204 research outputs found
Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Demoulin equilibrium
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 non-linear force-free coronal magnetic field
extrapolation code with the help of a known analytical solution. METHODS: The
non-linear force-free equations are numerically solved with the help of an
optimization principle. The method minimizes an integral over the force-free
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 force-freeness and divergence-freeness 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
force-free 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.Comment: 6 pages, 2 figures, Research Not
Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation
Extrapolation codes for modelling the magnetic field in the corona in
cartesian geometry do not take the curvature of the Sun's surface into account
and can only be applied to relatively small areas, \textit{e.g.}, a single
active region. We apply a method for nonlinear force-free coronal magnetic
field modelling of photospheric vector magnetograms in spherical geometry which
allows us to study the connectivity between multi-active regions. We use vector
magnetograph data from the Synoptic Optical Long-term Investigations of the Sun
survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic
field, where we study three neighbouring magnetically connected active regions
(ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively.
We compare the magnetic field topologies and the magnetic energy densities and
study the connectivities between the active regions(ARs). We have studied the
time evolution of magnetic field over the period of three days and found no
major changes in topologies as there was no major eruption event. From this
study we have concluded that active regions are much more connected
magnetically than the electric current.Comment: Solar Physic
Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm
We compare the performance of two alternative algorithms which aim to
construct a force-free magnetic field given suitable boundary conditions. For
this comparison, we have implemented both algorithms on the same finite element
grid which uses Whitney forms to describe the fields within the grid cells. The
additional use of conjugate gradient and multigrid iterations result in quite
effective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithms
both perform well for the reconstruction of a known analytic force-free field.
For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotis
approach has some difficulties because it requires overdetermined boundary
information which may include inconsistencies. The Grad-Rubin code on the other
hand loses convergence for strong current densities. For the example we have
investigated, however, the maximum possible current density seems to be not far
from the limit beyond which a force free field cannot exist anymore for a given
normal magnetic field intensity on the boundary.Comment: 21 pages, 13 figure
A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests
Based on a second-order approximation of nonlinear force-free magnetic field
solutions in terms of uniformly twisted field lines derived in Paper I, we
develop here a numeric code that is capable to forward-fit such analytical
solutions to arbitrary magnetogram (or vector magnetograph) data combined with
(stereoscopically triangulated) coronal loop 3D coordinates. We test the code
here by forward-fitting to six potential field and six nonpotential field cases
simulated with our analytical model, as well as by forward-fitting to an
exactly force-free solution of the Low and Lou (1990) model. The
forward-fitting tests demonstrate: (i) a satisfactory convergence behavior
(with typical misalignment angles of ), (ii)
relatively fast computation times (from seconds to a few minutes), and (iii)
the high fidelity of retrieved force-free -parameters ( for simulations and for the Low and Lou model). The
salient feature of this numeric code is the relatively fast computation of a
quasi-forcefree magnetic field, which closely matches the geometry of coronal
loops in active regions, and complements the existing {\sl nonlinear force-free
field (NLFFF)} codes based on photospheric magnetograms without coronal
constraints.Comment: Solar PHysics, (in press), 25 pages, 11 figure
How to use magnetic field information for coronal loop identification?
The structure of the solar corona is dominated by the magnetic field because
the magnetic pressure is about four orders of magnitude higher than the plasma
pressure. Due to the high conductivity the emitting coronal plasma (visible
e.g. in SOHO/EIT) outlines the magnetic field lines. The gradient of the
emitting plasma structures is significantly lower parallel to the magnetic
field lines than in the perpendicular direction. Consequently information
regarding the coronal magnetic field can be used for the interpretation of
coronal plasma structures. We extrapolate the coronal magnetic field from
photospheric magnetic field measurements into the corona. The extrapolation
method depends on assumptions regarding coronal currents, e.g. potential fields
(current free) or force-free fields (current parallel to magnetic field). As a
next step we project the reconstructed 3D magnetic field lines on an EIT-image
and compare with the emitting plasma structures. Coronal loops are identified
as closed magnetic field lines with a high emissivity in EIT and a small
gradient of the emissivity along the magnetic field.Comment: 14 pages, 3 figure
Nonlinear force-free reconstruction of the global solar magnetic field: methodology
We present a novel numerical method that allows the calculation of nonlinear
force-free magnetostatic solutions above a boundary surface on which only the
distribution of the normal magnetic field component is given. The method relies
on the theory of force-free electrodynamics and applies directly to the
reconstruction of the solar coronal magnetic field for a given distribution of
the photospheric radial field component. The method works as follows: we start
with any initial magnetostatic global field configuration (e.g. zero, dipole),
and along the boundary surface we create an evolving distribution of tangential
(horizontal) electric fields that, via Faraday's equation, give rise to a
respective normal field distribution approaching asymptotically the target
distribution. At the same time, these electric fields are used as boundary
condition to numerically evolve the resulting electromagnetic field above the
boundary surface, modelled as a thin ideal plasma with non-reflecting,
perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear
force-free configuration that satisfies the given normal field distribution on
the boundary. This is different from existing methods relying on a fixed
boundary condition - the boundary evolves toward the a priori given one, at the
same time evolving the three-dimensional field solution above it. Moreover,
this is the first time a nonlinear force-free solution is reached by using only
the normal field component on the boundary. This solution is not unique, but
depends on the initial magnetic field configuration and on the evolutionary
course along the boundary surface. To our knowledge, this is the first time
that the formalism of force-free electrodynamics, used very successfully in
other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic
Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions
We examine the nonlinear magnetofrictional extrapolation scheme using the
solar active region model by Titov and D\'emoulin as test field. This model
consists of an arched, line-tied current channel held in force-free equilibrium
by the potential field of a bipolar flux distribution in the bottom boundary. A
modified version, having a parabolic current density profile, is employed here.
We find that the equilibrium is reconstructed with very high accuracy in a
representative range of parameter space, using only the vector field in the
bottom boundary as input. Structural features formed in the interface between
the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch
separatrix surface"-are reliably reproduced, as are the flux rope twist and the
energy and helicity of the configuration. This demonstrates that force-free
fields containing these basic structural elements of solar active regions can
be obtained by extrapolation. The influence of the chosen initial condition on
the accuracy of reconstruction is also addressed, confirming that the initial
field that best matches the external potential field of the model quite
naturally leads to the best reconstruction. Extrapolating the magnetogram of a
Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a
sequence of two opposing evolutionary phases which clearly indicate the
unstable nature of the configuration: a partial buildup of the flux rope with
rising free energy is followed by destruction of the rope, losing most of the
free energy.Comment: 14 pages, 10 figure
Shear-Flow Driven Current Filamentation: Two-Dimensional Magnetohydrodynamic Simulations
The process of current filamentation in permanently externally driven,
initially globally ideal plasmas is investigated by means of two-dimensional
Magnetohydrodynamic (MHD)-simulations. This situation is typical for
astrophysical systems like jets, the interstellar and intergalactic medium
where the dynamics is dominated by external forces. Two different cases are
studied. In one case, the system is ideal permanently and dissipative processes
are excluded. In the second case, a system with a current density dependent
resistivity is considered. This resistivity is switched on self-consistently in
current filaments and allows for local dissipation due to magnetic
reconnection. Thus one finds tearing of current filaments and, besides, merging
of filaments due to coalescence instabilities. Energy input and dissipation
finally balance each other and the system reaches a state of constant magnetic
energy in time.Comment: 32 Pages, 13 Figures. accepted, to appear in Physics of Plasmas
(049012
The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
The nonlinear force-free field (NLFFF) model is often used to describe the
solar coronal magnetic field, however a series of earlier studies revealed
difficulties in the numerical solution of the model in application to
photospheric boundary data. We investigate the sensitivity of the modeling to
the spatial resolution of the boundary data, by applying multiple codes that
numerically solve the NLFFF model to a sequence of vector magnetogram data at
different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active
Region 10978 on 2007 December 13. We analyze the resulting energies and
relative magnetic helicities, employ a Helmholtz decomposition to characterize
divergence errors, and quantify changes made by the codes to the vector
magnetogram boundary data in order to be compatible with the force-free model.
This study shows that NLFFF modeling results depend quantitatively on the
spatial resolution of the input boundary data, and that using more highly
resolved boundary data yields more self-consistent results. The free energies
of the resulting solutions generally trend higher with increasing resolution,
while relative magnetic helicity values vary significantly between resolutions
for all methods. All methods require changing the horizontal components, and
for some methods also the vertical components, of the vector magnetogram
boundary field in excess of nominal uncertainties in the data. The solutions
produced by the various methods are significantly different at each resolution
level. We continue to recommend verifying agreement between the modeled field
lines and corresponding coronal loop images before any NLFFF model is used in a
scientific setting.Comment: Accepted to ApJ; comments/corrections to this article are welcome via
e-mail, even after publicatio
Nonlinear force-free and potential field models of active-region and global coronal fields during the Whole Heliospheric Interval
Between 2008/3/24 and 2008/4/2, the three active regions NOAA active regions
10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term
Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they
traversed the solar disk. We use these measurements and the nonlinear
force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic
field for each active region and compare model field lines with images from the
Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope
(XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global
Oscillations Network Group (GONG) magnetograms provide information on the
global photospheric field and potential-field source-surface models based on
these maps describe the global coronal field during the Whole Heliospheric
Interval (WHI) and its neighboring rotations. Features of the modeled global
field, such as the coronal holes and streamer belt locations, are discussed in
comparison with extreme ultra-violet and coronagraph observations from STEREO.
The global field is found to be far from a minimum, dipolar state. From the
nonlinear models we compute physical quantities for the active regions such as
the photospheric magnetic and electric current fluxes, the free magnetic energy
and the relative helicity for each region each day where observations permit.
The interconnectivity of the three regions is addressed in the context of the
potential-field source-surface model. Using local and global quantities derived
from the models, we briefly discuss the different observed activity levels of
the regions.Comment: Accepted for publication in the Solar Physics Whole Heliospheric
Interval (WHI) topical issue. We had difficulty squeezing this paper into
arXiv's 15 Mb limit. The full paper is available here
ftp://gong2.nso.edu/dsds_user/petrie/PetrieCanouAmari.pd
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