M. Schüssler

Dynamical Interaction of Solar Magnetic Elements and Granular Convection: Results of a Numerical Simulation

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.

Emerging Flux Tubes in the Solar Convection Zone. II. The Influence of Initial Conditions

Numerical simulations of rising magnetic flux tubes in the solar convection zone have contributed significantly to our understanding of the basic properties of sunspot groups. They have provided an important clue to the operation of the solar dynamo by predicting strong (super-equipartition) magnetic fields near the bottom of the convection zone. We have investigated to what extent the simulation results (obtained on the basis of the thin flux tube approximation) depend on the assumptions made about the initial state of a magnetic flux tube at the start of the simulation. Two initial conditions used in the literature have been considered in detail: mechanical equilibrium (MEQ) and temperature balance (TBL). It turns out that the requirement of super-equipartition field strength is a robust feature of the simulations, largely independent of the choice of initial conditions: emergence of active regions at low latitudes and the correct dependence of their tilt angle (with respect to the east-west direction) as a function of heliographic latitude require an initial magnetic field strength on the order of 105 G. Other properties of rising flux tubes, such as the asymmetries of shape and field strength between the leading and following wings (with respect to the direction of rotation) of a rising loop, or the anchoring of part of the flux tube in the overshoot region, depend on the initial condition. Observed asymmetries in the magnetic flux distribution and of proper motions in emerging active regions favor MEQ over TBL as the proper initial condition. MEQ should also be preferred for other theoretical reasons: it allows for fewer free parameters, it requires no fine tuning for the tube geometry and background stratification in the overshoot region, and it can be easily made compatible with an encompassing model of the generation, storage, and eruption of the magnetic flux. We have also studied whether an external upflow (convective updraft) can trigger the eruption of an otherwise stably stored flux tube in the overshoot region. We find that a significant deformation and destabilization of a flux tube with equipartition field strength requires coherent upflow velocities of 20-50 m s-1 in the overshoot layer, which is an order of magnitude larger than current estimates for such velocities.

Dynamic Interaction of Convection with Magnetic Flux Sheets: First Results of a New MHD Code

Methods, tests, and first results of a new code for the simulation of solar magnetoconvection are presented. Special emphasis is laid on a reliable and economic treatment of small-scale structures like magnetic flux concentrations, current layers and shocks in 3-D, time-dependent simulations. The numerical grid is adjusted to the local resolution requirements using the method of Adaptive Mesh Refinement (AMR). We describe the implementation of the AMR technique in an MHD code and show a number of test cases. First results on the interaction of magnetic flux sheets with radiative, non-stationary convection in the solar atmosphere have been obtained with a 2-D version of the code. Besides recovering a number of basic features of previous models for such structures, we find a spectacular new phenomenon: strong bending of a flux sheet by asymmetric convective flow followed by rapid sweeping back due to buoyancy and magnetic tension. Such events may lead to the excitation of transversal MHD waves and therefore possibly contribute to heating the upper solar atmosphere.

Polarized radiation diagnostics of magnetohydrodynamic models of the solar atmosphere

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.

Some developments in the theory of magnetic flux concentrations in the solar atmosphere

Abstract Most of the magnetic flux in the solar photosphere is concentrated in small-scale structures of large field strength, called magnetic elements . We discuss briefly the observationally determined properties of magnetic elements and the theoretical concepts for the origin of magnetic flux filamentation and concentration. New results of model calculations for 2D magnetic flux sheets on the basis of numerical simulation of the compressible MHD equations including a full (grey) radiative transfer are presented. Synthetic Stokes profiles of spectral lines and continuum intensity distributions serve to compare the theoretical models with observational data. Among the key results are: (1) The upper layers of the magnetic structure become hotter than the environment due to radiative illumination effects; (2) a strong convective flow evolves with horizontal velocity of 2 km/s towards the flux sheet and a narrow “downflow jet” with velocity up to 6 km/s adjacent to the magnetic structure; (3) both flux sheet and non-magnetic environment oscillate with a period around 5 minutes. Comparison with observed properties of solar magnetic elements reveals: (4) Calculated and semi-empirical temperature profiles as function of height in the photosphere are in reasonable agreement; (5) the calculated velocity field around flux concentrations explains the area asymmetry of the observed Stokes V -profiles including their center-limb variation; (6) the calculated continuum intensity of a flux sheet model is compatible with the values inferred from high spatial resolution observations of bright points at solar disk center; (7) the observed center-limb variation of facular contrast at low or medium spatial resolution is reproduced by arranging calculated flux sheets in arrays. We stress the importance of MHD simulation models for the analysis and interpretation of data from future facilities for high spatial resolution observations like OSL and LEST .

Models of Magnetic Flux Sheets

We present results of numerical model calculations of magnetic flux concentrations in the solar photosphere. Using a 2D slab geometry we solve the nonlinear MHD equations for a compressible medium incorporating partial ionization effects and a full radiative transfer (grey, LTE). An adaptive Moving Finite Element code is employed. We are able to analyze our results by computing the profiles of the four Stokes parameters (of various spectral lines) emerging from the flux concentrations and comparing them with observations. We find good agreement between synthetic and observed Stokes V-profiles in the visible and infrared. A major new result is the appearance of a temperature enhancement in the upper layers in the upper layers of the flux concentration which are heated by illumination from the hot bottom. We obtain a large positive continuum intensity contrast of the flux sheet.

Dynamics of Erupting Magnetic Flux Tubes

The eruption of magnetic flux tubes from the overshoot layer due to instability and the dynamics of their subsequent rise through the solar convection zone are followed by numerical simulation. Special emphasis is put on the possibility of explaining observed regularities of the active regions at the surface (tilt angles, latitude of emergence, asymmetry between preceding and following parts, etc). Instability sets in with non-axisymmetric (undular) modes at azimuthal wavenumbers m = 1 and m = 2 if the field strength exceeds values of the order of 105 G. At the same time, such strong initial fields are required to reproduce the observable properties of sunspots and active regions. Consequently, a consistent picture of storage, instability and eruption of solar magnetic fields emerges.