bibcode: 2005ESASP.596E..16W Altcode: 2005ccmf.confE..16W No abstract at ADS Title: Magnetohydrodynamic Simulation from the Convection Zone to the Chromosphere Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.; Freytag, B. Bibcode: 2005ESASP.596E..65S Altcode: 2005ccmf.confE..65S No abstract at ADS Title: Dynamics of the Solar Magnetic Network: Two-dimensional MHD Simulations Authors: Hasan, S. S.; van Ballegooijen, A. A.; Kalkofen, W.; Steiner, O. Bibcode: 2005ApJ...631.1270H Altcode: 2005astro.ph..3525H The aim of this work is to identify the physical processes that occur in the network and contribute to its dynamics and heating. We model the network as consisting of individual flux tubes, each with a nonpotential field structure, that are located in intergranular lanes. With a typical horizontal size of about 150 km at the base of the photosphere, they expand upward and merge with their neighbors at a height of about 600 km. Above a height of approximately 1000 km the magnetic field starts to become uniform. Waves are excited in this medium by means of motions at the lower boundary. We focus on transverse driving, which generates both fast and slow waves within a flux tube and acoustic waves at the interface of the tube and the ambient medium. The acoustic waves at the interface are due to compression of the gas on one side of the flux tube and expansion on the other. These longitudinal waves are guided upward along field lines at the two sides of the flux tube, and their amplitude increases with height due to the density stratification. Being acoustic in nature, they produce a compression and significant shock heating of the plasma in the chromospheric part of the flux tube. For impulsive excitation with a time constant of 120 s, we find that a dominant feature of our simulations is the creation of vortical motions that propagate upward. We have identified an efficient mechanism for the generation of acoustic waves at the tube edge, which is a consequence of the sharp interface of the flux concentration. We examine some broad implications of our results. Title: Dynamics of the Magnetic Network on the Sun Authors: Hasan, S.; van Ballegoiijen, A.; Kalkofen, W.; Steiner, O. Bibcode: 2005AGUSMSH13C..08H Altcode: Observations have revealed the presence of a rich spectrum of waves with different periods in regions of the solar atmosphere called the "magnetic network" that are dominated by strong magnetic fields. This network is believed to be heated by dissipation of magnetohydrodynamic (MHD) waves, but the MHD processes involved in wave generation, propagation and dissipation are poorly understood. In this work we attempt to identify some of the processes that occur in the network and which contribute to its dynamics and heating. We model the network as consisting of individual magnetic elements or flux tubes, rooted in intergranular lanes, with a typical horizontal size of 100 km. They expand upward and merge with their neighbors at a height of about 600 km. Above this height the magnetic field becomes uniform. An equilibrium configuration based on the above model is constructed by solving the magnetostatic equations in 2-D. Waves are generated in this medium by means of motions at the lower boundary. We focus on transverse driving which generates fast waves within the flux tubes and acoustic waves at the interface of the tubes and the field-free medium, but not otherwise in the field-free gas. The acoustic waves at the interface are due to compression of the gas on one side of the flux tube and expansion on the other. These waves travel upward along the two sides of the (2D) flux tube and enter it, where they become longitudinal waves. For impulsive excitation with a time constant of 120 s, we find that a dominant feature is the creation of vortical motions that propagate upwards. We have identified a new and efficient mechanism for the generation of longitudinal waves and shock formation in the chromosphere. We examine the observational implications of our results and their broad applications to chromospheric heating and activity. Title: Connecting solar radiance variability to the solar dynamo with the virial theorem Authors: Steiner, O.; Ferriz-Mas, A. Bibcode: 2005AN....326..190S Altcode: The variability of solar radiance over a solar cycle is thought to result from a delicate balance between the radiative deficit of sunspots and the extra contribution of plage and network regions. Although the net effect is tiny, it must imply structural and thermal changes in the Sun or in partial layers of it as an unavoidable consequence of the virial theorem. Using the virial theorem for continua--including the magnetic field--it can be shown how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time scale. Title: Radiative properties of magnetic elements. II. Center to limb variation of the appearance of photospheric faculae Authors: Steiner, O. Bibcode: 2005A&A...430..691S Altcode: For the understanding of more complex numerical simulation results, a basic facular model is created consisting of a magnetic flux sheet embedded in a plane parallel atmosphere. The atmosphere within the flux sheet is similar to the external one but shifted in the downward direction to result in a Wilson depression of 150 km. It is shown that the horizontal spatial extension of the contrast enhancement produced by this model increases from center to limb from a few tenths to up to 1 arcsec as a consequence of enhanced radiation from the limbward surface outside (behind) the magnetic flux concentration. For a conceivable explanation of this radiative effect it is noted that a plasma parcel on the solar surface sideways of the flux sheet ``sees'' a more transparent sky in the direction towards the flux sheet compared to a direction away from it because of the rarefied atmosphere within the flux sheet. This facular model also produces a dark lane at the disk-center side (in front) of the flux sheet even though no flow is present. It it is due to the deep layers of the flux sheet that have a lower temperature gradient and are cooler than the surrounding atmosphere at equal geometrical depth. This implies that limb observations offer a glimpse of the ``cool bottom'' of magnetic elements. The center-to-limb variation of the size and the dark-lane effect derived from this basic model is recovered in a self-consistent, two-dimensional non-stationary simulation of a magnetic flux concentration. These findings are in excellent agreement with and provide an interpretation of recent observations of faculae at very high resolution by Lites et al. (2004, \solphys, 221, 65). Title: The deep roots of solar radiance variability . Authors: Steiner, O.; Ferriz-Mas, A. Bibcode: 2005MmSAI..76..789S Altcode: The variability of solar radiance over a solar cycle is thought to result from a delicate balance between the radiative deficit of sunspots and the extra contribution of plage and network regions. Although the net effect is tiny, it implies structural and thermal changes in the Sun or in partial layers of it as an unavoidable consequence of the virial theorem. Using the virial theorem for continua--including the magnetic field--it can be shown how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time scale. Title: Indications of shock waves in the solar photosphere Authors: Rybák, J.; Wöhl, H.; Kučera, A.; Hanslmeier, A.; Steiner, O. Bibcode: 2004A&A...420.1141R Altcode: High resolution observations of solar granulation near the solar limb are used in a search for hydrodynamic shocks caused by an abrupt braking of the fast (probably supersonic) horizontal flow of the granular plasma towards the intergranular lane. Shock signatures in the spectral line of Fe II 6456.38 Åof one particular observed shock event are investigated in detail. Evolution, amplitude, and spatial relation of the spectral line characteristics of the shock event are in agreement with predictions from numerical simulations for such shock phenomena in the solar photosphere. The dimensions and amplitudes of the observed shock signatures are comparable to predicted values when seeing and instrumental effects as well as a possible obliqueness of the shock front with respect to the observer's line-of-sight are taken into account. The temporal evolution of such an event is observed for the first time. The stable and declining phase of the event were studied for a time period of almost 2 min. A particular relationship was found between the shock event and a nearby G-band bright point located 2'' from the shock event. It is suggestive that the observed shock is a causal consequence of the magnetic flux concentration, traced by the G-band bright point. Such a type of shock can appear outside the flux concentrations as a consequence of a rapid flux-tube motion. Title: Connecting solar radiance variability to the solar dynamo with the virial theorem Authors: Steiner, Oskar Bibcode: 2004IAUS..223...77S Altcode: 2005IAUS..223...77S The variability of solar radiance over a solar cycle is thought to be a delicate balance between the radiative deficit of sunspots and the extra contribution of plage and network regions. Although the net effect is tiny, it must imply structural and thermal changes in the Sun or in partial layers of it as an unavoidable consequence of the virial theorem. Using the virial theorem for continua including the magnetic field it is shown, how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time-scale. Title: Understanding facular granules and lanes Authors: Steiner, Oskar Bibcode: 2004IAUS..223..299S Altcode: 2005IAUS..223..299S Recent high resolution observations by Lites et al. (2004) show details of facular granules at 0.12^{primeprime}, including dark facular lanes. For an interpretation of these data a basic facular model is constructed, consisting of a magnetic flux sheet embedded in a plane parallel atmosphere. While the maximum contrast originates from the "hot wall" of the flux-sheet depression, the model explains the wide brightening limbward of the facular magnetic field as due to a radiative transfer effect caused by the reduced opacity of the rarefied flux-sheet atmosphere. This model produces a dark, narrow lane centerward of the facular granule even in the absence of granular flow as a consequence of the cool deep layers of the magnetic flux sheet. These results carry over to a self-consistent simulation of a flux concentration in dynamic interaction with convective motion, where the dark lane deepens and broadens. Title: Distribution of magnetic flux density at the solar surface. Formulation and results from simulations Authors: Steiner, O. Bibcode: 2003A&A...406.1083S Altcode: A formal description of the distribution of magnetic flux density in a quiet Sun region supplemented by an example and an application is presented. We define a flux-based probability density, which is useful to reveal the presence of any strong-field component in the region. The corresponding flux-based probability distribution gives the fraction of the total absolute magnetic flux with a given field-strength limit. Application to the simulations of convective field intensification of Grossmann-Doerth et al. (1998) shows, that, depending on the strength of the initial homogeneous vertical field, 1-50% of the total magnetic flux within the computational domain of 3 arcsec width is concentrated into flux fibrils with a flux density exceeding 0.1 T. It is shown that a low efficiency of the flux-concentration process is compatible with new observations that suggest a large fraction of the surface magnetic field to have a flux density below 0.1 T. Title: Distribution of the Magnetic Flux Density at the Solar Surface Authors: Steiner, Oskar Bibcode: 2003ANS...324R..31S Altcode: 2003ANS...324..D07S No abstract at ADS Title: Solar Radiance Variability as a Direct Consequence of the Flux-tube Dynamo Authors: Steiner, Oskar Bibcode: 2003ANS...324..106S Altcode: 2003ANS...324..P12S No abstract at ADS Title: Convergence of a Solenoidal Discrete Rot-operator Authors: Steiner, Oskar Bibcode: 2003ANS...324...75S Altcode: 2003ANS...324..I20S No abstract at ADS Title: The contrast of magnetic elements across the solar spectrum Authors: Steiner, O.; Hauschildt, P. H.; Bruls, J. Bibcode: 2003AN....324..398S Altcode: No abstract at ADS Title: Multi-Grid Radiative Transfer Revisited Authors: Steiner, O. Bibcode: 2003ASPC..288...83S Altcode: 2003sam..conf...83S Multi-grid radiation transfer is an efficient method for solving a variety of radiation transfer problems, in particular problems of multiple spatial dimensions on scalar computers. This advantage is lost on massively parallel machines in which the computational grid can be directly mapped onto the processor array. Contrary to operator splitting methods, the convergence rate of the multi-grid method does not deteriorate with increasing spatial resolution of the computational grid. It is therefore well suited for high resolution problems, while performance at low resolution is not better than the best operator splitting methods.

There exists a considerable variety of basic multi-grid algorithms, which leave ample room for improvements of the few multi-grid radiation-transfer calculations that have been carried out so far. This poster is available under Poster Title: Large-Scale Flow in Two-Dimensional Simulation of Solar Convection Authors: Steiner, O. Bibcode: 2003IAUS..210P.C11S Altcode: No abstract at ADS Title: Spectral signature of magnetic flux tubes in sunspot penumbrae Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M. Bibcode: 2002A&A...393..305M Altcode: We study the polarization of spectral lines in the penumbra by integrating the radiative transfer equation of polarized light for a three-dimensional model atmosphere of a sunspot. In this model, the Evershed flow is confined to magnetic flux tubes which are embedded in a static background atmosphere, in accordance with the moving tube model of Schlichenmaier et al. (\cite{Schlichenmaier1998apjl},b). The gradients and/or discontinuities in the fluid velocity and the magnetic field at the flux tube boundaries give rise to asymmetric Stokes profiles. We concentrate on the Stokes-V profiles and study the net circular polarization (NCP) of two photospheric spectral lines of neutral iron, Fe I 630.25 nm and Fe I 1564.8 nm. The different behavior of these two lines, which are exemplary for atomic spectral lines with a large Landé factor and significantly different wavelength, is based on the difference in excitation potential of the corresponding atomic transitions and the fact that the wavelength dependence of the Doppler shift is linear, while that of the Zeeman splitting is quadratic. We find that the azimuthal variation of the NCP, N(psi, is a predominantly antisymmetric function of psi with respect to the line connecting disk center and spot center (line-of-symmetry) for the infrared line of Fe I 1564.8 nm, while the variation is predominantly symmetric for Fe I 630.25 nm. We show that the antisymmetric variation is caused by anomalous dispersion (Faraday pulsation) and the discontinuity in the azimuthal angle of the magnetic field, which is due to the relative inclination between flux tube and background field. We then compute synthetic NCP maps of a sunspot and compare them with observational results. Finally, the center-to-limb variation of the NCP, N(theta ), of these spectral lines is investigated. We show that the location of the zero-crossing point of N(theta ) on the center side of the line-of-symmetry represents a diagnostic tool to determine the inclination angle of the Evershed flow: A vanishing NCP on the center-side of the line-of-symmetry is an indirect evidence of downflows in the penumbra. Title: Net circular polarization of sunspot penumbrae - symmetry breaking by anomalous dispersion Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M. Bibcode: 2002ESASP.508..141M Altcode: 2002soho...11..141M We examine the polarization of spectral lines in the penumbra of sunspots by solving the radiative transfer equation of polarized light for a three-dimensional axially symmetric model atmosphere of a sunspot. The Evershed flow is confined to horizontal magnetic flux tubes obtained from MHD calculations. These are embedded in an inclined background magnetic field. In this work, we concentrate on the Stokes-V profiles and examine the net circular polarization (NCP), N = ∫V(λ)dλ, of two photospheric spectral lines of neutral iron, Fe I 630.25 nm and Fe I 1564.8 nm. Analyzing spectra at a fixed distance from the spot center, we find that the azimuthal variation of N, N(ψ), is an antisymmetric function of ψ w.r.t. to the line connecting disk center and spot center for Fe I 1564.8 nm, while the variation is predominantly symmetric for Fe I 630.25 nm. We show that the antisymmetric variation is caused by anomalous dispersion (rotation of the polarization vector in a magnetized plasma). The different inclination angles lead to a discontinuity in the azimuth of the magnetic field along the line-of-sight. We show that this discontinuity together with the effect of anomalous dispersion produced an antisymmetric component in N(ψ) which outweighs the symmetric component from the discontinuity for Fe I 1564.8 nm, while it is negligible for Fe I 630.25 nm. We finally compute synthetic NCP maps of a sunspot which offer an explanation for recent observational results. Title: Net circular polarization of sunspot penumbrae. Symmetry breaking through anomalous dispersion Authors: Schlichenmaier, R.; Müller, D. A. N.; Steiner, O.; Stix, M. Bibcode: 2002A&A...381L..77S Altcode: The net circular polarization, N, is used as a measure for the asymmetry of Stokes-V profiles: Nequiv int V(lambda ) d lambda , integrated over an absorption line. Exemplary for Fe I 630.2 nm and Fe I 1564.8 nm, we synthesize penumbral V-profiles that stem from a model atmosphere in which the Evershed flow is confined to horizontal flux tubes which are embedded in a magnetic field that has the same magnetic field strength as the flow channel, but is less inclined w.r.t. the surface normal. At the two points where a line-of-sight enters and leaves the flow channel, discontinuities in the inclination, gamma , the velocity v, and the azimuth, phi , of the magnetic field vector w.r.t. the plane perpendicular to the line-of-sight produce V-asymmetries. Assuming an axially symmetric penumbra, we investigate the azimuthal dependence N(psi ) for a mid-penumbral radius. We find: (1) Without including anomalous dispersion, N(psi ) is symmetric w.r.t. the line that connects disk center to the center of the spot. (2) Including anomalous dispersion, this symmetry is broken. We demonstrate that this is due to the difference in azimuth, triangle phi (psi ), between the flow channel and the background that varies along the penumbral circle. For Fe I 630.2 nm this effect is found to be of minor relevance leading to essentially symmetric N-maps, whereas strong asymmetries are predicted for Fe I 1564.8 nm. Our results provide an explanation for recent observational findings. Title: Time-slice diagrams of solar granulation Authors: Müller, D. A. N.; Steiner, O.; Schlichenmaier, R.; Brandt, P. N. Bibcode: 2001SoPh..203..211M Altcode: From a series of 1400 white-light images of solar granulation spanning a time period of 8.2 hours, skeletal plots of time-slice diagrams are derived showing intergranular lane positions as a function of time. The diagrams permit to automatically track, classify, and relate 42 186 granules. Recurrently fragmenting granules are found that survive by means of their descendants for more than 3 hours. Such long-lived active granules tend to have a mean spatial distance along the slice of about 10 Mm. This distance decreases with decreasing minimal required lifetime. Since active granules are expected to generate a steadily divergent flow over a long period of time, it is suggested to identify them as a source of the mesogranular flow. Deficiencies of the time-slice analysis are discussed. The relative frequency of different types of granules and the granule decay time as derived from the time-slice diagrams are compared with corresponding results of previous works. Title: Radiative properties of magnetic elements. I. Why are vec G-band bright points bright? Authors: Steiner, O.; Hauschildt, P. H.; Bruls, J. Bibcode: 2001A&A...372L..13S Altcode: Photospheric magnetic elements are most conspicuously visible in high-resolution G-band filtergrams. We show that their enhanced contrast in the G-band is due to a reduction of the CH abundance by dissociation in the deep photospheric layers of the flux tube, where it is hotter than in the surrounding atmosphere. As a consequence, the CH-lines weaken, allowing more of the continuum to ``shine'' through the forest of G-band CH-lines. We suggest that other molecular bands or atomic lines may exhibit a similar behaviour. Title: Understanding Small Solar Magnetic Structures: Comparing Numerical Simulations to Observations Authors: Leka, K. D.; Steiner, O. Bibcode: 2001ApJ...552..354L Altcode: We present direct comparisons of small magnetic structures observed in the solar photosphere with the results from numerical simulations of those structures. We compare diagnostic signatures derived from emergent Stokes polarization spectra from both the observed and model atmospheres, the former recorded with the National Solar Observatory/High Altitude Observatory Advanced Stokes Polarimeter, the latter from a fully dynamic MHD simulation of a magnetic flux sheet in a convective atmosphere. We focus on the asymmetries in the Stokes V spectra and find, first and foremost, that the asymmetries from the observed Stokes I and V in and around solar pores and azimuth centers (ACs) are quantitatively comparable to those derived from the simulation. We also find enhanced Stokes V asymmetry on the periphery of pores and ACs. We interpret this as a consequence of strong downdrafts in the surroundings of these magnetic structures, accompanied by the expansion of the magnetic field lines with height above these field-free downdrafts (the ``canopy effect''). The magnetic canopy can be present whether or not there is a continuum signature (i.e., a dark ``pore''). Not surprisingly, the patterns and magnitudes of asymmetries scale with the size of the magnetic element. In the interior of the pores and ACs, we find evidence for mixed up- and downflows, with little spatial correlation between the zero-crossing shift of the V profile and the V amplitude. Finally, we report on asymmetries observed in the linear polarization Plin(λ)=[Q(λ)2+U(λ)2]1/2, finding further support for the presence of the magnetic canopy from those diagnostics. We additionally present expectations for spectropolarimetric observations at significantly higher spatial resolution. Title: Why are G-Band Bright Points Bright? Authors: Steiner, O.; Bruls, J.; Hauschildt, P. H. Bibcode: 2001ASPC..236..453S Altcode: 2001aspt.conf..453S No abstract at ADS Title: The Formation of Asymmetric Stokes V Profiles in the Presence of a Magnetopause Authors: Steiner, O. Bibcode: 2001ASPC..236..587S Altcode: 2001aspt.conf..587S No abstract at ADS Title: Chromosphere: Magnetic Canopy Authors: Steiner, O. Bibcode: 2000eaa..bookE2264S Altcode: The magnetic canopy is a layer of magnetic field which is directed parallel to the solar surface and located in the low CHROMOSPHERE, overlying a field-free region of the SOLAR PHOTOSPHERE. It has a field strength of the order of 0.01 T and covers a large area fraction of the solar surface. The magnetic canopy can be compared with the canopy of the rain forest: the tree-trunks correspond to the ... Title: The formation of asymmetric Stokes V profiles in the presence of a magnetopause Authors: Steiner, Oskar Bibcode: 2000SoPh..196..245S Altcode: A magnetopause that separates two regimes of different flow, additional to the separation of a magnetic field from a field-free plasma, gives rise to the formation of asymmetric Stokes profiles. Using a simple two-layer model atmosphere, where one layer comprises a magnetic field, the other being field-free, it is shown by analytical derivation that a wide variety of Stokes V profiles can be produced, having amplitude asymmetries δa in the range −∞≤δa≤∞. These include two-humped V profiles, which have two lobes of equal sign. For the most simple models, the asymmetry depends on the ratio of continuum intensity to the Planck radiation intensity of the magnetic layer at the wavelength of the spectral line under consideration, and on the line depth. Two-humped profiles (|δa|>1) require the temperature of the magnetic layer to surpass the temperature of the line-core forming region, implying a temperature inversion, so that the V profile is partially in emission. The confrontation of this formation scenario with properties of observed one-lobe profiles of quiet-Sun network regions is inconclusive due to insufficient spatial resolution and lack of a sufficient sample of simultaneously recorded Stokes spectral lines of varying line depths. It seems, however, to be in good agreement with the observed frequent occurrence of abnormal V profiles of the very strong Na i D2 and D2 spectral line. A possible observational verification for the present formation scenario of abnormal Stokes V profiles and a novel method of Stokes inversion are discussed. Title: Strong Stokes V asymmetries of photospheric spectral lines: What can they tell us about the magnetic field structure? Authors: Grossmann-Doerth, U.; Schüssler, M.; Sigwarth, M.; Steiner, O. Bibcode: 2000A&A...357..351G Altcode: In an attempt to identify the mechanism responsible for the extremely asymmetric Stokes V profiles which were recently observed we analyzed several simple atmospheric configurations with separated layers of mass flow and magnetic field. We found that under appropriate conditions the models are capable of producing the observed one-lobe profiles. Title: Flux Tube Dynamics Authors: Steiner, O. Bibcode: 1999ASPC..184...38S Altcode: We propose that the observed fragmentation of magnetic elements is due to their inherent liability to the interchange instability. The convective collapse and numerical simulations of the formation of intense magnetic flux sheets including spectral signatures of the formation process are discussed. We suggest that the mean downflow measured in magnetic elements is due to a fraction of an ensemble of magnetic elements being in the formation phase at any given time. It is shown that observed Stokes V profiles of magnetic elements are actua lly an average of spatially strongly varying profiles with a delicate balance of positive and negative contributions to the area asymmetry. Title: Understanding Small Solar Magnetic Elements: Comparing Models and Observations Authors: Leka, K. D.; Steiner, O.; Grossmann-Doerth, U. Bibcode: 1999AAS...194.5507L Altcode: 1999BAAS...31R.911L We perform direct comparisons of high-resolution spectropolarimetric observations with a full MHD model of the magnetized solar atmosphere. In this manner we investigate the evolution and dynamics of small magnetic elements by fully utilizing the diagnostics available with Stokes spectropolarimetry, both computed and observed. The model is a 2-D time-dependent numerical simulation of a small (~ 600 km diameter) magnetic feature embedded in a non-magnetized atmosphere (Steiner et al., 1998). At select time-steps, synthetic emergent Stokes I and V profiles are computed using a polarized radiation transfer code. The data consist of Stokes I and V spectra from the Advanced Stokes Polarimeter for seventeen small magnetic elements located near disk-center. For both the observed and computed Stokes spectra, diagnostics are computed including the emergent continuum intensity, V-crossing shift, and amplitude and area asymmetries of the V-profile. We find that it is possible to differentiate between salient processes occurring in the magnetic atmosphere (strong flows, gradients, etc.) by their spectropolarimetric signature; from this, we determine the dominant processes present in the observed magnetic structures. The results are extremely encouraging. We find good qualitative agreement between the amplitude and area asymmetries and their spatial variation. Quantitatively, the agreement is surprisingly good in many cases. While limitations exist for both the model and observations, this stringent test allows us to comment on the dynamics and possible evolutionary differences present in the observed magnetic features. This work is funded in part by NSF grant ATM-9710782. Reference: - Steiner, O., Grossmann-Doerth, U., Knolker, M., Schussler, M.: 1998, ApJ 495, 468 Title: Small Scale Magnetic Flux Tubes in the Photosphere: A Simulation Perspective Authors: Steiner, O. Bibcode: 1999ASPC..183...17S Altcode: 1999hrsp.conf...17S No abstract at ADS Title: 2D radiative equilibrium models of magnetic flux tubes Authors: Hasan, S. S.; Kalkofen, W.; Steiner, O. Bibcode: 1999ASSL..243..409H Altcode: 1999sopo.conf..409H No abstract at ADS Title: The formation of extremely asymmetric Stokes V profiles Authors: Steiner, O.; Grossmann-Doerth, U.; Schüssler, M.; Sigwarth, M. Bibcode: 1999AGAb...15R..10S Altcode: 1999AGM....15..A11S Recent polarimetric observations at high spatial resolution (< 1 arcsec) and with high polarimetric accuracy (noise of Stokes V/I_c < 3 cdot 10^{-4}) have revealed that about 10% of all Stokes V profiles of a quiet Sun region have an abnormal shape that strongly deviates from the more common, nearly antisymmetric profiles. 35% of the abnormal Stokes V profiles are of one-wing type, where the profile shows essentially one lobe only. We show, that a strongly asymmetric Stokes V profile can be obtained when the atmosphere, in which the profile is formed, is divided into two or more layers of different magnetic, flow, and thermal properties. A simple configuration of that kind (sometimes referred to as magnetic canopy) consists of a layer of plasma at rest with a magnetic field component parallel to the line of sight, located on top of a field-free layer with downdraft. The Stokes V asymmetry in this case sensitively depends on the position of the layers interface and may assume values up to about 80%. An asymmetry of nearly 100% (corresponding to a one-wing profile) is obtained when the plasma below the magnetic canopy is relatively cool, giving rise to the formation of a strong, redshifted spectral line in the field-free plasma beneath the canopy. If the core of this line is formed at lower temperature than the temperature of the canopy layer, the red wing of the resulting Stokes V profile is driven into emission, leading to a ``pathological'' V profile. Title: Meso and supergranulation in two-dimensional simulation of solar convection Authors: Steiner, O. Bibcode: 1999AGAb...15...92S Altcode: 1999AGM....15..P10S A two-dimensional hydrodynamic simulation of a thin surface layer of the solar convection zone, encompassing a horizontal span of 150 Mm and a depth of 1 Mm, is carried out. An additional 0.5 Mm height includes the photospheric layer. Radiation transfer using the OPAL Rosseland mean opacity is taken into account as well as Hydrogen ionization. The simulation shows granule evolution of the well known dichotomous character: granules either dissolve by shrinking or they fragment into smaller granules. The maximum horizontal granule size in the simulation is about 3.5 Mm. The Fourier decomposition of the horizontal velocity near the solar surface (tau_c = 1) shows a local maximum in amplitude at around 5-7 Mm, which we identify with mesogranular flow. The maximum amplitude is found at 50 Mm, corresponding to supergranular flow. Cork tracks visualize these findings. The occurrence of supergranules in this shallow simulation domain supports recent results from local helioseismology, suggesting that supergranulation pertains to a thin surface layer only. We discuss possible interpretation of the simulation results. Title: Convective intensification of solar surface magnetic fields: results of numerical experiments Authors: Grossmann-Doerth, U.; Schuessler, M.; Steiner, O. Bibcode: 1998A&A...337..928G Altcode: The concentration of magnetic flux by convective flows in the solar surface layers is studied by means of two-dimensional numerical simulations with radiative transfer. We follow the evolution of an initially homogeneous, vertical magnetic field, starting from an evolved state of simulated solar granulation. The results of three simulation runs with initial field strengths, B_0, of 100 G, 200 G, and 400 G, respectively, are shown. In all cases, horizontal convective flows rapidly sweep magnetic flux into the intergranular downflow channels. The field is further amplified up to kilogauss values by partial evacuation due to a strongly accelerated downflow within the magnetic structure. The value of the field strength reached at a given depth and the size of the flux concentrations grows with the initial field strength (i.e., the amount of magnetic flux within the computional box). In the case of B_0 = 400 G, the downflow within the flux concentration becomes so strong that it `bounces' off the high density plasma in the deeper layers; the resulting upflow leads to a strong, upward moving shock and to the dispersal of the flux sheet after a lifetime of about 200 s. In the cases with less magnetic flux (B_0 100 G, 200 G), the downflow is less vigorous and the flux concentrations persist to the end of the simulation (about 5 minutes). Radiation diagnostics in the continuum and in spectral lines predicts observable signatures of the intensification process. The accelerated downflow leads to a conspicuous Doppler shift and a negative area asymmetry of Stokes V-profiles of spectral lines, while the intensification of the magnetic field may be detectable through the `magnetic line ratio' method in the visible and by direct Zeeman splitting of magnetically sensitive lines in the infrared wavelength ranges. Title: On the reliability of Stokes diagnostics of magnetic elements away from solar disc centre Authors: Solanki, S. K.; Steiner, O.; Buente, M.; Murphy, G.; Ploner, S. R. O. Bibcode: 1998A&A...333..721S Altcode: {The spectropolarimetric signature of models of small-scale magnetic features is well understood at the centre of the solar disc, but has been little studied near the solar limb, mainly because the detailed geometry of the flux tubes must then be taken into account in a realistic analysis. We present multi-ray calculations of Stokes profiles through arrays of 2-D magnetohydrostatic models of small flux tubes. We compare the Stokes profile shapes and Stokes based diagnostics (Q to V ratio, V amplitude, magnetic line ratio, centre of gravity wavelengths, etc.) resulting from plane-parallel and 2-D flux-tube models at different limb distances for two lines in the visible and an infrared H-band line. For the visible lines around 5250 Angstroms all the diagnostics we have studied, with the exception of the Q and U to V ratio, are significantly affected by the finite size of the flux tubes and the passage of the rays through non-magnetic material near the limb. We show that magnetic filling factors and the global magnetic flux may be underestimated using the usual calibration techniques. In addition, near the solar limb the magnetic line ratio can move into a regime that is forbidden according to simpler models. The spatially averaged longitudinal field derived from the centre-of-gravity method also becomes strongly model dependent. The thermal structure of the non-magnetic atmosphere appears to play a particularly important role in determining the values of these diagnostic parameters. The infrared line at 1.5648 mu m, on the one hand, reacts little to the external atmosphere and provides superior diagnostics of both the magnetic field strength and filling factor. On the other hand, for a flux tube with a sharp boundary this line shows little dependence on the flux-tube diameter, in contrast to the earlier findings of Zayer et al. (1989). } Title: Dynamical Interaction of Solar Magnetic Elements and Granular Convection: Results of a Numerical Simulation Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler, M. Bibcode: 1998ApJ...495..468S Altcode: Nonstationary convection in the solar photosphere and its interaction with photospheric magnetic structures (flux sheets in intergranular lanes) have been simulated using a numerical code for two-dimensional MHD with radiative energy transfer. Dynamical phenomena are identified in the simulations, which may contribute to chromospheric and coronal heating. Among these are the bending and horizontal displacement of a flux sheet by convective flows and the excitation and propagation of shock waves both within and outside the magnetic structure. Observational signatures of these phenomena are derived from calculated Stokes profiles of Zeeman-sensitive spectral lines. We suggest that the extended red wings of the observed Stokes V profiles are due to downward coacceleration of magnetized material in a turbulent boundary layer between the flux sheet and the strong external downflow. Upward-propagating shocks in magnetic structures should be detectable if a time resolution of about 10 s is achieved, together with a spatial resolution that allows one to isolate individual magnetic structures. Determination of the complicated internal dynamics of magnetic elements requires observations with a spatial resolution better than 100 km in the solar photosphere. Title: Computational methods for astrophysical fluid flow Authors: Steiner, O.; Gautschy, A. Bibcode: 1998cmaf.conf.....S Altcode: No abstract at ADS Title: Numerical simulations of magnetic flux sheets. Authors: Steiner, O.; Knölker, M.; Schüssler, M. Bibcode: 1997smf..conf...31S Altcode: Non-stationary convection in the solar photosphere and its interaction with photospheric magnetic structures (flux sheets in intergranular lanes) has been simulated using a numerical code for two-dimensional MHD with radiative transfer. Dynamical phenomena, which may contribute to chromospheric and coronal heating, like bending and horizontal displacement of a flux sheet by convective flows as well as the excitation and propagation of shock waves within and outside the magnetic structure are found. Observational signature of transversal displacement and shocks are derived. It is shown that upward propagating shocks in magnetic structures should be detectable. The evolution of an initially homogeneous vertical magnetic field is followed, starting from an evolved state of a two-dimensional numerical simulation of solar granulation. Title: Convective intensification of magnetic fields at the solar surface. Authors: Steiner, O. Bibcode: 1996NAWG.1996..185S Altcode: The evolution of an initially homogeneous vertical magnetic field is followed, starting from an evolved state of a 2D numerical simulation of solar granulation. The field is concentrated in the intergranular lane by the combined action of flux expulsion and field intensification by the downflow. A flux sheet forms with a maximum field strength of 1600 G at the solar surface, a value well above the equipartition field strength of about 700 G. The rapid downflow within the flux sheet bounces off the high density plasma in the deeper layers of the flux sheet; the resulting upflow leads to a strong, upward moving shock and to the destruction of the flux sheet after a lifetime of about 200 s. Title: Polarized Radiation Diagnostics of Magnetohydrodynamic Models of the Solar Atmosphere Authors: Steiner, O.; Grossmann-Doerth, U.; Schüssler, M.; Knölker, M. Bibcode: 1996SoPh..164..223S Altcode: Solar magnetic elements and their dynamical interaction with the convective surface layers of the Sun are numerically simulated. Radiation transfer in the photosphere is taken into account. A simulation run over 18.5 minutes real time shows that the granular flow is capable of moving and bending a magnetic flux sheet (the magnetic element). At times it becomes inclined by up to 30° with respect to the vertical around the level τ5000 = 1 and it moves horizontally with a maximal velocity of 4 km/s. Shock waves form outside and within the magnetic flux sheet. The latter cause a distinctive signature in a time series of synthetic Stokes V-profiles. Such shock events occur with a mean frequency of about 2.5 minutes. A time resolution of at least 10 seconds in Stokes V recordings is needed to reveal an individual shock event by observation. Title: Convective intensification of photospheric magnetic fields. Authors: Schüssler, M.; Grossmann-Doerth, U.; Steiner, O.; Knölker, M. Bibcode: 1996AGAb...12...89S Altcode: No abstract at ADS Title: Simulation of the Interaction of Convective Flow with Magnetic Elements in the Solar Atmosphere. Authors: Steiner, O.; Grossmann-Doerth, U.; Knoelker, M.; Schuessler, M. Bibcode: 1995RvMA....8...81S Altcode: No abstract at ADS Title: Dynamic interaction of convection with magnetic flux sheets: first results of a new MHD code Authors: Steiner, O.; Knölker, M.; Schüssler, M. Bibcode: 1994ASIC..433..441S Altcode: No abstract at ADS Title: Flux Tube Shredding Its Infrared Signature Authors: Bunte, M.; Steiner, O.; Solanki, S. K.; Pizzo, V. J. Bibcode: 1994IAUS..154..459B Altcode: No abstract at ADS Title: Theoretical Models of Magnetic Flux Tubes: Structure and Dynamics Authors: Steiner, O. Bibcode: 1994IAUS..154..407S Altcode: No abstract at ADS Title: The upper photosphere and lower chromosphere of small-scale magnetic features Authors: Solanki, S. K.; Bruls, J. H. M. J.; Steiner, O.; Ayres, T.; Livingston, W.; Uitenbroek, H. Bibcode: 1994ASIC..433...91S Altcode: No abstract at ADS Title: MHD simulations with adaptive mesh refinement Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler, M. Bibcode: 1994smf..conf..282S Altcode: No abstract at ADS Title: Simulation of magneto-convection with radiative transfer Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler, M. Bibcode: 1994smf..conf..286S Altcode: No abstract at ADS Title: Centre-to-limb variation of the Stokes V asymmetry in solar magnetic flux tubes Authors: Buente, M.; Solanki, S. K.; Steiner, O. Bibcode: 1993A&A...268..736B Altcode: The center-to-limb variation (CLV) of synthetic Stokes V line profiles of the spectral lines Fe 15250.22 A and Fe I 5083.35 A is computed and compared with observations. The basic elements of the hydromagnetic model used to calculate the Stokes V profiles consist of a vertical cylindrical flux tube surrounded by a field-free plasma in stationary motion with a downflow along the tube boundary and an upflow further away from it. It is shown that an array of such magnetic flux tubes reproduces the peculiar observed CLV of the Stokes V asymmetry, in particular the sign reversal of the asymmetry near the limb. We determine a minimum number of model components needed for the reproduction of the Stokes V area asymmetry and study the influence of various free model parameters on it. Satisfactory agreement between synthetic and observed Stokes V profiles can only be achieved by including a considerable amount of realism into the model such as a granular temperature-velocity correlation. This suggests that the basic picture of magnetic structures in the quiet solar network and active region plages is correct. Title: On the interchange instability of solar magnetic flux tubes. I - The influence of magnetic tension and internal gas pressure Authors: Buente, M.; Steiner, O.; Pizzo, V. J. Bibcode: 1993A&A...268..299B Altcode: Small magnetic flux tubes at the solar surface are known to be interchange-unstable. Previous studies of this instability have focused on evacuated tubes in the thin tube approximation, thereby neglecting magnetic tension forces and internal atmospheres. We have extended the analysis to study the influence of these two missing components. An internal atmosphere can either have a stabilizing or destabilizing effect, depending upon the details of the prescribed gas pressure stratification. Magnetic tension forces in general stabilize the tubes by reducing the curvature of the boundary. For evacuated numerical models we find that the instability can be suppressed by a critical whirl flow of 2.2 km/s surrounding the tubes. This is considerably lower than previously found for evacuated thin tube structures. For tubes in temperature equilibrium with their surroundings this critical whirl velocity is even lower, while temperature differences at equal geometric height increase its value. The sharp interface between the magnetic field and the whirl flow is due to the Kelvin-Helmholtz instability (KHI). However, the boundary layer of finite width at the tube surface might suppress the KHI, and hence make the whirl flow mechanism feasible, if the tube is highly evacuated at the relevant height of the atmosphere. Title: CA II K Line Diagnostics of Two Dimensional Models of the Solar Chromosphere Authors: Solanki, S. K.; Buente, M.; Steiner, O.; Uitenbroek, H. Bibcode: 1992ASPC...26..294S Altcode: 1992csss....7..294S No abstract at ADS Title: MHD simulations with adaptive mesh refinement. Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler, M. Bibcode: 1992AGAb....7..213S Altcode: No abstract at ADS Title: Two-dimensional models of the solar chromosphere. I - The CA II K line as a diagnostic: 1.5-D radiative transfer Authors: Solanki, S. K.; Steiner, O.; Uitenbroeck, H. Bibcode: 1991A&A...250..220S Altcode: Ca II K line calculations for a 5-level atom and partial frequency redistribution along multiple rays passing through 2D MHD models of magnetic flux tubes in the solar atmosphere are presented. Temperature stratifications corresponding to various empirical chromospheric models are incorporated into the models. The influence of a number of model parameters on individual and spatially averaged line profiles is considered in detail. The profiles are also compared with observations. It is found that the present models can, at least qualitatively, reproduce a wide variety of observations if the temperature within the magnetic component lies between that of model F of Vernazza et al. (1981) and of model VALP of Ayres et al. (1986) and if the temperature in the nonmagnetic part of the atmosphere corresponds to that of the COOLC model of Ayres et al. Observations that are consistent with this model are presented. Title: Fast solution of radiative transfer problems using a method of multiple grids Authors: Steiner, O. Bibcode: 1991A&A...242..290S Altcode: A method of multiple grids of the second kind is used to solve two basic radiative transfer problems: the spectral line transfer in a homogeneous slab of two-level atoms and a two-dimensional LTE model atmosphere in radiative equilibrium. The employed multigrid method (W-cycle) alternately performs coarse-grid corrections and smoothing steps, the latter in the form of an accelerated Lambda-iteration. The new iterative method preserves all the advantages of approximate operator techniques, but convergence is considerably improved. In all the relevant examples of line transfer calculations made, the multigrid method is faster by a factor that varies from 4 to more than 20 with respect to the CPU time needed by an accelerated Lambda-iteration based on a nonlocal approximate operator. The two-dimensional slab problem even shows speedup factors as high as 40. Grid refinement generally improves the convergence rate. Title: Center-to-limb variation of the Stokes V asymmetry in solar magnetic flux tubes. Authors: Bünte, M.; Steiner, O.; Solanki, S. K. Bibcode: 1991sopo.work..468B Altcode: The center-to-limb-variation of synthetic Stokes V line profiles of the spectral line Fe I 5250.22 Å is presented and compared with observations. These synthetic profiles are calculated using models that contain the main features of the current basic pictures of small scale magnetic fields on the Sun. Title: Fast Solution of Radiative Transfer Problems with a Multi-Grid Method Authors: Steiner, O. Bibcode: 1991ASIC..341...19S Altcode: 1991sabc.conf...19S No abstract at ADS Title: How magnetic is the solar chromosphere? Authors: Solanki, S. K.; Steiner, O. Bibcode: 1990A&A...234..519S Altcode: The lower solar chromosphere is thought to have a very inhomogeneous temperature structure, with hot magnetic flux tubes surrounded by cool (T less than 4000 K) nonmagnetic gas (Ayres et al., 1986). The effect of such a thermally bifurcated atmosphere on the structure of the magnetic field in the chromosphere is considered. It is shown that magnetic flux tubes expand much more rapidly if the atmosphere is thermally bifurcated than if it is homogeneous. They merge and form a magnetic canopy with an almost horizontal base which does not exceed approximately 800-1000 km above tau = 1, irrespective of the magnetic filling factor. Hence the middle and upper chromosphere is filled with a magnetic field almost everywhere on the sun. The consequences of this result both for the sun and for other late type stars are discussed. Title: Structure of solar magnetic fluxtubes from the inversion of Stokes spectra at disk center Authors: Keller, C. U.; Steiner, O.; Stenflo, J. O.; Solanki, S. K. Bibcode: 1990A&A...233..583K Altcode: The paper presents an inversion procedure that derives the temperature stratification, the turbulent velocity, and the magnetic field strength of the photospheric layers of small-scale magnetic fields from observed Stokes V spectra and the continuum intensity. The inversion is based on the determination of a small number of model flux parameters by a nonlinear least squares fitting algorithm. The minimization of the sum of the squared differences between observed and synthetic observables makes it possible to determine the temperature stratification and the magnetic field strength. Title: A rapidly converging temperature correction procedure using operator perturbation Authors: Steiner, O. Bibcode: 1990A&A...231..278S Altcode: The Lambda-operator perturbation technique, known in NLTE line transfer calculations, is used for improving the temperature correction procedure. The approach presented here makes use of the formal solution to the radiative transfer equation and is capable of treating line blanketing effects by considering line opacity distribution functions. The method is shown to overcome all the problems related to the classical Lambda-iteration. Title: Model calculations of solar magnetic fluxtubes and radiative transfer Authors: Steiner, Oskar Urs Bibcode: 1990PhDT.......358S Altcode: No abstract at ADS Title: Model Calculations of the Photospheric Layers of Solar Magnetic Fluxtubes Authors: Steiner, O.; Stenflo, J. O. Bibcode: 1990IAUS..138..181S Altcode: No abstract at ADS Title: A parametric survey of model solar fluxtubes Authors: Steiner, O.; Pizzo, V. J. Bibcode: 1989A&A...211..447S Altcode: A parametric survey of numerically-generated, axially-symmetric two-dimensional magnetostatic fluxtubes is conducted to quantify the sensitivity of the properties of fluxtube models. It is found that heating of a static fluxtube atmosphere leads to an increase in the gas pressure above the level where the heating occurs, causing the fluxtube to fan out more rapidly with height. The heating also leads an increase in the opacity, causing to an upward shift in the surfaces of constant optical depth in the tube. The magnitude of these effects depends upon the temperature excess in the tube relative to that in the surrounding photosphere and upon the level in the tube atmosphere where heating is introduced. The consequences of these results for fluxtube models are discussed. Title: Numerical models for solar magnetic fluxtubes Authors: Steiner, O.; Pneuman, G. W.; Stenflo, J. O. Bibcode: 1986A&A...170..126S Altcode: A fully self-consistent method for constructing magnetostatic solutions for magnetic fluxtubes is presented, and the method is applied to three untwisted fluxtube configurations, two in which a sheet current exists at the surface of the tube, and one in which the the internal magnetic field varies continuously as a Gaussian. Convergence was obtained in all three cases, though the rate of convergence and accuracy of the solution were superior for the continuous field distribution case. For twisted fluxtubes, a maximum twist compatible with equilibrium is found for a given configuration, and the merging height is shown to decrease slightly with increased twist and to increase if the twist is concentrated more toward the surface of the tube.