Magnetostatic modelling from SUNRISE/IMaX: Application to an active region observed with SUNRISE II 

Thomas Wiegelmann Submitted: 20170113 10:08
Magnetostatic models may overcome some of the issues facing forcefree magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quietSun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloonborne solar observatory in June 2013 as boundary condition for a magnetostatic model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magnetostatic extrapolation approach, which has been applied earlier (Paper I) to a quiet Sun region observed with Sunrise I. In an active region the signaltonoiseratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magnetostatic equilibria. The high spatial resolution of IMaX (110130 km, pixel size 40 km) enables us to model the nonforcefree layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents.
Authors: T. Wiegelmann, T. Neukirch, D.H. Nickeler, S.K. Solanki, P. Barthol, A. Gandorfer, L. Gizon, J. Hirzberger, T.L. Riethmüller, M. van Noort, J. Blanco Rodríguez, J. C. Del Toro Iniesta, D. Orozco Suárez, W. Schmidt, V. Martínez Pillet, M. Knölker
Projects: Other

Publication Status: ApJS, accepted
Last Modified: 20170113 13:22



Magnetostatic modelling of the mixed plasma Beta solar atmosphere based on SUNRISE/IMaX data 

Thomas Wiegelmann Submitted: 20151119 07:12
Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of nonnegligible plasma beta. We use highresolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magnetostatic magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be forcefree (the Lorentzforce vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken selfconsistently into account and compensate the nonvanishing Lorentzforce. Above a certain height (about 2 Mm) the nonmagnetic forces become very weak and consequently the magnetic field becomes almost forcefree. Here we apply a linear approach, where the electric current density consists of a superposition of a fieldline parallel current and a current perpendicular to the Sun's gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a nonlinear model.
Authors: T. Wiegelmann, T. Neukirch, D.H. Nickeler, S.K. Solanki, V. Martinez Pillet, J.M. Borrero
Projects: None

Publication Status: ApJ, accepted
Last Modified: 20151120 15:38



Solar Forcefree Magnetic Fields 

Thomas Wiegelmann Submitted: 20120828 05:13
The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all nonmagnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the forcefree field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are coaligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the socalled linear forcefree field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear forcefree coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from groundbased (for example SOLIS) and spaceborn (for example Hinode and SDO) instruments. If we can obtain accurate forcefree coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUVimages of the radiating coronal plasma.
Authors: Thomas Wiegelmann, Takashi Sakurai
Projects: None

Publication Status: Accepted for publication in Living Reviews in Solar Physics
Last Modified: 20120828 12:30



Magnetic loops in the quiet Sun 

Thomas Wiegelmann Submitted: 20101004 03:12
We investigate the fine structure of magnetic fields in the atmosphere of the quiet Sun. We use photospheric magnetic field measurements from {sc Sunrise}/IMaX with unprecedented spatial resolution to extrapolate the photospheric magnetic field into higher layers of the solar atmosphere with the help of potential and forcefree extrapolation techniques. We find that most magnetic loops which reach into the chromosphere or higher have one foot point in relatively strong magnetic field regions in the photosphere. 91% of the magnetic energy in the mid chromosphere (at a height of 1 Mm) is in field lines, whose stronger foot point has a strength of more than 300 G, i.e. above the equipartition field strength with convection. The loops reaching into the chromosphere and corona are also found to be asymmetric in the sense that the weaker foot point has a strength B < 300 G and is located in the internetwork. Such loops are expected to be strongly dynamic and have short lifetimes, as dictated by the properties of the internetwork fields.
Authors: Thomas Wiegelmann, Sami K Solanki, Juan Borrero, Valentin Martinez Pillet, J. C. del Toro Iniesta, Vicente Domingo, J. A. Bonet Navarro, Peter Barthol, Achim Gandorfer, Michael Knoelker, Wolfgang Schmidt, Alan M. Title
Projects: None

Publication Status: accepted for ApJL Sunrise special issue
Last Modified: 20101004 18:07



Thin current sheets caused by plasma flow gradients in space and astrophysical plasma 

Thomas Wiegelmann Submitted: 20100818 04:22
Strong gradients in plasma flows play a major role in space and astrophysical plasmas. A typical situation is that a static plasma equilibrium is surrounded by a plasma flow, which can lead to strong plasma flow gradients at the separatrices between field lines with different magnetic topologies, e.g., planetary magnetospheres, helmet streamers in the solar corona, or at the boundary between the heliosphere and interstellar medium. Within this work we make a first step to understand the influence of these flows towards the occurrence of current sheets in a stationary state situation. We concentrate here on incompressible plasma flows and 2D equilibria, which allow us to find analytic solutions of the stationary magnetohydrodynamics equations (SMHD). First we solve the magnetohydrostatic (MHS) equations with the help of a GradShafranov equation and then we transform these static equilibria into a stationary state with plasma flow. We are in particular interested to study SMHDequilibria with strong plasma flow gradients perpendicular to separatrices. We find that induced thin current sheets occur naturally in such situations. The strength of the induced currents depend on the Alfvén Mach number and its gradient, and on the magnetic field.
Authors: Dieter H. Nickeler, Thomas Wiegelmann
Projects: None

Publication Status: Ann. Geophys., 28, 15231532, 2010, DOI: 10.5194/angeo2815232010
Last Modified: 20100818 10:20



Nonlinear forcefree modelling: influence of inaccuracies in the measured magnetic vector 

Thomas Wiegelmann Submitted: 20091215 04:45
Context: Solar magnetic fields are regularly extrapolated into
the corona starting from photospheric magnetic measurements
that can suffer from significant uncertainties.
Aims: Here we study how inaccuracies introduced into the maps of
the photospheric magnetic vector from the inversion of ideal and
noisy Stokes parameters influence the extrapolation of nonlinear
forcefree magnetic fields.
Methods: We compute nonlinear forcefree magnetic fields based on
simulated vector magnetograms, which have been produced by the
inversion of Stokes profiles, computed froma 3D radiation MHD
simulation snapshot. These extrapolations are compared with
extrapolations starting directly from the field in the MHD simulations,
which is our reference. We investigate how line formation
and instrumental effects such as noise, limited spatial resolution and
the effect of employing a filter instrument influence the resulting magnetic
field structure. The comparison is done qualitatively by visual inspection
of the magnetic field distribution and quantitatively by different metrics.
Results: The reconstructed field is most accurate if ideal Stokes data are inverted
and becomes less accurate if instrumental effects and noise are included.
The results demonstrate that the nonlinear forcefree field extrapolation
method tested here is relatively insensitive to the effects of noise in measured
polarization spectra at levels consistent with presentday instruments.
Conclusions heading: Our results show that we can reconstruct the coronal
magnetic field as a nonlinear forcefree field from realistic photospheric
measurements with an accuracy of a few percent, at least in the absence of sunspots.
Authors: T. Wiegelmann, L. Yelles Chaouche, S. K. Solanki, A. Lagg
Projects: Hinode/SOT

Publication Status: Astronomy and Astrophysics, accepted,
Last Modified: 20091215 12:20



Solar stereoscopy ? where are we and what developments do we require to progress? 

Thomas Wiegelmann Submitted: 20090825 05:20
Observations from the two STEREOspacecraft
give us for the first time the possibility to use stereoscopic methods to reconstruct the 3D solar corona. Classical stereoscopy works best for solid objects with clear edges. Consequently an application of classical stereoscopic methods to the faint structures visible in the optically thin coronal plasma is by no means straight forward and several problems have to be treated adequately: 1) First there is the problem of identifying onedimensional structures ? e.g. active region
coronal loops or polar plumes from the two individual EUVimages observed with STEREO/EUVI. 2) As a next step one
has the association problem to find corresponding structures
in both images. This becomes more difficult as the angle
between STEREOA and B increases. 3) Within the reconstruction problem stereoscopic methods are used to compute the 3Dgeometry of the identified structures. Without any prior assumptions, e.g., regarding the footpoints of coronal loops, the reconstruction problem has not one unique solution. 4) One has to estimate the reconstruction error or accuracy of the reconstructed 3Dstructure, which depends on the accuracy of the identified structures in 2D, the separation angle between the spacecraft, but also on the location, e.g., for eastwest directed coronal loops the reconstruction error is highest close to the loop top. 5) Eventually we are not
only interested in the 3Dgeometry of loops or plumes, but
also in physical parameters like density, temperature, plasma flow, magnetic field strength etc. Helpful for treating some of these problems are coronal magnetic field models extrapolated from photospheric measurements, because observed EUVloops outline the magnetic field. This feature has been used for a new method dubbed "magnetic stereoscopy". As examples we show recent application to active region loops.
Authors: T. Wiegelmann, B. Inhester, L. Feng
Projects: STEREO

Publication Status: Annales Geophysicae, Volume 27, Issue 7, pp.29252936, 2009
Last Modified: 20090825 09:00



Subject will be restored when possible 

Thomas Wiegelmann Submitted: 20080108 08:10
The solar magnetic field is key to understanding the physical processes in the
solar atmosphere. Nonlinear forcefree codes have been shown to be
useful in extrapolating the coronal field upward from underlying vector
boundary data. However, we can only measure the magnetic field vector
routinely with high accuracy in the photosphere, and unfortunately these data
do not fulfill the forcefree condition. We must therefore apply some
transformations to these data before nonlinear forcefree extrapolation codes
can be selfconsistently applied. To this end, we have developed a
minimization procedure that yields a more chromospherelike field, using the
measured photospheric field vectors as input. The procedure includes
forcefree consistency integrals, spatial smoothing, and  newly included in
the version presented here  an improved match to the field direction as
inferred from fibrils as can be observed in, {it e.g.}, chromospheric Hα
images.
We test the procedure using a model activeregion field that included buoyancy
forces at the photospheric level. The proposed preprocessing method allows us
to approximate the chromospheric vector field to within a few degrees and the
free energy in the coronal field to within one percent.
Authors: Wiegelmann, T; Thalmann, J.K.; Schrijver, C.J.; DeRosa, M.L.; Metcalf, T.R.
Projects: Hinode/SOT

Publication Status: Solar Physics, accepted
Last Modified: 20080108 09:53



Testing nonlinear forcefree coronal magnetic field extrapolations with the TitovDemoulin equilibrium 

Thomas Wiegelmann Submitted: 20061221 09:32
CONTEXT:
As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona.
AIMS:
We test the quality of a nonlinear forcefree coronal magnetic field extrapolation code with the help of a known analytical solution.
METHODS:
The nonlinear forcefree equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the forcefree and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the
computational box in Case I or only on the bottom boundary in Case II. We check the quality
of the reconstruction by computing how well forcefreeness and divergencefreeness are fulfilled
and by comparing the numerical solution with the analytical solution. The comparison is
done with magnetic field line plots and several quantitative measures, like the vector correlation,
Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy.
RESULTS:
For Case I the reconstructed magnetic field shows good agreement with the original magnetic
field topology, whereas in Case II there are considerable deviations from the exact solution. This is
corroborated by the quantitative measures, which are significantly better for Case I.
CONCLUSIONS:
Despite the strong nonlinearity of the considered forcefree equilibrium, the optimization
method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly
on the consistency of the input data, which is given only if the known solution is provided also at
the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram.
Authors: T. Wiegelmann, B. Inhester, B. Kliem, G. Valori and T. Neukirch
Projects: None

Publication Status: A&A, Vol. 453, 737741 (2006)
Last Modified: 20061221 09:54




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