A. Vögler

Simulations of magneto-convection in the solar photosphere: Equations, methods and results of the MURaM code

We have developed a 3D magnetohydrodynamics simulation code for applications in the solar convection zone and photosphere. The code includes a non-local and non-grey radiative transfer module and takes into account the effects of partial ionization. Its parallel design is based on domain decomposition, which makes it suited for use on parallel computers with distributed memory architecture. We give a description of the equations and numerical methods and present the results of the simulation of a solar plage region. Starting with a uniform vertical field of 200 G, the processes of flux expulsion and convective field amplification lead to a dichotomy of strong, mainly vertical fields embedded in the granular downflow network and weak, randomly oriented fields filling the hot granular upflows. The strong fields form a magnetic network with thin, sheet- like structures extending along downflow lanes and micropores with diameters of up to 1000 km which form occasionally at vertices where several downflow lanes merge. At the visible surface around optical depth unity, the strong field concentrations are in pressure balance with their weakly magnetized surroundings and reach field strengths of up to 2 kG, strongly exceeding the values corresponding to equipartition with the kinetic energy density of the convective motions. As a result of the channelling of radiation, small flux concentrations stand out as bright features, while the larger micropores appear dark in brightness maps owing to the suppression of the convective energy transport. The overall shape of the magnetic network changes slowly on a timescale much larger than the convective turnover time, while the magnetic flux is constantly redistributed within the network leading to continuous formation and dissolution of flux concentrations.The interaction between convective flows and magnetic fields in the solar photosphere and uppermost layers of the convection zone is crucial for many aspects of solar activity and plays an important role in the heating of the upper layers of the solar atmosphere. Since the photosphere is the region where radiation takes over from convection as the dominant energy transport mechanism, the energy exchange between gas and radiation has a significant influence on the photospheric energy balance. It determines the temperature structure of the photosphere and is responsible for the entropy drop which acts as the main driver of convection, so any realistic simulation of the solar photosphere must include an accurate modelling of radiative transfer effects.In this thesis we carried out three-dimensional magnetohydrodynamical simulations in order to study the interaction between convection, magnetic fields and radiation field in photospheric Plage regions. We modified and extended already existing MHD code in order to adapt it to the requirements of realistic photospheric simulations. A radiative transfer module was developed, which solves the radiative transfer equation under the assumption of local thermal equilibrium and accounts for the frequency dependence of the radiation field by means of opacity binning. Further modifications were made regarding the inclusion of partial ionization effects, the development of an open lower boundary condition, and the stabilization of the numerical scheme in simulations of strongly stratified media using the concept of hyperdiffusivities. We carried out comprehensive tests of the opacity-binning method, which confirm the applicability of the method in realistic simulations and show that the advantage over a grey radiative transfer is most pronounced when horizontal inhomogeneities in the upper photosphere lead to significant lateral radiative heating and cooling.The simulation of a typical solar Plage region with an average magnetic field strength of 200 Gauss in a box extending 6 mm in both horizontal and 1.4 mm in the vertical direction, using a resolution of 288 x 288 x 100 gridpoints, shows the amplification of a homogeneous initial field and the formation of a magnetic network embedded in the network of intergranular downflows. The magnetic field forms thin, sheet-like structures as well as micropores with diameters up to 1000 km and maximum field strengths around 2000 Gauss. Morphology, time evolution, and statistical properties of magnetic structures are analyzed and the relation between field strength and brightness of magnetic features is studied.A comparison of simulations using the frequency dependent (non-grey) radiative transfer with grey simulations shows that the non-grey effects lead to a significant reduction of temperature fluctuations in the upper photosphere and enhance the heating of magnetic elements due to the increased absorption of hot radiation.

A solar surface dynamo

Context. Observations indicate that the “quiet” solar photosphere outside active regions contains considerable amounts of magnetic energy and magnetic flux, with mixed polarity on small scales. The origin of this flux is unclear. Aims. We test whether local dynamo action of the near-surface convection (granulation) can generate a significant contribution to the observed magnetic flux. Methods. We have carried out MHD simulations of solar surface convection, including the effects of strong stratification, compressibility, partial ionization, radiative transfer, as well as an open lower boundary. Results. Exponential growth of a weak magnetic seed field (with vanishing net flux through the computational box) is found in a simulation run with a magnetic Reynolds number of aboutxa02600. The magnetic energy approaches saturation at a level of a few percent of the total kinetic energy of the convective motions. Near the visible solar surface, the (unsigned) magnetic flux density reaches at least a value of about 25xa0G. Conclusions. A realistic flow topology of stratified, compressible, non-helical surface convection without enforced recirculation is capable of turbulent local dynamo action near the solar surface.

Magnetoconvection in a sunspot umbra

Results from a realistic simulation of three-dimensional radiative magnetoconvection in a strong background magnetic field corresponding to the conditions in sunspot umbrae are shown. The convective energy transport is dominated by narrow upflow plumes with adjacent downflows, which become almost field-free near the surface layers. The strong external magnetic field forces the plumes to assume a cusplike shape in their top parts, where the upflowing plasma loses its buoyancy. The resulting bright features in intensity images correspond well (in terms of brightness, size, and lifetime) to the observed umbral dots in the central parts of sunspot umbrae. Most of the simulated umbral dots have a horizontally elongated form with a central dark lane. Above the cusp, most plumes show narrow upflow jets, which are driven by the pressure of the piled-up plasma below. The large velocities and low field strengths in the plumes are effectively screened from spectroscopic observation because the surfaces of equal optical depth are locally elevated, so that spectral lines are largely formed above the cusp. Our simulations demonstrate that nearly field-free upflow plumes and umbral dots are a natural result of convection in a strong, initially monolithic magnetic field.Results from a realistic simulation of three-dimensional radiative magnetoconvection in a strong background magnetic field corresponding to the conditions in sunspot umbrae are shown. The convective energy transport is dominated by narrow upflow plumes with adjacent downflows, which become almost field-free near the surface layers. The strong external magnetic field forces the plumes to assume a cusplike shape in their top parts, where the upflowing plasma loses its buoyancy. The resulting bright features in intensity images correspond well (in terms of brightness, size, and lifetime) to the observed umbral dots in the central parts of sunspot umbrae. Most of the simulated umbral dots have a horizontally elongated form with a central dark lane. Above the cusp, most plumes show narrow upflow jets, which are driven by the pressure of the piled-up plasma below. The large velocities and low field strengths in the plumes are effectively screened from spectroscopic observation because the surfaces of equal optical depth are locally elevated, so that spectral lines are largely formed above the cusp. Our simulations demonstrate that nearly field-free upflow plumes and umbral dots are a natural result of convection in a strong, initially monolithic magnetic field.

Approximations for non-grey radiative transfer in numerical simulations of the solar photosphere

Realistic simulations of solar (magneto-)convection require an accurate treatment of the non-grey character of the radiative energy transport. Owing to the large number of spectral lines in the solar atmosphere, statistical representations of the line opacities have to be used in order to keep the problem numerically tractable. We consider two statistical approaches, the opacity distribution function (ODF) concept and the multigroup (or opacity binning) method and provide a quantitative assessment of the errors that arise from the application of these methods in the context of 2D/3D simulations. In a first step, the ODF- and multigroup methods are applied to a 1D model-atmosphere and the resulting radiative heating rates are compared. A number of 4−6 frequency bins is found to warrant a satisfactory modeling of the radiative energy exchange. Further tests in 2D model-atmospheres show the applicability of the multigroup method in realistic situations and underline the importance of a non-grey treatment. Furthermore, we address the question of an appropriate opacity average in multigroup calculations and discuss the significance of velocity gradients for the radiative heating rates.

Magnetic flux in the internetwork quiet Sun

We report a direct comparison of the amplitudes of Stokes spectra of the Fe uf769 630 nm and 1.56 µm lines produced by realistic MHD simulations with simultaneous observations in the same spectral regions. The Stokes spectra were synthesized in snapshots with a mixed polarity magnetic field having a spatially averaged strength, � B� , between 10 and 30 G. The distribution of Stokes V amplitudes depends sensitively onB� . A quiet inter-network region was observed at the German VTT simultane- ously with TIP (1.56 µm) and POLIS (630 nm). We find that the Stokes V amplitudes of both infrared and visible observations are best reproduced by the simulation snapshot withB� = 20 G. In observations with 1 �� resolution, up to 2/3 of the magnetic flux can remain undetected.

On the fractal dimension of small-scale magnetic structures in the Sun

We compare, by means of fractal analyses, the shapes of observed small-scale magnetic structures on the Sun with those of magnetic features resulting from numerical simulations of magnetoconvection. The observations were obtained with the “Gottingen” Fabry-Perot spectrometer at the Vacuum Tower Telescope at the Observatorio del Teide on Tenerife. Magnetograms with 0

Effects of non-grey radiative transfer on 3D simulations of solar magneto-convection

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Disrupting the subscription journals’ business model for the necessary large-scale transformation to open access

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RX J004717.4-251811 : The first eclipsing X-ray binary outside the Local Group

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Generation of bisymmetric magnetic fields in galaxies with tidal interaction

5 spatial resolution were obtained from two-dimensional Stokes V polarimetry in the