244 research outputs found
Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data
We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to
model the force-free coronal field above a solar active region, assuming
magnetic forces to dominate. We take measurement uncertainties caused by, e.g.,
noise and the particular inversion technique into account. After searching for
the optimum modeling parameters for the particular data sets, we compare the
resulting nonlinear force-free model fields. We show the degree of agreement of
the coronal field reconstructions from the different data sources by comparing
the relative free energy content, the vertical distribution of the magnetic
pressure and the vertically integrated current density. Though the longitudinal
and transverse magnetic flux measured by the VSM and HMI is clearly different,
we find considerable similarities in the modeled fields. This indicates the
robustness of the algorithm we use to calculate the nonlinear force-free fields
against differences and deficiencies of the photospheric vector maps used as an
input. We also depict how much the absolute values of the total force-free,
virial and the free magnetic energy differ and how the orientation of the
longitudinal and transverse components of the HMI- and VSM-based model volumes
compares to each other.Comment: 9 pages, 5 figure
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
An optimization principle for the computation of MHD equilibria in the solar corona
AIMS: We develop an optimization principle for computing stationary MHD
equilibria. METHODS: Our code for the self-consistent computation of the
coronal magnetic fields and the coronal plasma uses non-force-free MHD
equilibria. Previous versions of the code have been used to compute non-linear
force-free coronal magnetic fields from photospheric measurements. The program
uses photospheric vector magnetograms and coronal EUV images as input. We
tested our reconstruction code with the help of a semi-analytic
MHD-equilibrium. The quality of the reconstruction was judged by comparing the
exact and reconstructed solution qualitatively by magnetic field-line plots and
EUV-images and quantitatively by several different numerical criteria. RESULTS:
Our code is able to reconstruct the semi-analytic test equilibrium with high
accuracy. The stationary MHD optimization code developed here has about the
same accuracy as its predecessor, a non-linear force-free optimization code.
The computing time for MHD-equilibria is, however, longer than for force-free
magnetic fields. We also extended a well-known class of nonlinear force-free
equilibria to the non-force-free regime for purposes of testing the code.
CONCLUSIONS: We demonstrate that the code works in principle using tests with
analytical equilibria, but it still needs to be applied to real data.Comment: 6 pages, 3 figure
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
How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?
The SDO/HMI instruments provide photospheric vector magnetograms with a high
spatial and temporal resolution. Our intention is to model the coronal magnetic
field above active regions with the help of a nonlinear force-free
extrapolation code. Our code is based on an optimization principle and has been
tested extensively with semi-analytic and numeric equilibria and been applied
before to vector magnetograms from Hinode and ground based observations.
Recently we implemented a new version which takes measurement errors in
photospheric vector magnetograms into account. Photospheric field measurements
are often due to measurement errors and finite nonmagnetic forces inconsistent
as a boundary for a force-free field in the corona. In order to deal with these
uncertainties, we developed two improvements: 1.) Preprocessing of the surface
measurements in order to make them compatible with a force-free field 2.) The
new code keeps a balance between the force-free constraint and deviation from
the photospheric field measurements. Both methods contain free parameters,
which have to be optimized for use with data from SDO/HMI. Within this work we
describe the corresponding analysis method and evaluate the force-free
equilibria by means of how well force-freeness and solenoidal conditions are
fulfilled, the angle between magnetic field and electric current and by
comparing projections of magnetic field lines with coronal images from SDO/AIA.
We also compute the available free magnetic energy and discuss the potential
influence of control parameters.Comment: 17 Pages, 6 Figures, Sol. Phys., accepte
Spatially and Spectrally Resolved Observations of a Zebra Pattern in Solar Decimetric Radio Burst
We present the first interferometric observation of a zebra-pattern radio
burst with simultaneous high spectral (~ 1 MHz) and high time (20 ms)
resolution. The Frequency-Agile Solar Radiotelescope (FASR) Subsystem Testbed
(FST) and the Owens Valley Solar Array (OVSA) were used in parallel to observe
the X1.5 flare on 14 December 2006. By using OVSA to calibrate the FST the
source position of the zebra pattern can be located on the solar disk. With the
help of multi-wavelength observations and a nonlinear force-free field (NLFFF)
extrapolation, the zebra source is explored in relation to the magnetic field
configuration. New constraints are placed on the source size and position as a
function of frequency and time. We conclude that the zebra burst is consistent
with a double-plasma resonance (DPR) model in which the radio emission occurs
in resonance layers where the upper hybrid frequency is harmonically related to
the electron cyclotron frequency in a coronal magnetic loop.Comment: Accepted for publication in Ap
On the Relation of Hard X-ray Peak Flux and Outburst Waiting Time in the Black Hole Transient GX 339-4
Aims. In this work we re-investigated the empirical relation between the hard
X-ray peak flux and the outburst waiting time found previously in the black
hole transient GX 339-4. We tested the relation using the observed hard X-ray
peak flux of the 2007 outburst of GX 339-4, clarified issues about faint
flares, and estimated the lower limit of hard X-ray peak flux for the next
outburst. Methods. We included Swift/BAT data obtained in the past four years.
Together with the CGRO/BATSE and RXTE/HEXTE light curves, the observations used
in this work cover a period of 18 years. Results. The observation of the 2007
outburst confirms the empirical relation discovered before. This strengthens
the apparent link between the mass in the accretion disk and the peak
luminosity of the brightest hard state that the black hole transient can reach.
We also show that faint flares with peak fluxes smaller than about 0.12 crab do
not affect the empirical relation. We predict that the hard X-ray peak flux of
the next outburst should be larger than 0.65 crab, which will make it at least
the second brightest in the hard X-ray since 1991.Comment: 4 pages, 3 figures, accepted by A&
Coronal Magnetic Field Structure and Evolution for Flaring AR 11117 and its Surroundings
In this study, photospheric vector magnetograms obtained with the Synoptic
Optical Long-term Investigations of the Sun survey (SOLIS), are used as
boundary conditions to model the three-dimensional nonlinear force-free (NLFF)
coronal magnetic fields as a sequence of nonlinear force-free equilibria in
spherical geometry. We study the coronal magnetic field structure inside active
regions and its temporal evolution. We compare the magnetic field configuration
obtained from NLFF extrapolation before and after flaring event in active
region (AR) 11117 and its surroundings observed on 27 October 2010. We compare
the magnetic field topologies and the magnetic energy densities and study the
connectivities between AR 11117 and its surroundings. During the investigated
time period, we estimate the change in free magnetic energy from before to
after the flare to be 1.74x10^{32}erg which represents about 13.5% of nonlinear
force-free magnetic energy before the flare. In this study, we find that
electric currents from AR 11117 to its surroundings were disrupted after the
flare.Comment: 14 pages, 14 figures, Accepted by Solar Physics Journa
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
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