wiegelmann

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Author name code: wiegelmann
ADS astronomy entries on 2022-09-14
author:"Wiegelmann, Thomas"

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Title: Mini-filament eruption, QSL reconnection, and
reconnection-driven outflows: IRIS and AIA/HMI/SDO observations
and modelling
Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus;
Xie, Haixia; Wiegelmann, Thomas
2022cosp...44.2533M Altcode:
We will present unique observations of a mini-filament eruption
associated with cancelling magnetic fluxes of a small-scale loop system
known as a coronal bright point. The event is uniquely recorded in
both the imaging and spectroscopic data taken with the Interface
Region Imaging Spectrograph (IRIS). The study aims at providing
a better understanding of the physical processes driving these
ubiquitous small-scale eruptions. We also analysed images taken in the
extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA)
and line-of-sight magnetic-field data from the Helioseismic Magnetic
Imager (HMI) onboard the Solar Dynamics Observatory. As the observations
can only give an inkling about the possible physical processes at play,
we also employed a non-linear force-free field (NLFFF) relaxation
approach based on the HMI magnetogram time series. Furthermore, we
computed the squashing factor, Q, in different horizontal planes of
the NLFFF model. This allowed us to further investigate the evolution
of the magnetic-field structures involved in the eruption process.

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Title: Effects of Initial Conditions on Magnetic Reconnection in a
Solar Transient
Authors: Agarwal, Satyam; Bhattacharyya, Ramit; Wiegelmann, Thomas
2022SoPh..297...91A Altcode:
Coronal magnetic field extrapolations are necessary to understand
the magnetic field morphology of the source region in solar coronal
transients. The extrapolation models are broadly classified into
nonforce-free and force-free, depending on whether the model allows
for a Lorentz force or not. Presently, these models are employed
to carry out state-of-the-art data-driven and data-constrained
magnetohydrodynamics (MHD) simulations to explore magnetic reconnection
(MR)—the underlying cause of the transients. It is then imperative
to study the influence of different extrapolation models on simulated
evolution. For this purpose, the numerical model EULAG-MHD is employed
to carry out simulations with different initial magnetic and velocity
fields obtained through nonforce-free and force-free extrapolations. The
selected active region is NOAA 11977, hosting a C6.6 class eruptive
flare. Both extrapolations are found to be in good agreement with
the observed line-of-sight and transverse magnetic fields. Further,
a morphological comparison on the global scale and particularly for
selected topologies, such as a magnetic null point and a hyperbolic flux
tube (HFT), suggests that similar magnetic field line structures are
reproducible in both models, although the extent of agreement between
the two varies. Astoundingly, generation of a three-dimensional
null near the HFT is observed in all the simulations, inferring
the evolution to be independent of the particular initial field
configuration. Moreover, the magnetic field lines (MFLs) undergoing
MRs at the null point and HFT evolve similarly, further confirming
the near independence of reconnection details on the chosen initial
conditions. Consequently, both the extrapolation techniques can be
suitable for initiating data-driven and data-constrained simulations.

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Title: Active region chromospheric magnetic fields. Observational
inference versus magnetohydrostatic modelling
Authors: Vissers, G. J. M.; Danilovic, S.; Zhu, X.; Leenaarts, J.;
Díaz Baso, C. J.; da Silva Santos, J. M.; de la Cruz Rodríguez,
J.; Wiegelmann, T.
2022A&A...662A..88V Altcode: 2021arXiv210902943V
Context. A proper estimate of the chromospheric magnetic fields is
thought to improve modelling of both active region and coronal mass
ejection evolution. However, because the chromospheric field is not
regularly obtained for sufficiently large fields of view, estimates
thereof are commonly obtained through data-driven models or field
extrapolations, based on photospheric boundary conditions alone and
involving pre-processing that may reduce details and dynamic range in
the magnetograms. Aims: We investigate the similarity between
the chromospheric magnetic field that is directly inferred from
observations and the field obtained from a magnetohydrostatic (MHS)
extrapolation based on a high-resolution photospheric magnetogram. Methods: Based on Swedish 1-m Solar Telescope Fe I 6173 Å and
Ca II 8542 Å observations of NOAA active region 12723, we employed
the spatially regularised weak-field approximation (WFA) to derive
the vector magnetic field in the chromosphere from Ca II, as well as
non-local thermodynamic equilibrium (non-LTE) inversions of Fe I and Ca
II to infer a model atmosphere for selected regions. Milne-Eddington
inversions of Fe I serve as photospheric boundary conditions for the
MHS model that delivers the three-dimensional field, gas pressure,
and density self-consistently. Results: For the line-of-sight
component, the MHS chromospheric field generally agrees with the
non-LTE inversions and WFA, but tends to be weaker by 16% on average
than these when larger in magnitude than 300 G. The observationally
inferred transverse component is systematically stronger, up to an
order of magnitude in magnetically weaker regions, but the qualitative
distribution with height is similar to the MHS results. For either
field component, the MHS chromospheric field lacks the fine structure
derived from the inversions. Furthermore, the MHS model does not
recover the magnetic imprint from a set of high fibrils connecting
the main polarities. Conclusions: The MHS extrapolation and
WFA provide a qualitatively similar chromospheric field, where the
azimuth of the former is better aligned with Ca II 8542 Å fibrils than
that of the WFA, especially outside strong-field concentrations. The
amount of structure as well as the transverse field strengths are,
however, underestimated by the MHS extrapolation. This underscores the
importance of considering a chromospheric magnetic field constraint in
data-driven modelling of active regions, particularly in the context
of space weather predictions.

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Title: Eruptions from coronal bright points: A spectroscopic
view by IRIS of a mini-filament eruption, QSL reconnection, and
reconnection-driven outflows
Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus;
Wiegelmann, Thomas; Xie, Haixia
2022A&A...660A..45M Altcode: 2022arXiv220200370M
Context. Our study investigates a mini-filament eruption associated with
cancelling magnetic fluxes. The eruption originates from a small-scale
loop complex commonly known as a coronal bright point (CBP). The
event is uniquely recorded in both the imaging and spectroscopic data
taken with the Interface Region Imaging Spectrograph (IRIS). 
Aims: The investigation aims to gain a better understanding of the
physical processes driving these ubiquitous small-scale eruptions. Methods: We analysed IRIS spectroscopic and slit-jaw imaging
observations as well as images taken in the extreme-ultraviolet
channels of the Atmospheric Imaging Assembly (AIA) and line-of-sight
magnetic-field data from the Helioseismic Magnetic Imager (HMI) on
board the Solar Dynamics Observatory. As the observations can only
indicate the possible physical processes at play, we also employed a
non-linear force-free field (NLFFF) relaxation approach based on the
HMI magnetogram time series. This allowed us to further investigate
the evolution of the magnetic-field structures involved in the eruption
process. Results: We identified a strong small-scale brightening
as a micro-flare in a CBP, recorded in emission from chromospheric to
flaring plasmas. The mini-eruption is manifested via the ejection of hot
(CBP loops) and cool (mini-filament) plasma recorded in both the imaging
and spectroscopic data. The micro-flare is preceded by the appearance
of an elongated bright feature in the IRIS slit-jaw 1400 Å images,
located above the polarity inversion line. The micro-flare starts
with an IRIS pixel size brightening and propagates bi-directionally
along the elongated feature. We detected, in both the spectral and
imaging IRIS data and AIA data, strong flows along and at the edges of
the elongated feature; we believe that these represent reconnection
outflows. Both edges of the elongated feature that wrap around the
edges of the erupting MF evolve into a J-type shape, creating a
sigmoid appearance. A quasi-separatrix layer (QSL) is identified in
the vicinity of the polarity inversion line by computing the squashing
factor, Q, in different horizontal planes of the NLFFF model. 
Conclusions: This CBP spectro-imaging study provides further evidence
that CBPs represent downscaled active regions and, as such, they may
make a significant contribution to the mass and energy balance of
the solar atmosphere. They are the sources of all range of typical
active-region features, including magnetic reconnection along QSLs,
(mini-)filament eruptions, (micro-)flaring, reconnection outflows,
etc. The QSL reconnection site has the same spectral appearance
as the so-called explosive events identified by strong blue- and
red-shifted emission, thus providing an answer to an outstanding
question regarding the true nature of this spectral phenomenon. Movies associated to Figs. A.1 and A.2 are available at <A
href="https://www.aanda.org/10.1051/0004-6361/202142439/olm">https://www.aanda.org</A>

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Title: Coronal magnetic field evolution over cycle 24
Authors: Chifu, I.; Inhester, B.; Wiegelmann, T.
2022A&A...659A.174C Altcode: 2022arXiv220103853C
Context. The photospheric magnetic field vector is continuously derived
from measurements, while reconstruction of the three-dimensional
(3D) coronal magnetic field requires modelling with photospheric
measurements as a boundary condition. For decades, the cycle variation
of the magnetic field in the photosphere has been investigated. Until
now, there has been no study of the evolution of the coronal magnetic
flux in the corona or of the evolution of solar cycle magnetic free
energy. Aims: The aim of this paper is to analyze the temporal
variation of the magnetic field and free magnetic energy in the solar
corona for solar cycle 24 and the behavior of the magnetic field in the
two hemispheres. We want to investigate whether or not we can obtain
better estimates of the magnetic field at Earth using the nonlinear
force-free field extrapolation method. Methods: To model the
magnetic field over cycle 24 we apply the nonlinear force-free field
(NLFFF) optimization method to the entire set of the synoptic vector
magnetic maps derived from observations made using the Heliospheric and
Magnetic Imager (HMI) on board Solar Dynamic Observatory (SDO). 
Results: From our results, we find that during solar cycle 24, the
maximum of the Sun's dynamics is different than the sunspot number
(SSN) maximum peak. The major contribution to the total unsigned flux
is provided by the flux coming from the magnetic field structures other
than sunspots (MSOS) within latitudes of −30° and +30°. The magnetic
flux variation during solar cycle 24 shows a different evolution in
the corona than in the photosphere. We find a correlation value of
0.8 between the derived magnetic energy from our model and the flare
energy index derived from observations. On average, cycle 24 had a
higher number of sunspots in the northern hemisphere (NH) but stronger
flux in the southern hemisphere (SH) which could more effectively
reach the higher layers of the atmosphere. The coupling between the
hemispheres increases with height. The strongest asymmetries in the
unsigned magnetic flux are between the two SSN peaks.

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Title: Magnetohydrostatic Modeling of the Solar Atmosphere
Authors: Zhu, Xiaoshuai; Neukirch, Thomas; Wiegelmann, Thomas
2022arXiv220315356Z Altcode:
Understanding structures and evolutions of the magnetic fields and
plasma in multiple layers on the Sun is very important. A force-free
magnetic field which is an accurate approximation of the solar corona
due to the low plasma $\beta$ has been widely studied and used
to model the coronal magnetic structure. While the force-freeness
assumption is well satisfied in the solar corona, the lower atmosphere
is not force-free given the high plasma $\beta$. Therefore, a
magnetohydrostatic (MHS) equilibrium which takes into account plasma
forces, such as pressure gradient and gravitational force, is considered
to be more appropriate to describe the lower atmosphere. This paper
reviews both analytical and numerical extrapolation methods based on
the MHS assumption for calculating the magnetic fields and plasma in
the solar atmosphere from measured magnetograms.

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Title: Multiwavelength Signatures of Episodic Nullpoint Reconnection
in a Quadrupolar Magnetic Configuration and the Cause of Failed Flux
Rope Eruption
Authors: Mitra, Prabir K.; Joshi, Bhuwan; Veronig, Astrid M.;
Wiegelmann, Thomas
2022ApJ...926..143M Altcode: 2021arXiv211214412M
In this paper, we present multiwavelength observations of the
triggering of a failed-eruptive M-class flare from active region
NOAA 11302 and investigate the possible reasons for the associated
failed eruption. Photospheric observations and nonlinear force-free
field extrapolated coronal magnetic field revealed that the flaring
region had a complex quadrupolar configuration with a preexisting
coronal nullpoint situated above the core field. Prior to the onset
of the M-class flare, we observed multiple periods of small-scale
flux enhancements in GOES and RHESSI soft X-ray observations from the
location of the nullpoint. The preflare configuration and evolution
reported here are similar to the configurations presented in the
breakout model, but at much lower coronal heights. The core of the
flaring region was characterized by the presence of two flux ropes in a
double-decker configuration. During the impulsive phase of the flare,
one of the two flux ropes initially started erupting, but resulted in
a failed eruption. Calculation of the magnetic decay index revealed a
saddle-like profile where the decay index initially increased to the
torus-unstable limits within the heights of the flux ropes, but then
decreased rapidly and reached negative values, which was most likely
responsible for the failed eruption of the initially torus-unstable
flux rope.

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Title: Toward a fast and consistent approach to modeling solar
magnetic fields in multiple layers
Authors: Zhu, X.; Wiegelmann, T.
2022A&A...658A..37Z Altcode: 2021arXiv210912789Z
 Aims: We aim to develop a fast and consistent extrapolation
method for modeling multiple layers of the solar atmosphere. Methods: The new approach combines the magnetohydrostatic (MHS)
extrapolation, which models the solar low atmosphere in a flat box,
together with the nonlinear force-free field (NLFFF) extrapolation,
which models the solar corona with a chromospheric vector magnetogram
deduced from the MHS extrapolation. We tested our code with a
snapshot of a radiative magnetohydrodynamic simulation of a solar
flare and we conducted quantitative comparisons based on several
metrics. Results: Following a number of test runs, we found
an optimized configuration for the combination of two extrapolations
with a 5.8-Mm-high box for the MHS extrapolation and a magnetogram at a
height of 1 Mm for the NLFFF extrapolation. The new approach under this
configuration has the capability to reconstruct the magnetic fields
in multi-layers accurately and efficiently. Based on figures of merit
that are used to assess the performance of different extrapolations
(NLFFF extrapolation, MHS extrapolation, and the combined one), we
find the combined extrapolation reaches the same level of accuracy
as the MHS extrapolation and they are both better than the NLFFF
extrapolation. The combined extrapolation is moderately efficient for
application to magnetograms with high resolution.

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Title: Solar force-free magnetic fields
Authors: Wiegelmann, Thomas; Sakurai, Takashi
2021LRSP...18....1W Altcode: 2012arXiv1208.4693W
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 non-magnetic forces such as plasma pressure gradients
and gravity can be neglected in the lowest order. This model assumption
is called the force-free field assumption, as the Lorentz force
vanishes. This can be obtained by either vanishing electric currents
(leading to potential fields) or the currents are co-aligned 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 so-called linear force-free field approximation. In the
generic case, however, the relationship 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 force-free 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 a large
area of research, as accurate measurements of the photospheric field
are available from ground-based observatories such as the Synoptic
Optical Long-term Investigations of the Sun and the Daniel K. Inouye
Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar
Dynamics Observatory. If we can obtain accurate force-free 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., EUV images of the radiating coronal plasma.

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Title: Linking the Sun to the Heliosphere Using Composition Data
and Modelling
Authors: Parenti, Susanna; Chifu, Iulia; Del Zanna, Giulio; Edmondson,
Justin; Giunta, Alessandra; Hansteen, Viggo H.; Higginson, Aleida;
Laming, J. Martin; Lepri, Susan T.; Lynch, Benjamin J.; Rivera, Yeimy
J.; von Steiger, Rudolf; Wiegelmann, Thomas; Wimmer-Schweingruber,
Robert F.; Zambrana Prado, Natalia; Pelouze, Gabriel
2021SSRv..217...78P Altcode: 2021arXiv211006111P
Our understanding of the formation and evolution of the corona and
the heliosphere is linked to our capability of properly interpret the
data from remote sensing and in-situ observations. In this respect,
being able to correctly connect in-situ observations with their source
regions on the Sun is the key for solving this problem. In this work
we aim at testing a diagnostics method for this connectivity.

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Title: Global coronal and heliospheric magnetic field modelling for
Solar Orbiter
Authors: Wiegelmann, Thomas; Neukirch, Thomas; Chifu, Iulia; Inhester,
Bernd
2021EGUGA..2311005W Altcode:
Computing the solar coronal magnetic field and plasmaenvironment
is an important research topic on it's own rightand also important
for space missions like Solar Orbiter toguide the analysis of
remote sensing and in-situ instruments.In the inner solar corona
plasma forces can be neglected andthe field is modelled under the
assumption of a vanishingLorentz-force. Further outwards (above
about two solar radii)plasma forces and the solar wind flow has to
be considered.Finally in the heliosphere one has to consider that the
Sunis rotating and the well known Parker-spiral forms.We have developed
codes based on optimization principlesto solve nonlinear force-free,
magneto-hydro-static andstationary MHD-equilibria. In the present
work we want toextend these methods by taking the solar rotation
into account.

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Title: Preprocessing of magnetograms for magnetohydrostatic
extrapolations
Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas; Inhester, Bernd
2021EGUGA..23.1973Z Altcode:
Magnetohydrostatic (MHS) extrapolations are developed to model 3D
magnetic fields and plasma structures in the solar low atmosphere by
using measured vector magnetic fields on the photosphere. However,
the photospheric magnetogram may be inconsistent with the MHS
assumption. By applying Gauss" theorem to an isolated active region,
we obtain a set of surface integrals of the magnetogram as criteria
for a MHS system. The integrals are a subset of Aly"s criteria for a
force-free field (FFF). Based on the new criteria, we preprocess the
magnetogram to make it more consistent with the MHS assumption and,
at the same time, close to the original data. As a byproduct, we also
find the boundary integral that is used to compute the energy of a
FFF usually underestimates the magnetic energy of an active region.

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Title: An overall view of temperature oscillations in the solar
chromosphere with ALMA
Authors: Jafarzadeh, S.; Wedemeyer, S.; Fleck, B.; Stangalini, M.;
Jess, D. B.; Morton, R. J.; Szydlarski, M.; Henriques, V. M. J.; Zhu,
X.; Wiegelmann, T.; Guevara Gómez, J. C.; Grant, S. D. T.; Chen,
B.; Reardon, K.; White, S. M.
2021RSPTA.37900174J Altcode: 2021RSTPA.379..174J; 2020arXiv201001918J
By direct measurements of the gas temperature, the Atacama Large
Millimeter/submillimeter Array (ALMA) has yielded a new diagnostic
tool to study the solar chromosphere. Here, we present an overview
of the brightness-temperature fluctuations from several high-quality
and high-temporal-resolution (i.e. 1 and 2 s cadence) time series
of images obtained during the first 2 years of solar observations
with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz)
and 1.25 mm (239 GHz), respectively. The various datasets represent
solar regions with different levels of magnetic flux. We perform
fast Fourier and Lomb-Scargle transforms to measure both the spatial
structuring of dominant frequencies and the average global frequency
distributions of the oscillations (i.e. averaged over the entire field
of view). We find that the observed frequencies significantly vary from
one dataset to another, which is discussed in terms of the solar regions
captured by the observations (i.e. linked to their underlying magnetic
topology). While the presence of enhanced power within the frequency
range 3-5 mHz is found for the most magnetically quiescent datasets,
lower frequencies dominate when there is significant influence from
strong underlying magnetic field concentrations (present inside and/or
in the immediate vicinity of the observed field of view). We discuss
here a number of reasons which could possibly contribute to the power
suppression at around 5.5 mHz in the ALMA observations. However,
it remains unclear how other chromospheric diagnostics (with an
exception of Hα line-core intensity) are unaffected by similar
effects, i.e. they show very pronounced 3-min oscillations dominating
the dynamics of the chromosphere, whereas only a very small fraction
of all the pixels in the 10 ALMA datasets analysed here show peak power
near 5.5 mHz. This article is part of the Theo Murphy meeting issue
`High-resolution wave dynamics in the lower solar atmosphere'.

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Title: Preprocessing of vector magnetograms for magnetohydrostatic
extrapolations
Authors: Zhu, X.; Wiegelmann, T.; Inhester, B.
2020A&A...644A..57Z Altcode: 2020arXiv201006174Z
Context. Understanding the 3D magnetic field as well as the plasma
in the chromosphere and transition region is important. One way is to
extrapolate the magnetic field and plasma from the routinely measured
vector magnetogram on the photosphere based on the assumption of the
magnetohydrostatic (MHS) state. However, photospheric data may be
inconsistent with the MHS assumption. Therefore, we must study the
restriction on the photospheric magnetic field, which is required by
the MHS system. Moreover, the data should be transformed accordingly
before MHS extrapolations can be applied. Aims: We aim to
obtain a set of surface integrals as criteria for the MHS system and
use this set of integrals to preprocess a vector magnetogram. 
Methods: By applying Gauss' theorem and assuming an isolated active
region on the Sun, we related the magnetic energy and forces in the
volume to the surface integral on the photosphere. The same method was
applied to obtain restrictions on the photospheric magnetic field as
necessary criteria for a MHS system. We used an optimization method to
preprocess the data to minimize the deviation from the criteria as well
as the measured value. Results: By applying the virial theorem
to the active region, we find the boundary integral that is used to
compute the energy of a force-free field usually underestimates the
magnetic energy of a large active region. We also find that the MHS
assumption only requires the x-, y-component of net Lorentz force and
the z-component of net torque to be zero. These zero components are part
of Aly's criteria for a force-free field. However, other components of
net force and torque can be non-zero values. According to new criteria,
we preprocess the magnetogram to make it more consistent with the MHS
system and, at the same time close, to the original data.

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Title: Coordination within the remote sensing payload on the Solar
Orbiter mission
Authors: Auchère, F.; Andretta, V.; Antonucci, E.; Bach, N.;
Battaglia, M.; Bemporad, A.; Berghmans, D.; Buchlin, E.; Caminade,
S.; Carlsson, M.; Carlyle, J.; Cerullo, J. J.; Chamberlin, P. C.;
Colaninno, R. C.; Davila, J. M.; De Groof, A.; Etesi, L.; Fahmy,
S.; Fineschi, S.; Fludra, A.; Gilbert, H. R.; Giunta, A.; Grundy,
T.; Haberreiter, M.; Harra, L. K.; Hassler, D. M.; Hirzberger, J.;
Howard, R. A.; Hurford, G.; Kleint, L.; Kolleck, M.; Krucker, S.;
Lagg, A.; Landini, F.; Long, D. M.; Lefort, J.; Lodiot, S.; Mampaey,
B.; Maloney, S.; Marliani, F.; Martinez-Pillet, V.; McMullin, D. R.;
Müller, D.; Nicolini, G.; Orozco Suarez, D.; Pacros, A.; Pancrazzi,
M.; Parenti, S.; Peter, H.; Philippon, A.; Plunkett, S.; Rich, N.;
Rochus, P.; Rouillard, A.; Romoli, M.; Sanchez, L.; Schühle, U.;
Sidher, S.; Solanki, S. K.; Spadaro, D.; St Cyr, O. C.; Straus, T.;
Tanco, I.; Teriaca, L.; Thompson, W. T.; del Toro Iniesta, J. C.;
Verbeeck, C.; Vourlidas, A.; Watson, C.; Wiegelmann, T.; Williams,
D.; Woch, J.; Zhukov, A. N.; Zouganelis, I.
2020A&A...642A...6A Altcode:
Context. To meet the scientific objectives of the mission, the Solar
Orbiter spacecraft carries a suite of in-situ (IS) and remote sensing
(RS) instruments designed for joint operations with inter-instrument
communication capabilities. Indeed, previous missions have shown that
the Sun (imaged by the RS instruments) and the heliosphere (mainly
sampled by the IS instruments) should be considered as an integrated
system rather than separate entities. Many of the advances expected
from Solar Orbiter rely on this synergistic approach between IS and
RS measurements. Aims: Many aspects of hardware development,
integration, testing, and operations are common to two or more
RS instruments. In this paper, we describe the coordination effort
initiated from the early mission phases by the Remote Sensing Working
Group. We review the scientific goals and challenges, and give an
overview of the technical solutions devised to successfully operate
these instruments together. Methods: A major constraint for the
RS instruments is the limited telemetry (TM) bandwidth of the Solar
Orbiter deep-space mission compared to missions in Earth orbit. Hence,
many of the strategies developed to maximise the scientific return from
these instruments revolve around the optimisation of TM usage, relying
for example on onboard autonomy for data processing, compression,
and selection for downlink. The planning process itself has been
optimised to alleviate the dynamic nature of the targets, and an
inter-instrument communication scheme has been implemented which can
be used to autonomously alter the observing modes. We also outline the
plans for in-flight cross-calibration, which will be essential to the
joint data reduction and analysis. Results: The RS instrument
package on Solar Orbiter will carry out comprehensive measurements
from the solar interior to the inner heliosphere. Thanks to the close
coordination between the instrument teams and the European Space
Agency, several challenges specific to the RS suite were identified
and addressed in a timely manner.

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Title: Models and data analysis tools for the Solar Orbiter mission
Authors: Rouillard, A. P.; Pinto, R. F.; Vourlidas, A.; De Groof, A.;
Thompson, W. T.; Bemporad, A.; Dolei, S.; Indurain, M.; Buchlin, E.;
Sasso, C.; Spadaro, D.; Dalmasse, K.; Hirzberger, J.; Zouganelis, I.;
Strugarek, A.; Brun, A. S.; Alexandre, M.; Berghmans, D.; Raouafi,
N. E.; Wiegelmann, T.; Pagano, P.; Arge, C. N.; Nieves-Chinchilla,
T.; Lavarra, M.; Poirier, N.; Amari, T.; Aran, A.; Andretta, V.;
Antonucci, E.; Anastasiadis, A.; Auchère, F.; Bellot Rubio, L.;
Nicula, B.; Bonnin, X.; Bouchemit, M.; Budnik, E.; Caminade, S.;
Cecconi, B.; Carlyle, J.; Cernuda, I.; Davila, J. M.; Etesi, L.;
Espinosa Lara, F.; Fedorov, A.; Fineschi, S.; Fludra, A.; Génot,
V.; Georgoulis, M. K.; Gilbert, H. R.; Giunta, A.; Gomez-Herrero, R.;
Guest, S.; Haberreiter, M.; Hassler, D.; Henney, C. J.; Howard, R. A.;
Horbury, T. S.; Janvier, M.; Jones, S. I.; Kozarev, K.; Kraaikamp,
E.; Kouloumvakos, A.; Krucker, S.; Lagg, A.; Linker, J.; Lavraud,
B.; Louarn, P.; Maksimovic, M.; Maloney, S.; Mann, G.; Masson, A.;
Müller, D.; Önel, H.; Osuna, P.; Orozco Suarez, D.; Owen, C. J.;
Papaioannou, A.; Pérez-Suárez, D.; Rodriguez-Pacheco, J.; Parenti,
S.; Pariat, E.; Peter, H.; Plunkett, S.; Pomoell, J.; Raines, J. M.;
Riethmüller, T. L.; Rich, N.; Rodriguez, L.; Romoli, M.; Sanchez,
L.; Solanki, S. K.; St Cyr, O. C.; Straus, T.; Susino, R.; Teriaca,
L.; del Toro Iniesta, J. C.; Ventura, R.; Verbeeck, C.; Vilmer, N.;
Warmuth, A.; Walsh, A. P.; Watson, C.; Williams, D.; Wu, Y.; Zhukov,
A. N.
2020A&A...642A...2R Altcode:
Context. The Solar Orbiter spacecraft will be equipped with a wide
range of remote-sensing (RS) and in situ (IS) instruments to record
novel and unprecedented measurements of the solar atmosphere and
the inner heliosphere. To take full advantage of these new datasets,
tools and techniques must be developed to ease multi-instrument and
multi-spacecraft studies. In particular the currently inaccessible
low solar corona below two solar radii can only be observed
remotely. Furthermore techniques must be used to retrieve coronal
plasma properties in time and in three dimensional (3D) space. Solar
Orbiter will run complex observation campaigns that provide interesting
opportunities to maximise the likelihood of linking IS data to their
source region near the Sun. Several RS instruments can be directed
to specific targets situated on the solar disk just days before
data acquisition. To compare IS and RS, data we must improve our
understanding of how heliospheric probes magnetically connect to the
solar disk. Aims: The aim of the present paper is to briefly
review how the current modelling of the Sun and its atmosphere
can support Solar Orbiter science. We describe the results of a
community-led effort by European Space Agency's Modelling and Data
Analysis Working Group (MADAWG) to develop different models, tools,
and techniques deemed necessary to test different theories for the
physical processes that may occur in the solar plasma. The focus here
is on the large scales and little is described with regards to kinetic
processes. To exploit future IS and RS data fully, many techniques have
been adapted to model the evolving 3D solar magneto-plasma from the
solar interior to the solar wind. A particular focus in the paper is
placed on techniques that can estimate how Solar Orbiter will connect
magnetically through the complex coronal magnetic fields to various
photospheric and coronal features in support of spacecraft operations
and future scientific studies. Methods: Recent missions such as
STEREO, provided great opportunities for RS, IS, and multi-spacecraft
studies. We summarise the achievements and highlight the challenges
faced during these investigations, many of which motivated the Solar
Orbiter mission. We present the new tools and techniques developed
by the MADAWG to support the science operations and the analysis of
the data from the many instruments on Solar Orbiter. Results:
This article reviews current modelling and tool developments that ease
the comparison of model results with RS and IS data made available
by current and upcoming missions. It also describes the modelling
strategy to support the science operations and subsequent exploitation
of Solar Orbiter data in order to maximise the scientific output
of the mission. Conclusions: The on-going community effort
presented in this paper has provided new models and tools necessary
to support mission operations as well as the science exploitation of
the Solar Orbiter data. The tools and techniques will no doubt evolve
significantly as we refine our procedure and methodology during the
first year of operations of this highly promising mission.

---------------------------------------------------------
Title: The Solar Orbiter Science Activity Plan. Translating solar
and heliospheric physics questions into action
Authors: Zouganelis, I.; De Groof, A.; Walsh, A. P.; Williams, D. R.;
Müller, D.; St Cyr, O. C.; Auchère, F.; Berghmans, D.; Fludra,
A.; Horbury, T. S.; Howard, R. A.; Krucker, S.; Maksimovic, M.;
Owen, C. J.; Rodríguez-Pacheco, J.; Romoli, M.; Solanki, S. K.;
Watson, C.; Sanchez, L.; Lefort, J.; Osuna, P.; Gilbert, H. R.;
Nieves-Chinchilla, T.; Abbo, L.; Alexandrova, O.; Anastasiadis, A.;
Andretta, V.; Antonucci, E.; Appourchaux, T.; Aran, A.; Arge, C. N.;
Aulanier, G.; Baker, D.; Bale, S. D.; Battaglia, M.; Bellot Rubio,
L.; Bemporad, A.; Berthomier, M.; Bocchialini, K.; Bonnin, X.; Brun,
A. S.; Bruno, R.; Buchlin, E.; Büchner, J.; Bucik, R.; Carcaboso,
F.; Carr, R.; Carrasco-Blázquez, I.; Cecconi, B.; Cernuda Cangas, I.;
Chen, C. H. K.; Chitta, L. P.; Chust, T.; Dalmasse, K.; D'Amicis, R.;
Da Deppo, V.; De Marco, R.; Dolei, S.; Dolla, L.; Dudok de Wit, T.;
van Driel-Gesztelyi, L.; Eastwood, J. P.; Espinosa Lara, F.; Etesi,
L.; Fedorov, A.; Félix-Redondo, F.; Fineschi, S.; Fleck, B.; Fontaine,
D.; Fox, N. J.; Gandorfer, A.; Génot, V.; Georgoulis, M. K.; Gissot,
S.; Giunta, A.; Gizon, L.; Gómez-Herrero, R.; Gontikakis, C.; Graham,
G.; Green, L.; Grundy, T.; Haberreiter, M.; Harra, L. K.; Hassler,
D. M.; Hirzberger, J.; Ho, G. C.; Hurford, G.; Innes, D.; Issautier,
K.; James, A. W.; Janitzek, N.; Janvier, M.; Jeffrey, N.; Jenkins,
J.; Khotyaintsev, Y.; Klein, K. -L.; Kontar, E. P.; Kontogiannis,
I.; Krafft, C.; Krasnoselskikh, V.; Kretzschmar, M.; Labrosse, N.;
Lagg, A.; Landini, F.; Lavraud, B.; Leon, I.; Lepri, S. T.; Lewis,
G. R.; Liewer, P.; Linker, J.; Livi, S.; Long, D. M.; Louarn, P.;
Malandraki, O.; Maloney, S.; Martinez-Pillet, V.; Martinovic, M.;
Masson, A.; Matthews, S.; Matteini, L.; Meyer-Vernet, N.; Moraitis,
K.; Morton, R. J.; Musset, S.; Nicolaou, G.; Nindos, A.; O'Brien,
H.; Orozco Suarez, D.; Owens, M.; Pancrazzi, M.; Papaioannou, A.;
Parenti, S.; Pariat, E.; Patsourakos, S.; Perrone, D.; Peter, H.;
Pinto, R. F.; Plainaki, C.; Plettemeier, D.; Plunkett, S. P.; Raines,
J. M.; Raouafi, N.; Reid, H.; Retino, A.; Rezeau, L.; Rochus, P.;
Rodriguez, L.; Rodriguez-Garcia, L.; Roth, M.; Rouillard, A. P.;
Sahraoui, F.; Sasso, C.; Schou, J.; Schühle, U.; Sorriso-Valvo, L.;
Soucek, J.; Spadaro, D.; Stangalini, M.; Stansby, D.; Steller, M.;
Strugarek, A.; Štverák, Š.; Susino, R.; Telloni, D.; Terasa, C.;
Teriaca, L.; Toledo-Redondo, S.; del Toro Iniesta, J. C.; Tsiropoula,
G.; Tsounis, A.; Tziotziou, K.; Valentini, F.; Vaivads, A.; Vecchio,
A.; Velli, M.; Verbeeck, C.; Verdini, A.; Verscharen, D.; Vilmer, N.;
Vourlidas, A.; Wicks, R.; Wimmer-Schweingruber, R. F.; Wiegelmann,
T.; Young, P. R.; Zhukov, A. N.
2020A&A...642A...3Z Altcode: 2020arXiv200910772Z
Solar Orbiter is the first space mission observing the solar plasma
both in situ and remotely, from a close distance, in and out of the
ecliptic. The ultimate goal is to understand how the Sun produces
and controls the heliosphere, filling the Solar System and driving
the planetary environments. With six remote-sensing and four in-situ
instrument suites, the coordination and planning of the operations are
essential to address the following four top-level science questions:
(1) What drives the solar wind and where does the coronal magnetic field
originate?; (2) How do solar transients drive heliospheric variability?;
(3) How do solar eruptions produce energetic particle radiation that
fills the heliosphere?; (4) How does the solar dynamo work and drive
connections between the Sun and the heliosphere? Maximising the
mission's science return requires considering the characteristics
of each orbit, including the relative position of the spacecraft
to Earth (affecting downlink rates), trajectory events (such
as gravitational assist manoeuvres), and the phase of the solar
activity cycle. Furthermore, since each orbit's science telemetry
will be downloaded over the course of the following orbit, science
operations must be planned at mission level, rather than at the level
of individual orbits. It is important to explore the way in which those
science questions are translated into an actual plan of observations
that fits into the mission, thus ensuring that no opportunities are
missed. First, the overarching goals are broken down into specific,
answerable questions along with the required observations and the
so-called Science Activity Plan (SAP) is developed to achieve this. The
SAP groups objectives that require similar observations into Solar
Orbiter Observing Plans, resulting in a strategic, top-level view of
the optimal opportunities for science observations during the mission
lifetime. This allows for all four mission goals to be addressed. In
this paper, we introduce Solar Orbiter's SAP through a series of
examples and the strategy being followed.

---------------------------------------------------------
Title: An Optimization Principle for Computing Stationary MHD
Equilibria with Solar Wind Flow
Authors: Wiegelmann, Thomas; Neukirch, Thomas; Nickeler, Dieter H.;
Chifu, Iulia
2020SoPh..295..145W Altcode: 2020arXiv201002945W
In this work we describe a numerical optimization method for computing
stationary MHD equilibria. The newly developed code is based on a
nonlinear force-free optimization principle. We apply our code to
model the solar corona using synoptic vector magnetograms as boundary
condition. Below about two solar radii the plasma β and Alfvén Mach
number MA are small and the magnetic field configuration
of stationary MHD is basically identical to a nonlinear force-free
field, whereas higher up in the corona (where β and MA are
above unity) plasma and flow effects become important and stationary
MHD and force-free configuration deviate significantly. The new
method allows for the reconstruction of the coronal magnetic field
further outwards than with potential field, nonlinear force-free or
magnetostatic models. This way the model might help to provide the
magnetic connectivity for joint observations of remote sensing and
in-situ instruments on Solar Orbiter and Parker Solar Probe.

---------------------------------------------------------
Title: PMI: The Photospheric Magnetic Field Imager
Authors: Staub, Jan; Fernandez-Rico, German; Gandorfer, Achim; Gizon,
Laurent; Hirzberger, Johann; Kraft, Stefan; Lagg, Andreas; Schou,
Jesper; Solanki, Sami K.; del Toro Iniesta, Jose Carlos; Wiegelmann,
Thomas; Woch, Joachim
2020JSWSC..10...54S Altcode:
We describe the design and the capabilities of the Photospheric Magnetic
field Imager (PMI), a compact and lightweight vector magnetograph,
which is being developed for ESA's Lagrange mission to the Lagrange
L5 point. After listing the design requirements and give a scientific
justification for them, we describe the technical implementation and
the design solution capable of fulfilling these requirements. This is
followed by a description of the hardware architecture as well as the
operations principle. An outlook on the expected performance concludes
the paper.

---------------------------------------------------------
Title: The Solar Orbiter EUI instrument: The Extreme Ultraviolet
Imager
Authors: Rochus, P.; Auchère, F.; Berghmans, D.; Harra, L.; Schmutz,
W.; Schühle, U.; Addison, P.; Appourchaux, T.; Aznar Cuadrado,
R.; Baker, D.; Barbay, J.; Bates, D.; BenMoussa, A.; Bergmann, M.;
Beurthe, C.; Borgo, B.; Bonte, K.; Bouzit, M.; Bradley, L.; Büchel,
V.; Buchlin, E.; Büchner, J.; Cabé, F.; Cadiergues, L.; Chaigneau,
M.; Chares, B.; Choque Cortez, C.; Coker, P.; Condamin, M.; Coumar,
S.; Curdt, W.; Cutler, J.; Davies, D.; Davison, G.; Defise, J. -M.;
Del Zanna, G.; Delmotte, F.; Delouille, V.; Dolla, L.; Dumesnil, C.;
Dürig, F.; Enge, R.; François, S.; Fourmond, J. -J.; Gillis, J. -M.;
Giordanengo, B.; Gissot, S.; Green, L. M.; Guerreiro, N.; Guilbaud,
A.; Gyo, M.; Haberreiter, M.; Hafiz, A.; Hailey, M.; Halain, J. -P.;
Hansotte, J.; Hecquet, C.; Heerlein, K.; Hellin, M. -L.; Hemsley, S.;
Hermans, A.; Hervier, V.; Hochedez, J. -F.; Houbrechts, Y.; Ihsan,
K.; Jacques, L.; Jérôme, A.; Jones, J.; Kahle, M.; Kennedy, T.;
Klaproth, M.; Kolleck, M.; Koller, S.; Kotsialos, E.; Kraaikamp, E.;
Langer, P.; Lawrenson, A.; Le Clech', J. -C.; Lenaerts, C.; Liebecq,
S.; Linder, D.; Long, D. M.; Mampaey, B.; Markiewicz-Innes, D.;
Marquet, B.; Marsch, E.; Matthews, S.; Mazy, E.; Mazzoli, A.; Meining,
S.; Meltchakov, E.; Mercier, R.; Meyer, S.; Monecke, M.; Monfort,
F.; Morinaud, G.; Moron, F.; Mountney, L.; Müller, R.; Nicula, B.;
Parenti, S.; Peter, H.; Pfiffner, D.; Philippon, A.; Phillips, I.;
Plesseria, J. -Y.; Pylyser, E.; Rabecki, F.; Ravet-Krill, M. -F.;
Rebellato, J.; Renotte, E.; Rodriguez, L.; Roose, S.; Rosin, J.;
Rossi, L.; Roth, P.; Rouesnel, F.; Roulliay, M.; Rousseau, A.; Ruane,
K.; Scanlan, J.; Schlatter, P.; Seaton, D. B.; Silliman, K.; Smit,
S.; Smith, P. J.; Solanki, S. K.; Spescha, M.; Spencer, A.; Stegen,
K.; Stockman, Y.; Szwec, N.; Tamiatto, C.; Tandy, J.; Teriaca, L.;
Theobald, C.; Tychon, I.; van Driel-Gesztelyi, L.; Verbeeck, C.;
Vial, J. -C.; Werner, S.; West, M. J.; Westwood, D.; Wiegelmann, T.;
Willis, G.; Winter, B.; Zerr, A.; Zhang, X.; Zhukov, A. N.
2020A&A...642A...8R Altcode:
Context. The Extreme Ultraviolet Imager (EUI) is part of the remote
sensing instrument package of the ESA/NASA Solar Orbiter mission
that will explore the inner heliosphere and observe the Sun from
vantage points close to the Sun and out of the ecliptic. Solar Orbiter
will advance the "connection science" between solar activity and the
heliosphere. Aims: With EUI we aim to improve our understanding
of the structure and dynamics of the solar atmosphere, globally as well
as at high resolution, and from high solar latitude perspectives. 
Methods: The EUI consists of three telescopes, the Full Sun Imager and
two High Resolution Imagers, which are optimised to image in Lyman-α
and EUV (17.4 nm, 30.4 nm) to provide a coverage from chromosphere
up to corona. The EUI is designed to cope with the strong constraints
imposed by the Solar Orbiter mission characteristics. Limited telemetry
availability is compensated by state-of-the-art image compression,
onboard image processing, and event selection. The imposed power
limitations and potentially harsh radiation environment necessitate
the use of novel CMOS sensors. As the unobstructed field of view of
the telescopes needs to protrude through the spacecraft's heat shield,
the apertures have been kept as small as possible, without compromising
optical performance. This led to a systematic effort to optimise the
throughput of every optical element and the reduction of noise levels
in the sensor. Results: In this paper we review the design
of the two elements of the EUI instrument: the Optical Bench System
and the Common Electronic Box. Particular attention is also given to
the onboard software, the intended operations, the ground software,
and the foreseen data products. Conclusions: The EUI will
bring unique science opportunities thanks to its specific design,
its viewpoint, and to the planned synergies with the other Solar
Orbiter instruments. In particular, we highlight science opportunities
brought by the out-of-ecliptic vantage point of the solar poles,
the high-resolution imaging of the high chromosphere and corona,
and the connection to the outer corona as observed by coronagraphs.

---------------------------------------------------------
Title: Eruptive-Impulsive Homologous M-class Flares Associated with
Double-decker Flux Rope Configuration in Minisigmoid of NOAA 12673
Authors: Mitra, Prabir K.; Joshi, Bhuwan; Veronig, Astrid M.; Chandra,
Ramesh; Dissauer, K.; Wiegelmann, Thomas
2020ApJ...900...23M Altcode: 2020arXiv200711810M
We present a multiwavelength analysis of two homologous, short-lived,
impulsive flares of GOES class M1.4 and M7.3 that occurred from a very
localized minisigmoid region within the active region NOAA 12673 on
2017 September 7. Both flares were associated with initial jetlike
plasma ejection that for a brief amount of time moved toward the east
in a collimated manner before drastically changing direction toward
the southwest. Nonlinear force-free field extrapolation reveals the
presence of a compact double-decker flux rope configuration in the
minisigmoid region prior to the flares. A set of open field lines
originating near the active region that were most likely responsible
for the anomalous dynamics of the erupted plasma gave the earliest
indication of an emerging coronal hole near the active region. The
horizontal field distribution suggests a rapid decay of the field
above the active region, implying high proneness of the flux rope
system toward eruption. In view of the low coronal double-decker flux
ropes and compact extreme ultraviolet brightening beneath the filament,
along with associated photospheric magnetic field changes, our analysis
supports the combination of initial tether-cutting reconnection and
subsequent torus instability for driving the eruption.

---------------------------------------------------------
Title: Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX
vector magnetogram
Authors: Zhu, X.; Wiegelmann, T.; Solanki, S. K.
2020A&A...640A.103Z Altcode: 2020arXiv200514332Z
Context. High-resolution magnetic field measurements are routinely
only done in the solar photosphere. Higher layers, such as the
chromosphere and corona, can be modeled by extrapolating these
photospheric magnetic field vectors upward. In the solar corona,
plasma forces can be neglected and the Lorentz force vanishes. This
is not the case in the upper photosphere and chromosphere where
magnetic and nonmagnetic forces are equally important. One way to
deal with this problem is to compute the plasma and magnetic field
self-consistently, in lowest order with a magnetohydrostatic (MHS)
model. The non-force-free layer is rather thin and MHS models require
high-resolution photospheric magnetic field measurements as the lower
boundary condition. Aims: We aim to derive the magnetic field,
plasma pressure, and density of AR11768 by applying the newly developed
extrapolation technique to the SUNRISE/IMaX data embedded in SDO/HMI
magnetogram. Methods: We used an optimization method for the MHS
modeling. The initial conditions consist of a nonlinear force-free field
(NLFFF) and a gravity-stratified atmosphere. During the optimization
procedure, the magnetic field, plasma pressure, and density are computed
self-consistently. Results: In the non-force-free layer, which
is spatially resolved by the new code, Lorentz forces are effectively
balanced by the gas pressure gradient force and gravity force. The
pressure and density are depleted in strong field regions, which is
consistent with observations. Denser plasma, however, is also observed
at some parts of the active region edges. In the chromosphere, the
fibril-like plasma structures trace the magnetic field nicely. Bright
points in SUNRISE/SuFI 3000 Å images are often accompanied by the
plasma pressure and electric current concentrations. In addition, the
average of angle between MHS field lines and the selected chromospheric
fibrils is 11.8°, which is smaller than those computed from the NLFFF
model (15.7°) and linear MHS model (20.9°). This indicates that the
MHS solution provides a better representation of the magnetic field
in the chromosphere.

---------------------------------------------------------
Title: Magnetohydrostatic modelling of the solar atmosphere: Test
and application
Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas
2020EGUGA..22.2695Z Altcode:
Both magnetic field and plasma play important roles in activities in
the solar atmosphere. Unfortunately only the magnetic fields in the
photosphere are routinely measured precisely. We aim to extrapolate
these photospheric vector magnetograms upwards into the solar
atmosphere. In this work we are mainly interested in reconstructing the
upper solar photosphere and chromosphere. In these layers magnetic
and non-magnetic forces are equally important. Consequently we
have to compute an equilibrium of plasma and magnetic forces with a
magnetohydrostatic model. A optimization approach which minimize a
functional defined by the magnetohydrostatic equations is used in the
model. In this talk/poster, I will present a strict test of the new
code with a radiative MHD simulation and its first application to a
high resolution vector magnetogram measured by SUNRISE/IMaX.

---------------------------------------------------------
Title: Relative magnetic helicity dissipation during the major flares
Authors: Wang, Quan; Yang, Shangbin; Zhang, Mei; Wiegelmann, Thomas
2020EGUGA..2218835W Altcode:
Magnetic helicity is conserved in ideal magnetic fluid and is still
approximately conserved in the process of fast magnetic reconnection
when the magnetic Reynolds number is large enough. We can derive the
magnetic helicity injecting into corona from the magnetic helicity
flux through photoshpere. A statistical research is carried out to
investigate the dissipation of magnetic helicity during the major
flares. We choose 69M-up flares from 16 major flare-productive active
regions in 24th cycle to research the helicity in corona. Among these
flares, 19 is X-up flares. We utilize Differential Affine Velocity
Estimator for Vector Magnetograms (DAVE4VM) and 12-min successive vector
magnetograms from Helioseismic and Magnetic Imager (HMI) on board
the Solar Dynamics Observatory (SDO) to derive the flux of magnetic
helicity through photosphere. At the same time, we extrapolate the
vector magnetic field in corona to calculate the relative helicity by
the suppose of Non-linear Force Free Field (NLFFF). The calculation
window is 12-18 minutes before and after flares. A well correlation
is shown between the magnetic free energy and magnetic helicity, the
threshold of triggering M-up flare is the change of magnetic helicity
above 2×1042Mx2 and the change of magnetic free energy above 3 ×
1031erg . Considering one fifth of magnetic helicity injecting into
corona, the dissipation of magnetic helicity during the flares is
6-7 %, which is corresponding to the result of previous numerical
simulation results, which strongly support that the magnetic helicity
is approximate conserved during the major flares.

---------------------------------------------------------
Title: An optimization principle for computing stationary MHD
equilibria with solar wind flow
Authors: Wiegelmann, Thomas; Neukirch, Thomas; Nickeler, Dieter;
Chifu, Iulia
2020EGUGA..22.3029W Altcode:
Knowledge about the magnetic field and plasma environment
is importantfor almost all physical processes in the solar
atmosphere. Precisemeasurements of the magnetic field vector are done
routinely only inthe photosphere, e.g. by SDO/HMI. These measurements
are used asboundary condition for modelling the solar chromosphere
and corona,whereas some model assumptions have to be made. In the
low-plasma-betacorona the Lorentz-force vanishes and the magnetic
fieldis reconstructed with a nonlinear force-free model. In the
mixed-betachromosphere plasma forces have to be taken into account
with thehelp of a magnetostatic model. And finally for modelling the
globalcorona far beyond the source surface the solar wind flow has tobe
incorporated within a stationary MHD model.To do so, we generalize
a nonlinear force-free and magneto-static optimizationcode by the
inclusion of a field aligned compressible plasma flow.Applications
are the implementation of the solar wind onglobal scale. This allows
to reconstruct the coronal magnetic field furtheroutwards than with
potential field, nonlinear force-free and magneto-static models.This way
the model might help in future to provide the magnetic connectivityfor
joint observations of remote sensing and in-situ instruments on
SolarOrbiter and Parker Solar Probe.

---------------------------------------------------------
Title: The SO/PHI instrument on Solar Orbiter and its data products
Authors: Solanki, Sami K.; Hirzberger, Johann; Wiegelmann, Thomas;
Gandorfer, Achim; Woch, Joachim; del Toro Iniesta, José Carlos
2020EGUGA..2217904S Altcode:
A central instrument of Solar Orbiter is the Polarimetric and
Helioseismic Imager, SO/PHI. It is a vector magnetograph that also
provides data for helioseismology. SO/PHI is composed of two telescopes,
a full-disk telescope (FDT) and a high-resolution telescope (HRT). The
HRT will observe at a resolution as high as 200 km on the solar
surface, while the FDT will obtain the magnetic field and velocity of
the full solar disc whenever it observes. SO/PHI will be the first
solar spectro-polarimeter to leave the Sun-Earth line, opening up
some unique perspectives, such as the first detailed view of the solar
poles. This will allow not just a more precise and exact mapping of the
polar magnetic field than possible so far, but will also enable us to
follow the dynamics of individual magnetic features at high latitudes
and to determine solar surface and sub-surface flows right up to the
poles. In addition to its standard data products (vector magnetograms,
continuum images and maps of the line-of-sight velocity), SO/PHI will
also provide higher-level data products. These will include synoptic
charts, local magnetic field extrapolations starting from HRT data and
global magnetic field extrapolations (from FDT data) with potential
field source-surface (PFSS) models and possibly also non-potential
models such as NLFFF (non-linear force-free fields), magnetostatics
and MHD. The SO/PHI data products will usefully complement the data
taken by other instruments on Solar Orbiter and on Solar Probe, as
well as instruments on the ground or in Earth orbit. Combining with
observations by Earth-based and near-Earth telescopes will enable
new types of investigations, such as stereoscopic polarimetry and
stereoscopic helioseismology.

---------------------------------------------------------
Title: Analytical Three-dimensional Magnetohydrostatic Equilibrium
Solutions for Magnetic Field Extrapolation Allowing a Transition
from Non-force-free to Force-free Magnetic Fields
Authors: Neukirch, Thomas; Wiegelmann, Thomas
2019SoPh..294..171N Altcode: 2019arXiv191111084N
For the extrapolation of magnetic fields into the solar corona from
measurements taken in the photosphere (or chromosphere) force-free
magnetic fields are typically used. This does not take into account that
the lower layers of the solar atmosphere are not force-free. While
some numerical extrapolation methods using magnetohydrostatic
magnetic fields have been suggested, a complementary and numerically
comparatively cheap method is to use analytical magnetohydrostatic
equilibria to extrapolate the magnetic field. In this paper, we
present a new family of solutions for a special class of analytical
three-dimensional magnetohydrostatic equilibria, which can be of use
for such magnetic field extrapolation. The new solutions allow for the
more flexible modeling of a transition from non-force-free to (linear)
force-free magnetic fields. In particular, the height and width of the
region where this transition takes place can be specified by choosing
appropriate model parameters.

---------------------------------------------------------
Title: Testing magnetohydrostatic extrapolation with radiative MHD
simulation of a solar flare
Authors: Zhu, X.; Wiegelmann, T.
2019A&A...631A.162Z Altcode: 2019arXiv191003523Z
Context. On the sun, the magnetic field vector is measured routinely
solely in the photosphere. By using these photospheric measurements as a
boundary condition, we developed magnetohydrostatic (MHS) extrapolation
to model the solar atmosphere. The model makes assumptions about the
relative importance of magnetic and non-magnetic forces. While the
solar corona is force-free, this is not the case with regard to the
photosphere and chromosphere. Aims: The model has previously been
tested with an exact equilibria. Here we present a more challenging and
more realistic test of our model with the radiative magnetohydrodynamic
simulation of a solar flare. Methods: By using the optimization
method, the MHS model computes the magnetic field, plasma pressure
and density self-consistently. The nonlinear force-free field (NLFFF)
and gravity-stratified atmosphere along the field line are assumed
as the initial conditions for optimization. Results: Compared
with the NLFFF, the MHS model provides an improved magnetic field not
only in magnitude and direction, but also in magnetic connectivity. In
addition, the MHS model is capable of recovering the main structure
of plasma in the photosphere and chromosphere.

---------------------------------------------------------
Title: CME-HSS Interaction and Characteristics Tracked from Sun
to Earth
Authors: Heinemann, Stephan G.; Temmer, Manuela; Farrugia, Charles J.;
Dissauer, Karin; Kay, Christina; Wiegelmann, Thomas; Dumbović, Mateja;
Veronig, Astrid M.; Podladchikova, Tatiana; Hofmeister, Stefan J.;
Lugaz, Noé; Carcaboso, Fernando
2019SoPh..294..121H Altcode: 2019arXiv190810161H
In a thorough study, we investigate the origin of a remarkable plasma
and magnetic field configuration observed in situ on June 22, 2011, near
L1, which appears to be a magnetic ejecta (ME) and a shock signature
engulfed by a solar wind high-speed stream (HSS). We identify the
signatures as an Earth-directed coronal mass ejection (CME), associated
with a C7.7 flare on June 21, 2011, and its interaction with a HSS,
which emanates from a coronal hole (CH) close to the launch site of the
CME. The results indicate that the major interaction between the CME and
the HSS starts at a height of 1.3 R⊙ up to 3 R⊙. Over
that distance range, the CME undergoes a strong north-eastward
deflection of at least 30∘ due to the open magnetic field
configuration of the CH. We perform a comprehensive analysis for the
CME-HSS event using multi-viewpoint data (from the Solar TErrestrial
RElations Observatories, the Solar and Heliospheric Observatory and the
Solar Dynamics Observatory), and combined modeling efforts (nonlinear
force-free field modeling, Graduated Cylindrical Shell CME modeling,
and the Forecasting a CME's Altered Trajectory - ForeCAT model). We aim
at better understanding its early evolution and interaction process as
well as its interplanetary propagation and related in situ signatures,
and finally the resulting impact on the Earth's magnetosphere.

---------------------------------------------------------
Title: The Magnetic Properties of Heating Events on High-temperature
Active-region Loops
Authors: Ugarte-Urra, Ignacio; Crump, Nicholas A.; Warren, Harry P.;
Wiegelmann, Thomas
2019ApJ...877..129U Altcode: 2019arXiv190411976U
Understanding the relationship between the magnetic field and coronal
heating is one of the central problems of solar physics. However,
studies of the magnetic properties of impulsively heated loops have
been rare. We present results from a study of 34 evolving coronal loops
observed in the Fe XVIII line component of 94 Å filter images obtained
by the Atmospheric Imaging Assembly (AIA)/Solar Dynamics Observatory
(SDO) from three active regions with different magnetic conditions. We
show that the peak intensity per unit cross section of the loops depends
on their individual magnetic and geometric properties. The intensity
scales proportionally to the average field strength along the loop (B
avg) and inversely with the loop length (L) for a combined
dependence of {({B}avg}/L)}0.52+/- 0.13. These
loop properties are inferred from magnetic extrapolations of the
photospheric Helioseismic and Magnetic Imager (HMI)/SDO line-of-sight
and vector magnetic field in three approximations: potential and two
nonlinear force-free (NLFF) methods. Through hydrodynamic modeling
(enthalpy-based thermal evolution loop (EBTEL) model) we show that
this behavior is compatible with impulsively heated loops with a
volumetric heating rate that scales as {ɛ }{{H}}∼
{B}avg}0.3+/- 0.2/{L}0.2{+/-
0.10.2}.

---------------------------------------------------------
Title: Linking the Sun to the heliosphere using composition data
and modelling: coronal jets as a test case
Authors: Wimmer-Schweingruber, Robert F.; Parenti, Susanna; Del Zanna,
G.; Edmondson, J.; Giunta, A.; Hansteen, V. H.; Higginson, A.; Lepri,
S.; Laming, M.; Lynch, B. J.; von Steiger, R. E.; Wiegelmann, T.;
Zambrana Prado, N.
2019shin.confE.231W Altcode:
Understanding the formation and evolution of the solar wind is still
a priority in the Solar and Heliospheric communities. We expect
a significant progress in terms of observations with the upcoming
Solar Orbiter mission (launch in 2020), which will provide detailed
in-situ measurements of the solar wind and several remote-sensing
observations. However, real progress will only be possible if we
improve our understanding of the physical link between what measured
in-situ and its source regions on the Sun. In this respect, the plasma
chemical and charge-state compositions are considered good diagnostic
tools. In this paper we present results obtained from an extensive team
work aiming at providing solid diagnostics for linking the in-situ and
the remote sensing measurements. For our test cases, we selected two
periods when a single active region produced, close to its sunspot,
jets which had a counterpart signature in the Heliosphere in the form
of type-III radio bursts. These jets therefore marked magnetically
open regions expanding in the heliosphere. Firstly, we looked for
signatures of the open field associated with the active regions in
in-situ data from ACE and WIND, finding potential tracers. Secondly,
we studied the magnetic topology of the full Sun and Heliosphere with
extrapolations of photospheric data and MHD modeling. We found that
the open field area is consistent with the source and evolution of the
jets, as observed with EUV imagers (SDO/AIA, STEREO/EUVI). Thirdly, we
analysed remote sensing EUV spectroscopic observations to measure the
plasma conditions (densities, temperatures and chemical composition)
whenever available. We then modeled the solar wind and charge
state evolution with the solar distance along the open fields to
establish a link between the in-situ signatures and the remote sensing
observations. We discuss the various difficulties associated with such
studies, and highlight how Solar Orbiter measurements can improve them.

---------------------------------------------------------
Title: Nonlinear magnetohydrostatic modeling of an active region
based on a SUNRISE/IMaX vector magnetogram
Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas
2019EGUGA..21.3986Z Altcode:
For modelling the upper solar photosphere and chromosphere, plasma
forces are important. Therefore a nonlinear magnetohydrostatic (NLMHS)
model is a better approximation of the physical state in these layers
than a nonlinear force-free (NLFF) model. The latter one is only valid
in the low plasma-beta corona. The magnetohydrostatic model computes
self-consistently the magnetic field and plasma distribution. We
intensively tested the new code with exact equilibria (Zhu &amp;
Wiegelmann, 2018, ApJ, 866, 130) and the NLMHS code has been able
to meaningfully recover the plasma density, pressure and magnetic
field. Here we present a first application of our new code to an active
region (AR 11768), which was observed by IMaX during the second flight
of the balloon-borne SUNRISE solar observatory in 2013. The high spatial
resolution IMaX vector magnetogram was embedded in SDO/HMI data to cover
the entire active region. We were able to model the non-force-free layer
in the lower atmosphere. Our model shows strongly localized electric
currents and Lorentz forces and self-consistently the corresponding
plasma distribution. Such features require the use of a NLMHS model
and cannot be reconstructed with linear MHS or NLFFF models.

---------------------------------------------------------
Title: Global coronal magnetic field modelling for Solar Orbiter
Authors: Wiegelmann, Thomas; Inhester, Bernd; Chifu, Iulia
2019EGUGA..21.3311W Altcode:
Modelling the solar coronal magnetic field in 3D is an interesting
research topic on its own right. But field models are also important
for combining the analysis of data from remote sensing and in-situ
instrument on Solar Orbiter by providing the magnetic connectivity. A
well tested and frequently applied method is to use photospheric
field measurements, e.g. synoptic vector magnetograms from SDO/HMI,
and extrapolate them into the solar corona under the assumption that
the field is force-free. We do this by a nonlinear force-free code,
based on minimizing a functional. The method is very flexible and
allows to incorporate loop shapes from coronal images. Ongoing projects
are to go beyond the force-free approximation, which is necessary in
the outer solar corona beyond the source surface. A first step are
magneto-static extrapolations (including plasma pressure gradient and
gravity force). In a second step we compute stationary MHD-equilibria
which additionally consider the solar wind flow.

---------------------------------------------------------
Title: Reconstructing nonlinear force-free fields by a constrained
optimization
Authors: Nasiri, S.; Wiegelmann, T.
2019JASTP.182..181N Altcode:
It seems that the potential and linear force-free magnetic fields
are inadequate to represent the observed magnetic events occurring
in different regions of the solar corona. To reconstruct the
nonlinear force-free fields from the solar surface magnetograms,
various analytical and numerical methods have already been examined
by different authors. Here, using the Lagrange multiplier technique,
a constrained optimization approach for reconstructing force-free
magnetic fields is proposed. In the optimization procedure the
solenoidal property is considered as a constraint on the initial
non-force-free field. In the Wheatland et al. (2000) method as an
unconstrained optimization, both solenoidal and force-free conditions
are fulfilled approximately. In contrast, the constrained optimization
method, up to numerical precision, leads us to a nearly force-free
magnetic field with exactly zero divergence. The solutions are obtained
and tested by the Low and Lou (1990) semi-analytic solution.

---------------------------------------------------------
Title: On the extrapolation of magneto-hydro-static equilibria on
the sun: model and tests
Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas
2018csc..confE.133Z Altcode:
Modeling the interface region between solar photosphere and corona is
challenging, because the relative importance of magnetic and plasma
forces change by several orders of magnitude. While the solar corona
can be modeled by the force-free assumption, we need to take care
about plasma forces (pressure gradient and gravity) in photosphere
and chromosphere, here within the magneto-hydro-static (MHS) model. We
solve the MHS equations with the help of an optimization principle and
use vector magnetogram as boundary condition. Positive pressure and
density are ensured by replacing them with two new basic variables. The
Lorentz force during optimization is used to update the plasma pressure
on the bottom boundary, which makes the new extrapolation works even
without pressure measurement on the photosphere. Our code is tested
by using a linear MHS model as reference. From the detailed analyses,
we find that the newly developed MHS extrapolation not only recovers
the plasma distribution at high accuracy. but also gives the better
fit magnetic field than the nonlinear force-free extrapolation.

---------------------------------------------------------
Title: Observations of solar chromospheric heating at sub-arcsec
spatial resolution
Authors: Smitha, H. N.; Chitta, L. P.; Wiegelmann, T.; Solanki, S. K.
2018A&A...617A.128S Altcode: 2018arXiv180701078S
A wide variety of phenomena such as gentle but persistent
brightening, dynamic slender features (∼100 km), and compact
(∼1″) ultraviolet (UV) bursts are associated with the heating of
the solar chromosphere. High spatio-temporal resolution is required to
capture the finer details of the likely magnetic reconnection-driven,
rapidly evolving bursts. Such observations are also needed to reveal
their similarities to large-scale flares, which are also thought to be
reconnection driven, and more generally their role in chromospheric
heating. Here we report observations of chromospheric heating in
the form of a UV burst obtained with the balloon-borne observatory
SUNRISE. The observed burst displayed a spatial morphology similar
to that of a large-scale solar flare with a circular ribbon. While
the co-temporal UV observations at 1.5″ spatial resolution and
24 s cadence from the Solar Dynamics Observatory showed a compact
brightening, the SUNRISE observations at diffraction-limited spatial
resolution of 0.1″ at 7 s cadence revealed a dynamic substructure
of the burst that it is composed of an extended ribbon-like feature
and a rapidly evolving arcade of thin (∼0.1″) magnetic loop-like
features, similar to post-flare loops. Such a dynamic substructure
reveals the small-scale nature of chromospheric heating in these
bursts. Furthermore, based on magnetic field extrapolations, this
heating event is associated with a complex fan-spine magnetic
topology. Our observations strongly hint at a unified picture of
magnetic heating in the solar atmosphere from some large-scale
flares to small-scale bursts, all associated with such a magnetic
topology. The movie associated to Fig. 2 is available at <A
href="https://www.aanda.org/10.1051/0004-6361/201833276/olm">https://www.aanda.org/</A>

---------------------------------------------------------
Title: On the Extrapolation of Magnetohydrostatic Equilibria on
the Sun
Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas
2018ApJ...866..130Z Altcode: 2018arXiv180902168Z
Modeling the interface region between the solar photosphere and corona
is challenging because the relative importance of magnetic and plasma
forces change by several orders of magnitude. While the solar corona
can be modeled by the force-free assumption, we need to take plasma
forces into account (pressure gradient and gravity) in photosphere and
chromosphere, here within the magnetohydrostatic (MHS) model. We solve
the MHS equations with the help of an optimization principle and use
vector magnetogram as the boundary condition. Positive pressure and
density are ensured by replacing them with two new basic variables. The
Lorentz force during optimization is used to update the plasma pressure
on the bottom boundary, which makes the new extrapolation work even
without pressure measurements on the photosphere. Our code is tested
using a linear MHS model as reference. From the detailed analyses, we
find that the newly developed MHS extrapolation recovers the reference
model at high accuracy. The MHS extrapolation is, however, numerically
more expensive than the nonlinear force-free field extrapolation
and consequently one should limit their application to regions where
plasma forces become important, e.g., in a layer of about 2 Mm above
the photosphere.

---------------------------------------------------------
Title: Global Non-Potential Magnetic Models of the Solar Corona
During the March 2015 Eclipse
Authors: Yeates, Anthony R.; Amari, Tahar; Contopoulos, Ioannis; Feng,
Xueshang; Mackay, Duncan H.; Mikić, Zoran; Wiegelmann, Thomas; Hutton,
Joseph; Lowder, Christopher A.; Morgan, Huw; Petrie, Gordon; Rachmeler,
Laurel A.; Upton, Lisa A.; Canou, Aurelien; Chopin, Pierre; Downs,
Cooper; Druckmüller, Miloslav; Linker, Jon A.; Seaton, Daniel B.;
Török, Tibor
2018SSRv..214...99Y Altcode: 2018arXiv180800785Y
Seven different models are applied to the same problem of simulating
the Sun's coronal magnetic field during the solar eclipse on 2015
March 20. All of the models are non-potential, allowing for free
magnetic energy, but the associated electric currents are developed
in significantly different ways. This is not a direct comparison
of the coronal modelling techniques, in that the different models
also use different photospheric boundary conditions, reflecting
the range of approaches currently used in the community. Despite
the significant differences, the results show broad agreement in the
overall magnetic topology. Among those models with significant volume
currents in much of the corona, there is general agreement that the
ratio of total to potential magnetic energy should be approximately
1.4. However, there are significant differences in the electric current
distributions; while static extrapolations are best able to reproduce
active regions, they are unable to recover sheared magnetic fields in
filament channels using currently available vector magnetogram data. By
contrast, time-evolving simulations can recover the filament channel
fields at the expense of not matching the observed vector magnetic
fields within active regions. We suggest that, at present, the best
approach may be a hybrid model using static extrapolations but with
additional energization informed by simplified evolution models. This
is demonstrated by one of the models.

---------------------------------------------------------
Title: Toward a Quantitative Comparison of Magnetic Field
Extrapolations and Observed Coronal Loops
Authors: Warren, Harry P.; Crump, Nicholas A.; Ugarte-Urra, Ignacio;
Sun, Xudong; Aschwanden, Markus J.; Wiegelmann, Thomas
2018ApJ...860...46W Altcode: 2018arXiv180500281W
It is widely believed that loops observed in the solar atmosphere
trace out magnetic field lines. However, the degree to which magnetic
field extrapolations yield field lines that actually do follow loops
has yet to be studied systematically. In this paper, we apply three
different extrapolation techniques—a simple potential model, a
nonlinear force-free (NLFF) model based on photospheric vector data,
and an NLFF model based on forward fitting magnetic sources with
vertical currents—to 15 active regions that span a wide range of
magnetic conditions. We use a distance metric to assess how well each
of these models is able to match field lines to the 12202 loops traced
in coronal images. These distances are typically 1″-2″. We also
compute the misalignment angle between each traced loop and the local
magnetic field vector, and find values of 5°-12°. We find that the
NLFF models generally outperform the potential extrapolation on these
metrics, although the differences between the different extrapolations
are relatively small. The methodology that we employ for this study
suggests a number of ways that both the extrapolations and loop
identification can be improved.

---------------------------------------------------------
Title: Global non-potential coronal magnetic field models
Authors: Wiegelmann, Thomas
2018EGUGA..20.1787W Altcode:
Knowledge of the Sun's large scale magnetic field is an important
research topic on its own right, but also important to guide
future space missions like Parker Solar Probe and Solar Orbiter. To
combine remote sensing and in-situ measurements from these mission,
information regarding the magnetic connectivity is essential. Within an
international collaboration we compared several static and evolutionary
corona models: non-linear force-free, magneto-static, evolutionary
magneto- frictional, full MHD and zero-beta MHD. The models agree
on the amount of open flux, streamer location and broad magnetic
topology. They disagree on the shape of helmet streamers and electric
currents. Static models are better in active regions, evolutionary
models better to model filaments. Our advice is to combine static
extrapolations with energisation from evolutionary models.

---------------------------------------------------------
Title: Magnetic Braids in Eruptions of a Spiral Structure in the
Solar Atmosphere
Authors: Huang, Zhenghua; Xia, Lidong; Nelson, Chris J.; Liu, Jiajia;
Wiegelmann, Thomas; Tian, Hui; Klimchuk, James A.; Chen, Yao; Li, Bo
2018ApJ...854...80H Altcode: 2018arXiv180105967H
We report on high-resolution imaging and spectral observations of
eruptions of a spiral structure in the transition region, which
were taken with the Interface Region Imaging Spectrograph, and the
Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic
Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The eruption
coincided with the appearance of two series of jets, with velocities
comparable to the Alfvén speeds in their footpoints. Several pieces of
evidence of magnetic braiding in the eruption are revealed, including
localized bright knots, multiple well-separated jet threads, transition
region explosive events, and the fact that all three of these are
falling into the same locations within the eruptive structures. Through
analysis of the extrapolated 3D magnetic field in the region, we found
that the eruptive spiral structure corresponded well to locations
of twisted magnetic flux tubes with varying curl values along their
lengths. The eruption occurred where strong parallel currents,
high squashing factors, and large twist numbers were obtained. The
electron number density of the eruptive structure is found to be ∼3 ×
1012 cm-3, indicating that a significant amount
of mass could be pumped into the corona by the jets. Following the
eruption, the extrapolations revealed a set of seemingly relaxed loops,
which were visible in the AIA 94 Å channel, indicating temperatures
of around 6.3 MK. With these observations, we suggest that magnetic
braiding could be part of the mechanisms explaining the formation of
solar eruption and the mass and energy supplement to the corona.

---------------------------------------------------------
Title: Coronal Magnetic Field Models
Authors: Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete
2018smf..book..249W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetic topological analysis of coronal bright points
Authors: Galsgaard, K.; Madjarska, M. S.; Moreno-Insertis, F.; Huang,
Z.; Wiegelmann, T.
2017A&A...606A..46G Altcode: 2017arXiv170704174G
Context. We report on the first of a series of studies on coronal
bright points which investigate the physical mechanism that generates
these phenomena. Aims: The aim of this paper is to understand
the magnetic-field structure that hosts the bright points. 
Methods: We use longitudinal magnetograms taken by the Solar Optical
Telescope with the Narrowband Filter Imager. For a single case,
magnetograms from the Helioseismic and Magnetic Imager were added
to the analysis. The longitudinal magnetic field component is used
to derive the potential magnetic fields of the large regions around
the bright points. A magneto-static field extrapolation method is
tested to verify the accuracy of the potential field modelling. The
three dimensional magnetic fields are investigated for the presence
of magnetic null points and their influence on the local magnetic
domain. Results: In nine out of ten cases the bright point
resides in areas where the coronal magnetic field contains an opposite
polarity intrusion defining a magnetic null point above it. We find that
X-ray bright points reside, in these nine cases, in a limited part of
the projected fan-dome area, either fully inside the dome or expanding
over a limited area below which typically a dominant flux concentration
resides. The tenth bright point is located in a bipolar loop system
without an overlying null point. Conclusions: All bright points
in coronal holes and two out of three bright points in quiet Sun regions
are seen to reside in regions containing a magnetic null point. An as
yet unidentified process(es) generates the brigh points in specific
regions of the fan-dome structure. The movies are available at <A
href="http://www.aanda.org/10.1051/0004-6361/201731041/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Coronal Magnetic Field Models
Authors: Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete
2017SSRv..210..249W Altcode: 2015SSRv..tmp...75W
Coronal magnetic field models use photospheric field measurements
as boundary condition to model the solar corona. We review in this
paper the most common model assumptions, starting from MHD-models,
magnetohydrostatics, force-free and finally potential field models. Each
model in this list is somewhat less complex than the previous one and
makes more restrictive assumptions by neglecting physical effects. The
magnetohydrostatic approach neglects time-dependent phenomena and
plasma flows, the force-free approach neglects additionally the
gradient of the plasma pressure and the gravity force. This leads
to the assumption of a vanishing Lorentz force and electric currents
are parallel (or anti-parallel) to the magnetic field lines. Finally,
the potential field approach neglects also these currents. We outline
the main assumptions, benefits and limitations of these models both
from a theoretical (how realistic are the models?) and a practical
viewpoint (which computer resources to we need?). Finally we address
the important problem of noisy and inconsistent photospheric boundary
conditions and the possibility of using chromospheric and coronal
observations to improve the models.

---------------------------------------------------------
Title: The Plasma Parameters and Geometry of Cool and Warm Active
Region Loops
Authors: Xie, Haixia; Madjarska, Maria S.; Li, Bo; Huang, Zhenghua;
Xia, Lidong; Wiegelmann, Thomas; Fu, Hui; Mou, Chaozhou
2017ApJ...842...38X Altcode: 2017arXiv170502564X
How the solar corona is heated to high temperatures remains an unsolved
mystery in solar physics. In the present study we analyze observations
of 50 whole active region loops taken with the Extreme-ultraviolet
Imaging Spectrometer on board the Hinode satellite. Eleven loops were
classified as cool loops (&lt;1 MK) and 39 as warm loops (1-2 MK). We
study their plasma parameters, such as densities, temperatures,
filling factors, nonthermal velocities, and Doppler velocities. We
combine spectroscopic analysis with linear force-free magnetic field
extrapolation to derive the 3D structure and positioning of the loops,
their lengths and heights, and the magnetic field strength along
the loops. We use density-sensitive line pairs from Fe xii, Fe xiii,
Si x, and Mg vii ions to obtain electron densities by taking special
care of intensity background subtraction. The emission measure loci
method is used to obtain the loop temperatures. We find that the loops
are nearly isothermal along the line of sight. Their filling factors
are between 8% and 89%. We also compare the observed parameters with
the theoretical Rosner-Tucker-Vaiana (RTV) scaling law. We find that
most of the loops are in an overpressure state relative to the RTV
predictions. In a follow-up study, we will report a heating model of a
parallel-cascade-based mechanism and will compare the model parameters
with the loop plasma and structural parameters derived here.

---------------------------------------------------------
Title: Coronal magnetic field extrapolation
Authors: Wiegelmann, Thomas
2017EGUGA..19.2788W Altcode:
The solar corona is structured by the solar magnetic field and
to understand physical processes in the solar corona it is key to
get information about the coronal magnetic field. Due to the low
plasma beta of the coronal plasma, the magnetic forces dominate
and other plasma forces can be neglected in lowest order. In
this approach the Lorentz-force vanishes and the magnetic
field is force-free. Unfortunately we do not have routine direct
measurements of the magnetic field in the solar corona, but in the
photosphere, e.g. from SDO/HMI. These photospheric magnetic field
measurements are then extrapolated into the higher layers of the solar
atmosphere. Because of the high conductivity of the coronal plasma,
EUV-images, e.g. from SDO/AIA or STEREO/SECCHI, outline the magnetic
field lines and these coronal images are used to validate and improve
coronal magnetic field models. The models provide the 3D-magnetic
field structure and can be used to compute the free magnetic energy
and helicity. Both quantities are important to understand the onset
of coronal eruptions.

---------------------------------------------------------
Title: Slender Ca II H Fibrils Mapping Magnetic Fields in the Low
Solar Chromosphere
Authors: Jafarzadeh, S.; Rutten, R. J.; Solanki, S. K.; Wiegelmann, T.;
Riethmüller, T. L.; van Noort, M.; Szydlarski, M.; Blanco Rodríguez,
J.; Barthol, P.; del Toro Iniesta, J. C.; Gandorfer, A.; Gizon, L.;
Hirzberger, J.; Knölker, M.; Martínez Pillet, V.; Orozco Suárez,
D.; Schmidt, W.
2017ApJS..229...11J Altcode: 2016arXiv161003104J
A dense forest of slender bright fibrils near a small solar active
region is seen in high-quality narrowband Ca II H images from the SuFI
instrument onboard the Sunrise balloon-borne solar observatory. The
orientation of these slender Ca II H fibrils (SCF) overlaps with the
magnetic field configuration in the low solar chromosphere derived
by magnetostatic extrapolation of the photospheric field observed
with Sunrise/IMaX and SDO/HMI. In addition, many observed SCFs are
qualitatively aligned with small-scale loops computed from a novel
inversion approach based on best-fit numerical MHD simulation. Such
loops are organized in canopy-like arches over quiet areas that differ
in height depending on the field strength near their roots.

---------------------------------------------------------
Title: Magneto-static Modeling from Sunrise/IMaX: Application to an
Active Region Observed with Sunrise II
Authors: Wiegelmann, T.; Neukirch, T.; Nickeler, D. H.; Solanki, S. K.;
Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; Riethmüller,
T. L.; van Noort, M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.;
Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
2017ApJS..229...18W Altcode: 2017arXiv170101458N; 2017arXiv170101458W
Magneto-static models may overcome some of the issues facing force-free
magnetic field extrapolations. So far they have seen limited use
and have faced problems when applied to quiet-Sun 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 balloon-borne solar observatory in 2013
June as boundary conditions for a magneto-static 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 magneto-static extrapolation approach, which was applied
earlier to a quiet-Sun region observed with Sunrise I. In an active
region the signal-to-noise-ratio 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 magneto-static equilibria. The high spatial resolution of IMaX
(110-130 km, pixel size 40 km) enables us to model the non-force-free
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 us to model intrinsic nonlinear structures
like strongly localized electric currents.

---------------------------------------------------------
Title: Electric Current Filamentation Induced by 3D Plasma Flows in
the Solar Corona
Authors: Nickeler, Dieter H.; Wiegelmann, Thomas; Karlický, Marian;
Kraus, Michaela
2017ApJ...837..104N Altcode: 2017arXiv170203986N
Many magnetic structures in the solar atmosphere evolve rather slowly,
so they can be assumed as (quasi-)static or (quasi-)stationary
and represented via magnetohydrostatic (MHS) or stationary
magnetohydrodynamic (MHD) equilibria, respectively. While exact 3D
solutions would be desired, they are extremely difficult to find in
stationary MHD. We construct solutions with magnetic and flow vector
fields that have three components depending on all three coordinates. We
show that the noncanonical transformation method produces quasi-3D
solutions of stationary MHD by mapping 2D or 2.5D MHS equilibria to
corresponding stationary MHD states, that is, states that display
the same field-line structure as the original MHS equilibria. These
stationary MHD states exist on magnetic flux surfaces of the original 2D
MHS states. Although the flux surfaces and therefore also the equilibria
have a 2D character, these stationary MHD states depend on all three
coordinates and display highly complex currents. The existence of
geometrically complex 3D currents within symmetric field-line structures
provides the basis for efficient dissipation of the magnetic energy
in the solar corona by ohmic heating. We also discuss the possibility
of maintaining an important subset of nonlinear MHS states, namely
force-free fields, by stationary flows. We find that force-free
fields with nonlinear flows only arise under severe restrictions of
the field-line geometry and of the magnetic flux density distribution.

---------------------------------------------------------
Title: Nonlinear Force-free Coronal Magnetic Stereoscopy
Authors: Chifu, Iulia; Wiegelmann, Thomas; Inhester, Bernd
2017ApJ...837...10C Altcode: 2017arXiv170904177C
Insights into the 3D structure of the solar coronal magnetic field have
been obtained in the past by two completely different approaches. The
first approach are nonlinear force-free field (NLFFF) extrapolations,
which use photospheric vector magnetograms as boundary condition. The
second approach uses stereoscopy of coronal magnetic loops observed in
EUV coronal images from different vantage points. Both approaches have
their strengths and weaknesses. Extrapolation methods are sensitive
to noise and inconsistencies in the boundary data, and the accuracy
of stereoscopy is affected by the ability of identifying the same
structure in different images and by the separation angle between the
view directions. As a consequence, for the same observational data,
the 3D coronal magnetic fields computed with the two methods do not
necessarily coincide. In an earlier work (Paper I) we extended our
NLFFF optimization code by including stereoscopic constrains. The method
was successfully tested with synthetic data, and within this work, we
apply the newly developed code to a combined data set from SDO/HMI,
SDO/AIA, and the two STEREO spacecraft. The extended method (called
S-NLFFF) contains an additional term that monitors and minimizes the
angle between the local magnetic field direction and the orientation
of the 3D coronal loops reconstructed by stereoscopy. We find that
when we prescribe the shape of the 3D stereoscopically reconstructed
loops, the S-NLFFF method leads to a much better agreement between the
modeled field and the stereoscopically reconstructed loops. We also
find an appreciable decrease by a factor of two in the angle between
the current and the magnetic field. This indicates the improved quality
of the force-free solution obtained by S-NLFFF.

---------------------------------------------------------
Title: Sources of the Slow Solar Wind During the Solar Cycle 23/24
Minimum
Authors: Kilpua, E. K. J.; Madjarska, M. S.; Karna, N.; Wiegelmann,
T.; Farrugia, C.; Yu, W.; Andreeova, K.
2016SoPh..291.2441K Altcode: 2016arXiv160605142K; 2016SoPh..tmp..149K
We investigate the characteristics and the sources of the slow
(&lt;450 kms−1) solar wind during the four years (2006 -
2009) of low solar activity between Solar Cycles 23 and 24. We used a
comprehensive set of in-situ observations in the near-Earth solar wind
(Wind and ACE) and removed the periods when large-scale interplanetary
coronal mass ejections were present. The investigated period features
significant variations in the global coronal structure, including
the frequent presence of low-latitude active regions in 2006 - 2007,
long-lived low- and mid-latitude coronal holes in 2006 - mid-2008
and mostly the quiet Sun in 2009. We examined Carrington rotation
averages of selected solar plasma, charge state, and compositional
parameters and distributions of these parameters related to the quiet
Sun, active region Sun, and the coronal hole Sun. While some of the
investigated parameters (e.g. speed, the C+6/C+4
and He/H ratios) show clear variations over our study period and with
solar wind source type, some (Fe/O) exhibit very little changes. Our
results highlight the difficulty of distinguishing between the slow
solar wind sources based on the inspection of solar wind conditions.

---------------------------------------------------------
Title: Comparison of CME/Shock Propagation Models with Heliospheric
Imaging and In Situ Observations
Authors: Zhao, Xinhua; Liu, Ying D.; Inhester, Bernd; Feng, Xueshang;
Wiegelmann, Thomas; Lu, Lei
2016ApJ...830...48Z Altcode: 2016arXiv160705533Z
The prediction of the arrival time for fast coronal mass ejections
(CMEs) and their associated shocks is highly desirable in space weather
studies. In this paper, we use two shock propagation models, I.e.,
Data Guided Shock Time Of Arrival (DGSTOA) and Data Guided Shock
Propagation Model (DGSPM), to predict the kinematical evolution of
interplanetary shocks associated with fast CMEs. DGSTOA is based on the
similarity theory of shock waves in the solar wind reference frame,
and DGSPM is based on the non-similarity theory in the stationary
reference frame. The inputs are the kinematics of the CME front at the
maximum speed moment obtained from the geometric triangulation method
applied to STEREO imaging observations together with the Harmonic
Mean approximation. The outputs provide the subsequent propagation
of the associated shock. We apply these models to the CMEs on 2012
January 19, January 23, and March 7. We find that the shock models
predict reasonably well the shock’s propagation after the impulsive
acceleration. The shock’s arrival time and local propagation speed at
Earth predicted by these models are consistent with in situ measurements
of WIND. We also employ the Drag-Based Model (DBM) as a comparison,
and find that it predicts a steeper deceleration than the shock models
after the rapid deceleration phase. The predictions of DBM at 1 au
agree with the following ICME or sheath structure, not the preceding
shock. These results demonstrate the applicability of the shock models
used here for future arrival time prediction of interplanetary shocks
associated with fast CMEs.

---------------------------------------------------------
Title: Erratum: “Evolution of Magnetic Field and Energy in A
Major Eruptive Active Region Based on SDO/HMI Observation” (<A
href="http://dx.doi.org/10.1088/0004-637x/748/2/77 ">2012, ApJ,
748, 77</A>)
Authors: Sun, Xudong; Hoeksema, J. Todd; Liu, Yang; Wiegelmann,
Thomas; Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia
2016ApJ...828...65S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Relationship Between Sunspot Rotation and a Major Solar
Eruption on 12 July 2012
Authors: Wang, Rui; Liu, Ying D.; Wiegelmann, Thomas; Cheng, Xin;
Hu, Huidong; Yang, Zhongwei
2016SoPh..291.1159W Altcode: 2016SoPh..tmp...49W
We present an analysis of Solar Dynamics Observatory (SDO) observations
of an X1.4 class flare on 12 July 2012 (SOL2012-07-12T15:37L082C105),
which was associated with a pronounced sunspot rotation in the
associated active region. Based on the magnetograms taken with the
Helioseismic and Magnetic Imager (HMI) on the SDO, we measured the
rotational speed of the sunspot. We also used a technique, called
the differential affine velocity estimator for vector magnetograms
(DAVE4VM), to determine the horizontal velocities and the magnetic
helicity flux transport. The helicity flux rate due to shearing motion
changed sign after the onset of the eruption. A high correlation between
the sunspot rotation speed and the change in the total accumulated
helicity was found. We also calculated the net fluxes of the respective
magnetic polarities and the net vertical currents. The net current in
the region of interest showed a synchronous change with the sunspot
rotation rate. The magnetic configurations of the sigmoid filament
in the active region and the associated possible interaction between
different structures were further investigated by means of a nonlinear
force-free field extrapolation. We identified a possible magnetic
reconnection region from the three-dimensional magnetic fields and its
association with EUV structures. These results suggest that the major
eruption of this active region was connected with the sunspot rotation.

---------------------------------------------------------
Title: Structure, Stability, and Evolution of Magnetic Flux Ropes
from the Perspective of Magnetic Twist
Authors: Liu, Rui; Kliem, Bernhard; Titov, Viacheslav S.; Chen, Jun;
Wang, Yuming; Wang, Haimin; Liu, Chang; Xu, Yan; Wiegelmann, Thomas
2016ApJ...818..148L Altcode: 2015arXiv151202338L
We investigate the evolution of NOAA Active Region (AR) 11817 during
2013 August 10-12, when it developed a complex field configuration
and produced four confined, followed by two eruptive, flares. These
C-and-above flares are all associated with a magnetic flux rope (MFR)
located along the major polarity inversion line, where shearing and
converging photospheric flows are present. Aided by the nonlinear
force-free field modeling, we identify the MFR through mapping magnetic
connectivities and computing the twist number {{ T }}w
for each individual field line. The MFR is moderately twisted (|
{{ T }}w| \lt 2) and has a well-defined boundary of high
squashing factor Q. We found that the field line with the extremum |
{{ T }}w| is a reliable proxy of the rope axis, and that
the MFR's peak | {{ T }}w| temporarily increases within
half an hour before each flare while it decreases after the flare peak
for both confined and eruptive flares. This pre-flare increase in | {{
T }}w| has little effect on the AR's free magnetic energy or
any other parameters derived for the whole region, due to its moderate
amount and the MFR's relatively small volume, while its decrease after
flares is clearly associated with the stepwise decrease in the whole
region's free magnetic energy due to the flare. We suggest that {{ T
}}w may serve as a useful parameter in forewarning the onset
of eruption, and therefore, the consequent space weather effects. The
helical kink instability is identified as the prime candidate onset
mechanism for the considered flares.

---------------------------------------------------------
Title: Structure, Stability and Evolution of a Magnetic Flux Rope
Authors: Liu, R.; Kliem, B.; Titov, V. S.; Chen, J.; Wang, Y.; Wang,
H.; Liu, C.; Xu, Y.; Wiegelmann, T.
2015AGUFMSH13D2457L Altcode:
We investigate the evolution of NOAA Active Region 11817 during
2013 August 10--12, when it developed a complex field configuration
and produced four confined, followed by two eruptive, flares. These
C-and-above flares are all associated with a magnetic flux rope (MFR)
located along the major polarity inversion line, where shearing and
converging photospheric flows are present. With the aid of nonlinear
force-free field modeling, we identify the MFR through mapping
magnetic connectivities and computing the twist number Tw for each
individual field line. The MFR is moderately twisted (Tw &lt; 2)
and has a well-defined boundary of high squashing factor Q. Its axis
coincides with the field line with the peak Tw in the rope. We find
that the MFR's peak Tw temporarily increases within half an hour before
each flare while it decreases after the flare peak for both confined
and eruptive flares. This pre-flare increase in Tw has little effect
on the active region's free magnetic energy or any other parameters
derived for the whole region, due to its moderate amount and the MFR's
relatively small volume, while its decrease after flares is clearly
associated with the stepwise decrease in free magnetic energy due
to the flare. We suggest that Tw may serve as a useful parameter in
prewarning the onset of eruption, and therefore, the consequent space
weather effects. The helical kink instability is identified as the
prime candidate onset mechanism for the considered flares.

---------------------------------------------------------
Title: Magneto-static Modeling of the Mixed Plasma Beta Solar
Atmosphere Based on Sunrise/IMaX Data
Authors: Wiegelmann, T.; Neukirch, T.; Nickeler, D. H.; Solanki,
S. K.; Martínez Pillet, V.; Borrero, J. M.
2015ApJ...815...10W Altcode: 2015arXiv151105568W
Our aim is to model the three-dimensional magnetic field structure
of the upper solar atmosphere, including regions of non-negligible
plasma beta. We use high-resolution photospheric magnetic field
measurements from SUNRISE/IMaX as the boundary condition for a
magneto-static magnetic field model. The high resolution of IMaX
allows us to resolve the interface region between the photosphere
and corona, but modeling this region is challenging for the following
reasons. While the coronal magnetic field is thought to be force-free
(the Lorentz force 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 self-consistently taken into
account and compensate for the non-vanishing Lorentz force. Above a
certain height (about 2 Mm) the non-magnetic forces become very weak
and consequently the magnetic field becomes almost force-free. Here,
we apply a linear approach where the electric current density consists
of a superposition of a field-line 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
toward a nonlinear model.

---------------------------------------------------------
Title: The Influence of Spatial resolution on Nonlinear Force-free
Modeling
Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.;
Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori,
G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.;
Régnier, S.
2015ApJ...811..107D Altcode: 2015arXiv150805455D
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/Solar Optical Telescope
Spectro-Polarimeter 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.

---------------------------------------------------------
Title: A Circular-ribbon Solar Flare Following an Asymmetric Filament
Eruption
Authors: Liu, Chang; Deng, Na; Liu, Rui; Lee, Jeongwoo; Pariat,
Étienne; Wiegelmann, Thomas; Liu, Yang; Kleint, Lucia; Wang, Haimin
2015ApJ...812L..19L Altcode: 2015arXiv150908414L
The dynamic properties of flare ribbons and the often associated
filament eruptions can provide crucial information on the flaring
coronal magnetic field. This Letter analyzes the GOES-class X1.0 flare
on 2014 March 29 (SOL2014-03-29T17:48), in which we found an asymmetric
eruption of a sigmoidal filament and an ensuing circular flare
ribbon. Initially both EUV images and a preflare nonlinear force-free
field model show that the filament is embedded in magnetic fields with
a fan-spine-like structure. In the first phase, which is defined by a
weak but still increasing X-ray emission, the western portion of the
sigmoidal filament arches upward and then remains quasi-static for
about five minutes. The western fan-like and the outer spine-like
fields display an ascending motion, and several associated ribbons
begin to brighten. Also found is a bright EUV flow that streams down
along the eastern fan-like field. In the second phase that includes the
main peak of hard X-ray (HXR) emission, the filament erupts, leaving
behind two major HXR sources formed around its central dip portion
and a circular ribbon brightened sequentially. The expanding western
fan-like field interacts intensively with the outer spine-like field,
as clearly seen in running difference EUV images. We discuss these
observations in favor of a scenario where the asymmetric eruption of
the sigmoidal filament is initiated due to an MHD instability and
further facilitated by reconnection at a quasi-null in corona; the
latter is in turn enhanced by the filament eruption and subsequently
produces the circular flare ribbon.

---------------------------------------------------------
Title: Comparison between the eruptive X2.2 flare on 2011 February
15 and confined X3.1 flare on 2014 October 24
Authors: Jing, Ju; Xu, Yan; Lee, Jeongwoo; Nitta, Nariaki V.; Liu,
Chang; Park, Sung-Hong; Wiegelmann, Thomas; Wang, Haimin
2015RAA....15.1537J Altcode:
We compare two contrasting X-class flares in terms of magnetic free
energy, relative magnetic helicity and decay index of the active regions
(ARs) in which they occurred. The events in question are the eruptive
X2.2 flare from AR 11158 accompanied by a halo coronal mass ejection
(CME) and the confined X3.1 flare from AR 12192 with no associated
CME. These two flares exhibit similar behavior of free magnetic energy
and helicity buildup for a few days preceding them. A major difference
between the two flares is found to lie in the time-dependent change
of magnetic helicity of the ARs that hosted them. AR 11158 shows a
significant decrease in magnetic helicity starting ∼4 hours prior
to the flare, but no apparent decrease in helicity is observed in AR
12192. By examining the magnetic helicity injection rates in terms
of sign, we confirmed that the drastic decrease in magnetic helicity
before the eruptive X2.2 flare was not caused by the injection of
reversed helicity through the photosphere but rather the CME-related
change in the coronal magnetic field. Another major difference we find
is that AR 11158 had a significantly larger decay index and therefore
weaker overlying field than AR 12192. These results suggest that the
coronal magnetic helicity and the decay index of the overlying field
can provide a clue about the occurrence of CMEs.

---------------------------------------------------------
Title: Coronal magnetic field modeling using stereoscopy constraints
Authors: Chifu, I.; Inhester, B.; Wiegelmann, T.
2015A&A...577A.123C Altcode:
 Aims: Nonlinear force-free field (NLFFF) extrapolation has been
used extensively in the past to extrapolate solar surface magnetograms
to stationary coronal field models. In theoretical tests with known
boundary conditions, the nonlinear boundary value problem can be
solved reliably. However, if the magnetogram is measured with errors,
the extrapolation often yields field lines that disagree with the
shapes of simultaneously observed and stereoscopically reconstructed
coronal loops. We here propose an extension to an NLFFF extrapolation
scheme that remedies this deficiency in that it incorporates the
loop information in the extrapolation procedure. Methods: We
extended the variational formulation of the NLFFF optimization code
by an additional term that monitors and minimizes the difference of
the local magnetic field direction and the orientation of 3D plasma
loops. We tested the performance of the new code with a previously
reported semi-analytical force-free solution. Results: We
demonstrate that there is a range of force-free and divergence-free
solutions that comply with the boundary measurements within some error
bound. With our new approach we can obtain the solution out of this
set the coronal fields which is well aligned with given loops. 
Conclusions: We conclude that the shape of coronal loops reconstructed
by stereoscopy may lead to an important stabilization of coronal NLFFF
field solutions when, as is typically the case, magnetic surface
measurements with limited precision do not allow determining the
solution solely from photospheric field measurements.

---------------------------------------------------------
Title: Multiwavelength Observations of a Partially Eruptive Filament
on 2011 September 8
Authors: Zhang, Q. M.; Ning, Z. J.; Guo, Y.; Zhou, T. H.; Cheng, X.;
Ji, H. S.; Feng, L.; Wiegelmann, T.
2015ApJ...805....4Z Altcode: 2015arXiv150302933Z
In this paper, we report our multiwavelength observations of a partial
filament eruption event in NOAA active region (AR) 11283 on 8 September
2011. A magnetic null point and the corresponding spine and separatrix
surface are found in the AR. Beneath the null point, a sheared arcade
supports the filament along the highly complex and fragmented polarity
inversion line. After being activated, the sigmoidal filament erupted
and split into two parts. The major part rose at speeds of 90-150 km
s-1 before reaching the maximum apparent height of ∼115
Mm. Afterward, it returned to the solar surface in a bumpy way at speeds
of 20-80 km s-1. The rising and falling motions were clearly
observed in the extreme-ultraviolet, UV, and Hα wavelengths. The
failed eruption of the main part was associated with an M6.7 flare
with a single hard X-ray source. The runaway part of the filament,
however, separated from and rotated around the major part for ∼1 turn
at the eastern leg before escaping from the corona, probably along
large-scale open magnetic field lines. The ejection of the runaway
part resulted in a very faint coronal mass ejection that propagated
at an apparent speed of 214 km s-1 in the outer corona. The
filament eruption also triggered a transverse kink-mode oscillation of
the adjacent coronal loops in the same AR. The amplitude and period
of the oscillation were 1.6 Mm and 225 s. Our results are important
for understanding the mechanisms of partial filament eruptions, and
provide new constraints to theoretical models. The multiwavelength
observations also shed light on space weather prediction.

---------------------------------------------------------
Title: Effect of the Size of the Computational Domain on Spherical
Nonlinear Force-Free Modeling of a Coronal Magnetic Field Using
SDO/HMI Data
Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J.
2015SoPh..290.1159T Altcode: 2014arXiv1409.1775T; 2015SoPh..tmp...23T
The solar coronal magnetic field produces solar activity, including
extremely energetic solar flares and coronal mass ejections
(CMEs). Knowledge of the structure and evolution of the magnetic field
of the solar corona is important for investigating and understanding
the origins of space weather. Although the coronal field remains
difficult to measure directly, there is considerable interest in
accurate modeling of magnetic fields in and around sunspot regions on
the Sun using photospheric vector magnetograms as boundary data. In
this work, we investigate effects of the size of the domain chosen
for coronal magnetic field modeling on resulting model solutions. We
applied a spherical nonlinear force-free optimization procedure to
vector magnetogram data of the Helioseismic and Magnetic Imager (HMI)
onboard the Solar Dynamics Observatory (SDO). We selected a particular
observation in which there were four active regions observed on 9 March
2012 at 20:55 UT. The results imply that quantities such as magnetic
flux density, electric current density, and free magnetic energy density
of active regions of interest are significantly different from the
corresponding quantities obtained in the same region with a larger
computational domain. The difference is even more pronounced in the
regions that are connected to the outside of the domain.

---------------------------------------------------------
Title: Effect of Size of the Computational Domain on Nonlinear
Force-Free Modeling of Coronal Magnetic Field Using SDO/HMI Data
Authors: Asfaw, T. T.; Wiegelmann, T.; MacNeice, P. J.
2014AGUFMSH21A4083A Altcode:
The solar coronal magnetic field produces solar activity, including
extremely energetic solar flares and coronal mass ejections
(CMEs). Knowledge of the structure and evolution of the magnetic field
of the solar corona is important for investigating and understanding the
origins of space weather. Although the coronal field remains difficult
to measure directly, there is considerable interest in accurate
modeling of magnetic fields in and around sunspot regions on the Sun
using photospheric vector magnetograms as boundary data. In this work,
we investigate effects of the size of the domain chosen for coronal
magnetic field modeling on resulting model solution. We apply spherical
Optimization procedure to vector magnetogram data of Helioseismic and
Magnetic Imager (HMI) onboardSolar Dynamics Observatory (SDO) with four
Active Region observed on 09 March 2012 at 20:55UT. The results imply
that quantities like magnetic flux density, electric current density
and free magnetic energy density of ARs of interest are significantly
different from the corresponding quantities obtained in the same region
within the wider field of view. The difference is even more pronounced
in the regions where there are connections to outside the domain.

---------------------------------------------------------
Title: The magnetic field in the solar atmosphere
Authors: Wiegelmann, Thomas; Thalmann, Julia K.; Solanki, Sami K.
2014A&ARv..22...78W Altcode: 2014arXiv1410.4214W
This publication provides an overview of magnetic fields in the solar
atmosphere with the focus lying on the corona. The solar magnetic field
couples the solar interior with the visible surface of the Sun and with
its atmosphere. It is also responsible for all solar activity in its
numerous manifestations. Thus, dynamic phenomena such as coronal mass
ejections and flares are magnetically driven. In addition, the field
also plays a crucial role in heating the solar chromosphere and corona
as well as in accelerating the solar wind. Our main emphasis is the
magnetic field in the upper solar atmosphere so that photospheric and
chromospheric magnetic structures are mainly discussed where relevant
for higher solar layers. Also, the discussion of the solar atmosphere
and activity is limited to those topics of direct relevance to the
magnetic field. After giving a brief overview about the solar magnetic
field in general and its global structure, we discuss in more detail
the magnetic field in active regions, the quiet Sun and coronal holes.

---------------------------------------------------------
Title: Global Solar Free Magnetic Energy and Electric Current Density
Distribution of Carrington Rotation 2124
Authors: Tadesse, Tilaye; Pevtsov, Alexei A.; Wiegelmann, T.; MacNeice,
P. J.; Gosain, S.
2014SoPh..289.4031T Altcode: 2013arXiv1310.5790T
Solar eruptive phenomena, like flares and coronal mass ejections
(CMEs), are governed by magnetic fields. To describe the structure of
these phenomena one needs information on the magnetic flux density and
the electric current density vector components in three dimensions
throughout the atmosphere. However, current spectro-polarimetric
measurements typically limit the determination of the vector magnetic
field to only the photosphere. Therefore, there is considerable
interest in accurate modeling of the solar coronal magnetic field
using photospheric vector magnetograms as boundary data. In this work,
we model the coronal magnetic field for global solar atmosphere using
nonlinear force-free field (NLFFF) extrapolation codes implemented to
a synoptic maps of photospheric vector magnetic field synthesized from
the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term
Investigations of the Sun (SOLIS) as boundary condition. Using
the resulting three-dimensional magnetic field, we calculate the
three-dimensional electric current density and magnetic energy
throughout the solar atmosphere for Carrington rotation 2124 using our
global extrapolation code. We found that spatially, the low-lying,
current-carrying core field demonstrates a strong concentration of
free energy in the active-region core, from the photosphere to the
lower corona (about 70 Mm). The free energy density appears largely
co-spatial with the electric current distribution.

---------------------------------------------------------
Title: Three-dimensional Magnetic Restructuring in Two Homologous
Solar Flares in the Seismically Active NOAA AR 11283
Authors: Liu, Chang; Deng, Na; Lee, Jeongwoo; Wiegelmann, Thomas;
Jiang, Chaowei; Dennis, Brian R.; Su, Yang; Donea, Alina; Wang, Haimin
2014ApJ...795..128L Altcode: 2014arXiv1409.6391L
We carry out a comprehensive investigation comparing the
three-dimensional magnetic field restructuring, flare energy release,
and the helioseismic response of two homologous flares, the 2011
September 6 X2.1 (FL1) and September 7 X1.8 (FL2) flares in NOAA AR
11283. In our analysis, (1) a twisted flux rope (FR) collapses onto the
surface at a speed of 1.5 km s-1 after a partial eruption
in FL1. The FR then gradually grows to reach a higher altitude and
collapses again at 3 km s-1 after a fuller eruption in
FL2. Also, FL2 shows a larger decrease of the flux-weighted centroid
separation of opposite magnetic polarities and a greater change
of the horizontal field on the surface. These imply a more violent
coronal implosion with corresponding more intense surface signatures
in FL2. (2) The FR is inclined northward and together with the ambient
fields, it undergoes a southward turning after both events. This agrees
with the asymmetric decay of the penumbra observed in the peripheral
regions. (3) The amounts of free magnetic energy and nonthermal electron
energy released during FL1 are comparable to those of FL2 within the
uncertainties of the measurements. (4) No sunquake was detected in FL1;
in contrast, FL2 produced two seismic emission sources S1 and S2 both
lying in the penumbral regions. Interestingly, S1 and S2 are connected
by magnetic loops, and the stronger source S2 has a weaker vertical
magnetic field. We discuss these results in relation to the implosion
process in the low corona and the sunquake generation.

---------------------------------------------------------
Title: MHD flows at astropauses and in astrotails
Authors: Nickeler, D. H.; Wiegelmann, T.; Karlický, M.; Kraus, M.
2014ASTRP...1...51N Altcode: 2015arXiv150105122N
The geometrical shapes and the physical properties of stellar wind -
interstellar medium interaction regions form an important stage for
studying stellar winds and their embedded magnetic fields as well as
cosmic ray modulation. Our goal is to provide a proper representation
and classification of counter-flow configurations and counter-flow
interfaces in the frame of fluid theory. In addition we calculate flows
and large-scale electromagnetic fields based on which the large-scale
dynamics and its role as possible background for particle acceleration,
e.g., in the form of anomalous cosmic rays, can be studied. We find
that for the definition of the boundaries, which are determining the
astropause shape, the number and location of magnetic null points
and stagnation points is essential. Multiple separatrices can exist,
forming a highly complex environment for the interstellar and stellar
plasma. Furthermore, the formation of extended tail structures
occur naturally, and their stretched field and streamlines provide
surroundings and mechanisms for the acceleration of particles by
field-aligned electric fields.

---------------------------------------------------------
Title: Quasi-static Three-dimensional Magnetic Field Evolution in
Solar Active Region NOAA 11166 Associated with an X1.5 Flare
Authors: Vemareddy, P.; Wiegelmann, T.
2014ApJ...792...40V Altcode: 2014arXiv1406.7823V
We study the quasi-static evolution of coronal magnetic fields
constructed from the non-linear force-free field (NLFFF) approximation
aiming to understand the relation between the magnetic field topology
and ribbon emission during an X1.5 flare in active region (AR) NOAA
11166. The flare with a quasi-elliptical and two remote ribbons
occurred on 2011 March 9 at 23:13 UT over a positive flux region
surrounded by negative flux at the center of the bipolar AR. Our
analysis of the coronal magnetic structure with potential and NLFFF
solutions unveiled the existence of a single magnetic null point
associated with a fan-spine topology and is co-spatial with the hard
X-ray source. The footpoints of the fan separatrix surface agree
with the inner edge of the quasi-elliptical ribbon and the outer
spine is linked to one of the remote ribbons. During the evolution,
the slow footpoint motions stressed the field lines along the polarity
inversion line and caused electric current layers in the corona around
the fan separatrix surface. These current layers trigger magnetic
reconnection as a consequence of dissipating currents, which are
visible as cusp-shaped structures at lower heights. The reconnection
process reorganized the magnetic field topology whose signatures
are observed at the separatrices/quasi-separatrix layer structure
in both the photosphere and the corona during the pre-to-post flare
evolution. In agreement with previous numerical studies, our results
suggest that the line-tied footpoint motions perturb the fan-spine
system and cause null point reconnection, which eventually causes the
flare emission at the footpoints of the field lines.

---------------------------------------------------------
Title: Self-consistent stationary MHD shear flows in the solar
atmosphere as electric field generators
Authors: Nickeler, D. H.; Karlický, M.; Wiegelmann, T.; Kraus, M.
2014A&A...569A..44N Altcode: 2014arXiv1407.3227N
Context. Magnetic fields and flows in coronal structures, for
example, in gradual phases in flares, can be described by 2D and
3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD)
equilibria. Aims: Within a physically simplified, but exact
mathematical model, we study the electric currents and corresponding
electric fields generated by shear flows. Methods: Starting
from exact and analytically calculated magnetic potential fields,
we solved the nonlinear MHD equations self-consistently. By applying
a magnetic shear flow and assuming a nonideal MHD environment, we
calculated an electric field via Faraday's law. The formal solution
for the electromagnetic field allowed us to compute an expression
of an effective resistivity similar to the collisionless Speiser
resistivity. Results: We find that the electric field can be
highly spatially structured, or in other words, filamented. The electric
field component parallel to the magnetic field is the dominant component
and is high where the resistivity has a maximum. The electric field is a
potential field, therefore, the highest energy gain of the particles can
be directly derived from the corresponding voltage. In our example of a
coronal post-flare scenario we obtain electron energies of tens of keV,
which are on the same order of magnitude as found observationally. This
energy serves as a source for heating and acceleration of particles.

---------------------------------------------------------
Title: Well-observed Dynamics of Flaring and Peripheral Coronal
Magnetic Loops during an M-class Limb Flare
Authors: Shen, Jinhua; Zhou, Tuanhui; Ji, Haisheng; Wiegelmann,
Thomas; Inhester, Bernd; Feng, Li
2014ApJ...791...83S Altcode:
In this paper, we present a variety of well-observed dynamic behaviors
for the flaring and peripheral magnetic loops of the M6.6 class extreme
limb flare that occurred on 2011 February 24 (SOL2011-02-24T07:20)
from EUV observations by the Atmospheric Imaging Assembly on the Solar
Dynamics Observatory and X-ray observations by RHESSI. The flaring loop
motion confirms the earlier contraction-expansion picture. We find that
the U-shaped trajectory delineated by the X-ray corona source of the
flare roughly follows the direction of a filament eruption associated
with the flare. Different temperature structures of the coronal source
during the contraction and expansion phases strongly suggest different
kinds of magnetic reconnection processes. For some peripheral loops,
we discover that their dynamics are closely correlated with the filament
eruption. During the slow rising to abrupt, fast rising of the filament,
overlying peripheral magnetic loops display different responses. Two
magnetic loops on the elbow of the active region had a slow descending
motion followed by an abrupt successive fast contraction, while magnetic
loops on the top of the filament were pushed outward, slowly being
inflated for a while and then erupting as a moving front. We show that
the filament activation and eruption play a dominant role in determining
the dynamics of the overlying peripheral coronal magnetic loops.

---------------------------------------------------------
Title: Statistical Study of Free Magnetic Energy and Flare
Productivity of Solar Active Regions
Authors: Su, J. T.; Jing, J.; Wang, S.; Wiegelmann, T.; Wang, H. M.
2014ApJ...788..150S Altcode: 2014arXiv1405.2131S
Photospheric vector magnetograms from the Helioseismic and Magnetic
Imager on board the Solar Dynamic Observatory are utilized as the
boundary conditions to extrapolate both nonlinear force-free and
potential magnetic fields in solar corona. Based on the extrapolations,
we are able to determine the free magnetic energy (FME) stored in active
regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We
compare FME with the ARs' flare index (FI) and find that there is
a weak correlation (&lt;60%) between FME and FI. FME shows slightly
improved flare predictability relative to the total unsigned magnetic
flux of ARs in the following two aspects: (1) the flare productivity
predicted by FME is higher than that predicted by magnetic flux and
(2) the correlation between FI and FME is higher than that between FI
and magnetic flux. However, this improvement is not significant enough
to make a substantial difference in time-accumulated FI, rather than
individual flare, predictions.

---------------------------------------------------------
Title: Temporal Evolution of the Magnetic Topology of the NOAA Active
Region 11158
Authors: Zhao, Jie; Li, Hui; Pariat, Etienne; Schmieder, Brigitte;
Guo, Yang; Wiegelmann, Thomas
2014ApJ...787...88Z Altcode: 2014arXiv1404.5004Z
We studied the temporal evolution of the magnetic topology of the active
region (AR) 11158 based on the reconstructed three-dimensional magnetic
fields in the corona. The non-linear force-free field extrapolation
method was applied to the 12 minute cadence data obtained with the
Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory
during 5 days. By calculating the squashing degree factor Q in the
volume, the derived quasi-separatrix layers (QSLs) show that this AR has
an overall topology, resulting from a magnetic quadrupole, including a
hyperbolic flux tube (HFT) configuration that is relatively stable at
the timescale of the flare (~1-2 hr). A strong QSL, which corresponds
to some highly sheared arcades that might be related to the formation
of a flux rope, is prominent just before the M6.6 and X2.2 flares,
respectively. These facts indicate the close relationship between the
strong QSL and the high flare productivity of AR 11158. In addition,
with a close inspection of the topology, we found a small-scale HFT
that has an inverse tear-drop structure above the aforementioned
QSL before the X2.2 flare. It indicates the existence of magnetic
flux rope at this place. Even though a global configuration (HFT)
is recognized in this AR, it turns out that the large-scale HFT only
plays a secondary role during the eruption. In conclusion, we dismiss
a trigger based on the breakout model and highlight the central role
of the flux rope in the related eruption.

---------------------------------------------------------
Title: A Comparison Between Nonlinear Force-Free Field and Potential
Field Models Using Full-Disk SDO/HMI Magnetogram
Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J.; Inhester,
B.; Olson, K.; Pevtsov, A.
2014SoPh..289..831T Altcode: 2012arXiv1212.5639T
Measurements of magnetic fields and electric currents in the
pre-eruptive corona are crucial to the study of solar eruptive
phenomena, like flares and coronal mass ejections (CMEs). However,
spectro-polarimetric measurements of certain photospheric lines
permit a determination of the vector magnetic field only at the
photosphere. Therefore, there is considerable interest in accurate
modeling of the solar coronal magnetic field using photospheric vector
magnetograms as boundary data. In this work, we model the coronal
magnetic field above multiple active regions with the help of a
potential field and a nonlinear force-free field (NLFFF) extrapolation
code over the full solar disk using Helioseismic and Magnetic Imager
(SDO/HMI) data as boundary conditions. We compare projections of the
resulting magnetic field lines with full-disk coronal images from
the Atmospheric Imaging Assembly (SDO/AIA) for both models. This
study has found that the NLFFF model reconstructs the magnetic
configuration closer to observation than the potential field model
for full-disk magnetic field extrapolation. We conclude that many
of the trans-equatorial loops connecting the two solar hemispheres
are current-free.

---------------------------------------------------------
Title: Evolution of a Magnetic Flux Rope and its Overlying Arcade
Based on Nonlinear Force-free Field Extrapolations
Authors: Jing, Ju; Liu, Chang; Lee, Jeongwoo; Wang, Shuo; Wiegelmann,
Thomas; Xu, Yan; Wang, Haimin
2014ApJ...784L..13J Altcode:
Dynamic phenomena indicative of slipping reconnection and magnetic
implosion were found in a time series of nonlinear force-free field
(NLFFF) extrapolations for the active region 11515, which underwent
significant changes in the photospheric fields and produced five C-class
flares and one M-class flare over five hours on 2012 July 2. NLFFF
extrapolation was performed for the uninterrupted 5 hour period from
the 12 minute cadence vector magnetograms of the Helioseismic and
Magnetic Imager on board the Solar Dynamic Observatory. According
to the time-dependent NLFFF model, there was an elongated, highly
sheared magnetic flux rope structure that aligns well with an Hα
filament. This long filament splits sideways into two shorter segments,
which further separate from each other over time at a speed of 1-4 km
s-1, much faster than that of the footpoint motion of the
magnetic field. During the separation, the magnetic arcade arching over
the initial flux rope significantly decreases in height from ~4.5 Mm
to less than 0.5 Mm. We discuss the reality of this modeled magnetic
restructuring by relating it to the observations of the magnetic
cancellation, flares, a filament eruption, a penumbra formation,
and magnetic flows around the magnetic polarity inversion line.

---------------------------------------------------------
Title: First use of synoptic vector magnetograms for global nonlinear,
force-free coronal magnetic field models
Authors: Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.;
Pevtsov, A. A.
2014A&A...562A.105T Altcode: 2013arXiv1309.5853T
Context. The magnetic field permeating the solar atmosphere is
generally thought to provide the energy for much of the activity
seen in the solar corona, such as flares, coronal mass ejections
(CMEs), etc. To overcome the unavailability of coronal magnetic field
measurements, photospheric magnetic field vector data can be used to
reconstruct the coronal field. Currently, there are several modelling
techniques being used to calculate three-dimensional field lines into
the solar atmosphere. Aims: For the first time, synoptic maps
of a photospheric-vector magnetic field synthesized from the vector
spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations
of the Sun (SOLIS) are used to model the coronal magnetic field and
estimate free magnetic energy in the global scale. The free energy
(i.e., the energy in excess of the potential field energy) is one of
the main indicators used in space weather forecasts to predict the
eruptivity of active regions. Methods: We solve the nonlinear
force-free field equations using an optimization principle in spherical
geometry. The resulting three-dimensional magnetic fields are used
to estimate the magnetic free energy content Efree =
Enlfff - Epot, which is the difference of the
magnetic energies between the nonpotential field and the potential field
in the global solar corona. For comparison, we overlay the extrapolated
magnetic field lines with the extreme ultraviolet (EUV) observations
by the atmospheric imaging assembly (AIA) on board the Solar Dynamics
Observatory (SDO). Results: For a single Carrington rotation
2121, we find that the global nonlinear force-free field (NLFFF)
magnetic energy density is 10.3% higher than the potential one. Most
of this free energy is located in active regions.

---------------------------------------------------------
Title: Topological study of active region 11158
Authors: Zhao, Jie; Li, Hui; Pariat, Etienne; Schmieder, Brigitte;
Guo, Yang; Wiegelmann, Thomas
2014IAUS..300..479Z Altcode:
With the cylindrical equal area (CEA) projection data from the
Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics
Observatory (SDO), we reconstructed the three-dimensional (3D)
magnetic fields in the corona, using a non-linear force-free field
(NLFFF) extrapolation method every 12 minutes during five days, to
calculate the squashing degree factor Q in the volume. The results
show that this AR has an hyperbolic flux tube (HFT) configuration,
a typical topology of quadrupole, which is stable even during the two
large flares (M6.6 and X2.2 class flares).

---------------------------------------------------------
Title: Force-free Field Modeling of Twist and Braiding-induced
Magnetic Energy in an Active-region Corona
Authors: Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T.
2014ApJ...780..102T Altcode: 2013arXiv1311.3413T
The theoretical concept that braided magnetic field lines in the solar
corona may dissipate a sufficient amount of energy to account for the
brightening observed in the active-region (AR) corona has only recently
been substantiated by high-resolution observations. From the analysis
of coronal images obtained with the High Resolution Coronal Imager,
first observational evidence of the braiding of magnetic field lines
was reported by Cirtain et al. (hereafter CG13). We present nonlinear
force-free reconstructions of the associated coronal magnetic field
based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager
vector magnetograms. We deliver estimates of the free magnetic energy
associated with a braided coronal structure. Our model results suggest
(~100 times) more free energy at the braiding site than analytically
estimated by CG13, strengthening the possibility of the AR corona
being heated by field line braiding. We were able to appropriately
assess the coronal free energy by using vector field measurements and
we attribute the lower energy estimate of CG13 to the underestimated
(by a factor of 10) azimuthal field strength. We also quantify the
increase in the overall twist of a flare-related flux rope that was
noted by CG13. From our models we find that the overall twist of the
flux rope increased by about half a turn within 12 minutes. Unlike
another method to which we compare our results, we evaluate the
winding of the flux rope's constituent field lines around each other
purely based on their modeled coronal three-dimensional field line
geometry. To our knowledge, this is done for the first time here.

---------------------------------------------------------
Title: Evidence for Solar Tether-cutting Magnetic Reconnection from
Coronal Field Extrapolations
Authors: Liu, Chang; Deng, Na; Lee, Jeongwoo; Wiegelmann, Thomas;
Moore, Ronald L.; Wang, Haimin
2013ApJ...778L..36L Altcode: 2013arXiv1310.5098L
Magnetic reconnection is one of the primary mechanisms for triggering
solar eruptive events, but direct observation of this rapid process has
been a challenge. In this Letter, using a nonlinear force-free field
(NLFFF) extrapolation technique, we present a visualization of field
line connectivity changes resulting from tether-cutting reconnection
over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA
AR 11158. Evidence for the tether-cutting reconnection was first
collected through multiwavelength observations and then by analysis of
the field lines traced from positions of four conspicuous flare 1700
Å footpoints observed at the event onset. Right before the flare,
the four footpoints are located very close to the regions of local
maxima of the magnetic twist index. In particular, the field lines
from the inner two footpoints form two strongly twisted flux bundles
(up to ~1.2 turns), which shear past each other and reach out close to
the outer two footpoints, respectively. Immediately after the flare,
the twist index of regions around the footpoints diminishes greatly and
the above field lines become low-lying and less twisted (lsim0.6 turns),
overarched by loops linking the two flare ribbons formed later. About
10% of the flux (~3 × 1019 Mx) from the inner footpoints
undergoes a footpoint exchange. This portion of flux originates
from the edge regions of the inner footpoints that are brightened
first. These rapid changes of magnetic field connectivity inferred
from the NLFFF extrapolation are consistent with the tether-cutting
magnetic reconnection model.

---------------------------------------------------------
Title: Magnetic structure of solar active region NOAA 11158
Authors: Vemareddy, P.; Ambastha, A.; Wiegelmann, T.
2013BASI...41..183V Altcode: 2013arXiv1310.6895V
Magnetic fields in the solar corona are responsible for a wide range
of phenomena. However, any direct measurements of the coronal magnetic
fields are very difficult due to lack of suitable spectral lines, weak
magnetic fields, and high temperatures. Therefore, one extrapolates
photospheric field measurements into the corona. Owing to low coronal
plasma β, we can apply a force-free model in lowest order to study the
slow evolution of active region (AR) magnetic fields. On applying these
models to AR 11158 and compared with coronal plasma tracers, we found
that (1) the approximation of potential field to coronal structures
over large length scales is a reasonable one, 2) linear force-free
(LFF) assumption to AR coronal fields may not be applicable model
as it assumes uniform twist over the entire AR, and 3) for modeling
fields at sheared, stressed locations where energy release in the
form of flares are usually observed, non-linear force free fields
(NLFFF) seem to provide a good approximation. The maximum available
free-energy profile shows step-wise decrease that is sufficient to
power an M-class flare as observed.

---------------------------------------------------------
Title: Modeling coronal magnetic field using spherical geometry:
cases with several active regions
Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J.; Olson, K.
2013Ap&SS.347...21T Altcode: 2013Ap&SS.tmp..221T; 2013arXiv1301.7522T
The magnetic fields in the solar atmosphere structure the plasma,
store free magnetic energy and produce a wide variety of active
solar phenomena, like flare and coronal mass ejections (CMEs). The
distribution and strength of magnetic fields are routinely measured
in the solar surface (photosphere). Therefore, there is considerable
interest in accurately modeling the 3D structure of the coronal
magnetic field using photospheric vector magnetograms. Knowledge of
the 3D structure of magnetic field lines also help us to interpret
other coronal observations, e.g., EUV images of the radiating coronal
plasma. Nonlinear force-free field (NLFFF) models are thought to
be viable tools for those task. Usually those models use Cartesian
geometry. However, the spherical nature of the solar surface cannot
be neglected when the field of view is large. In this work, we model
the coronal magnetic field above multiple active regions using NLFFF
extrapolation code using vector magnetograph data from the Synoptic
Optical Long-term Investigations of the Sun survey (SOLIS)/Vector
Spectromagnetograph (VSM) as a boundary conditions. We compare
projections of the resulting magnetic field lines solutions with their
respective coronal EUV-images from the Atmospheric Imaging Assembly
(SDO/AIA) observed on October 15, 2011 and November 13, 2012. This study
has found that the NLFFF model in spherical geometry reconstructs the
magnetic configurations for several active regions which agrees to some
extent with observations. During October 15, 2011 observation, there are
substantial number of trans-equatorial loops carrying electric current.

---------------------------------------------------------
Title: Fragmentation of electric currents in the solar corona by
plasma flows
Authors: Nickeler, D. H.; Karlický, M.; Wiegelmann, T.; Kraus, M.
2013A&A...556A..61N Altcode: 2013arXiv1306.5155N
 Aims: We consider a magnetic configuration consisting of an
arcade structure and a detached plasmoid, resulting from a magnetic
reconnection process, as is typically found in connection with solar
flares. We study spontaneous current fragmentation caused by shear and
vortex plasma flows. Methods: An exact analytical transformation
method was applied to calculate self-consistent solutions of the
nonlinear stationary magnetohydrodynamic equations. The assumption
of incompressible field-aligned flows implies that both the Alfvén
Mach number and the mass density are constant on field lines. We first
calculated nonlinear magnetohydrostatic equilibria with the help of
the Liouville method, emulating the scenario of a solar eruptive flare
configuration with plasmoids (magnetic ropes or current-carrying loops
in 3D) and flare arcade. Then a Mach number profile was constructed
that describes the upflow along the open magnetic field lines and
implements a vortex flow inside the plasmoid. This Mach number profile
was used to map the magnetohydrostatic equilibrium to the stationary
one. Results: We find that current fragmentation takes place
at different locations within our configuration. Steep gradients of
the Alfvén Mach number are required, implying the strong influence
of shear flows on current amplification and filamentation of the
magnetohydrostatic current sheets. Crescent- or ring-like structures
appear along the outer separatrix, butterfly structures between the
upper and lower plasmoids, and strong current peaks close the lower
boundary (photosphere). Furthermore, impressing an intrinsic small-scale
structure on the upper plasmoid results in strong fragmentation of the
plasmoid. Hence fragmentation of current sheets and plasmoids is an
inherent property of magnetohydrodynamic theory. Conclusions:
Transformations from magnetohydrostatic into magnetohydrodynamic
steady-states deliver fine-structures needed for plasma heating and
acceleration of particles and bulk plasma flows in dissipative events
that are typically connected to magnetic reconnection processes in
flares and coronal mass ejections.

---------------------------------------------------------
Title: Comparison of Force-free Coronal Magnetic Field Modeling
Using Vector Fields from Hinode and Solar Dynamics Observatory
Authors: Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T.
2013ApJ...769...59T Altcode: 2013arXiv1304.3619T
Photospheric magnetic vector maps from two different instruments
are used to model the nonlinear force-free coronal magnetic field
above an active region. We use vector maps inferred from polarization
measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic
Imager (HMI) and the Solar Optical Telescope's Spectropolarimeter (SP)
on board Hinode. Besides basing our model calculations on HMI data,
we use both SP data of original resolution and scaled down to the
resolution of HMI. This allows us to compare the model results based
on data from different instruments and to investigate how a binning
of high-resolution data affects the model outcome. The resulting
three-dimensional magnetic fields are compared in terms of magnetic
energy content and magnetic topology. We find stronger magnetic fields
in the SP data, translating into a higher total magnetic energy
of the SP models. The net Lorentz forces of the HMI and SP lower
boundaries verify their force-free compatibility. We find substantial
differences in the absolute estimates of the magnetic field energy but
similar relative estimates, e.g., the fraction of excess energy and
of the flux shared by distinct areas. The location and extension of
neighboring connectivity domains differ and the SP model fields tend
to be higher and more vertical. Hence, conclusions about the magnetic
connectivity based on force-free field models are to be drawn with
caution. We find that the deviations of the model solution when based
on the lower-resolution SP data are small compared to the differences
of the solutions based on data from different instruments.

---------------------------------------------------------
Title: Evolution of the Fine Structure of Magnetic Fields in the
Quiet Sun: Observations from Sunrise/IMaX and Extrapolations
Authors: Wiegelmann, Thomas; Solanki, Sami; Borrero, Juan; Peter,
Hardi; Sunrise Team
2013EGUGA..15.5251W Altcode:
Observations with the balloon-borne Sunrise/ Imaging Magnetograph
eXperiment (IMaX) provide high spatial resolution (roughly 100 km at
disk center) measurements of the magnetic field in the photosphere of
the quiet Sun. To investigate the magnetic structure of the chromosphere
and corona, we extrapolate these photospheric measurements into
the upper solar atmosphere and analyse a 22-minute long time series
with a cadence of 33 seconds. Using the extrapolated magnetic-field
lines as tracer, we investigate temporal evolution of the magnetic
connectivity in the quiet Sun's atmosphere. The majority of magnetic
loops are asymmetric in the sense that the photospheric field strength
at the loop footpoints is very different. We find that the magnetic
connectivity of the loops changes rapidly with a typical connection
recycling time of about 3 ± 1 minutes in the upper solar atmosphere and
12 ± 4 minutes in the photosphere. This is considerably shorter than
previously found. Nonetheless, our estimate of the energy released by
the associated magnetic-reconnection processes is not likely to be the
sole source for heating the chromosphere and corona in the quiet Sun.

---------------------------------------------------------
Title: Evolution of the Fine Structure of Magnetic Fields in the
Quiet Sun: Observations from Sunrise/IMaX and Extrapolations
Authors: Wiegelmann, T.; Solanki, S. K.; Borrero, J. M.; Peter,
H.; Barthol, P.; Gandorfer, A.; Martínez Pillet, V.; Schmidt, W.;
Knölker, M.
2013SoPh..283..253W Altcode:
Observations with the balloon-borne Sunrise/Imaging Magnetograph
eXperiment (IMaX) provide high spatial resolution (roughly 100 km at
disk center) measurements of the magnetic field in the photosphere of
the quiet Sun. To investigate the magnetic structure of the chromosphere
and corona, we extrapolate these photospheric measurements into
the upper solar atmosphere and analyze a 22-minute long time series
with a cadence of 33 seconds. Using the extrapolated magnetic-field
lines as tracer, we investigate temporal evolution of the magnetic
connectivity in the quiet Sun's atmosphere. The majority of magnetic
loops are asymmetric in the sense that the photospheric field strength
at the loop foot points is very different. We find that the magnetic
connectivity of the loops changes rapidly with a typical connection
recycling time of about 3±1 minutes in the upper solar atmosphere and
12±4 minutes in the photosphere. This is considerably shorter than
previously found. Nonetheless, our estimate of the energy released by
the associated magnetic-reconnection processes is not likely to be the
sole source for heating the chromosphere and corona in the quiet Sun.

---------------------------------------------------------
Title: Force-free coronal magnetic field modeling using vector fields
from Hinode and SDO
Authors: Thalmann, Julia K.; Tiwari, Sanjiv K.; Wiegelmann, Thomas
2013EGUGA..15.1368T Altcode:
Given the lack of routine direct measurements of the magnetic
field in the solar corona, force-free reconstruction methods are
a promising tool for the diagnostics of the magnetic structure
there. Routine photospheric magnetic field measurements which monitor
the temporal evolution of an active region and contain information on
the non-potentiality of the field above are used as an input. Based on
the assumption that magnetic forces dominate the solar atmosphere, these
models allow estimates of the total and free magnetic energy content and
the structure of the magnetic field above active regions. The outcome
of force-free field modeling strongly depends on the vector magnetic
field data used as boundary condition. We compare the model results
based on simultaneously observed vector maps from the Helioseismic and
Magnetic Imager (HMI) on board Solar Dynamics Observatory and from the
Solar Optical Telescope Spectropolarimeter (SP) on board Hinode. We
find substantial differences in the absolute estimates of the magnetic
field energy but very similar relative estimates, e.g., the fraction
of energy to be set free during an eruption or the fraction of flux
linking distinct areas within an active region. Our study reveals that
only relative estimates of coronal physical quantities from force-free
models might be save and conclusions about the magnetic field topology
might be drawn with caution.

---------------------------------------------------------
Title: Magnetic Energy Partition between the Coronal Mass Ejection
and Flare from AR 11283
Authors: Feng, L.; Wiegelmann, T.; Su, Y.; Inhester, B.; Li, Y. P.;
Sun, X. D.; Gan, W. Q.
2013ApJ...765...37F Altcode:
On 2011 September 6, an X-class flare and a halo coronal mass ejection
(CME) were observed from Earth erupting from the same active region
AR 11283. The magnetic energy partition between them has been
investigated. SDO/HMI vector magnetograms were used to obtain the
coronal magnetic field using the nonlinear force-free field (NLFFF)
extrapolation method. The free magnetic energies before and after the
flare were calculated to estimate the released energy available to
power the flare and the CME. For the flare energetics, thermal and
nonthermal energies were derived using the RHESSI and GOES data. To
obtain the radiative output, SDO/EVE data in the 0.1-37 nm waveband
were utilized. We have reconstructed the three-dimensional (3D)
periphery of the CME from the coronagraph images observed by STEREO-A,
B, and SOHO. The mass calculations were then based on a more precise
Thomson-scattering geometry. The subsequent estimate of the kinetic and
potential energies of the CME took advantage of the more accurate mass,
and the height and speed in a 3D frame. The released free magnetic
energy resulting from the NLFFF model is about 6.4 × 1031
erg, which has a possible upper limit of 1.8 × 1032 erg. The
thermal and nonthermal energies are lower than the radiative output
of 2.2 × 1031 erg from SDO/EVE for this event. The total
radiation covering the whole solar spectrum is probably a few times
larger. The sum of the kinetic and potential energy of the CME could go
up to 6.5 × 1031 erg. Therefore, the free energy is able
to power the flare and the CME in AR 11283. Within the uncertainty,
the flare and the CME may consume a similar amount of free energy.

---------------------------------------------------------
Title: 2D and 3D Polar Plume Analysis from the Three Vantage Positions
of STEREO/EUVI A, B, and SOHO/EIT
Authors: de Patoul, Judith; Inhester, Bernd; Feng, Li; Wiegelmann,
Thomas
2013SoPh..283..207D Altcode: 2011arXiv1111.4123D; 2011SoPh..tmp..415D
Polar plumes appear as elongated objects starting at the solar polar
regions. Here we analyze these objects from a sequence of images
taken simultaneously by the three spacecraft telescopes STEREO/EUVI A
and B, and SOHO/EIT. We establish a method capable of automatically
identifying plumes in solar EUV images close to the limb at 1.01 -
1.39 R⊙ in order to study their temporal evolution. This
plume-identification method is based on a multiscale Hough-wavelet
analysis. Then two methods to determine the 3D localization and
structure of the plumes are discussed: first, tomography using
filtered back-projection and including the differential rotation
of the Sun and, second, conventional stereoscopic triangulation. We
show that tomography and stereoscopy are complementary for studying
polar plumes. We also show that this systematic 2D identification and
the proposed methods of 3D reconstruction are well suited to identify
plumes individually and also to analyze the distribution of plumes and
inter-plume regions. Finally, the results are discussed, focusing on
plume position and cross-sectional area.

---------------------------------------------------------
Title: Full-disk nonlinear force-free field extrapolation of SDO/HMI
and SOLIS/VSM magnetograms
Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B.; MacNeice, P.;
Pevtsov, A.; Sun, X.
2013A&A...550A..14T Altcode: 2012arXiv1210.3668T
Context. The magnetic field configuration is essential for understanding
solar explosive phenomena, such as flares and coronal mass ejections. To
overcome the unavailability of coronal magnetic field measurements,
photospheric magnetic field vector data can be used to reconstruct the
coronal field. Two complications of this approach are that the measured
photospheric magnetic field is not force-free and that one has to apply
a preprocessing routine to achieve boundary conditions suitable for the
force-free modeling. Furthermore the nonlinear force-free extrapolation
code should take uncertainties into account in the photospheric field
data. They occur due to noise, incomplete inversions, or azimuth
ambiguity-removing techniques. Aims: Extrapolation codes in
Cartesian geometry for modeling the magnetic field in the corona do not
take the curvature of the Sun's surface into account and can only be
applied to relatively small areas, e.g., a single active region. Here
we apply a method for nonlinear force-free coronal magnetic field
modeling and preprocessing of photospheric vector magnetograms in
spherical geometry using the optimization procedure to full disk vector
magnetograms. We compare the analysis of the photospheric magnetic
field and subsequent force-free modeling based on full-disk vector
maps from Helioseismic and Magnetic Imager (HMI) onboard the solar
dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the
Synoptic Optical Long-term Investigations of the Sun (SOLIS). 
Methods: We used HMI and VSM photospheric magnetic field measurements
to model the force-free coronal field above multiple solar active
regions, assuming magnetic forces to dominate. We solved the nonlinear
force-free field equations by minimizing a functional in spherical
coordinates over a full disk and excluding the poles. After searching
for the optimum modeling parameters for the particular data sets, we
compared the resulting nonlinear force-free model fields. We compared
quantities, such as the total magnetic energy content, free magnetic
energy, the longitudinal distribution of the magnetic pressure,
and surface electric current density, using our spherical geometry
extrapolation code. Results: The magnetic field lines obtained
from nonlinear force-free extrapolation based on HMI and VSM data show
good agreement. However, the nonlinear force-free extrapolation based
on HMI data contain more total magnetic energy, free magnetic energy,
the longitudinal distribution of the magnetic pressure, and surface
electric current density than do the VSM data.

---------------------------------------------------------
Title: Double Power-law Distribution of Magnetic Energy in the Solar
Corona over an Active Region
Authors: Shen, Jinhua; Ji, Haisheng; Wiegelmann, Thomas; Inhester,
Bernd
2013ApJ...764...86S Altcode:
In this paper, we study the magnetic energy (ME) structure contained
in the solar corona over the active region NOAA 11158. The time period
is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which
an X-class flare occurred. The nonlinear force-free field (NLFFF)
and the potential field extrapolation are carried out to model the
coronal magnetic field over this active region, using high-quality
photospheric vector magnetograms observed by the Helioseismic and
Magnetic Imager on board the Solar Dynamics Observatory as boundary
conditions. We find that the volume distribution for the density of
the ME (B 2/8π) and the ohmic dissipation power (ODP, j
2/σ), in which j is the electric current density (c/4π∇
× B) and σ is the conductivity in the corona, can be readily fitted by
a broken-down double-power law. The turn-over density for the spectrum
of the ME and ODP is found to be fixed at ~1.0 × 104
erg cm-3 and ~2.0 × 10-15 W cm-3
(assuming σ = 105 Ω-1 m-1),
respectively. Compared with their first power-law spectra (fitted below
the corresponding turn-over value) which remain unchanged, the second
power-law spectra (fitted above the corresponding turn-over value) for
the NLFFF's ME and ODP show flare-associated changes. The potential
field remains steady. These results indicate that a magnetic field
with energy density larger than the turn-over energy density plays a
dominant role in powering the flare.

---------------------------------------------------------
Title: On the Comparison of Nonlinear Force-free Models Based on
Vector-magnetograms from Different Instruments
Authors: Thalmann, J. K.; Wiegelmann, T.; Tiwari, S. K.; Sun, X.
2012AGUFMSH41C2120T Altcode:
We investigate the three-dimensional structure of the magnetic field in
the outer solar atmosphere with the help of photospheric magnetic vector
maps based on measurements from the Helioseismic and Magnetic Imager
(HMI) on board the Solar Dynamics Observatory and of the Solar Optical
Telescope Spectral-polarimeter (SP) on board the Hinode spacecraft. HMI
and SP magnetic vector maps of NOAA AR 11382 on 21-22 December 2011
are used as lower boundary condition for nonlinear force-free field
reconstructions. We compare the resulting three-dimensional coronal
magnetic field models in terms of the energy content, the magnetic
pressure, the vertical distribution of the magnetic field and
associated electric current density, as well as the magnetic field
line configuration and compare the latter to the loops visible in
coronal images from the SDO Atmospheric Imaging Assembly.

---------------------------------------------------------
Title: Doppler shift of hot coronal lines in a moss area of an
active region
Authors: Dadashi, N.; Teriaca, L.; Tripathi, D.; Solanki, S. K.;
Wiegelmann, T.
2012A&A...548A.115D Altcode: 2012arXiv1211.5473D
The moss is the area at the footpoint of the hot (3 to 5 MK) loops
forming the core of the active region where emission is believed to
result from the heat flux conducted down to the transition region from
the hot loops. Studying the variation of Doppler shift as a function
of line formation temperatures over the moss area can give clues
on the heating mechanism in the hot loops in the core of the active
regions. We investigate the absolute Doppler shift of lines formed
at temperatures between 1 MK and 2 MK in a moss area within active
region NOAA 11243 using a novel technique that allows determining the
absolute Doppler shift of EUV lines by combining observations from
the SUMER and EIS spectrometers. The inner (brighter and denser) part
of the moss area shows roughly constant blue shift (upward motions)
of 5 km s-1 in the temperature range of 1 MK to 1.6 MK. For
hotter lines the blue shift decreases and reaches 1 km s-1
for Fe xv 284 Å (~2 MK). The measurements are discussed in relation
to models of the heating of hot loops. The results for the hot coronal
lines seem to support the quasi-steady heating models for nonsymmetric
hot loops in the core of active regions.

---------------------------------------------------------
Title: How Should One Optimize Nonlinear Force-Free Coronal Magnetic
Field Extrapolations from SDO/HMI Vector Magnetograms?
Authors: Wiegelmann, T.; Thalmann, J. K.; Inhester, B.; Tadesse, T.;
Sun, X.; Hoeksema, J. T.
2012SoPh..281...37W Altcode: 2012SoPh..tmp...67W; 2012arXiv1202.3601W
The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics
Observatory (SDO) provides 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 semianalytic
and numeric equilibria and applied to vector magnetograms from Hinode
and ground-based observations. Recently we implemented a new version
which takes into account measurement errors in photospheric vector
magnetograms. Photospheric field measurements are often affected by
measurement errors and finite nonmagnetic forces inconsistent for use
as a boundary for a force-free field in the corona. To deal with these
uncertainties, we developed two improvements: i) preprocessing of the
surface measurements to make them compatible with a force-free field,
and ii) new code which keeps a balance between the force-free constraint
and deviation from the photospheric field measurements. Both methods
contain free parameters, which must be optimized for use with data from
SDO/HMI. In this work we describe the corresponding analysis method
and evaluate the force-free equilibria by how well force-freeness and
solenoidal conditions are fulfilled, by the angle between magnetic
field and electric current, and by comparing projections of magnetic
field lines with coronal images from the Atmospheric Imaging Assembly
(SDO/AIA). We also compute the available free magnetic energy and
discuss the potential influence of control parameters.

---------------------------------------------------------
Title: Coronal Magnetic Field Structure and Evolution for Flaring
AR 11117 and Its Surroundings
Authors: Tadesse, Tilaye; Wiegelmann, T.; Inhester, B.; Pevtsov, A.
2012SoPh..281...53T Altcode: 2011arXiv1109.4889T; 2012SoPh..tmp...60T
In this study, photospheric vector magnetograms obtained with the
Synoptic Optical Long-term Investigations of the Sun (SOLIS) survey
are used as boundary conditions to model three-dimensional nonlinear
force-free (NLFF) coronal magnetic fields as a sequence of NLFF
equilibria in spherical geometry. We study the coronal magnetic field
structure inside an active region and its temporal evolution. We compare
the magnetic field configuration obtained from NLFF extrapolation
before and after the flaring event in active region (AR) 11117 and
its surroundings observed on 27 October 2010, and we also 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 1.74×1032 erg,
which represents about 13.5 % of the NLFF magnetic energy before the
flare. In this study, we find that electric currents from AR 11117 to
its surroundings were disrupted after the flare.

---------------------------------------------------------
Title: First 4D Reconstruction of an Eruptive Prominence Using Three
Simultaneous View Directions
Authors: Chifu, I.; Inhester, B.; Mierla, M.; Chifu, V.; Wiegelmann, T.
2012SoPh..281..121C Altcode: 2012SoPh..tmp..213C
Data from the STEREO (Solar Terrestrial Relations Observatory)
mission are intensively used for 3D reconstruction of solar coronal
structures. After the launch of the SDO (Solar Dynamic Observatory)
satellite, its additional observations give the possibility to have
a third eye for more accurate 3D reconstruction in the very low
corona (&lt; 1.5 R⊙). With our reconstruction code MBSR
(Multi-view B-spline Stereoscopic Reconstruction), we use three view
directions (STEREO A, B, and SDO) to perform the 3D reconstruction
and evolution of a prominence which triggered a CME on 1 August
2010. In the paper we present the reconstruction of this prominence
from the moment it starts to erupt until it leaves the field of view
of the coronagraph. We also determine the evolution of the leading
edge of the CME. Based on the temporal evolution, we analyze some of
its properties, such as velocity, acceleration, opening and rotation
angles and evolution of the cavity.

---------------------------------------------------------
Title: Modeling Magnetic Field Structure of a Solar Active Region
Corona Using Nonlinear Force-free Fields in Spherical Geometry
Authors: Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.;
Wiegelmann, T.
2012ApJ...760...47G Altcode: 2012arXiv1210.0998G
We test a nonlinear force-free field (NLFFF) optimization code
in spherical geometry using an analytical solution from Low and
Lou. Several tests are run, ranging from idealized cases where exact
vector field data are provided on all boundaries, to cases where noisy
vector data are provided on only the lower boundary (approximating
the solar problem). Analytical tests also show that the NLFFF code
in the spherical geometry performs better than that in the Cartesian
one when the field of view of the bottom boundary is large, say, 20°
× 20°. Additionally, we apply the NLFFF model to an active region
observed by the Helioseismic and Magnetic Imager on board the Solar
Dynamics Observatory (SDO) both before and after an M8.7 flare. For
each observation time, we initialize the models using potential field
source surface (PFSS) extrapolations based on either a synoptic chart
or a flux-dispersal model, and compare the resulting NLFFF models. The
results show that NLFFF extrapolations using the flux-dispersal model
as the boundary condition have slightly lower, therefore better,
force-free, and divergence-free metrics, and contain larger free
magnetic energy. By comparing the extrapolated magnetic field lines with
the extreme ultraviolet (EUV) observations by the Atmospheric Imaging
Assembly on board SDO, we find that the NLFFF performs better than
the PFSS not only for the core field of the flare productive region,
but also for large EUV loops higher than 50 Mm.

---------------------------------------------------------
Title: LEMUR: Large European module for solar Ultraviolet
Research. European contribution to JAXA's Solar-C mission
Authors: Teriaca, Luca; Andretta, Vincenzo; Auchère, Frédéric;
Brown, Charles M.; Buchlin, Eric; Cauzzi, Gianna; Culhane, J. Len;
Curdt, Werner; Davila, Joseph M.; Del Zanna, Giulio; Doschek, George
A.; Fineschi, Silvano; Fludra, Andrzej; Gallagher, Peter T.; Green,
Lucie; Harra, Louise K.; Imada, Shinsuke; Innes, Davina; Kliem,
Bernhard; Korendyke, Clarence; Mariska, John T.; Martínez-Pillet,
Valentin; Parenti, Susanna; Patsourakos, Spiros; Peter, Hardi; Poletto,
Luca; Rutten, Robert J.; Schühle, Udo; Siemer, Martin; Shimizu,
Toshifumi; Socas-Navarro, Hector; Solanki, Sami K.; Spadaro, Daniele;
Trujillo-Bueno, Javier; Tsuneta, Saku; Dominguez, Santiago Vargas;
Vial, Jean-Claude; Walsh, Robert; Warren, Harry P.; Wiegelmann,
Thomas; Winter, Berend; Young, Peter
2012ExA....34..273T Altcode: 2011ExA...tmp..135T; 2011arXiv1109.4301T
The solar outer atmosphere is an extremely dynamic environment
characterized by the continuous interplay between the plasma and the
magnetic field that generates and permeates it. Such interactions play a
fundamental role in hugely diverse astrophysical systems, but occur at
scales that cannot be studied outside the solar system. Understanding
this complex system requires concerted, simultaneous solar observations
from the visible to the vacuum ultraviolet (VUV) and soft X-rays, at
high spatial resolution (between 0.1” and 0.3”), at high temporal
resolution (on the order of 10 s, i.e., the time scale of chromospheric
dynamics), with a wide temperature coverage (0.01 MK to 20 MK,
from the chromosphere to the flaring corona), and the capability of
measuring magnetic fields through spectropolarimetry at visible and
near-infrared wavelengths. Simultaneous spectroscopic measurements
sampling the entire temperature range are particularly important. These
requirements are fulfilled by the Japanese Solar-C mission (Plan B),
composed of a spacecraft in a geosynchronous orbit with a payload
providing a significant improvement of imaging and spectropolarimetric
capabilities in the UV, visible, and near-infrared with respect to
what is available today and foreseen in the near future. The Large
European Module for solar Ultraviolet Research (LEMUR), described
in this paper, is a large VUV telescope feeding a scientific payload
of high-resolution imaging spectrographs and cameras. LEMUR consists
of two major components: a VUV solar telescope with a 30 cm diameter
mirror and a focal length of 3.6 m, and a focal-plane package composed
of VUV spectrometers covering six carefully chosen wavelength ranges
between 170 Å and 1270 Å. The LEMUR slit covers 280” on the Sun with
0.14” per pixel sampling. In addition, LEMUR is capable of measuring
mass flows velocities (line shifts) down to 2 km s - 1 or
better. LEMUR has been proposed to ESA as the European contribution
to the Solar C mission.

---------------------------------------------------------
Title: Solar Force-free Magnetic Fields
Authors: Wiegelmann, Thomas; Sakurai, Takashi
2012LRSP....9....5W Altcode:
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 non-magnetic forces like plasma pressure gradient and
gravity can be neglected in the lowest order. This model assumption
is called the force-free field assumption, as the Lorentz force
vanishes. This can be obtained by either vanishing electric currents
(leading to potential fields) or the currents are co-aligned 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 so-called linear force-free 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 force-free 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 ground-based (for example SOLIS) and space-born
(for example Hinode and SDO) instruments. If we can obtain accurate
force-free 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., EUV images of the radiating coronal plasma.

---------------------------------------------------------
Title: The Formation of a Magnetic Channel by Emergence of
Current-Carrying Magnetic Fields
Authors: Lim, E. -K.; Chae, J.; Jing, J.; Wang, H.; Wiegelmann, T.
2012ASPC..454..185L Altcode:
The term magnetic channel indicates a series of polarity reversals
separating elongated flux threads with opposite polarities. We studied
the formation process of the magnetic channel in AR 10930 using time
sequence SP data taken by SOT/Hinode. As a result, we detected both
upflows (-0.5 to -1.0 km s-1) and downflows (+1.5 to +2.0 km
s-1) within the channel site, and a pair of strong vertical
current threads of opposite polarity along the channel. We also analyzed
coronal magnetic fields computed from the non-linear force-free field
extrapolation, and found that the current density in the lower corona
increased as the channel structure evolved. These findings support
the idea that the magnetic channel represents the emergence of the
twisted flux tube.

---------------------------------------------------------
Title: Nonlinear Force-free Field Modeling of a Solar Active Region
Using SDO/HMI and SOLIS/VSM Data
Authors: Thalmann, J. K.; Pietarila, A.; Sun, X.; Wiegelmann, T.
2012AJ....144...33T Altcode: 2012arXiv1206.1141T
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 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 compare to each other.

---------------------------------------------------------
Title: Reconstruction of 3D Coronal Magnetic Structures from
THEMIS/MTR and Hinode/SOT Vector Maps
Authors: Schmieder, B.; Guo, Y.; Aulanier, G.; Démoulin, P.; Török,
T.; Bommier, V.; Wiegelmann, T.; Gosain, S.
2012ASPC..454..363S Altcode:
Coordinated campaigns using THEMIS, Hinode, and other instruments have
allowed us to study the magnetic fields of faculae, filaments, and
active regions. In a first case, we modelled the 3D magnetic field in a
flaring active region with a nonlinear force-free field extrapolation,
using magnetic vectors observed by THEMIS/MTR as boundary condition. In
order to construct a consistent bottom boundary for the model, we
first removed the 180 degree ambiguity of the transverse fields and
minimized the force and torque in the observed vector fields. We found
a twisted magnetic flux rope, well aligned with the polarity inversion
line and a part of an Hα filament, and located where a large flare is
initiated about two hours later. In a second case, Hinode/SOT allowed
us to detect fine flux concentrations in faculae, while MTR provided us
with magnetic information at different levels in the atmosphere. The
polarimetry analysis of the MTR and SOT data gave consistent results,
using both UNNOFIT and MELANIE inversion codes.

---------------------------------------------------------
Title: Evolution of Relative Magnetic Helicity and Current Helicity
in NOAA Active Region 11158
Authors: Jing, Ju; Park, Sung-Hong; Liu, Chang; Lee, Jeongwoo;
Wiegelmann, Thomas; Xu, Yan; Deng, Na; Wang, Haimin
2012ApJ...752L...9J Altcode:
Both magnetic and current helicities are crucial ingredients for
describing the complexity of active-region magnetic structure. In this
Letter, we present the temporal evolution of these helicities contained
in NOAA active region 11158 during five days from 2011 February 12
to 16. The photospheric vector magnetograms of the Helioseismic and
Magnetic Imager on board the Solar Dynamic Observatory were used as
the boundary conditions for the coronal field extrapolation under the
assumption of nonlinear force-free field, from which we calculated
both relative magnetic helicity and current helicity. We construct a
time-altitude diagram in which altitude distribution of the magnitude
of current helicity density is displayed as a function of time. This
diagram clearly shows a pattern of upwardly propagating current
helicity density over two days prior to the X2.2 flare on February
15 with an average propagation speed of ~36 m s-1. The
propagation is synchronous with the emergence of magnetic flux into
the photosphere, and indicative of a gradual energy buildup for the
X2.2 flare. The time profile of the relative magnetic helicity shows
a monotonically increasing trend most of the time, but a pattern
of increasing and decreasing magnetic helicity above the monotonic
variation appears prior to each of two major flares, M6.6 and X2.2,
respectively. The physics underlying this bump pattern is not fully
understood. However, the fact that this pattern is apparent in the
magnetic helicity evolution but not in the magnetic flux evolution
makes it a useful indicator in forecasting major flares.

---------------------------------------------------------
Title: First Results from the SUNRISE Mission
Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.;
Gandorfer, A.; Hirzberger, J.; Jafarzadeh, S.; Lagg, A.; Riethmüller,
T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; González,
M. J. M.; Pillet, V. M.; Khomenko, E.; Yelles Chaouche, L.; Iniesta,
J. C. d. T.; Domingo, V.; Palacios, J.; Knölker, M.; González,
N. B.; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt,
W.; Steiner, O.; Title, A. M.
2012ASPC..455..143S Altcode:
The SUNRISE balloon-borne solar observatory consists of a 1m aperture
Gregory telescope, a UV filter imager, an imaging vector polarimeter,
an image stabilization system, and further infrastructure. The first
science flight of SUNRISE yielded high-quality data that reveal the
structure, dynamics, and evolution of solar convection, oscillations,
and magnetic fields at a resolution of around 100 km in the quiet
Sun. Here we describe very briefly the mission and the first results
obtained from the SUNRISE data, which include a number of discoveries.

---------------------------------------------------------
Title: Rapid Changes of Photospheric Magnetic Field after
Tether-cutting Reconnection and Magnetic Implosion
Authors: Liu, Chang; Deng, N.; Liu, R.; Lee, J.; Wiegelmann, T.;
Jing, J.; Xu, Y.; Wang, S.; Wang, H.
2012AAS...22051605L Altcode:
A rapid and persistent change of the photospheric magnetic field
co-temporal with the impulsive phase of solar flare emissions has
been recognized as an important element of the flare process from both
observational and theoretical points of view. Using the state-of-the-art
photospheric vector magnetograms acquired by HMI and Hinode, we have
studied such a change associated with the 2011 February 13 M6.6 flare
in NOAA AR 11158. Our aim is not only to identify the field change
but also to understand it in the context of magnetic reconnection
involved with the flare. In our analysis, (1) the rapid change is
detected in a compact region lying at the central neutral line,
where the mean horizontal field strength increased significantly by
28% in 30 minutes. The field also becomes more sheared and inclined
to the surface. (2) Sunspot umbrae with opposite polarity lying on
the two sides of the compact region experienced sudden perturbations,
moving in opposite directions at an apparent velocity of 3 km/s against
the long-term evolution. (3) The field variation induces a downward
Lorentz-force change acting on the compact region and two opposite
horizontal components of the Lorentz-force change consistent with
the sunspot motions. (4) Four conspicuous UV flare kernels appear at
the event onset and are linked to ribbon-like hard X-ray emissions
in the impulsive phase. The compact region lies between the central
two kernels that are co-spatial with the central feet of the sigmoid
according to the nonlinear force-free field (NLFFF) model. (5) The
NLFFF model further shows that strong coronal currents are concentrated
immediately above the compact region and undergo apparent downward
collapse after the sigmoid eruption. These results are discussed in
favor of both the tether-cutting reconnection producing the flare and
the ensuing implosion (collapse) of the coronal field resulting from
the energy release.

---------------------------------------------------------
Title: Evolution of Coronal Relative Magnetic Helicity and Current
Helicity in NOAA Active Region 11158
Authors: Jing, Ju; Park, S.; Liu, C.; Wiegelmann, T.; Xu, Y.; Deng,
N.; Wang, H.
2012AAS...22041102J Altcode:
The evolution of relative magnetic helicity contained in an active
region is a crucial ingredient to describe the complexity in solar
atmosphere. In this paper we present the temporal evolution of relative
magnetic helicity (Hr) in NOAA active region 11158 during a 4-day
period of February 12-15, 2011. The photospheric vector magnetograms of
the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic
Observatory (SDO) are used as the boundary conditions to extrapolate
the three-dimensional (3D) non-linear force-free (NLFF) coronal magnetic
field, based on which Hr inside the 3D coronal volume is deduced. A bump
pattern in Hr prior to two major flares is noted and may be a precursor
of major flares. We compare the temporal variation of Hr with that of
the accumulated amount of helicity injected through the photosphere that
is inferred independently by tracking the apparent motion of magnetic
footpoints at the photosphere from a line-of-sight HMI magnetogram
series. The good consistency between Hr and the injected helicity
suggests that the helicity is generated largely below the photosphere
and is well conserved from the subsurface into the corona. In addition,
the altitude-time diagram of the average unsigned current helicity
displays a clear propagation pattern over two days prior to the X2.2
flare of February 15, with an average propagation rate of 36 m/s. The
propagation is synchronous with the emergence of magnetic flux, and
indicative of a gradual energy buildup for the flares.

---------------------------------------------------------
Title: A First Look at Magnetic Field Data Products from SDO/HMI
Authors: Liu, Y.; Scherrer, P. H.; Hoeksema, J. T.; Schou, J.; Bai,
T.; Beck, J. G.; Bobra, M.; Bogart, R. S.; Bush, R. I.; Couvidat,
S.; Hayashi, K.; Kosovichev, A. G.; Larson, T. P.; Rabello-Soares,
C.; Sun, X.; Wachter, R.; Zhao, J.; Zhao, X. P.; Duvall, T. L., Jr.;
DeRosa, M. L.; Schrijver, C. J.; Title, A. M.; Centeno, R.; Tomczyk,
S.; Borrero, J. M.; Norton, A. A.; Barnes, G.; Crouch, A. D.; Leka,
K. D.; Abbett, W. P.; Fisher, G. H.; Welsch, B. T.; Muglach, K.;
Schuck, P. W.; Wiegelmann, T.; Turmon, M.; Linker, J. A.; Mikić,
Z.; Riley, P.; Wu, S. T.
2012ASPC..455..337L Altcode:
The Helioseismic and Magnetic Imager (HMI; Scherrer &amp; Schou 2011)
is one of the three instruments aboard the Solar Dynamics Observatory
(SDO) that was launched on February 11, 2010 from Cape Canaveral,
Florida. The instrument began to acquire science data on March 24. The
regular operations started on May 1. HMI measures the Doppler velocity
and line-of-sight magnetic field in the photosphere at a cadence of
45 seconds, and the vector magnetic field at a 135-second cadence,
with a 4096× 4096 pixels full disk coverage. The vector magnetic
field data is usually averaged over 720 seconds to suppress the p-modes
and increase the signal-to-noise ratio. The spatial sampling is about
0".5 per pixel. HMI observes the Fe i 6173 Å absorption line, which
has a Landé factor of 2.5. These data are further used to produce
higher level data products through the pipeline at the HMI-AIA Joint
Science Operations Center (JSOC) - Science Data Processing (Scherrer et
al. 2011) at Stanford University. In this paper, we briefly describe the
data products, and demonstrate the performance of the HMI instrument. We
conclude that the HMI is working extremely well.

---------------------------------------------------------
Title: Evolution of Magnetic Field and Energy in a Major Eruptive
Active Region Based on SDO/HMI Observation
Authors: Sun, Xudong; Hoeksema, J. Todd; Liu, Yang; Wiegelmann,
Thomas; Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia
2012ApJ...748...77S Altcode: 2012arXiv1201.3404S
We report the evolution of the magnetic field and its energy in NOAA
active region 11158 over five days based on a vector magnetogram series
from the Helioseismic and Magnetic Imager (HMI) on board the Solar
Dynamic Observatory (SDO). Fast flux emergence and strong shearing
motion led to a quadrupolar sunspot complex that produced several
major eruptions, including the first X-class flare of Solar Cycle
24. Extrapolated nonlinear force-free coronal fields show substantial
electric current and free energy increase during early flux emergence
near a low-lying sigmoidal filament with a sheared kilogauss field
in the filament channel. The computed magnetic free energy reaches a
maximum of ~2.6 × 1032 erg, about 50% of which is stored
below 6 Mm. It decreases by ~0.3 × 1032 erg within 1 hr
of the X-class flare, which is likely an underestimation of the actual
energy loss. During the flare, the photospheric field changed rapidly:
the horizontal field was enhanced by 28% in the core region, becoming
more inclined and more parallel to the polarity inversion line. Such
change is consistent with the conjectured coronal field "implosion" and
is supported by the coronal loop retraction observed by the Atmospheric
Imaging Assembly (AIA). The extrapolated field becomes more "compact"
after the flare, with shorter loops in the core region, probably because
of reconnection. The coronal field becomes slightly more sheared in the
lowest layer, relaxes faster with height, and is overall less energetic.

---------------------------------------------------------
Title: On the Role of the Background Overlying Magnetic Field in
Solar Eruptions
Authors: Nindos, A.; Patsourakos, S.; Wiegelmann, T.
2012ApJ...748L...6N Altcode:
The primary constraining force that inhibits global solar eruptions is
provided by the overlying background magnetic field. Using magnetic
field data from both the Helioseismic and Magnetic Imager aboard the
Solar Dynamics Observatory and the spectropolarimeter of the Solar
Optical Telescope aboard Hinode, we study the long-term evolution of
the background field in active region AR11158 that produced three major
coronal mass ejections (CMEs). The CME formation heights were determined
using EUV data. We calculated the decay index -(z/B)(∂B/∂z) of the
magnetic field B (i.e., how fast the field decreases with height, z)
related to each event from the time of the active region emergence until
well after the CMEs. At the heights of CME formation, the decay indices
were 1.1-2.1. Prior to two of the events, there were extended periods
(of more than 23 hr) where the related decay indices at heights above
the CME formation heights either decreased (up to -15%) or exhibited
small changes. The decay index related to the third event increased (up
to 118%) at heights above 20 Mm within an interval that started 64 hr
prior to the CME. The magnetic free energy and the accumulated helicity
into the corona contributed the most to the eruptions by their increase
throughout the flux emergence phase (by factors of more than five and
more than two orders of magnitude, respectively). Our results indicate
that the initiation of eruptions does not depend critically on the
temporal evolution of the variation of the background field with height.

---------------------------------------------------------
Title: Magnetic Connectivity Between Active Regions 10987, 10988,
and 10989 by Means of Nonlinear Force-Free Field Extrapolation
Authors: Tadesse, Tilaye; Wiegelmann, T.; Inhester, B.; Pevtsov, A.
2012SoPh..277..119T Altcode: 2011SoPh..tmp..167T; 2011arXiv1104.2246T; 2011SoPh..tmp..236T;
2011SoPh..tmp..102T
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, 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 Spectromagnetograph (VSM) data
from the Synoptic Optical Long-term Investigations of the Sun (SOLIS)
survey 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. We have studied
the time evolution of the 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.

---------------------------------------------------------
Title: Relation between current sheets and vortex sheets in stationary
incompressible MHD
Authors: Nickeler, D. H.; Wiegelmann, T.
2012AnGeo..30..545N Altcode: 2012arXiv1203.5493N
Magnetohydrodynamic configurations with strong localized current
concentrations and vortices play an important role in the dissipation
of energy in space and astrophysical plasma. Within this work we
investigate the relation between current sheets and vortex sheets
in incompressible, stationary equilibria. For this approach it is
helpful that the similar mathematical structure of magnetohydrostatics
and stationary incompressible hydrodynamics allows us to transform
static equilibria into stationary ones. The main control function
for such a transformation is the profile of the Alfvén-Mach number
MA, which is always constant along magnetic field lines,
but can change from one field line to another. In the case of a global
constant MA, vortices and electric current concentrations are
parallel. More interesting is the nonlinear case, where MA
varies perpendicular to the field lines. This is a typical situation
at boundary layers like the magnetopause, heliopause, the solar wind
flowing around helmet streamers and at the boundary of solar coronal
holes. The corresponding current and vortex sheets show in some
cases also an alignment, but not in every case. For special density
distributions in 2-D, it is possible to have current but no vortex
sheets. In 2-D, vortex sheets of field aligned-flows can also exist
without strong current sheets, taking the limit of small Alfvén Mach
numbers into account. The current sheet can vanish if the Alfvén Mach
number is (almost) constant and the density gradient is large across
some boundary layer. It should be emphasized that the used theory is
not only valid for small Alfvén Mach numbers MA &lt;&lt;
1, but also for MA ≲ 1. Connection to other theoretical
approaches and observations and physical effects in space plasmas
are presented. Differences in the various aspects of theoretical
investigations of current sheets and vortex sheets are given.

---------------------------------------------------------
Title: Particle kinetic analysis of a polar jet from SECCHI COR data
Authors: Feng, L.; Inhester, B.; de Patoul, J.; Wiegelmann, T.; Gan,
W. Q.
2012A&A...538A..34F Altcode: 2011arXiv1112.2255F
 Aims: We analyze coronagraph observations of a polar jet observed
by the Sun Earth Connection Coronal and Heliospheric Investigation
(SECCHI) instrument suite onboard the Solar TErrestrial RElations
Observatory (STEREO) spacecraft. Methods: In our analysis
we compare the brightness distribution of the jet in white-light
coronagraph images with a dedicated kinetic particle model. We obtain
a consistent estimate of the time that the jet was launched from the
solar surface and an approximate initial velocity distribution in the
jet source. The method also allows us to check the consistency of the
kinetic model. In this first application, we consider only gravity as
the dominant force on the jet particles along the magnetic field. 
Results: We find that the kinetic model explains the observed brightness
evolution well. The derived initiation time is consistent with the jet
observations by the EUVI telescope at various wavelengths. The initial
particle velocity distribution is fitted by Maxwellian distributions
and we find deviations of the high-energy tail from the Maxwellian
distributions. We estimated the jet's total electron content to have
a mass between 3.2 × 1014 and 1.8 × 1015
g. Mapping the integrated particle number along the jet trajectory
to its source region and assuming a typical source region size, we
obtain an initial electron density between 8 × 109 and
5 × 1010 cm-3 that is characteristic for the
lower corona or the upper chromosphere. The total kinetic energy of all
particles in the jet source region amounts from 2.1 × 1028
to 2.4 × 1029 erg.

---------------------------------------------------------
Title: Computer Vision for the Solar Dynamics Observatory (SDO)
Authors: Martens, P. C. H.; Attrill, G. D. R.; Davey, A. R.; Engell,
A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar, S. H.;
Savcheva, A.; Su, Y.; Testa, P.; Wills-Davey, M.; Bernasconi, P. N.;
Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F.; Cirtain, J. W.;
DeForest, C. E.; Angryk, R. A.; De Moortel, I.; Wiegelmann, T.;
Georgoulis, M. K.; McAteer, R. T. J.; Timmons, R. P.
2012SoPh..275...79M Altcode: 2011SoPh..tmp..144M; 2011SoPh..tmp..213M; 2011SoPh..tmp....8M
In Fall 2008 NASA selected a large international consortium to produce
a comprehensive automated feature-recognition system for the Solar
Dynamics Observatory (SDO). The SDO data that we consider are all of the
Atmospheric Imaging Assembly (AIA) images plus surface magnetic-field
images from the Helioseismic and Magnetic Imager (HMI). We produce
robust, very efficient, professionally coded software modules that
can keep up with the SDO data stream and detect, trace, and analyze
numerous phenomena, including flares, sigmoids, filaments, coronal
dimmings, polarity inversion lines, sunspots, X-ray bright points,
active regions, coronal holes, EIT waves, coronal mass ejections
(CMEs), coronal oscillations, and jets. We also track the emergence and
evolution of magnetic elements down to the smallest detectable features
and will provide at least four full-disk, nonlinear, force-free magnetic
field extrapolations per day. The detection of CMEs and filaments is
accomplished with Solar and Heliospheric Observatory (SOHO)/Large
Angle and Spectrometric Coronagraph (LASCO) and ground-based Hα
data, respectively. A completely new software element is a trainable
feature-detection module based on a generalized image-classification
algorithm. Such a trainable module can be used to find features that
have not yet been discovered (as, for example, sigmoids were in the
pre-Yohkoh era). Our codes will produce entries in the Heliophysics
Events Knowledgebase (HEK) as well as produce complete catalogs for
results that are too numerous for inclusion in the HEK, such as the
X-ray bright-point metadata. This will permit users to locate data on
individual events as well as carry out statistical studies on large
numbers of events, using the interface provided by the Virtual Solar
Observatory. The operations concept for our computer vision system is
that the data will be analyzed in near real time as soon as they arrive
at the SDO Joint Science Operations Center and have undergone basic
processing. This will allow the system to produce timely space-weather
alerts and to guide the selection and production of quicklook images and
movies, in addition to its prime mission of enabling solar science. We
briefly describe the complex and unique data-processing pipeline,
consisting of the hardware and control software required to handle
the SDO data stream and accommodate the computer-vision modules, which
has been set up at the Lockheed-Martin Space Astrophysics Laboratory
(LMSAL), with an identical copy at the Smithsonian Astrophysical
Observatory (SAO).

---------------------------------------------------------
Title: Rapid Changes of Photospheric Magnetic Field after
Tether-cutting Reconnection and Magnetic Implosion
Authors: Liu, Chang; Deng, Na; Liu, Rui; Lee, Jeongwoo; Wiegelmann,
Thomas; Jing, Ju; Xu, Yan; Wang, Shuo; Wang, Haimin
2012ApJ...745L...4L Altcode: 2011arXiv1112.3598L
The rapid, irreversible change of the photospheric magnetic field
has been recognized as an important element of the solar flare
process. This Letter reports such a rapid change of magnetic fields
during the 2011 February 13 M6.6 flare in NOAA AR 11158 that we found
from the vector magnetograms of the Helioseismic and Magnetic Imager
(HMI) with 12 minute cadence. High-resolution magnetograms of Hinode
that are available at ~-5.5, -1.5, 1.5, and 4 hr relative to the flare
maximum are used to reconstruct a three-dimensional coronal magnetic
field under the nonlinear force-free field (NLFFF) assumption. UV
and hard X-ray images are also used to illuminate the magnetic field
evolution and energy release. The rapid change is mainly detected by
HMI in a compact region lying in the center of the magnetic sigmoid,
where the mean horizontal field strength exhibited a significant
increase of 28%. The region lies between the initial strong UV and
hard X-ray sources in the chromosphere, which are cospatial with the
central feet of the sigmoid according to the NLFFF model. The NLFFF
model further shows that strong coronal currents are concentrated
immediately above the region, and that, more intriguingly, the
coronal current system underwent an apparent downward collapse after
the sigmoid eruption. These results are discussed in favor of both
the tether-cutting reconnection producing the flare and the ensuing
implosion of the coronal field resulting from the energy release.

---------------------------------------------------------
Title: Nonlinear Force-Free Extrapolation of Vector Magnetograms
into the Corona
Authors: Thalmann, J. K.; Wiegelmann, T.; Sun, X.; Hoeksema, J. T.;
Liu, Y.; Tadesse, T.
2011AGUFMSH33C..05T Altcode:
To investigate the structure and evolution of the coronal magnetic
field, we extrapolate measurements of the photospheric magnetic
field vector into the corona based on the force-free assumption. A
complication of this approach is that the measured photospheric
magnetic field is not force-free and that one has to apply a
preprocessing routine in order to achieve boundary conditions suitable
for the force-free modelling. Furthermore the nonlinear force-free
extrapolation code takes errors in the photospheric field data into
account which occur due to noise, incomplete inversions or ambiguity
removing techniques. Within this work we compare extrapolations from
SDO/HMI and SOLIS vector magnetograms and explain how to find optimum
parameters for handling the data of a particular instrument. The
resulting coronal magnetic field lines are quantitatively compared
with coronal EUV-images from SDO/AIA.

---------------------------------------------------------
Title: Evolution of the fine structure of magnetic fields in the
quiet Sun: Combining Sunrise observations and modelling
Authors: Wiegelmann, T.; Solanki, S.; Borrero, J.; Martinez Pillet,
V.; Sunrise Team
2011AGUFMSH41B..06W Altcode:
Observations with the balloon borne SUNRISE/IMAX instrument provide
us with unprecedented high spatial resolution (pixel size 40 km)
measurements of the magnetic field in the photosphere of the quiet
Sun. To investigate the magnetic structure of the chromosphere and
corona we extrapolate these photospheric measurements into the upper
solar atmosphere and analyse a timeseries with a cadence of 33s. We find
that the majority of closed loops which reach into the chromosphere
or corona have one foot point in strong photospheric magnetic field
regions (B&gt;300 G). Most loops are asymmetric and the weaker foot
point is often located in the internetwork. We find that the magnetic
connectivity of the loops changes rapidly with a typical recycling
time of about 2 min in the upper solar atmosphere and 14 min in the
photosphere. We discuss, to which extend the observed topological
changes can be interpreted as evidence for magnetic reconnection and
the relevance of these processes for coronal heating.

---------------------------------------------------------
Title: Evolution of Magnetic Field in the Flaring Active Region AR
11158 Based on SDO/HMI Observation
Authors: Sun, X.; Hoeksema, J. T.; Liu, Y.; Wiegelmann, T.; Hayashi, K.
2011AGUFMSH31A1993S Altcode:
We report the evolution of magnetic field and its energy in NOAA
active region 11158 based on a vector magnetogram series from the
Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic
Observatory (SDO). Over 5 days, the quadrupolar sunspot complex
produced multiple eruptions, including the first X-class flare of the
current solar cycle. Extrapolated non-linear force-free coronal fields
suggest substantial electric current and free energy injection during
early flux emergence along a newly-formed, pronounced filament. About
75% of the inferred free energy is stored below 10 Mm; the total
decreased by 0.25E32 erg (10%) within 1 hour of the X-class flare,
which is likely an underestimation of the actual energy loss. During
the flare, photospheric flux underwent rapid redistribution: horizontal
flux density was enhanced by 28% in the AR core region. Extrapolation
shows that such change is consistent with the conjectured coronal field
"implosion". Multiple coronal loops retraction were indeed observed
for 5 minutes over 10 Mm during the impulsive phase. Modeling indicates
that the coronal field becomes more compact after the flare, its lower
layers more energetic but overall less so.

---------------------------------------------------------
Title: Nonpotentiality of Chromospheric Fibrils in NOAA Active
Regions 11092 and 9661
Authors: Jing, Ju; Yuan, Yuan; Reardon, Kevin; Wiegelmann, Thomas;
Xu, Yan; Wang, Haimin
2011ApJ...739...67J Altcode:
In this paper, we present a method to automatically segment
chromospheric fibrils from Hα observations and further identify their
orientation. We assume that chromospheric fibrils are aligned with the
magnetic field. By comparing the orientation of the fibrils with the
azimuth of the embedding chromospheric magnetic field extrapolated from
a potential field model, the shear angle, a measure of nonpotentiality,
along the fibrils is readily deduced. Following this approach, we make
a quantitative assessment of the nonpotentiality of fibrils in two NOAA
active regions (ARs): (1) the relatively simple AR 11092, observed with
very high resolution by Interferometric Bidimensional Spectrometer,
and (2) a β-γ-δ AR 9661, observed with median resolution by Big
Bear Solar Observatory before and after an X1.6 flare.

---------------------------------------------------------
Title: Evolution of Magnetic Field and Energy in A Major Eruptive
Active Region Based on SDO/HMI Observation
Authors: Sun, Xudong; Hoeksema, Todd; Liu, Yang; Wiegelmann, Thomas;
Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia
2011sdmi.confE..63S Altcode:
We report the evolution of magnetic field and its energy in NOAA
AR 11158 based on a vector magnetogram series from the Helioseismic
and Magnetic Imager (HMI). Fast flux emergence and strong shearing
motion created a quadrupolar sunspot complex that produced several
major eruptions, including the first X-class flare of solar cycle
24. Extrapolated non-linear force-free coronal field shows substantial
electric current and free energy increase during early flux emergence
along a newly-formed, low-lying filament with a typical 1000 G field
strength and 0.45 Mm^(-1) alpha-parameter at its center. The computed
magnetic free energy reaches a maximum of 2.62E32 erg, about 50%
stored below 6 Mm. This free energy decreases by 0.33E32 erg within
1 hour of the X-class flare, which is likely an underestimation of
the actual energy loss. During the flare, photospheric field changed
rapidly: the horizontal field was enhanced by 28% in the AR core
region. Such change is consistent with the conjectured coronal field
"implosion", and is in line with both the reconnection signatures
and the coronal loop retraction observed by the Atmospheric Image
Assembly (AIA). Extrapolation indicates that the coronal field relaxes
more rapidly with height after the flare and becomes overall less
energetic. These preliminary results demonstrate the capability to
quantitatively study the AR field topology and energetics using SDO
data- although difficulties still abound.

---------------------------------------------------------
Title: Estimating the Relative Helicity of Coronal Magnetic Fields
Authors: Thalmann, J. K.; Inhester, B.; Wiegelmann, T.
2011SoPh..272..243T Altcode:
To quantify changes of the solar coronal field connectivity during
eruptive events, one can use magnetic helicity, which is a measure of
the shear or twist of a current-carrying (non-potential) field. To
find a physically meaningful quantity, a relative measure, giving
the helicity of a current-carrying field with respect to a reference
(potential) field, is often evaluated. This requires a knowledge of the
three-dimensional vector potential. We present a method to calculate
the vector potential for a solenoidal magnetic field as the sum of a
Laplacian part and a current-carrying part. The only requirements are
the divergence freeness of the Laplacian and current-carrying magnetic
field and the sameness of their normal field component on the bounding
surface of the considered volume.

---------------------------------------------------------
Title: A filament supported by different magnetic field configurations
Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.;
Aulanier, G.; Török, T.; Bommier, V.
2011IAUS..273..328G Altcode:
A nonlinear force-free magnetic field extrapolation of vector
magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the
simultaneous existence of different magnetic configurations within
one active region filament: one part of the filament is supported by
field line dips within a flux rope, while the other part is located
in dips within an arcade structure. Although the axial field chirality
(dextral) and the magnetic helicity (negative) are the same along the
whole filament, the chiralities of the filament barbs at different
sections are opposite, i.e., right-bearing in the flux rope part and
left-bearing in the arcade part. This argues against past suggestions
that different barb chiralities imply different signs of helicity of
the underlying magnetic field. This new finding about the chirality of
filaments will be useful to associate eruptive filaments and magnetic
cloud using the helicity parameter in the Space Weather Science.

---------------------------------------------------------
Title: The Sun at high resolution: first results from the Sunrise
mission
Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller,
A.; Gandorfer, A.; Hirzberger, J.; Lagg, A.; Riethmüller, T. L.;
Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; Pillet, V. Martínez;
Khomenko, E.; del Toro Iniesta, J. C.; Domingo, V.; Palacios, J.;
Knölker, M.; González, N. Bello; Borrero, J. M.; Berkefeld, T.;
Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M.
2011IAUS..273..226S Altcode:
The Sunrise balloon-borne solar observatory consists of a 1m aperture
Gregory telescope, a UV filter imager, an imaging vector polarimeter,
an image stabilization system and further infrastructure. The first
science flight of Sunrise yielded high-quality data that reveal the
structure, dynamics and evolution of solar convection, oscillations
and magnetic fields at a resolution of around 100 km in the quiet
Sun. Here we describe very briefly the mission and the first results
obtained from the Sunrise data, which include a number of discoveries.

---------------------------------------------------------
Title: Nonpotentiality of Chromospheric Fibrils in the Active Regions
NOAA 9661 and NOAA 11092
Authors: Jing, Ju; Yuan, Y.; Reardon, K.; Wiegelmann, T.; Deng, N.;
Xu, Y.; Wang, H.
2011SPD....42.1738J Altcode: 2011BAAS..43S.1738J
We have developed a method to automatically segment chromospheric
fibrils from Halpha observations and further identify their
orientation. We assume that chromospheric fibrils are magnetic
field-aligned. By comparing the orientation of the fibrils with the
azimuth of the embedding chromospheric magnetic field extrapolated
from the photosphere or chromosphere with the help of a potential
field model, the shear angle, a measure of nonpotentiality, along
the fibrils is readily deduced. Following this approach, we make
a quantitative assessment of the nonpotentiality of fibrils in the
active region NOAA 9661 and NOAA 11092. The spatial distribution and
the histogram of the shear angle along fibrils are presented.

---------------------------------------------------------
Title: Evolution of Magnetic Field in the Flaring Active Region
11158 Observed by SDO/HMI
Authors: Sun, Xudong; Hoeksema, T.; Liu, Y.; Wiegelmann, T.;
Hayashi, K.
2011SPD....42.2101S Altcode: 2011BAAS..43S.2101S
We report the evolution of the magnetic field in NOAA AR11158 over 5
days (2011 Feb 12-16) using preliminary vector magnetograms from the
Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic
Observatory (SDO). This region consisted of two pairs of major
sunspots and displayed a complex quadrupolar field topology. It
produced multiple major flares and eruptions, including the first
X-class flare of the current solar cycle. Strong shear motion and flux
emergence were both present, with apparent emergence preceding each
major flare. We reconstruct the coronal field from a series of vector
data using a non-linear force-free (NLFF) extrapolation. The estimated
free magnetic energy shows a great increase during the early emergence
of the current-carrying flux, while a significant, permanent decrease (
0.5e32 erg, or 20%) is found after the X-class flare despite continuous
flux injection. We relate this decrease to a previously reported, sudden
change of the photospheric field after the flare. The extrapolated
coronal field structure correspondingly becomes more "compact": the
low-lying of field appears more sheared and stores more free energy,
and higher-altitude field decays faster with height and becomes more
potential. The coronal field overall becomes less-energetic.

---------------------------------------------------------
Title: Nonlinear force-free field extrapolation in spherical
geometry: improved boundary data treatment applied to a SOLIS/VSM
vector magnetogram
Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B.; Pevtsov, A.
2011A&A...527A..30T Altcode: 2010arXiv1011.6285T
Context. Understanding the 3D structure of coronal magnetic field
is important to understanding: the onset of flares and coronal mass
ejections, and the stability of active regions, and to monitoring
the magnetic helicity and free magnetic energy and other phenomena
in the solar atmosphere. Routine measurements of the solar magnetic
field are mainly carried out in the photosphere. Therefore, one has to
infer the field strength in the upper layers of the solar atmosphere
from the measured photospheric field based on the assumption that the
corona is force-free. Meanwhile, those measured data are inconsistent
with the above force-free assumption. Therefore, one has to apply some
transformations to these data before nonlinear force-free extrapolation
codes can be applied. Aims: Extrapolation codes in Cartesian
geometry for modelling the magnetic field in the corona do not take the
curvature of the Sun's surface into account and can only be applied to
relatively small areas, e.g., a single active region. Here we apply
a method for nonlinear force-free coronal magnetic field modelling
and preprocessing of photospheric vector magnetograms in spherical
geometry using the optimization procedure. Methods: We solve
the nonlinear force-free field equations by minimizing a functional
in spherical coordinates over a restricted area of the Sun. We extend
the functional by an additional term, which allows us to incorporate
measurement errors and treat regions lacking observational data. We
use vector magnetograph data from the Synoptic Optical Long-term
Investigations of the Sun survey (SOLIS) to model the coronal magnetic
field. We study two neighbouring magnetically connected active regions
observed on May 15 2009. Results: For vector magnetograms with
variable measurement precision and randomly scattered data gaps (e.g.,
SOLIS/VSM), the new code yields field models that satisfy the solenoidal
and force-free condition significantly better as it allows deviations
between the extrapolated boundary field and observed boundary data
within the measurement errors. Data gaps are assigned an infinite
error. We extend this new scheme to spherical geometry and apply it
for the first time to real data.

---------------------------------------------------------
Title: Mesogranulation and the Solar Surface Magnetic Field
Distribution
Authors: Yelles Chaouche, L.; Moreno-Insertis, F.; Martínez Pillet,
V.; Wiegelmann, T.; Bonet, J. A.; Knölker, M.; Bellot Rubio, L. R.;
del Toro Iniesta, J. C.; Barthol, P.; Gandorfer, A.; Schmidt, W.;
Solanki, S. K.
2011ApJ...727L..30Y Altcode: 2010arXiv1012.4481Y
The relation of the solar surface magnetic field with mesogranular
cells is studied using high spatial (≈100 km) and temporal (≈30
s) resolution data obtained with the IMaX instrument on board
SUNRISE. First, mesogranular cells are identified using Lagrange
tracers (corks) based on horizontal velocity fields obtained through
local correlation tracking. After ≈20 minutes of integration, the
tracers delineate a sharp mesogranular network with lanes of width
below about 280 km. The preferential location of magnetic elements in
mesogranular cells is tested quantitatively. Roughly 85% of pixels with
magnetic field higher than 100 G are located in the near neighborhood
of mesogranular lanes. Magnetic flux is therefore concentrated in
mesogranular lanes rather than intergranular ones. Second, magnetic
field extrapolations are performed to obtain field lines anchored in
the observed flux elements. This analysis, therefore, is independent
of the horizontal flows determined in the first part. A probability
density function (PDF) is calculated for the distribution of distances
between the footpoints of individual magnetic field lines. The PDF has
an exponential shape at scales between 1 and 10 Mm, with a constant
characteristic decay distance, indicating the absence of preferred
convection scales in the mesogranular range. Our results support
the view that mesogranulation is not an intrinsic convective scale
(in the sense that it is not a primary energy-injection scale of solar
convection), but also give quantitative confirmation that, nevertheless,
the magnetic elements are preferentially found along mesogranular lanes.

---------------------------------------------------------
Title: A comparison of preprocessing methods for solar force-free
magnetic field extrapolation
Authors: Fuhrmann, M.; Seehafer, N.; Valori, G.; Wiegelmann, T.
2011A&A...526A..70F Altcode: 2010arXiv1010.6015F
Context. Extrapolations of solar photospheric vector magnetograms into
three-dimensional magnetic fields in the chromosphere and corona are
usually done under the assumption that the fields are force-free. This
condition is violated in the photosphere itself and a thin layer in
the lower atmosphere above. The field calculations can be improved
by preprocessing the photospheric magnetograms. The intention here
is to remove a non-force-free component from the data. Aims:
We compare two preprocessing methods presently in use, namely the
methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann
et al. (2007, A&amp;A, 476, 349). Methods: The two preprocessing
methods were applied to a vector magnetogram of the recently observed
active region NOAA AR 10 953. We examine the changes in the magnetogram
effected by the two preprocessing algorithms. Furthermore, the original
magnetogram and the two preprocessed magnetograms were each used as
input data for nonlinear force-free field extrapolations by means of two
different methods, and we analyze the resulting fields. Results:
Both preprocessing methods managed to significantly decrease the
magnetic forces and magnetic torques that act through the magnetogram
area and that can cause incompatibilities with the assumption of
force-freeness in the solution domain. The force and torque decrease is
stronger for the Fuhrmann et al. method. Both methods also reduced the
amount of small-scale irregularities in the observed photospheric field,
which can sharply worsen the quality of the solutions. For the chosen
parameter set, the Wiegelmann et al. method led to greater changes
in strong-field areas, leaving weak-field areas mostly unchanged,
and thus providing an approximation of the magnetic field vector in
the chromosphere, while the Fuhrmann et al. method weakly changed
the whole magnetogram, thereby better preserving patterns present
in the original magnetogram. Both preprocessing methods raised the
magnetic energy content of the extrapolated fields to values above the
minimum energy, corresponding to the potential field. Also, the fields
calculated from the preprocessed magnetograms fulfill the solenoidal
condition better than those calculated without preprocessing.

---------------------------------------------------------
Title: Driving mechanism of a failed eruption
Authors: Guo, Y.; Ding, M. D.; Schmieder, B.; Li, H.; Törö, T.;
Wiegelmann, T.
2011ASInC...2..307G Altcode:
We find a magnetic flux rope before the M1.1 flare in active
region 10767 on 2005 May 27 by a nonlinear force-free field
extrapolation. TRACE observations of the filament eruption show that the
erupting structure performed a writhing deformation and stopped rising
at a certain height, suggesting that the flux rope converted some of its
twist into writhe and was confined in the corona. After calculating the
twist of the flux rope, we find that it was comparable to thresholds
of the helical kink instability found in numerical simulations. We
conclude that the activation and rise of the flux rope were triggered
and initially driven by the kink instability. The decay index of
the external magnetic field stays below the threshold for the torus
instability within a long height range. The confinement of the eruption
could be explained by the failure of the torus instability. Hard X-ray
sources at the peak of the M1.1 flare coincided with the footpoints
of the erupting helical structure, which indicates a high possibility
that hard X-ray sources were produced more efficiently in the flux rope.

---------------------------------------------------------
Title: First Result of Field Extrapolation Based on HMI Vector
Magnetic Data
Authors: Sun, X.; Hoeksema, J. T.; Wiegelmann, T.; Hayashi, K.; Liu, Y.
2010AGUFMSH11A1607S Altcode:
Magnetic field extrapolation based on photospheric field has long
been used to infer the coronal field. However, past studies are often
restrained by the line-of-sight nature of observation, or the inadequate
spatial/temporal resolution of the few available vector data. With the
new Helioseismic and Magnetic Imager (HMI), we are now able to produce
full-disk, high cadence (12 min), high resolution (1 arcsec) vector
data continuously for the first time. In this paper, we analyze a time
sequence of HMI vector data and apply several extrapolation methods
(potential-field model, nonlinear force-free model, MHD simulation,
etc.) to study the evolution of overlying field structure in lower
corona. Results from different methods are cross-compared and examined
against coronal observations. This study will provide insight to
modeling the coronal field with greater detail and better accuracy,
and eventually help the understanding of dynamic processes in solar
atmosphere.

---------------------------------------------------------
Title: Driving Mechanism and Onset Condition of a Confined Eruption
Authors: Guo, Y.; Ding, M. D.; Schmieder, B.; Li, H.; Török, T.;
Wiegelmann, T.
2010ApJ...725L..38G Altcode:
We study a confined eruption accompanied by an M1.1 flare in solar
active region (AR) NOAA 10767 on 2005 May 27, where a pre-eruptive
magnetic flux rope was reported in a nonlinear force-free field (NLFFF)
extrapolation. The observations show a strong writhing motion of the
erupting structure, suggesting that a flux rope was indeed present
and converted some of its twist into writhe in the course of the
eruption. Using the NLFFF extrapolation, we calculate the twist of
the pre-eruptive flux rope and find that it is in very good agreement
with thresholds of the helical kink instability found in numerical
simulations. We conclude that the activation and rise of the flux
rope were triggered and driven by the instability. Using a potential
field extrapolation, we also estimate the height distribution of the
decay index of the external magnetic field in the AR 1 hr prior to the
eruption. We find that the decay index stays below the threshold for
the torus instability for a significant height range above the erupting
flux rope. This provides a possible explanation for the confinement
of the eruption to the low corona.

---------------------------------------------------------
Title: Magnetic Loops in the Quiet Sun
Authors: Wiegelmann, T.; Solanki, S. K.; Borrero, J. M.; Martínez
Pillet, V.; del Toro Iniesta, J. C.; Domingo, V.; Bonet, J. A.;
Barthol, P.; Gandorfer, A.; Knölker, M.; Schmidt, W.; Title, A. M.
2010ApJ...723L.185W Altcode: 2010arXiv1009.4715W
We investigate the fine structure of magnetic fields in the atmosphere
of the quiet Sun. We use photospheric magnetic field measurements from
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 force-free extrapolation
techniques. We find that most magnetic loops that reach into the
chromosphere or higher have one footpoint in relatively strong magnetic
field regions in the photosphere. Ninety-one percent of the magnetic
energy in the mid-chromosphere (at a height of 1 Mm) is in field
lines, whose stronger footpoint 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 footpoint has a strength B &lt;
300 G and is located in the internetwork (IN). Such loops are expected
to be strongly dynamic and have short lifetimes, as dictated by the
properties of the IN fields.

---------------------------------------------------------
Title: The Formation of a Magnetic Channel by the Emergence of
Current-carrying Magnetic Fields
Authors: Lim, Eun-Kyung; Chae, Jongchul; Jing, Ju; Wang, Haimin;
Wiegelmann, Thomas
2010ApJ...719..403L Altcode: 2010arXiv1009.0420L
A magnetic channel—a series of polarity reversals separating elongated
flux threads with opposite polarities—may be a manifestation of
a highly non-potential magnetic configuration in active regions. To
understand its formation, we have carried out a detailed analysis of
the magnetic channel in AR 10930 using data taken by the Solar Optical
Telescope/Hinode. As a result, we found upflows (-0.5 to -1.0 km
s-1) and downflows (+1.5 to +2.0 km s-1) inside
and at both tips of the thread, respectively, and a pair of strong
vertical currents of opposite polarity along the channel. Moreover,
our analysis of the nonlinear force-free fields constructed from the
photospheric magnetic field indicates that the current density in the
lower corona may have gradually increased as a result of the continuous
emergence of the highly sheared flux along the channel. With these
results, we suggest that the magnetic channel originates from the
emergence of the twisted flux tube that has formed below the surface
before the emergence.

---------------------------------------------------------
Title: Thin current sheets caused by plasma flow gradients in space
and astrophysical plasma
Authors: Nickeler, D. H.; Wiegelmann, T.
2010AnGeo..28.1523N Altcode: 2010arXiv1008.2848N
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 2-D 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 Grad-Shafranov equation and then we transform these
static equilibria into a stationary state with plasma flow. We are
in particular interested to study SMHD-equilibria 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.

---------------------------------------------------------
Title: Nonlinear Force-free Modeling of Magnetic Fields in a Solar
Filament
Authors: Jing, Ju; Yuan, Yuan; Wiegelmann, Thomas; Xu, Yan; Liu, Rui;
Wang, Haimin
2010ApJ...719L..56J Altcode:
We present a striking filament pattern in the nonlinear force-free
(NLFF) chromospheric magnetic field of the active region NOAA
10956. The NLFF chromospheric field is extrapolated from the Hinode
high-resolution photospheric vector magnetogram using the weighted
optimization method. The modeled structure is characterized by a
highly sheared field with strong horizontal magnetic components and
has a virtually identical shape and location as the filament seen in
Hα. The modeled field strength agrees with the recent He I 10830 Å
observations by Kuckein et al.. The unequivocal resemblance between the
NLFF extrapolation and the Hα observation not only demonstrates the
ability of the NLFF field to reproduce chromospheric features, but also
provides a valuable diagnostic tool for the filament magnetic fields.

---------------------------------------------------------
Title: Re-flaring of a Post-flare Loop System Driven by Flux Rope
Emergence and Twisting
Authors: Cheng, X.; Ding, M. D.; Guo, Y.; Zhang, J.; Jing, J.;
Wiegelmann, T.
2010ApJ...716L..68C Altcode: 2010arXiv1005.1720C
In this Letter, we study in detail the evolution of the post-flare
loops on 2005 January 15 that occurred between two consecutive solar
eruption events, both of which generated a fast halo coronal mass
ejection (CME) and a major flare. The post-flare loop system, formed
after the first CME/flare eruption, evolved rapidly, as manifested by
the unusual accelerating rise motion of the loops. Through nonlinear
force-free field models, we obtain the magnetic structure over the
active region. It clearly shows that the flux rope below the loops also
kept rising, accompanied with increasing twist and length. Finally, the
post-flare magnetic configuration evolved to a state that resulted in
the second CME/flare eruption. This is an event in which the post-flare
loops can re-flare in a short period of ~16 hr following the first
CME/flare eruption. The observed re-flaring at the same location
is likely driven by the rapid evolution of the flux rope caused by
the magnetic flux emergence and the rotation of the sunspot. This
observation provides valuable information on CME/flare models and
their prediction.

---------------------------------------------------------
Title: How to deal with measurement errors and lacking data in
nonlinear force-free coronal magnetic field modelling?
Authors: Wiegelmann, T.; Inhester, B.
2010A&A...516A.107W Altcode:
Context. The measured solar photospheric magnetic field vector
is extrapolated into the solar corona under the assumption of a
force-free plasma. In the generic case this problem is nonlinear. Aims: We aim to improve an algorithm for computing the nonlinear
force-free coronal magnetic field. We are in particular interested
to incorporate measurement errors and to handle lacking data in
the boundary conditions. Methods: We solve the nonlinear
force-free field equations by minimizing a functional. Within this
work we extend the functional by an additional term, which allows
us to incorporate measurement errors and treat regions with lacking
observational data. We test the new code with the help of a well
known semi-analytic test case. We compare coronal magnetic field
extrapolations from ideal boundary conditions and boundary conditions
where the transversal magnetic field information is lacking or has
a poor signal-to-noise ratio in weak field regions. Results:
For ideal boundary conditions the new code gives the same result as
the old code. The advantage of the new approach, which includes an
error matrix, is visible only for non-ideal boundary conditions. The
force-free and solenoidal conditions are fulfilled significantly better
and the solutions agrees somewhat better with the exact solution. The
new approach also relaxes the boundary and allows a deviation from the
boundary data in poor signal-to-noise ratio areas. Conclusions:
The incorporation of measurement errors in the updated extrapolation
code significantly improves the quality of nonlinear force-free field
extrapolation from imperfect boundary conditions.

---------------------------------------------------------
Title: Free Magnetic Energy and Flare Productivity of Active Regions
Authors: Jing, Ju; Tan, C.; Yuan, Y.; Wang, B.; Wiegelmann, T.; Xu,
Y.; Wang, H.
2010AAS...21640415J Altcode: 2010BAAS...41..902J
In this study, the photospheric vector magnetograms, obtained with the
Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are
used as the boundary conditions to extrapolate the three-dimensional
non-linear force-free (NLFF) coronal magnetic fields. The observed
non-force-free photospheric magnetic fields are preprocessed towards the
nearly force-free chromospheric magnetic fields. The performance of the
preprocessing procedure is evaluated by comparing with chromospheric
magnetic fields obtained by the Vector SpectroMagnetograph instrument
located on the Synoptic Optical Long-term Investigations of the Sun
(SOLIS) Tower. Then the weighted optimization method is applied
to the preprocessed boundary data to extrapolate the NLFF fields
with which we are able to estimate the free magnetic energy stored
in the active regions. The magnitude scaling correlation between
the free magnetic energy and the soft X-ray flare index of active
regions is then studied. The latter quantifies the impending flare
production of active regions over the subsequent 1-, 2- and 3-day
time windows. Based on 75 samples, we find a positive correlation
between the free energy and the flare index. We also study the temporal
variation of free magnetic energy for three active regions, of which
two are flare-active and one is flare-quiet during the observation
over a period of several days. While the magnitude of free magnetic
energy unambiguously differentiates between the flare-active and the
flare-quiet regions, the temporal variation of free magnetic energy
does not exhibit a clear and consistent pre-flare pattern. This may
indicate that the trigger mechanism of flares is as important as the
energy storage in active regions.

---------------------------------------------------------
Title: Computer Vision for SDO: First Results from the SDO Feature
Finding Algorithms
Authors: Martens, Petrus C.; Attrill, G.; Davey, A.; Engell, A.;
Farid, S.; Grigis, P.; Kasper, J.; Korreck, K.; Saar, S.; Su, Y.;
Testa, P.; Wills-Davey, M.; Bernasconi, P.; Raouafi, N.; Georgoulis,
M.; Deforest, C.; Peterson, J.; Berghoff, T.; Delouille, V.; Hochedez,
J.; Mampaey, B.; Verbeek, C.; Cirtain, J.; Green, S.; Timmons, R.;
Savcheva, A.; Angryk, R.; Wiegelmann, T.; McAteer, R.
2010AAS...21630804M Altcode:
The SDO Feature Finding Team produces robust and very efficient
software modules that can keep up with the relentless SDO data stream,
and detect, trace, and analyze a large number of phenomena including:
flares, sigmoids, filaments, coronal dimmings, polarity inversion
lines, sunspots, X-ray bright points, active regions, coronal holes,
EIT waves, CME's, coronal oscillations, and jets. In addition we track
the emergence and evolution of magnetic elements down to the smallest
features that are detectable, and we will also provide at least four
full disk nonlinear force-free magnetic field extrapolations per day. During SDO commissioning we will install in the near-real time data
pipeline the modules that provide alerts for flares, coronal dimmings,
and emerging flux, as well as those that trace filaments, sigmoids,
polarity inversion lines, and active regions. We will demonstrate
the performance of these modules and illustrate their use for science
investigations.

---------------------------------------------------------
Title: An Attempt in Incorporating Local and Global Coronal Magnetic
Field Modeling
Authors: Sun, Xudong; Hoeksema, J. T.; Zhao, X.; Wiegelmann, T.
2010AAS...21640215S Altcode: 2010BAAS...41R.875S
Coronal field extrapolation models are based on observed photospheric
field data. The global models (eg. MHD and potential field source
surface model (PFSS)) study the large scale stable structures of the
corona, whereas local models (eg. non-linear force free field model
(NLFFF)) look at smaller scale events that are more dynamic, with more
drastic energy build up and release. While both have been successful at
explaining a variety of solar activities, fewer studies are devoted to
how these two types of models could be integrated, and how large scale
and small scale magnetic activities interact with each other. In this
study, we demonstrate our first attempt in this direction. We plan
to use (1) series of updated synchronic maps and the PFSS model and
(2) series of vector magnetograms with the NLFFF model to study the
magnetic structure before and after major solar events. If available,
results using the newest HMI data will also illustrate the prospect
of future studies.

---------------------------------------------------------
Title: Coexisting Flux Rope and Dipped Arcade Sections Along One
Solar Filament
Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.;
Aulanier, G.; Török, T.; Bommier, V.
2010ApJ...714..343G Altcode:
We compute the three-dimensional magnetic field of an active
region in order to study the magnetic configuration of active region
filaments. The nonlinear force-free field model is adopted to compute
the magnetic field above the photosphere, where the vector magnetic
field was observed by THEMIS/MTR on 2005 May 27. We propose a new
method to remove the 180° ambiguity of the transverse field. Next, we
analyze the implications of the preprocessing of the data by minimizing
the total force and torque in the observed vector fields. This step
provides a consistent bottom boundary condition for the nonlinear
force-free field model. Then, using the optimization method to compute
the coronal field, we find a magnetic flux rope along the polarity
inversion line. The magnetic flux rope aligns well with part of an Hα
filament, while the total distribution of the magnetic dips coincides
with the whole Hα filament. This implies that the magnetic field
structure in one section of the filament is a flux rope, while the
other is a sheared arcade. The arcade induced a left-bearing filament
in the magnetic field of negative helicity, which is opposite to the
chirality of barbs that a flux rope would induce in a magnetic field
of the same helicity sign. The field strength in the center of the flux
rope is about 700 G, and the twist of the field lines is ~1.4 turns.

---------------------------------------------------------
Title: Free Magnetic Energy and Flare Productivity of Active Regions
Authors: Jing, Ju; Tan, Changyi; Yuan, Yuan; Wang, Benjamin;
Wiegelmann, Thomas; Xu, Yan; Wang, Haimin
2010ApJ...713..440J Altcode:
In this study, the photospheric vector magnetograms, obtained with the
Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are
used as the boundary conditions to extrapolate the three-dimensional
nonlinear force-free (NLFF) coronal magnetic fields. The observed
non-force-free photospheric magnetic fields are preprocessed toward the
nearly force-free chromospheric magnetic fields. The performance of the
preprocessing procedure is evaluated by comparing with chromospheric
magnetic fields obtained by the Vector SpectroMagnetograph instrument
located on the Synoptic Optical Long-term Investigations of the
Sun Tower. Then, the weighted optimization method is applied to the
preprocessed boundary data to extrapolate the NLFF fields with which
we are able to estimate the free magnetic energy stored in the active
regions. The magnitude scaling correlation between the free magnetic
energy and the soft X-ray flare index (FI) of active regions is then
studied. The latter quantifies the impending flare production of active
regions over the subsequent 1, 2, and 3 day time windows. Based on
75 samples, we find a positive correlation between the free energy
and the FI. We also study the temporal variation of free magnetic
energy for three active regions, of which two are flare-active and
one is flare-quiet during the observation over a period of several
days. While the magnitude of free magnetic energy unambiguously
differentiates between the flare-active and the flare-quiet regions,
the temporal variation of free magnetic energy does not exhibit a
clear and consistent pre-flare pattern. This may indicate that the
trigger mechanism of flares is as important as the energy storage in
active regions.

---------------------------------------------------------
Title: Nonlinear force-free modelling: influence of inaccuracies in
the measured magnetic vector
Authors: Wiegelmann, T.; Yelles Chaouche, L.; Solanki, S. K.; Lagg, A.
2010A&A...511A...4W Altcode: 2009arXiv0912.3002W
Context. Solar magnetic fields are regularly extrapolated into the
corona starting from photospheric magnetic measurements that can
be affected by significant uncertainty. Aims: We study how
inaccuracies introduced into the maps of the photospheric magnetic
vector by the inversion of ideal and noisy Stokes parameters influence
the extrapolation of nonlinear force-free magnetic fields. 
Methods: We compute nonlinear force-free magnetic fields based on
simulated vector magnetograms, by the inversion of Stokes profiles
that were computed by a 3-D radiation MHD simulation snapshot. These
extrapolations are compared with extrapolations that originate directly
in 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 performed qualitatively by visually inspecting 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
force-free field extrapolation method tested here is relatively
insensitive to the effects of noise in measured polarization spectra
at levels consistent with present-day instruments. Conclusions:
Our results show that we can reconstruct the coronal magnetic field as
a nonlinear force-free field from realistic photospheric measurements
with an accuracy of a few percent, at least in the absence of sunspots.

---------------------------------------------------------
Title: Stereoscopic 3D reconstruction of polar plumes from the
three vantage positions of STEREO/SECCHI A, B and SOHO/EIT using
the Hough-wavelet transform
Authors: de Patoul, Judith; Feng, Li; Inhester, Bernd; Wiegelmann,
Thomas
2010cosp...38.2947D Altcode: 2010cosp.meet.2947D
We present the results from a method to determine the 3D position
and orientation of po-lar plumes from three corresponding images
observed simultaneously by three spacecrafts, STEREO/SECCHI A,
B, and SOHO/EIT. We have applied both conventional stereoscopic
triangulation and a new detection tool based on a combination of Hough
and wavelet trans-form. We show that the obtained plume orientation
can help to verify magnetic field models in the pole region where
surface observations are difficult and their extrapolation may be
problematic. This automatic and systematic 3D reconstruction is well
suited to identify plumes individually in time and to follow their
intensity variation. Typical lifetimes observed were found between
1-2 days. The plumes we have reconstructed were not always rooted at a
simultaneous EUV bright points and were sometime associated with a jet.

---------------------------------------------------------
Title: How do inaccuracies and unresolved structures in the measured
solar photospheric magnetic vector influence the accuracy of coronal
magnetic field models?
Authors: Wiegelmann, Thomas; Yelles, Lotfi; Solanki, Sami; Lagg,
Andreas
2010cosp...38.2827W Altcode: 2010cosp.meet.2827W
Solar magnetic fields are usually extrapolated into the corona
starting from photospheric mag-netic measurements that can suffer from
significant uncertainties caused by the presence of unresolved fine
structures due to a limited spatial resolution and by the limited
polarimet-ric accuracy and spectral resolution. We investigate
how these inaccuracies in the measured photospheric magnetic field
vector influence the accuracy of the extrapolated coronal mag-netic
field. We compare non-linear force-free coronal magnetic field
extrapolations from a 3-D radiation MHD simulation snapshot with
corresponding extrapolations from synthetic vector magnetograms. The
synthetic magnetograms contain instrumental effects such as noise,
limited spatial and spectral resolution and the effect of employing a
filter instrument. The parameters are chosen in particular to mimic the
effects of the Hinode/SOT and the future Solar Orbiter PHI instruments,
respectively. We discuss, how photospheric structures, which are
inherent in the MHD snapshot, but not resolved in the photospheric
magnetic field measurements, influence the quality of the computed
coronal magnetic field model.

---------------------------------------------------------
Title: Monitoring free magnetic energy in erupting active regions
Authors: Wiegelmann, Thomas; Thalmann, Julia; Jing, Ju; Wang, Haimin
2010cosp...38.2960W Altcode: 2010cosp.meet.2960W
In solar eruptions, like flares and coronal mass ejections, free
magnetic energy stored in the solar corona is converted into kinetic
energy. Unfortunately the coronal magnetic field cannot be measured
directly. We can, however, reconstruct the coronal magnetic field
from measurements of the photospheric magnetic field vector under
the reasonable assumption of a force-free coronal plasma. With
a procedure dubbed preprocessing we derive force-free consistent
boundary conditions, which are extrapolated into the solar corona
with a nonlinear force-free extrapolation code. The resulting 3D
coronal magnetic field allows us to derive the magnetic topology and
to computed the magnetic energy as well as an upper limited of the
free energy available for driving eruptive phenomena. We apply our
code to measurements from several ground based vector magnetographs,
e.g. the Solar Flare Telescope, SOLIS and the Big Bear Solar
Observatory. Within our studies we find a clear relationship between
the stored magnetic energy and the strength of eruptions. In most cases
not the entire free energy is converted to kinetic energy, but only a
fraction. Consequently, the post-flare magnetic field configuration
is usually not entirely current free, but significantly closer to a
potential field as before the flare.

---------------------------------------------------------
Title: On the propagation of the polar jets from SECCHI/STEREO images
Authors: Feng, Li; Inhester, Bernd; de Patoul, Judith; Wiegelmann,
Thomas
2010cosp...38.2936F Altcode: 2010cosp.meet.2936F
We present the propagation of the polar jets observed from the field
of view of EUVI, COR1 to COR2 on board STEREO. We provide a method to
test the free fall model both in 2D and 3D dimensions by comparing
the height-time images extracted from observations with the free
fall model. By assuming all the particles in polar jets are ejected
at the same time when it is initiated, this method could produce the
initial velocity distribution of the particles and tell us during the
propagation whether the particles are ionized/recombined or experience
some other processes. The derived 3D orientations of the polar jets are
used to test different magnetic field models around polar regions where
the observation and extrapolation are not reliable. The estimated 3D
leading edge velocities by different telescopes are also investigated.

---------------------------------------------------------
Title: Automated Feature and Event Detection with SDO AIA and HMI Data
Authors: Davey, Alisdair; Martens, P. C. H.; Attrill, G. D. R.;
Engell, A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar,
S. H.; Su, Y.; Testa, P.; Wills-Davey, M.; Savcheva, A.; Bernasconi,
P. N.; Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F. .; Cirtain,
J. W.; Deforest, C. E.; Angryk, R. A.; de Moortel, I.; Wiegelmann,
T.; Georgouli, M. K.; McAteer, R. T. J.; Hurlburt, N.; Timmons, R.
2010cosp...38.2878D Altcode: 2010cosp.meet.2878D
The Solar Dynamics Observatory (SDO) represents a new frontier in
quantity and quality of solar data. At about 1.5 TB/day, the data will
not be easily digestible by solar physicists using the same methods
that have been employed for images from previous missions. In order for
solar scientists to use the SDO data effectively they need meta-data
that will allow them to identify and retrieve data sets that address
their particular science questions. We are building a comprehensive
computer vision pipeline for SDO, abstracting complete metadata
on many of the features and events detectable on the Sun without
human intervention. Our project unites more than a dozen individual,
existing codes into a systematic tool that can be used by the entire
solar community. The feature finding codes will run as part of the SDO
Event Detection System (EDS) at the Joint Science Operations Center
(JSOC; joint between Stanford and LMSAL). The metadata produced will
be stored in the Heliophysics Event Knowledgebase (HEK), which will be
accessible on-line for the rest of the world directly or via the Virtual
Solar Observatory (VSO) . Solar scientists will be able to use the
HEK to select event and feature data to download for science studies.

---------------------------------------------------------
Title: Nonlinear force-free extrapolation of SDO/HMI vector
magnetograms in to the corona
Authors: Tadesse Asfaw, Tilaye; Wiegelmann, Thomas; Inhester, Bernd
2010cosp...38.2866T Altcode: 2010cosp.meet.2866T
SDO/HMI provides us high resolution full disk measurements of
the photospheric magnetic field vector.We compute the field in the
higher layers of the solar atmosphere from the measured photospheric
field under the assumption that the corona is force-free. However,
those measured data are inconsistent with the above force-free
assumption. Therefore, one has to apply some transformations
dubbed preprocessing to these data before nonlinear force-free
extrapolation codes can be applied. Our force-free code is based on an
optimization principle and takes the spherical geometry of the sun in to
account. Untill now, these extrapolations were applied only to a small
surface area of the Sun so that cartesian geometry could be applied. We
carry out both full disk computations as well as computations of active
regions. The code has been well tested with model equilibria and used
with the ground based observations from SOLIS. We plan to show first
Nonlinear force-free coronal magnetic fields extrapolated from SDO/HMI
in comparison with the coronal plasma in SDO/HMI.

---------------------------------------------------------
Title: Nonlinear force-free coronal magnetic field modelling and
preprocessing of vector magnetograms in spherical geometry
Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B.
2009A&A...508..421T Altcode: 2009arXiv0912.1514T
Context: Knowledge about the coronal magnetic field is important
to the understanding of many phenomena, such as flares and coronal
mass ejections. Routine measurements of the solar magnetic field
vector are traditionally carried out in the photosphere. We compute
the field in the higher layers of the solar atmosphere from the
measured photospheric field under the assumption that the corona
is force-free. However, those measured data are inconsistent with
the above force-free assumption. Therefore, one has to apply some
transformations to these data before nonlinear force-free extrapolation
codes can be applied. Aims: Extrapolation codes of cartesian
geometry for medelling the magnetic field in the corona do not take
the curvature of the Sun's surface into account. Here we develop a
method for nonlinear force-free coronal magnetic field medelling and
preprocessing of photospheric vector magnetograms in spherical geometry
using the optimization procedure. Methods: We describe a newly
developed code for the extrapolation of nonlinear force-free coronal
magnetic fields in spherical coordinates over a restricted area of
the Sun. The program uses measured vector magnetograms on the solar
photosphere as input and solves the force-free equations in the solar
corona. We develop a preprocessing procedure in spherical geometry
to drive the observed non-force-free data towards suitable boundary
conditions for a force-free extrapolation. Results: We test the
code with the help of a semi-analytic solution and assess the quality
of our reconstruction qualitatively by magnetic field line plots
and quantitatively with a number of comparison metrics for different
boundary conditions. The reconstructed fields from the lower boundary
data with the weighting function are in good agreement with the original
reference fields. We added artificial noise to the boundary conditions
and tested the code with and without preprocessing. The preprocessing
recovered all main structures of the magnetogram and removed small-scale
noise. The main test was to extrapolate from the noisy photospheric
vector magnetogram with and without preprocessing. The preprocessing was
found to significantly improve the agreement between the extrapolated
and the exact field.

---------------------------------------------------------
Title: Internetwork Horizontal Magnetic Fields in the Quiet Sun
Chromosphere: Results from a Joint Hinode/VTT Study
Authors: Lagg, A.; Ishikawa, R.; Merenda, L.; Wiegelmann, T.; Tsuneta,
S.; Solanki, S. K.
2009ASPC..415..327L Altcode:
We present results from a joint Hinode/VTT campaign (May
2008). Spectropolarimetric data of a quiet Sun super-granular network
cell at a heliocentric angle of 28° in the He I 10830 Å line were
analyzed using an inversion code incorporating Hanle and Zeeman effects
(HeLIx^+) to retrieve magnetic field strength and direction in the upper
chromosphere. Simultaneously recorded Hinode SOT/SP data reveal the
photospheric magnetic field morphology, clearly showing magnetic flux
concentrations in the internetwork. The photospheric magnetic field
maps are used to feed potential field extrapolations similar to the
work by Schrijver &amp; Title (2003). The extrapolated magnetic field
structure is compared with the magnetic field configuration resulting
from the He 10830 inversions. These inversions also reveal horizontal
magnetic structures extending over a length of up to 20 Mm above the
internetwork, indicative of the presence of a magnetic canopy. The
photospheric magnetic flux concentrations in the internetwork are
obviously not sufficiently strong to prevent the formation of a canopy
at chromospheric heights.

---------------------------------------------------------
Title: Coronal hole boundaries evolution at small scales. I. EIT
195 Å and TRACE 171 Å view
Authors: Madjarska, M. S.; Wiegelmann, T.
2009A&A...503..991M Altcode: 2009arXiv0906.2556M
Aims: We aim to study the small-scale evolution at the boundaries of an
equatorial coronal hole connected with a channel of open magnetic flux
to the polar region and an “isolated” one in the extreme-ultraviolet
spectral range. We determine the spatial and temporal scale of these
changes. Methods: Imager data from TRACE in the Fe ix/x 171
Å passband and EIT on-board Solar and Heliospheric Observatory in
the Fe xii 195 Å passband were analysed. Results: We found
that small-scale loops known as bright points play an essential role
in coronal hole boundary evolution at small scales. Their emergence
and disappearance continuously expand or contract coronal holes. The
changes appear to be random on a time scale comparable to the lifetime
of the loops seen at these temperatures. No signature was found
for a major energy release during the evolution of the loops. Conclusions: Although coronal holes seem to maintain their general
shape during a few solar rotations, a closer look at their day-by-day
and even hour-by-hour evolution demonstrates significant dynamics. The
small-scale loops (10´´-40´´ and smaller) which are abundant along
coronal hole boundaries contribute to the small-scale evolution of
coronal holes. Continuous magnetic reconnection of the open magnetic
field lines of the coronal hole and the closed field lines of the
loops in the quiet Sun is more likely to take place. Movies are
only available in electronic form at http://www.aanda.org

---------------------------------------------------------
Title: Stereoscopic Polar Plume Reconstructions from STEREO/SECCHI
Images
Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wilhelm, K.;
Wiegelmann, T.; Podlipnik, B.; Howard, R. A.; Plunkett, S. P.; Wuelser,
J. P.; Gan, W. Q.
2009ApJ...700..292F Altcode: 2009arXiv0908.2365F
We present stereoscopic reconstructions of the location and
inclination of polar plumes of two data sets based on the two
simultaneously recorded images taken by the EUVI telescopes in the
SECCHI instrument package onboard the Solar TErrestrial RElations
Observatory spacecraft. The 10 plumes investigated show a superradial
expansion in the coronal hole in three dimensions (3D) which is
consistent with the two-dimensional results. Their deviations from the
local meridian planes are rather small with an average of 6fdg47. By
comparing the reconstructed plumes with a dipole field with its axis
along the solar rotation axis, it is found that plumes are inclined
more horizontally than the dipole field. The lower the latitude is, the
larger is the deviation from the dipole field. The relationship between
plumes and bright points has been investigated and they are not always
associated. For the first data set, based on the 3D height of plumes
and the electron density derived from SUMER/SOHO Si VIII line pair,
we found that electron densities along the plumes decrease with height
above the solar surface. The temperature obtained from the density
scale height is 1.6-1.8 times larger than the temperature obtained
from Mg IX line ratios. We attribute this discrepancy to a deviation
of the electron and the ion temperatures. Finally, we have found that
the outflow speeds studied in the O VI line in the plumes corrected
by the angle between the line of sight and the plume orientation are
quite small with a maximum of 10 km s-1. It is unlikely
that plumes are a dominant contributor to the fast solar wind.

---------------------------------------------------------
Title: Solar stereoscopy - where are we and what developments do we
require to progress?
Authors: Wiegelmann, T.; Inhester, B.; Feng, L.
2009AnGeo..27.2925W Altcode: 2009arXiv0912.1267W
Observations from the two STEREO-spacecraft give us for the first
time the possibility to use stereoscopic methods to reconstruct the
3-D 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
one-dimensional structures - e.g. active region coronal loops or polar
plumes- from the two individual EUV-images 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 STEREO-A and B increases. 3) Within the reconstruction
problem stereoscopic methods are used to compute the 3-D-geometry
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 3-D-structure, which depends
on the accuracy of the identified structures in 2-D, the separation
angle between the spacecraft, but also on the location, e.g., for
east-west directed coronal loops the reconstruction error is highest
close to the loop top. 5) Eventually we are not only interested in the
3-D-geometry 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 EUV-loops
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.

---------------------------------------------------------
Title: Hanle Effect Diagnostics of the Coronal Magnetic Field:
A Test Using Realistic Magnetic Field Configurations
Authors: Raouafi, N. -E.; Solanki, S. K.; Wiegelmann, T.
2009ASPC..405..429R Altcode: 2008arXiv0801.2202R
Our understanding of coronal phenomena, such as coronal plasma
thermodynamics, faces a major handicap caused by missing coronal
magnetic field measurements. Several lines in the UV wavelength range
present suitable sensitivity to determine the coronal magnetic field
via the Hanle effect. The latter is a largely unexplored diagnostic
of coronal magnetic fields with a very high potential. Here we study
the magnitude of the Hanle-effect signal to be expected outside the
solar limb due to the Hanle effect in polarized radiation from the
H I Lyα and β lines, which are among the brightest lines in the
off-limb coronal FUV spectrum. For this purpose we use a magnetic field
structure obtained by extrapolating the magnetic field starting from
photospheric magnetograms. The diagnostic potential of these lines for
determining the coronal magnetic field, as well as their limitations
are studied. We show that these lines, in particular H I Lyβ, are
useful for such measurements.

---------------------------------------------------------
Title: Computer Vision for The Solar Dynamics Observatory
Authors: Martens, Petrus C.; Angryk, R. A.; Bernasconi, P. N.; Cirtain,
J. W.; Davey, A. R.; DeForest, C. E.; Delouille, V. A.; De Moortel,
I.; Georgoulis, M. K.; Grigis, P. C.; Hochedez, J. E.; Kasper, J.;
Korreck, K. E.; Reeves, K. K.; Saar, S. H.; Savcheva, A.; Su, Y.;
Testa, P.; Wiegelmann, T.; Wills-Davey, M.
2009SPD....40.1711M Altcode:
NASA funded a large international consortium last year to produce
a comprehensive system for automated feature recognition in SDO
images. The data we consider are all AIA and EVE data plus surface
magnetic field images from HMI. Helioseismology is addressed by another
group. We will produce robust and very efficient software modules
that can keep up with the relentless SDO data stream and detect, trace,
and analyze a large number of phenomena, including: flares, sigmoids,
filaments, coronal dimmings, polarity inversion lines, sunspots,
X-ray bright points, active regions, coronal holes, EIT waves, CME's,
coronal oscillations, and jets. In addition we will track the emergence
and evolution of magnetic elements down to the smallest features
that are detectable, and we will also provide at least four full
disk nonlinear force-free magnetic field extrapolations per day. A completely new software element that rounds out this suite is a
trainable feature detection module, which employs a generalized image
classification algorithm to produce the texture features of the images
analyzed. A user can introduce a number of examples of the phenomenon
looked and the software will return images with similar features. We
have tested a proto-type on TRACE data, and were able to "train" the
algorithm to detect sunspots, active regions, and loops. Such a module
can be used to find features that have not even been discovered yet,
as, for example, sigmoids were in the pre-Yohkoh era. Our codes
will produce entries in the Helio Events Knowledge base, and that will
permit users to locate data on individual events as well as carry out
statistical studies on large numbers of events, using the interface
provided by the Virtual Solar Observatory.

---------------------------------------------------------
Title: Formation Heights of Extreme Ultraviolet Lines in an Active
Region Derived by Correlation of Doppler Velocity and Magnetic Field
Authors: Guo, Y.; Ding, M. D.; Jin, M.; Wiegelmann, T.
2009ApJ...696.1526G Altcode: 2009arXiv0903.4343G
We study the correlation heights, which indicate the formation height of
Extreme Ultraviolet (EUV) lines in an active region using observations
from the EUV Imaging Spectrometer and Solar Optical Telescope on
board Hinode. The nonlinear force-free field optimization method
is adopted to extrapolate the three-dimensional magnetic fields to
higher layers. Three subregions with different characteristics are
selected in the active region for this study. The results show that
the formation heights in different subregions vary with their different
magnetic fields or velocity patterns. After solving the line blending
problem between the He II 256.32 Å and Si X 256.37 Å lines by the
double Gaussian curve fitting, we find that the transition region
lies higher in a strong magnetic area. In a preflare heating area,
there possibly exist multithermal loops as implied by comparing the
Doppler velocity and the magnetic field on the solar disk.

---------------------------------------------------------
Title: Temporal Evolution of Free Magnetic Energy Associated with
Four X-Class Flares
Authors: Jing, Ju; Chen, P. F.; Wiegelmann, Thomas; Xu, Yan; Park,
Sung-Hong; Wang, Haimin
2009ApJ...696...84J Altcode:
We study the temporal variation of free magnetic energy
E free around the time of four X-class flares. The
high-cadence photospheric vector magnetograms obtained by the digital
vector magnegograph system at the Big Bear Solar Observatory are
used as the boundary conditions to reconstruct the three-dimensional
nonlinear force-free (NLFF) coronal field. In order to remove the
effect of the net Lorentz force and torque acting in the photosphere,
the vector magnetograms are preprocessed using the method devised by
Wiegelmann et al.. Then a well-tested multigrid-like optimization
code by Wiegelmann is applied to the preprocessed boundary data to
extrapolate the NLFF coronal field with which we are able to estimate
the free energy E free. In all the four events, we find
a significant drop of E free starting ~15 minutes before
the peak time of the associated nonthermal flare emission, although
long-term trend varies from event to event. We discuss the physical
implication of the result, i.e., the magnetic relaxation is already
going on in the corona well before the flare reconnection.

---------------------------------------------------------
Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953:
A Critical Assessment
Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan,
J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.;
Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.;
Inhester, B.; Tadesse, T.
2009SPD....40.3102D Altcode:
Nonlinear force-free field (NLFFF) modeling seeks to provide accurate
representations of the structure of the magnetic field above solar
active regions, from which estimates of physical quantities of interest
(e.g., free energy and helicity) can be made. However, the suite of
NLFFF algorithms have failed to arrive at consistent solutions when
applied to (thus far, two) cases using the highest-available-resolution
vector magnetogram data from Hinode/SOT-SP (in the region of the
modeling area of interest) and line-of-sight magnetograms from
SOHO/MDI (where vector data were not available). One issue is that
NLFFF models require consistent, force-free vector magnetic boundary
data, and vector magnetogram data sampling the photosphere do not
satisfy this requirement. Consequently, several problems have arisen
that are believed to affect such modeling efforts. We use AR 10953
to illustrate these problems, namely: (1) some of the far-reaching,
current-carrying connections are exterior to the observational field
of view, (2) the solution algorithms do not (yet) incorporate the
measurement uncertainties in the vector magnetogram data, and/or (3)
a better way is needed to account for the Lorentz forces within the
layer between the photosphere and coronal base. In light of these
issues, we conclude that it remains difficult to derive useful and
significant estimates of physical quantities from NLFFF models.

---------------------------------------------------------
Title: A Critical Assessment of Nonlinear Force-Free Field Modeling
of the Solar Corona for Active Region 10953
Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham;
Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar;
Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann,
Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas;
Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester,
Bernd; Tadesse, Tilaye
2009ApJ...696.1780D Altcode: 2009arXiv0902.1007D
Nonlinear force-free field (NLFFF) models are thought to be viable
tools for investigating the structure, dynamics, and evolution of
the coronae of solar active regions. In a series of NLFFF modeling
studies, we have found that NLFFF models are successful in application
to analytic test cases, and relatively successful when applied
to numerically constructed Sun-like test cases, but they are less
successful in application to real solar data. Different NLFFF models
have been found to have markedly different field line configurations
and to provide widely varying estimates of the magnetic free energy in
the coronal volume, when applied to solar data. NLFFF models require
consistent, force-free vector magnetic boundary data. However,
vector magnetogram observations sampling the photosphere, which is
dynamic and contains significant Lorentz and buoyancy forces, do not
satisfy this requirement, thus creating several major problems for
force-free coronal modeling efforts. In this paper, we discuss NLFFF
modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT,
STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process
illustrate three such issues we judge to be critical to the success of
NLFFF modeling: (1) vector magnetic field data covering larger areas
are needed so that more electric currents associated with the full
active regions of interest are measured, (2) the modeling algorithms
need a way to accommodate the various uncertainties in the boundary
data, and (3) a more realistic physical model is needed to approximate
the photosphere-to-corona interface in order to better transform the
forced photospheric magnetograms into adequate approximations of nearly
force-free fields at the base of the corona. We make recommendations
for future modeling efforts to overcome these as yet unsolved problems.

---------------------------------------------------------
Title: Free Magnetic Energy and Flare Productivity of Active Regions
Authors: Jing, Ju; Tan, C.; Wiegelmann, T.; Xu, Y.; Wang, H.
2009SPD....40.2009J Altcode:
We study the magnitude scaling correlation between coronal free magnetic
energy and flare productivity of active regions. The vector magnetograms
from Hinode are used as the boundary conditions to extrapolate the
3-dimensional nonlinear force-free (NLFF) coronal magnetic fields and
the potential fields. Free magnetic energy of NLFF fields is calculated
as the excess magnetic energy above the potential fields over the
volume of the computational box. For each active region, we select one
vector magnetogram in which the active region is viewed as close to the
disk center as possible. The flare productivity of active regions is
quantified by the soft X-ray flare index for two different time windows:
one covers the entire disk passage of active regions, the other covers
3 days starting from the time of the analyzed magnetogram. Based on the
limited samples we have studied so far, we find a positive correlation
between free energy and flare index. The correlation confirms the
physical link between the quantities and carries important statistical
information for the flare forecasting. The work is supported by
NSF under grant ATM 07-16950 and NASA under grant NNX08AQ89G.

---------------------------------------------------------
Title: Source region of the 18 November 2003 coronal mass ejection
that led to the strongest magnetic storm of cycle 23
Authors: Srivastava, Nandita; Mathew, Shibu K.; Louis, Rohan E.;
Wiegelmann, Thomas
2009JGRA..114.3107S Altcode: 2008arXiv0812.5046S; 2009JGRA..11403107S
The superstorm of 20 November 2003 was associated with a high-speed
coronal mass ejection (CME) which originated in the NOAA AR 10501 on 18
November. This coronal mass ejection had severe terrestrial consequences
leading to a geomagnetic storm with Dst index of -472 nT, the strongest
of the current solar cycle. In this paper, we attempt to understand
the factors that led to the coronal mass ejection on 18 November. We
have also studied the evolution of the photospheric magnetic field of
NOAA AR 10501, the source region of this coronal mass ejection. For
this purpose, the Michelson Doppler Imager line-of-sight magnetograms
and vector magnetograms from Solar Flare Telescope, Mitaka, obtained
during 17-19 November 2003 were analyzed. In particular, quantitative
estimates of the temporal variation in magnetic flux, energy, and
magnetic field gradient were estimated for the source active region. The
evolution of these quantities was studied for the 3-day period with an
objective to understand the preflare configuration leading up to the
moderate flare which was associated with the geoeffective coronal mass
ejection. We also examined the chromospheric images recorded in H 
α from Udaipur Solar Observatory to compare the flare location
with regions of different magnetic field and energy. Our observations
provide evidence that the flare associated with the CME occurred at a
location marked by high magnetic field gradient which led to release
of free energy stored in the active region.

---------------------------------------------------------
Title: Multiple-spacecraft study of an extended magnetic structure
in the solar wind
Authors: Ruan, P.; Korth, A.; Marsch, E.; Inhester, B.; Solanki, S.;
Wiegelmann, T.; Zong, Q. -G.; Bucik, R.; Fornacon, K. -H.
2009JGRA..114.2108R Altcode: 2009JGRA..11402108R
An extended magnetic structure was observed consecutively by five
spacecraft (ACE, WIND, STEREO A and B, and CLUSTER) in the solar wind on
15 January 2007. The similar bipolar magnetic field variations from five
spacecraft suggest that the magnetic structure is two-dimensional. The
abrupt disappearance of the beam electrons in the core of the structure
suggests that the core of the structure is magnetically isolated from
the surrounding environment. Our analysis shows that this magnetic
structure is a magnetic flux rope, which extends over at least 180 R
E in space. The length and orientation of the flux rope were
determined by a local minimum variance analysis (MVA) from individual
spacecraft observations of the magnetic field and a timing analysis
based on the joint observations by all five spacecraft. The results
show that the orientation of the flux rope stays constant in space
and time. The flux rope is embedded in a corotating interaction region
(CIR), which followed a magnetic cloud.

---------------------------------------------------------
Title: Magnetic Field Extrapolation of Flaring Active Regions
Authors: Thalmann, J. K.; Wiegelmann, T.
2009CEAB...33..131T Altcode:
The solar corona is structured by magnetic fields. As direct
measurements of the coronal magnetic field are not routinely available,
it is extrapolated from photospheric vector magnetograms. When magnetic
flux emerges from below the solar surface and expands into the corona,
the coronal magnetic field is destabilized, leading to explosive
phenomena like flares or coronal mass ejections. Our aim is to get
insights in the coronal magnetic field structure in active regions and
to study its temporal evolution. We are in particular interested to
investigate the magnetic configuration of active regions in the course
of flares. Therefore, we study the temporal evolution of the flaring
active regions NOAA 10540 and NOAA 10960 as observed in January 2004 and
June 2007, respectively. We are in particular interested in the free
magnetic energy available to power the flares associated with it. To
investigate AR 10540 we used photospheric vector magnetograms measured
with the Solar Flare Telescope VectorMagnetograph and for AR 10960 we
used data provided by the Synoptic Optical Long-term Investigations of
the Sun VectorSpectroMagnetograph. We extrapolated these measurements
into the corona with the help of a nonlinear force-free field model
based on a well-tested multigrid-like optimization code with which
we were able to estimate the energy content of the 3D coronal fields,
as well as an upper limit for its free magnetic energy.

---------------------------------------------------------
Title: Nonlinear Force-Free Magnetic Field Modeling of the Solar
Corona: A Critical Assessment
Authors: De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.;
Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung,
M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2008AGUFMSH41A1604D Altcode:
Nonlinear force-free field (NLFFF) modeling promises to provide accurate
representations of the structure of the magnetic field above solar
active regions, from which estimates of physical quantities of interest
(e.g., free energy and helicity) can be made. However, the suite of
NLFFF algorithms have so far failed to arrive at consistent solutions
when applied to cases using the highest-available-resolution vector
magnetogram data from Hinode/SOT-SP (in the region of the modeling
area of interest) and line-of-sight magnetograms from SOHO/MDI (where
vector data were not been available). It is our view that the lack of
robust results indicates an endemic problem with the NLFFF modeling
process, and that this process will likely continue to fail until (1)
more of the far-reaching, current-carrying connections are within the
observational field of view, (2) the solution algorithms incorporate
the measurement uncertainties in the vector magnetogram data, and/or
(3) a better way is found to account for the Lorentz forces within
the layer between the photosphere and coronal base. In light of these
issues, we conclude that it remains difficult to derive useful and
significant estimates of physical quantities from NLFFF models.

---------------------------------------------------------
Title: A First Step Towards a Nonlinear and Self-consistent Modelling
of the Interface Region Between Photosphere, Chromosphere and Corona
Authors: Wiegelmann, T.; Neukirch, T.
2008AGUFMSH51C..02W Altcode:
The interface region between the solar photosphere and corona
is an interesting environment which is, however, difficult to
model. Low and high plasma-beta regions are present in this layer
side by side and require that the magnetic field and plasma are
modelled self-consistently in one model. A popular simplification
used to model the low beta solar corona is the assumption of
force-free magnetic fields, but this approach is not justified
in the mixed beta interface region. We can, however, generalize
numerical schemes developed for nonlinear force-free magnetic field
extrapolations. Here we report a first step towards such an approach
based on an optimization principle which solves the non-force-free
magneto-hydrostatic equations by minimizing a functional. As a result we
get a self-consistent equilibrium of magnetic field, plasma density and
plasma pressure. Measured quantities, e.g. the photospheric magnetic
field vector, are used as boundary condition. We test our code with
the help of a semi-analytic magneto-hydro-static equilibrium. The
quality of the reconstruction was judged by comparing the exact and
reconstructed solution qualitatively by magnetic field-line plots
and artificial plasma-images and quantitatively by several different
numerical criteria. Our code is able to reconstruct this semi-analytic
test equilibrium with high accuracy. The strongly varying plasma-beta
environment requires, however, a smaller time step and longer computing
time compared with low beta force-free field extrapolations.

---------------------------------------------------------
Title: A MHS model in the solar corona
Authors: Ruan, P.; Wiegelmann, T.; Inhester, B.; Neukirch, T.
2008AGUFMSH13B1521R Altcode:
Since direct measurements of the solar coronal magnetic field and
plasma are extremely difficult and inaccurate, we use a modeling
approach based on observational quantities, e.g. the measured
photospheric magnetic field, to reconstruct the structure of the
global solar corona.An analytic magnetohydrostatic (MHS) model
(Neukirch 95) was taken to extrapolate the magnetic field in the
corona from photospheric magnetic field measurement from the Wilcox
Solar Observatory. The boundary conditions are given by a synoptic
magnetogram on the photosphere and by a source surface at the outer
boundary. In the model, the electric current density was decomposed into
two components: one component is aligned with the magnetic field lines,
whereas the other component flows in spherical shells. The second
component of the current generates finite Lorentz forces, which are
balanced by the plasma pressure gradient and the gravity force. So
the 3D distribution of the magnetic field and plasma can be derived
self-consistently in one model. The magnetic field distribution of
our model differs noticeably from both potential and force-free field
models for the same boundary conditions. The plasma density in the
MHS model is higher in the equatorial plane than in the polar region,
which gives a reasonable result.

---------------------------------------------------------
Title: Evolution of two Flaring Active Regions With CME Association
Authors: Thalmann, J. K.; Wiegelmann, T.
2008AGUFMSH23B1642T Altcode:
We study the coronal magnetic field structure of two active regions, one
during solar activity minimum (June 2007) and another one during a more
active time (January 2004). The temporal evolution was explored with the
help of nonlinear force-free coronal magnetic field extrapolations of
SOLIS/VSM and NAOJ/SFT photospheric vector magnetograms. We study the
active region NOAA 10960 observed on 2007 June 7 with three SOLIS/VSM
snapshots taken during a small C1.0 flare of time cadence 10 minutes
and six snapshots during a quiet period. The total magnetic energy in
the active region was approximately 3 × 1025 J. Before the flare the
free magnetic energy was about 5~% of the potential field energy. A part
of this excess energy was released during the flare, producing almost
a potential configuration at the beginning of the quiet period. The
return to an almost potential structure can be assigned to a CME as
recorded by the SoHO/LASCO instrument on 2007 June 07 around 10 minutes
after the flare peaked, so that whatever magnetic helicity was bodily
removed from the structure. This was compared with active region 10540
observed on 2004 January 18 -- 21, which was analyzed with the help
of vector magnetograph data from the Solar Flare Telescope in Japan
of time cadence of about 1 day. The free energy was Efree≈ 66~%
of the total energy which was sufficiently high to power a M6.1 flare
on January 20, which was associated with a CME 20 minutes later. The
activity of AR 10540 was significantly higher than for AR 10960,
as was the total magnetic energy. Furthermore, we found the common
feature that magnetic energy accumulates before the flare/CME and a
significant part of the excess energy is released during the eruption.

---------------------------------------------------------
Title: 3D Reconstruction of Polar Plumes From STEREO/SECCHI Images.
Authors: Feng, L.; de Patoul, J.; Inhester, B.; Wiegelmann, T.
2008AGUFMSH44A..05F Altcode:
We provide a newly developed approach to determine the 3D structure of
high latitude open magnetic fields as visible in polar plumes. Our data
are image pairs taken by the SECCHI-EUVI telescopes on board of the
two STEREO spacecraft. From these image pairs we identify the plumes
by two different methods. The first method identifies the plume axes by
the local intensity maxima and the second method uses image processing
tools such as the Hough Transform. The Hough Transform transfers plumes
from images into points, called Hough coordinates, which can directly
be used to calculate the 3D location of the plume. The automatic plume
detection by the Hough transform method is well suited to study their
temporal evolution. The capability of our code has been investigated
with synthetic images taken from a 3D magnetohydrostatic corona model
(Neukirch, 1995) and we apply our methods to study polar plumes observed
from two vantage viewpoints. We identify the locations of the footpoints
of the polar plumes in the photosphere as well as their inclination
relative to the line-of-sight and to their local radial direction. The
relationship between plume and bright point are investigated. With the
help of SOHO/SUMER observations we derive the density scale height in
the plumes. We found that plumes are not the main contributor to the
fast solar wind.

---------------------------------------------------------
Title: Study of Magnetic Channel Structure in Active Region 10930
Authors: Wang, Haimin; Jing, Ju; Tan, Changyi; Wiegelmann, Thomas;
Kubo, Masahito
2008ApJ...687..658W Altcode:
The concept of "magnetic channel" was first introduced by Zirin
&amp; Wang. They were defined as a series of oppositely directed
vertical-field inversions separated by extremely narrow elongated
transverse fields. In this paper, we utilized unprecedented filtergraph
and spectropolarimetry observations from Hinode, and studied the
evolution and physical properties of channel structure of AR 10930
in detail. We found the following: (1) Channels are associated with
new flux emergence in the middle of existing penumbra connecting
the δ sunspot. (2) The width of each channel is in the order of 1”
or less. (3) The line-of-sight magnetic gradient is highest in the
channel, 2.4-4.9 G km-1. (4) The fields are highly sheared
and inclined with a median shear angle around 64° and inclination angle
around 25°. (5) Using nonlinear force-free field (NLFF) extrapolation,
we derive a near surface current system carrying electric current
in the order of 5 × 1011 A. (6) The X3.4 flare on 2006
December 13 occurred during the period that the channels rapidly
formed, but a few hours before the maximum phase of channel structure
development. Based on the observational evidence, we propose that the
channels are formed during the emergence of a sequence of magnetic
bipoles that are squeezed in the compact penumbra of the δ sunspot
and they are highly nonpotential. Formation of channels might be a
precursor of major flares.

---------------------------------------------------------
Title: Plasma Flows Guided by Strong Magnetic Fields in the Solar
Corona
Authors: Marsch, Eckart; Tian, Hui; Sun, Jian; Curdt, Werner;
Wiegelmann, Thomas
2008ApJ...685.1262M Altcode:
In this study new results are presented regarding the relationships
between the coronal magnetic field and the intensities and Doppler
shifts of ultraviolet emission lines. This combination of magnetic
field and spectroscopic data is used here to study material flows in
association with the coronal field. We introduce the term "coronal
circulation" to describe this flow, and to indicate that the plasma is
not static but flows everywhere in the extended solar atmosphere. The
blueshifts and redshifts often seen in transition region and coronal
ultraviolet emission lines are interpreted as corresponding to upflows
and downflows of the plasma on open (funnels) and closed (loops) coronal
magnetic field lines, which tightly confine and strongly lead the flows
in the low-beta plasma. Evidence for these processes exists in the
ubiquitous redshifts mostly seen at both legs of loops on all scales,
and the sporadic blueshifts occurring in strong funnels. Therefore,
there is no static magnetically stratified plasma in the corona, since
panta rhei, but rather a continuous global plasma circulation, being
the natural perpetuation of photospheric convection which ultimately
is the driver.

---------------------------------------------------------
Title: Loop Morphology and Flows and their Relation to the Magnetic
Field
Authors: Teriaca, L.; Wiegelmann, T.; Lagg, A.; Solanki, S. K.; Curdt,
W.; Sekii, T.
2008ASPC..397..196T Altcode:
In November 2006 we obtained several rasters of a large sunspot
and its trailing region using the SUMER spectrometer on SOHO. The
observations consist of spectroheliograms in the continuum around
142 nm and in several spectral lines formed between 80000 K and
0.6 MK, covering the temperature range from the chromosphere to
the lower corona. The observed profiles provide LOS velocity and
Doppler width maps. TRACE images in the EUV passbands and in the 160
nm continuum provide a clear picture of the coronal loops and the
chromosphere near their footpoints. The same target was also observed
by all the instruments aboard Hinode and, in particular, by the SOT
spectro-polarimeter measuring the photospheric magnetic vector. We
combined SOT and MDI data (covering a larger FOV) to infer the coronal
magnetic field of the active region by a nonlinear force-free field
extrapolation. The observed radiance and velocity patterns at the
various heights/temperatures throughout the solar atmosphere are
compared with the field topology.

---------------------------------------------------------
Title: First nonlinear force-free field extrapolations of SOLIS/VSM
data
Authors: Thalmann, J. K.; Wiegelmann, T.; Raouafi, N. -E.
2008A&A...488L..71T Altcode: 2008arXiv0809.1428T
Aims: We study the coronal magnetic field structure inside active
regions and its temporal evolution. We attempt to compare the magnetic
configuration of an active region in a very quiet period with that
for the same region during a flare. Methods: Probably for
the first time, we use vector magnetograph data from the Synoptic
Optical Long-term Investigations of the Sun survey (SOLIS) to model
the coronal magnetic field as a sequence of nonlinear force-free
equilibria. We study the active region NOAA 10960 observed on 2007
June 7 with three snapshots taken during a small C1.0 flare of time
cadence 10 min and six snapshots during a quiet period. Results:
The total magnetic energy in the active region was approximately 3 ×
1025 J. Before the flare the free magnetic energy was about
5% of the potential field energy. A part of this excess energy was
released during the flare, producing almost a potential configuration
at the beginning of the quiet period. Conclusions: During the
investigated period, the coronal magnetic energy was only a few percent
higher than that of the potential field and consequently only a small
C1.0 flare occurred. This was compared with an earlier investigated
active region 10540, where the free magnetic energy was about 60% higher
than that of the potential field producing two M-class flares. However,
the free magnetic energy accumulates before and is released during
the flare which appears to be the case for both large and small flares.

---------------------------------------------------------
Title: Preprocessing of Hinode/SOT Vector Magnetograms for Nonlinear
Force-Free Coronal Magnetic Field Modeling
Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa,
M. L.; Metcalf, T. R.
2008ASPC..397..198W Altcode: 2008arXiv0801.2884W
The solar magnetic field is key to understanding the physical processes
in the solar atmosphere. Nonlinear force-free codes have been shown
to be useful in extrapolating the coronal field from underlying vector
boundary data (for an overview see Schrijver et al. (2006)). However,
we can only measure the magnetic field vector routinely with high
accuracy in the photosphere with, e.g., Hinode/SOT, and unfortunately
these data do not fulfill the force-free consistency condition as
defined by Aly (1989). We must therefore apply some transformations
to these data before nonlinear force-free extrapolation codes can be
legitimately applied. To this end, we have developed a minimization
procedure that uses the measured photospheric field vectors as input
to approximate a more chromospheric like field (The method was dubbed
preprocessing. See Wiegelmann et al. (2006) for details). The procedure
includes force-free consistency integrals and spatial smoothing. The
method has been intensively tested with model active regions (see
Metcalf et al. 2008) and been applied to several ground based vector
magnetogram data before. Here we apply the preprocessing program to
photospheric magnetic field measurements with the Hinode/SOT instrument.

---------------------------------------------------------
Title: 3D Magnetic Field Configuration of the 2006 December 13 Flare
Extrapolated with the Optimization Method
Authors: Guo, Y.; Ding, M. D.; Wiegelmann, T.; Li, H.
2008ApJ...679.1629G Altcode:
The photospheric vector magnetic field of the active region NOAA
10930 was obtained with the Solar Optical Telescope (SOT) on board
the Hinode satellite with a very high spatial resolution (about
0.3”). Observations of the two-ribbon flare on 2006 December 13 in
this active region provide us a good sample to study the magnetic
field configuration related to the occurrence of the flare. Using the
optimization method for nonlinear force-free field (NLFFF) extrapolation
proposed by Wheatland et al. and recently developed by Wiegelmann, we
derive the three-dimensional (3D) vector magnetic field configuration
associated with this flare. The general topology can be described
as a highly sheared core field and a quasi-potential envelope arch
field. The core field clearly shows some dips supposed to sustain a
filament. Free energy release in the flare, calculated by subtracting
the energy contained in the NLFFF and the corresponding potential
field, is 2.4 × 1031 ergs, which is ~2% of the preflare
potential field energy. We also calculate the shear angles, defined
as the angles between the NLFFF and potential field, and find that
they become larger at some particular sites in the lower atmosphere,
while they become significantly smaller in most places, implying that
the whole configuration gets closer to the potential field after the
flare. The Ca II H line images obtained with the Broadband Filter Imager
(BFI) of the SOT and the 1600 Å images with the Transition Region and
Coronal Explorer (TRACE) show that the preflare heating occurs mainly
in the core field. These results provide evidence in support of the
tether-cutting model of solar flares.

---------------------------------------------------------
Title: Evolution of the flaring active region NOAA 10540 as a sequence
of nonlinear force-free field extrapolations
Authors: Thalmann, J. K.; Wiegelmann, T.
2008A&A...484..495T Altcode:
Context: The solar corona is structured by magnetic fields. As direct
measurements of the coronal magnetic field are not routinely available,
it is extrapolated from photospheric vector magnetograms. When
magnetic flux emerges from below the solar surface and expands into
the corona, the coronal magnetic field is destabilized, leading to
explosive phenomena like flares or coronal mass ejections. Aims:
We study the temporal evolution of the flaring active region NOAA
10540 and are in particular interested in the free magnetic energy
available to power the flares associated with it. Methods: We
extrapolated photospheric vector magnetograms measured with the Solar
Flare Telescope, located in Tokyo, into the corona with the help of a
nonlinear force-free field model. This coronal magnetic field model is
based on a well-tested multigrid-like optimization code with which we
were able to estimate the energy content of the 3D coronal field, as
well as an upper limit for its free magnetic energy. Furthermore, the
evolution of the energy density with height and time was studied. Results: The coronal magnetic field energy in active region 10540
increases slowly during the three days before an M6.1 flare and drops
significantly after it. We estimated the energy that was set free
during this event as ∝1025 J. A sequence of nonlinear
force-free extrapolations of the coronal magnetic field shows a build
up of magnetic energy before a flare and release of energy during the
flare. The drop in magnetic energy of the active region is sufficient
to power an M6.1 flare.

---------------------------------------------------------
Title: First stereoscopic polar plume reconstructions from
STEREO/SECCHI images
Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.;
Podlipnik, B.; Howard, R.; Plunkett, S.; Wuelser, J.; Gan, W.
2008AGUSMSH23A..01F Altcode:
We present the first stereoscopic reconstruction of the
three-dimensional structures of polar plumes based on the two
simultaneously recorded images taken by the EUVI telescopes in
the SECCHI instrument package onboard the recently launched STEREO
mission. The reconstructed polar plumes were observed on April 7th,
2007 when the two spacecraft were well below the solar equatorial
plane, an appropriate time for the observation of the plumes in the
south polar coronal hole. The heliocentric separation of the two
spacecraft was 3.6 degrees at that time. We determine locations of
the footpoints of five EUV polar plumes on the solar surface as well
as their inclinations relative to the line-of-sight and to their
local radial directions. The five plumes are all within 21 degrees
of the south pole and their inclinations to the line-of-sight of
STEREO A(head) and radial directions are on average 107 degrees and
28 degrees, respectively. A simple dipole model for the south pole's
magnetic field does not provide a good correspondence with the obtained
inclinations. Of the three plumes in front of the limb only one is
associated with an EUV bright point.

---------------------------------------------------------
Title: Changes of Magnetic Structure in 3-D Associated with the X3.4
Flare of 2006 December 13
Authors: Jing, J.; Wiegelmann, T.; Suematsu, Y.; Kubo, M.; Wang, H.
2008AGUSMSP51C..02J Altcode:
Recent observations demonstrated that sunspot structure can change
rapidly and irreversibly after flares. One of the most puzzling results
is the increase in magnetic shear around flaring magnetic polarity
inversion line after flares. However, all these observations were
made at the photosphere level. We study the altitude variation of the
non-potentiality of the magnetic fields associated with the 4B/X3.4
flare of 2006 December 13. The vector magnetograms with unprecedented
quality from Hinode before and after the flare are used as the boundary
conditions to extrapolate the 3-dimensional non-linear force-free
magnetic fields and the potential fields. The former are computed
with the optimization algorithm and the latter with Green's function
method. At the photosphere boundary, magnetic shear increases after the
flare in a local area close to the flaring magnetic polarity inversion
line. Two measures of the magnetic non-potentiality, the weighted mean
shear θw and the total magnetic shear θwB, are calculated in this area
at progressively higher altitude. By comparing their altitude variation
profiles before and after the flare, we find that the non-potentiality
of the local area increases after the flare below ~8 Mm and decreases
from that height to ~70 Mm. Beyond 70 Mm, the magnetic fields approach
potential for both times.

---------------------------------------------------------
Title: Non-Linear Force-Free Field Modeling of a Solar Active Region
Around the Time of a Major Flare and Coronal Mass Ejection
Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes,
G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann,
T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
M.; Kusano, K.; Régnier, S.; Thalmann, J.
2008AGUSMSP31A..06D Altcode:
Solar flares and coronal mass ejections are associated with rapid
changes in coronal magnetic field connectivity and are powered by
the partial dissipation of electrical currents that run through
the solar corona. A critical unanswered question is whether the
currents involved are induced by the advection along the photosphere
of pre-existing atmospheric magnetic flux, or whether these currents
are associated with newly emergent flux. We address this problem by
applying nonlinear force-free field (NLFFF) modeling to the highest
resolution and quality vector-magnetographic data observed by the
recently launched Hinode satellite on NOAA Active Region 10930 around
the time of a powerful X3.4 flare in December 2006. We compute 14
NLFFF models using 4 different codes having a variety of boundary
conditions. We find that the model fields differ markedly in geometry,
energy content, and force-freeness. We do find agreement of the best-fit
model field with the observed coronal configuration, and argue (1)
that strong electrical currents emerge together with magnetic flux
preceding the flare, (2) that these currents are carried in an ensemble
of thin strands, (3) that the global pattern of these currents and
of field lines are compatible with a large-scale twisted flux rope
topology, and (4) that the ~1032~erg change in energy associated with
the coronal electrical currents suffices to power the flare and its
associated coronal mass ejection. We discuss the relative merits of
these models in a general critique of our present abilities to model
the coronal magnetic field based on surface vector field measurements.

---------------------------------------------------------
Title: A first step in reconstructing the solar corona
self-consistently with a magnetohydrostatic model during solar
activity minimum
Authors: Ruan, P.; Wiegelmann, T.; Inhester, B.; Neukirch, T.; Solanki,
S. K.; Feng, L.
2008A&A...481..827R Altcode:
Aims: We compute the distribution of the magnetic field and the plasma
in the global corona with a self-consistent magnetohydrostatic (MHS)
model. Methods: Because direct measurements of the solar coronal
magnetic field and plasma are extremely difficult and inaccurate, we
use a modeling approach based on observational quantities, e.g. the
measured photospheric magnetic field, to reconstruct the structure
of the global solar corona. We take an analytic magnetohydrostatic
model to extrapolate the magnetic field in the corona from photospheric
magnetic field measurement. In the model, the electric current density
can be decomposed into two components: one component is aligned with the
magnetic field lines, whereas the other component flows in spherical
shells. The second component of the current produces finite Lorentz
forces that are balanced by the pressure gradient and the gravity
force. We derive the 3D distribution of the magnetic field and plasma
self-consistently in one model. The boundary conditions are given by
a synoptic magnetogram on the inner boundary and by a source surface
model at the outer boundary. Results: The density in the model is
higher in the equatorial plane than in the polar region. We compare the
magnetic field distribution of our model with potential and force-free
field models for the same boundary conditions and find that our model
differs noticeably from both. We discuss how to apply the model and
how to improve it.

---------------------------------------------------------
Title: Theoretical modeling for the stereo mission
Authors: Aschwanden, Markus J.; Burlaga, L. F.; Kaiser, M. L.; Ng,
C. K.; Reames, D. V.; Reiner, M. J.; Gombosi, T. I.; Lugaz, N.;
Manchester, W.; Roussev, I. I.; Zurbuchen, T. H.; Farrugia, C. J.;
Galvin, A. B.; Lee, M. A.; Linker, J. A.; Mikić, Z.; Riley, P.;
Alexander, D.; Sandman, A. W.; Cook, J. W.; Howard, R. A.; Odstrčil,
D.; Pizzo, V. J.; Kóta, J.; Liewer, P. C.; Luhmann, J. G.; Inhester,
B.; Schwenn, R. W.; Solanki, S. K.; Vasyliunas, V. M.; Wiegelmann, T.;
Blush, L.; Bochsler, P.; Cairns, I. H.; Robinson, P. A.; Bothmer,
V.; Kecskemety, K.; Llebaria, A.; Maksimovic, M.; Scholer, M.;
Wimmer-Schweingruber, R. F.
2008SSRv..136..565A Altcode: 2006SSRv..tmp...75A
We summarize the theory and modeling efforts for the STEREO mission,
which will be used to interpret the data of both the remote-sensing
(SECCHI, SWAVES) and in-situ instruments (IMPACT, PLASTIC). The
modeling includes the coronal plasma, in both open and closed magnetic
structures, and the solar wind and its expansion outwards from the Sun,
which defines the heliosphere. Particular emphasis is given to modeling
of dynamic phenomena associated with the initiation and propagation
of coronal mass ejections (CMEs). The modeling of the CME initiation
includes magnetic shearing, kink instability, filament eruption, and
magnetic reconnection in the flaring lower corona. The modeling of CME
propagation entails interplanetary shocks, interplanetary particle
beams, solar energetic particles (SEPs), geoeffective connections,
and space weather. This review describes mostly existing models of
groups that have committed their work to the STEREO mission, but is by
no means exhaustive or comprehensive regarding alternative theoretical
approaches.

---------------------------------------------------------
Title: Segmentation of Loops from Coronal EUV Images
Authors: Inhester, B.; Feng, L.; Wiegelmann, T.
2008SoPh..248..379I Altcode: 2008arXiv0801.3240I
We present a procedure to extract bright loop features from solar
EUV images. In terms of image intensities, these features are
elongated ridge-like intensity maxima. To discriminate the maxima,
we need information about the spatial derivatives of the image
intensity. Commonly, the derivative estimates are strongly affected
by image noise. We therefore use a regularized estimation of the
derivative, which is then used to interpolate a discrete vector field
of ridge points; these "ridgels" are positioned on the ridge center and
have the intrinsic orientation of the local ridge direction. A scheme
is proposed to connect ridgels to smooth, spline-represented curves
that fit the observed loops. Finally, a half-automated user interface
allows one to merge or split curves or eliminate or select loop fits
obtained from this procedure. In this paper we apply our tool to one
of the first EUV images observed by the SECCHI instrument onboard the
recently launched STEREO spacecraft. We compare the extracted loops
with projected field lines computed from near-simultaneous magnetograms
measured by the SOHO/MDI Doppler imager. The field lines were calculated
by using a linear force-free field model. This comparison allows one to
verify faint and spurious loop connections produced by our segmentation
tool and it also helps to prove the quality of the magnetic-field
model where well-identified loop structures comply with field-line
projections. We also discuss further potential applications of our
tool such as loop oscillations and stereoscopy.

---------------------------------------------------------
Title: Changes of Magnetic Structure in Three Dimensions Associated
with the X3.4 Flare of 2006 December 13
Authors: Jing, Ju; Wiegelmann, Thomas; Suematsu, Yoshinori; Kubo,
Masahito; Wang, Haimin
2008ApJ...676L..81J Altcode:
Recent observations demonstrated that sunspot structure can change
rapidly and irreversibly after flares. One of the most puzzling results
is the increase in magnetic shear around the flaring magnetic polarity
inversion line after flares. However, all these observations were
made at the photosphere level. In this Letter, we study the altitude
variation of the nonpotentiality of the magnetic fields associated
with the 4B/X3.4 flare of 2006 December 13. The vector magnetograms
with unprecedented quality from Hinode before and after the flare are
used as the boundary conditions to extrapolate the three-dimensional
nonlinear force-free magnetic fields and the potential fields. The
former are computed with the optimization algorithm and the latter with
the Green's function method. At the photosphere boundary, magnetic shear
increases after the flare in a local area close to the flaring magnetic
polarity inversion line. Two measures of the magnetic nonpotentiality,
the weighted mean shear θw and the total magnetic shear
θwB, are calculated in this area at progressively higher
altitude. By comparing their altitude variation profiles before and
after the flare, we find that the nonpotentiality of the local area
increases after the flare below ~8 Mm and decreases from that height
to ~70 Mm. Beyond 70 Mm, the magnetic fields approach potential for
both times.

---------------------------------------------------------
Title: Nonlinear Force-free Field Modeling of a Solar Active Region
around the Time of a Major Flare and Coronal Mass Ejection
Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.;
Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.;
Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
M.; Kusano, K.; Régnier, S.; Thalmann, J. K.
2008ApJ...675.1637S Altcode: 2007arXiv0712.0023S
Solar flares and coronal mass ejections are associated with rapid
changes in field connectivity and are powered by the partial dissipation
of electrical currents in the solar atmosphere. A critical unanswered
question is whether the currents involved are induced by the motion of
preexisting atmospheric magnetic flux subject to surface plasma flows or
whether these currents are associated with the emergence of flux from
within the solar convective zone. We address this problem by applying
state-of-the-art nonlinear force-free field (NLFFF) modeling to the
highest resolution and quality vector-magnetographic data observed
by the recently launched Hinode satellite on NOAA AR 10930 around
the time of a powerful X3.4 flare. We compute 14 NLFFF models with
four different codes and a variety of boundary conditions. We find
that the model fields differ markedly in geometry, energy content,
and force-freeness. We discuss the relative merits of these models in
a general critique of present abilities to model the coronal magnetic
field based on surface vector field measurements. For our application
in particular, we find a fair agreement of the best-fit model field
with the observed coronal configuration, and argue (1) that strong
electrical currents emerge together with magnetic flux preceding the
flare, (2) that these currents are carried in an ensemble of thin
strands, (3) that the global pattern of these currents and of field
lines are compatible with a large-scale twisted flux rope topology,
and (4) that the ~1032 erg change in energy associated with
the coronal electrical currents suffices to power the flare and its
associated coronal mass ejection.

---------------------------------------------------------
Title: Nonlinear force-free modeling of the solar coronal magnetic
field
Authors: Wiegelmann, T.
2008JGRA..113.3S02W Altcode: 2008arXiv0801.2902W
The coronal magnetic field is an important quantity because the magnetic
field dominates the structure of the solar corona. Unfortunately,
direct measurements of coronal magnetic fields are usually not
available. The photospheric magnetic field is measured routinely with
vector magnetographs. These photospheric measurements are extrapolated
into the solar corona. The extrapolated coronal magnetic field
depends on assumptions regarding the coronal plasma, for example,
force-freeness. Force-free means that all nonmagnetic forces like
pressure gradients and gravity are neglected. This approach is well
justified in the solar corona owing to the low plasma beta. One has
to take care, however, about ambiguities, noise and nonmagnetic forces
in the photosphere, where the magnetic field vector is measured. Here
we review different numerical methods for a nonlinear force-free
coronal magnetic field extrapolation: Grad-Rubin codes, upward
integration method, MHD relaxation, optimization, and the boundary
element approach. We briefly discuss the main features of the different
methods and concentrate mainly on recently developed new codes.

---------------------------------------------------------
Title: Can We Improve the Preprocessing of Photospheric Vector
Magnetograms by the Inclusion of Chromospheric Observations?
Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa,
M. L.; Metcalf, T. R.
2008SoPh..247..249W Altcode: 2008arXiv0801.2707W; 2008SoPh..tmp...27W
The solar magnetic field is key to understanding the physical processes
in the solar atmosphere. Nonlinear force-free 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 force-free condition. We
must therefore apply some transformations to these data before nonlinear
force-free extrapolation codes can be self-consistently applied. To
this end, we have developed a minimization procedure that yields a more
chromosphere-like field, using the measured photospheric field vectors
as input. The procedure includes force-free 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, for example, chromospheric Hα images. We test
the procedure using a model active-region 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.

---------------------------------------------------------
Title: Nonlinear Force-Free Modeling of Coronal Magnetic
Fields. II. Modeling a Filament Arcade and Simulated Chromospheric
and Photospheric Vector Fields
Authors: Metcalf, Thomas R.; De Rosa, Marc L.; Schrijver, Carolus J.;
Barnes, Graham; van Ballegooijen, Adriaan A.; Wiegelmann, Thomas;
Wheatland, Michael S.; Valori, Gherardo; McTtiernan, James M.
2008SoPh..247..269M Altcode: 2008SoPh..tmp...17M
We compare a variety of nonlinear force-free field (NLFFF) extrapolation
algorithms, including optimization, magneto-frictional, and Grad -
Rubin-like codes, applied to a solar-like reference model. The model
used to test the algorithms includes realistic photospheric Lorentz
forces and a complex field including a weakly twisted, right helical
flux bundle. The codes were applied to both forced "photospheric" and
more force-free "chromospheric" vector magnetic field boundary data
derived from the model. When applied to the chromospheric boundary data,
the codes are able to recover the presence of the flux bundle and the
field's free energy, though some details of the field connectivity are
lost. When the codes are applied to the forced photospheric boundary
data, the reference model field is not well recovered, indicating
that the combination of Lorentz forces and small spatial scale
structure at the photosphere severely impact the extrapolation of the
field. Preprocessing of the forced photospheric boundary does improve
the extrapolations considerably for the layers above the chromosphere,
but the extrapolations are sensitive to the details of the numerical
codes and neither the field connectivity nor the free magnetic energy in
the full volume are well recovered. The magnetic virial theorem gives
a rapid measure of the total magnetic energy without extrapolation
though, like the NLFFF codes, it is sensitive to the Lorentz forces in
the coronal volume. Both the magnetic virial theorem and the Wiegelmann
extrapolation, when applied to the preprocessed photospheric boundary,
give a magnetic energy which is nearly equivalent to the value derived
from the chromospheric boundary, but both underestimate the free
energy above the photosphere by at least a factor of two. We discuss
the interpretation of the preprocessed field in this context. When
applying the NLFFF codes to solar data, the problems associated with
Lorentz forces present in the low solar atmosphere must be recognized:
the various codes will not necessarily converge to the correct, or
even the same, solution.

---------------------------------------------------------
Title: Nonlinear force-free field models
Authors: Wiegelmann, Thomas; Thalmann, Julia; Inhester, Bernd
2008cosp...37.3462W Altcode: 2008cosp.meet.3462W
The photospheric magnetic field vector is routinely measured with high
accuracy from ground based and space born instruments. We use these
measurements to prescribe suitable boundary conditions for modelling
the coronal magnetic field. Because of the low-beta plasma the magnetic
field is in lowest order assumed to be force-free in the corona and
upper chromosphere, but not in the high-beta photosphere. We developed
a program package which contains a preprocessing program and a nonlinear
force-free coronal magnetic extrapolation code. Both programs are based
on optimization principles. The preprocessing routine uses the measured
photospheric vector magnetogram as input and approximates the magnetic
field vector in the force-free upper chromosphere. These data are used
as boundary condition for a nonlinear force-free extrapolation of the
coronal magnetic field. We applied our method to study the temporal
evolution of a flaring active region as a sequence of nonlinear
force-free equilibria. We found that magnetic energy was build up
before the occurance of a flare and released after it. Furthermore,
the 3D-magnetic field model allows us to trace the temporal evolution
of the energy flows in the flaring region.

---------------------------------------------------------
Title: Optimization Approach for the Computation of 3D
Magnetohydrostatic Coronal Equilibria From Multi-Spacecraft
Observations
Authors: Neukirch, T.; Wiegelmann, T.; Ruan, P.; Inhester, B.
2007AGUFMSH14B..05N Altcode:
We cannot measure the 3D coronal magnetic field and plasma
pressure/density distribution directly. To derive these quantities we
propose a modelling approach based on observational data from multiple
instruments. Our aim is to use measurements of the photospheric magnetic
field vector (e.g. from Hinode/SOT and in future from SDO/HMI) and
plasma images from two viewpoints -as provided by STEREO- as input for
a newly developed magnetohydrostatic optimization code. The resulting 3D
magnetic field and plasma distribution is a self-consistent equilibrium
within the magnetohydrostatic approach. Here we test our code with the
help of an exact magnetohydrostatic equilibrium and extracted synthetic
observational data, which allow us to evaluate the accuracy of our
method. We find that the method reconstructs the equilibrium accurately,
with residual forces of the order of the discretisation error of the
exact solution. The correlation with the reference solution is better
than 99.9 percent and the magnetic energy is computed accurately with
an error of less than 0.1 percent. We are planning to use this method
with real observational data as input as soon as possible.

---------------------------------------------------------
Title: First Stereoscopic Coronal Loop Reconstructions from STEREO
SECCHI Images
Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.;
Podlipnik, B.; Howard, R. A.; Wuelser, J. -P.
2007ApJ...671L.205F Altcode: 2008arXiv0802.0773F
We present the first reconstruction of the three-dimensional shape of
magnetic loops in an active region from two different vantage points
based on simultaneously recorded images. The images were taken by the
two EUVI telescopes of the SECCHI instrument on board the recently
launched STEREO spacecraft when the heliocentric separation of the
two space probes was 12°. We demonstrate that these data allow us to
obtain a reliable three-dimensional reconstruction of sufficiently
bright loops. The result is compared with field lines derived from
a coronal magnetic field model extrapolated from a photospheric
magnetogram recorded nearly simultaneously by SOHO MDI. We attribute
discrepancies between reconstructed loops and extrapolated field lines
to the inadequacy of the linear force-free field model used for the
extrapolation.

---------------------------------------------------------
Title: Nonlinear Force-Free Field Extrapolation of NOAA AR 0696
Authors: Thalmann, J. K.; Wiegelmann, T.
2007AGUFMSH13A1095T Altcode:
We investigate the 3D coronal magnetic field structure of NOAA AR 0696
in the period of November 09-11, 2004, before and after an X2.5 flare
(occurring around 02:13 UT on November 10, 2004). The coronal magnetic
field dominates the structure of the solar corona and consequently plays
a key role for the understanding of the initiation of flares. The most
accurate presently available method to derive the coronal magnetic
field is currently the nonlinear force-free field extrapolation
from measurements of the photospheric magnetic field vector. These
vector-magnetograms were processed from stokes I, Q, U, and V
measurements of the Big Bear Solar Observatory and extrapolated into
the corona with the nonlinear force-free optimization code developed by
Wiegelmann (2004). We analyze the corresponding time series of coronal
equilibria regarding topology changes of the 3D coronal magnetic field
during the flare. Furthermore, quantities such as the temporal evolution
of the magnetic energy and helicity are computed.

---------------------------------------------------------
Title: First Stereoscopic Coronal Loop Reconstructions From
STEREO/SECCHI Images
Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.;
Podlipnik, B.; Howard, R. A.
2007AGUFMSH41B..06F Altcode:
We for the first time use simultaneously observed EUV images to
reconstruct the 3D shape of magnetic loops which emerge from an active
region. The images were taken by the two EUVI cameras of the SECCHI
telescopes onboard the STEREO spacecraft. At the time the data was
taken, the heliocentric separation of the two STEREO probes was 12
degrees. We show that under these conditions it is possible to obtain
a reliable three- dimensional reconstruction of sufficiently bright
loops as they usually emerge from an active region. The result is
compared with field lines derived from a coronal magnetic field model
extrapolated from a surface magnetogram. The magnetogram was abserved
by SOHO/MDI only 9 seconds before the the EUV images were taken.

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Title: Can we Improve the Preprocessing of Photospheric
Vectormagnetograms by the Inclusion of Chromospheric Observations?
Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa,
M. L.; Metcalf, T. R.
2007AGUFMSH51C..02W Altcode:
The solar magnetic field is key to understanding the physical
processes in the solar atmosphere. Unfortunately, we can measure
the magnetic field vector routinely with high accuracy only in the
photosphere with, e.g., Hinode/SOT and in future with SDO/HMI. These
measurements are extrapolated into the corona under the assumption
that the field is force-free. That condition is not fulfilled in the
photosphere, but is in the chromosphere and corona. In order to make
the observed boundary data consistent with the force-free assumption,
we therefore have to apply some transformations before nonlinear
force-free extrapolation codes can be legitimately applied. We develop
a minimization procedure that uses the measured photospheric field
vectors as input to approximate a more chromospheric-like field. The
procedure includes force-free 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,
e.g., chromospheric H-alpha images. We test the procedure using a model
active-region field that included buoyancy forces at the photospheric
level. We apply the combined preprocessing and nonlinear force-free
extrapolation method to compute the coronal magnetic field in an active
region measured with the Hinode/SOT instrument.

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Title: Optimization approach for the computation of magnetohydrostatic
coronal equilibria in spherical geometry
Authors: Wiegelmann, T.; Neukirch, T.; Ruan, P.; Inhester, B.
2007A&A...475..701W Altcode: 2008arXiv0801.2916W
Context: This paper presents a method which can be used to calculate
models of the global solar corona from observational data. Aims: We present an optimization method for computing nonlinear
magnetohydrostatic equilibria in spherical geometry with the aim
to obtain self-consistent solutions for the coronal magnetic field,
the coronal plasma density and plasma pressure using observational
data as input. Methods: Our code for the self-consistent
computation of the coronal magnetic fields and the coronal plasma
solves the non-force-free magnetohydrostatic equilibria using
an optimization method. Previous versions of the code have been
used to compute non-linear force-free coronal magnetic fields from
photospheric measurements in Cartesian and spherical geometry, and
magnetostatic-equilibria in Cartesian geometry. We test our code
with the help of a known analytic 3D equilibrium solution of the
magnetohydrostatic equations. The detailed comparison between the
numerical calculations and the exact equilibrium solutions is made by
using magnetic field line plots, plots of density and pressure and some
of the usual quantitative numerical comparison measures. Results:
We find that the method reconstructs the equilibrium accurately,
with residual forces of the order of the discretisation error of
the analytic solution. The correlation with the reference solution
is better than 99.9% and the magnetic energy is computed accurately
with an error of &lt;0.1%. Conclusions: We applied the method
so far to an analytic test case. We are planning to use this method
with real observational data as input as soon as possible.

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Title: Non-linear Force-free Modeling Of Coronal Magnetic Fields
Authors: Metcalf, Thomas R.; De Rosa, M. L.; Schrijver, C. J.; Barnes,
G.; van Ballegooijen, A.; Wiegelmann, T.; Wheatland, M. S.; Valori,
G.; McTiernan, J. M.
2007AAS...210.9102M Altcode: 2007BAAS...39..204M
We compare a variety of nonlinear force-free field (NLFFF)
extrapolation algorithms, including optimization, magneto-frictional,
and Grad-Rubin-like codes, applied to a solar-like reference
model. The model used to test the algorithms includes realistic
photospheric Lorentz forces and a complex field including a weakly
twisted, right helical flux bundle. The codes were applied to both
forced "photospheric” and more force-free "chromospheric” vector
magnetic field boundary data derived from the model. When applied to
the chromospheric boundary data, the codes are able to recover
the presence of the flux bundle and the field's free energy, though
some details of the field connectivity are lost. When the codes are
applied to the forced photospheric boundary data, the reference
model field is not well recovered, indicating that the Lorentz
forces on the photosphere severely impact the extrapolation of the
field. Preprocessing of the photospheric boundary does improve the
extrapolations considerably, although the results depend sensitively
on the details of the numerical codes. When applying the NLFFF codes
to solar data, the problems associated with Lorentz forces present in
the low solar atmosphere must be recognized: the various codes will
not necessarily converge to the correct, or even the same, solution.

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Title: Magnetic Stereoscopy of Coronal Loops in NOAA 8891
Authors: Feng, L.; Wiegelmann, T.; Inhester, B.; Solanki, S.; Gan,
W. Q.; Ruan, P.
2007SoPh..241..235F Altcode:
The Solar TErrestrial RElations Observatory (STEREO) requires powerful
tools for the three-dimensional (3D) reconstruction of the solar
corona. Here we test such a program with data from SOHO and TRACE. By
taking advantage of solar rotation, a newly developed stereoscopy tool
for the reconstruction of coronal loops is applied to the solar active
region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic
reconstruction is composed of three steps. First, we identify loop
structures in two TRACE images observed from two vantage viewpoints
approximately 17 degrees apart, which corresponds to observations
made about 30 hours apart. In the second step, we extrapolate the
magnetic field in the corona with the linear force-free field model
from the photospheric line-of-sight SOHO/MDI data. Finally, combining
the extrapolated field lines and one-dimensional loop curves from two
different viewpoints, we obtain the 3D loop structures with the magnetic
stereoscopy tool. We demonstrate that by including the magnetic modeling
this tool is more powerful than pure geometrical stereoscopy, especially
in resolving the ambiguities generated by classical stereoscopy. This
work will be applied to the STEREO mission in the near future.

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Title: Computing Nonlinear Force-Free Coronal Magnetic Fields in
Spherical Geometry
Authors: Wiegelmann, T.
2007SoPh..240..227W Altcode: 2006astro.ph.12124W
We describe a newly developed code for the extrapolation of nonlinear
force-free coronal magnetic fields in spherical coordinates. The program
uses measured vector magnetograms on the solar photosphere as input and
solves the force-free equations in the solar corona. The method is based
on an optimization principle and the heritage of the newly developed
code is a corresponding method in Cartesian geometry. We test the newly
developed code with the help of a semi-analytic solution and rate the
quality of our reconstruction qualitatively by magnetic field line
plots and quantitatively with a number of comparison metrics. We find
that we can reconstruct the original test field with high accuracy. The
method is fast if the computation is limited to low co-latitudes (say
30°≤θ≤150°), but it becomes significantly slower if the polar
regions are included.

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Title: Evolution of a Coronal Loop System
Authors: Tsiropoula, G.; Tziotziou, K.; Wiegelmann, T.; Zachariadis,
Th.; Gontikakis, C.; Dara, H.
2007SoPh..240...37T Altcode:
The temporal variation of a loop system that appears to be changing
rapidly is examined. The analyzed data were obtained on 15 May 1999,
with the Transition Region and Coronal Explorer (TRACE) during an
observing campaign and consist of observations in the Fe IX/Fe X 171
Å and Fe XII 195 Å passbands taken at a cadence of ∼10 min. The
special interest in this loop system is that it looks like one expanding
loop; however, careful examination reveals that the loop consists of
several strands and that new loop strands become visible successively
at higher altitudes and lower loop strands fade out during the one hour
of our observations. These strands have different widths, densities,
and temperatures and are most probably consisting of, at least, a few
unresolved thinner threads. Several geometric and physical parameters
are derived for two of the strands and an effort is made to determine
their 3D structure based on the extrapolation of the magnetic field
lines. Electron density estimates allow us to derive radiative and
conductive cooling times and to conclude that these loop strands are
cooling by radiation.

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Title: Evolution of coronal hole boundaries seen in EIT 195 Å and
TRACE 171 Å images
Authors: Madjarska, M. S.; Wiegelmann, T.
2007msfa.conf..249M Altcode:
We aim at studying the spatial and temporal scales of the small-scale
evolution of coronal hole boundaries using EUV observations from TRACE
(171 Å) and EIT (195 Å) on-board SoHO with a spatial resolution of
1" and 5.5", respectively, and various time cadences. We found that
small-scale loops known as bright points may play an essential role in
coronal hole boundaries evolution. Their emergence and disappearance
continuously expand or contract coronal holes. The changes appear to
be random on a time scale comparable with the lifetime of the loops
seen at these temperatures. No signature was found for a major energy
release during the evolution of the loops.

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Title: Magnetic stereoscopy of coronal loops in NOAA 8891
Authors: Feng, L.; Wiegelmann, T.; Inhester, B.
2007msfa.conf..269F Altcode:
We present an application of the magnetic stereoscopy tool to the
coronal loops observed by TRACE in the active region NOAA 8891. Designed
for the newly launched STEREO mission, this tool aims to reconstruct the
3D geometry of coronal loops. Taking advantage of the solar rotation,
two TRACE images observed one day apart are looked as STEREO-A and
STEREO-B EUVI images. Combining with the extrapolated magnetic field
lines in the corona from photospheric MDI data, the 3D geometry is
reconstructed with the identified loop pair.

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Title: Modeling large-scale coronal structures
Authors: Ruan, P.; Wiegelmann, T.; Inhester, B.
2007msfa.conf..363R Altcode:
Current measurements provide the photospheric magnetic field (e.g.,
from MDI on SOHO) and line-of-sight integrated 2D coronal images
(e.g., EIT). Our aim is to use these observations to reconstruct the
3D structure of the solar corona. Here we do the reconstruction in two
steps. We compute a global coronal magnetic field model with the help of
a potential or linear force-free model. In a subsequent step we model
the coronal plasma radiation with the help of scaling laws. Scaling
laws which relate loop emissivities with plasma parameters will be
tested with these models.

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Title: Nonlinear Force-Free Magnetic Field Modelling For VIM On SO
Authors: Wiegelmann, T.; Solanki, S. K.; Yelles, L.; Lagg, A.
2007ESASP.641E..19W Altcode:
The aim of this work is to investigate how photon noise and errors
in the retrieval of solar magnetic parameters from measured Stokes
profiles influences the extrapolartion of nonlinear force-free
coronal magnetic fields from photospheric vector magnetograms. To
do so we use a nonlinear force-free extrapolation code based on an
optimization principle. The extrapolation methods has been extensively
tested and applied to data from various telescopes. Here we apply the
code artificial vector magnetograms obtained from 3-D radiation-MHD
simulations. As a reference case we compute the coronal magnetic field
from an ideal magnetogram and compare the result with more realistic
magnetograms based on simulated Solar Orbiter/VIM-measurements. We
investigate the effect of noise, ambiguities, spatial resolution,
inversion mechanism, of Stokes profiles etc. We rate the quality of
the reconstructed coronal magnetic field qualitatively by magnetic
field line plots and quantitatively by a number of comparison metrices,
e.g., the vector correlation with the exact solution and how accurate
the free magnetic energy is computed. Not surprisingly, the instrument
effects and noise influence the quality of the nonlinear force-free
coronal magnetic field model. The extrapolations from realistic vector
magnetograms show a reasonable agreement with the ideal reconstruction,
however, and are in particular significantly better than extrapolations
based on line-of-sight magnetograms only. High quality VIM data
will thus allow reasonably accurate extrapolations that can serve
as the basis for magnetic coupling science through a comparison with
observations from EUS and EUI.

---------------------------------------------------------
Title: Measuring the Magnetic Vector with the He I 10830 Å Line:
A Rich New World
Authors: Solanki, S. K.; Lagg, A.; Aznar Cuadrado, R.; Orozco Suárez,
D.; Collados, M.; Wiegelmann, T.; Woch, J.; Sasso, C.; Krupp, N.
2006ASPC..358..431S Altcode:
The triplet of the He I transitions around 10830 Å not only shows a
rich variety of Stokes profiles, but also allows the full magnetic
vector in the upper chromosphere to be probed, thus revealing
the magnetic structure of loops, current sheets, finely structured
supersonic downflows, the chromospheric layers of sunspots (supporting
the presence of uncombed fields in the penumbra), flares, and the
quiet Sun. A very brief overview of some of the observations and
results obtained so far is given.

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Title: An optimization principle for the computation of MHD equilibria
in the solar corona
Authors: Wiegelmann, T.; Neukirch, T.
2006A&A...457.1053W Altcode: 2006astro.ph.12625W
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.

---------------------------------------------------------
Title: Testing non-linear force-free coronal magnetic field
extrapolations with the Titov-Démoulin equilibrium
Authors: Wiegelmann, T.; Inhester, B.; Kliem, B.; Valori, G.;
Neukirch, T.
2006A&A...453..737W Altcode: 2006astro.ph.12650W
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.

---------------------------------------------------------
Title: Magnetic Stereoscopy
Authors: Wiegelmann, T.; Inhester, B.
2006SoPh..236...25W Altcode: 2006astro.ph.12636W
The space mission Solar TErrestrial RElations Observatory (STEREO)
will provide images from two viewpoints. An important aim of the
STEREO mission is to get a 3D view of the solar corona. We develop
a program for the stereoscopic reconstruction of 3D coronal loops
from images taken with the two STEREO spacecraft. A pure geometric
triangulation of coronal features leads to ambiguities because the
dilute plasma emissions complicates the association of features in
image 1 with features in image 2. As a consequence of these problems,
the stereoscopic reconstruction is not unique and multiple solutions
occur. We demonstrate how these ambiguities can be resolved with the
help of different coronal magnetic field models (potential, linear,
and non-linear force-free fields). The idea is that, due to the high
conductivity in the coronal plasma, the emitting plasma outlines
the magnetic field lines. Consequently, the 3D coronal magnetic
field provides a proxy for the stereoscopy, which allows to eliminate
inconsistent configurations. The combination of stereoscopy and magnetic
modelling is more powerful than one of these tools alone. We test our
method with the help of a model active region and plan to apply it to
the solar case as soon as STEREO data become available.

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Title: Nonlinear Force-Free Magnetic Field Extrapolations: Comparison
of the Grad Rubin and Wheatland Sturrock Roumeliotis Algorithm
Authors: Inhester, Bernd; Wiegelmann, Thomas
2006SoPh..235..201I Altcode: 2008arXiv0801.3237I
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.

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Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part
I: A Quantitative Comparison of Methods
Authors: Schrijver, Carolus J.; De Rosa, Marc L.; Metcalf, Thomas R.;
Liu, Yang; McTiernan, Jim; Régnier, Stéphane; Valori, Gherardo;
Wheatland, Michael S.; Wiegelmann, Thomas
2006SoPh..235..161S Altcode:
We compare six algorithms for the computation of nonlinear force-free
(NLFF) magnetic fields (including optimization, magnetofrictional,
Grad-Rubin based, and Green's function-based methods) by evaluating
their performance in blind tests on analytical force-free-field models
for which boundary conditions are specified either for the entire
surface area of a cubic volume or for an extended lower boundary
only. Figures of merit are used to compare the input vector field to
the resulting model fields. Based on these merit functions, we argue
that all algorithms yield NLFF fields that agree best with the input
field in the lower central region of the volume, where the field and
electrical currents are strongest and the effects of boundary conditions
weakest. The NLFF vector fields in the outer domains of the volume
depend sensitively on the details of the specified boundary conditions;
best agreement is found if the field outside of the model volume is
incorporated as part of the model boundary, either as potential field
boundaries on the side and top surfaces, or as a potential field in
a skirt around the main volume of interest. For input field (B) and
modeled field (b), the best method included in our study yields an
average relative vector error En = « |B−b|»/« |B|» of
only 0.02 when all sides are specified and 0.14 for the case where only
the lower boundary is specified, while the total energy in the magnetic
field is approximated to within 2%. The models converge towards the
central, strong input field at speeds that differ by a factor of one
million per iteration step. The fastest-converging, best-performing
model for these analytical test cases is the Wheatland, Sturrock, and
Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann
(2004).

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Title: Preprocessing of Vector Magnetograph Data for a Nonlinear
Force-Free Magnetic Field Reconstruction
Authors: Wiegelmann, T.; Inhester, B.; Sakurai, T.
2006SoPh..233..215W Altcode: 2006astro.ph.12641W
Knowledge regarding the coronal magnetic field is important for
the understanding of many phenomena, like flares and coronal mass
ejections. Because of the low plasma beta in the solar corona,
the coronal magnetic field is often assumed to be force-free and
we use photospheric vector magnetograph data to extrapolate the
magnetic field into the corona with the help of a nonlinear force-free
optimization code. Unfortunately, the measurements of the photospheric
magnetic field contain inconsistencies and noise. In particular,
the transversal components (say Bx and By) of
current vector magnetographs have their uncertainties. Furthermore,
the magnetic field in the photosphere is not necessarily force free
and often not consistent with the assumption of a force-free field
above the magnetogram. We develop a preprocessing procedure to drive
the observed non-force-free data towards suitable boundary conditions
for a force-free extrapolation. As a result, we get a data set which
is as close as possible to the measured data and consistent with the
force-free assumption.

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Title: 3D visualization techniques for the STEREO-mission
Authors: Wiegelmann, T.; Podlipnik, B.; Inhester, B.; Feng, L.;
Ruan, P.
2006cosp...36..656W Altcode: 2006cosp.meet..656W
The forthcoming STEREO-mission will observe the Sun from two different
viewpoints We expect about 2GB data per day which ask for suitable
data presentation techniques A key feature of STEREO is that it will
provide for the first time a 3D-view of the Sun and the solar corona
In our normal environment we see objects three dimensional because
the light from real 3D objects needs different travel times to our
left and right eye As a consequence we see slightly different images
with our eyes which gives us information about the depth of objects
and a corresponding 3D impression Techniques for the 3D-visualization
of scientific and other data on paper TV computer screen cinema etc
are well known e g two colour anaglyph technique shutter glasses
polarization filters and head-mounted displays We discuss advantages
and disadvantages of these techniques and how they can be applied
to STEREO-data The 3D-visualization techniques are not limited to
visual images but can be also used to show the reconstructed coronal
magnetic field and energy and helicity distribution In the advent
of STEREO we test the method with data from SOHO which provides us
different viewpoints by the solar rotation This restricts the analysis
to structures which remain stationary for several days Real STEREO-data
will not be affected by these limitations however

---------------------------------------------------------
Title: Coupling of photospheric and coronal magnetic fields
Authors: Wiegelmann, T.; Inhester, B.
2006cosp...36..436W Altcode: 2006cosp.meet..436W
Information regarding the magnetic field are essential to understand the
coupling of the solar interior with the photosphere and atmosphere The
photospheric magnetic field is measured routinely with line-of-sight and
vector magnetographs Direct measurements of chromospheric and coronal
magnetic fields are usually not available except for a few individual
cases We can however extrapolate the photospheric magnetic field
into the corona This is by no means an easy task as the extrapolated
magnetic field depends on assumptions regarding the coronal plasma
e g force-freeness Force-free means that all non-magnetic forces e
g pressure gradients and gravity are neglected While this assumption
is well justified in the solar corona due to the low plasma beta the
magnetic field is not force-free on the photosphere Ambiguities and
noise in the transversal magnetic field measurements are an additional
complication for reliable coronal magnetic field extrapolations A
helpful property is that the emitting coronal plasma outlines the
magnetic field lines As a consequence we can test and improve coronal
magnetic field models by a comparison with coronal EUV-images This
approach is in particular attractive if EUV-images from different
viewpoints as provided by STEREO are available Photospheric magnetic
field measurements and EUV-images are combined for a consistent 3D
reconstruction of coronal magnetic fields and the coronal plasma

---------------------------------------------------------
Title: Non-Linear Force-Free Magnetic Fields
Authors: Wiegelmann, T.
2005ESASP.596E..80W Altcode: 2005ccmf.confE..80W
No abstract at ADS

---------------------------------------------------------
Title: Magnetic Loops: a Comparison of Extrapolations from the
Photosphere with Chromospheric Measurements
Authors: Wiegelmann, T.; Lagg, A.; Solanki, S.; Inhester, B.; Woch, J.
2005ESASP.596E...7W Altcode: 2005ccmf.confE...7W
No abstract at ADS

---------------------------------------------------------
Title: How To Use Magnetic Field Information For Coronal Loop
Identification
Authors: Wiegelmann, T.; Inhester, B.; Lagg, A.; Solanki, S. K.
2005SoPh..228...67W Altcode: 2008arXiv0801.4573W
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.

---------------------------------------------------------
Title: Comparing magnetic field extrapolations with measurements of
magnetic loops
Authors: Wiegelmann, T.; Lagg, A.; Solanki, S. K.; Inhester, B.;
Woch, J.
2005A&A...433..701W Altcode: 2008arXiv0801.4519W
We compare magnetic field extrapolations from a photospheric magnetogram
with the observationally inferred structure of magnetic loops in
a newly developed active region. This is the first time that the
reconstructed 3D-topology of the magnetic field is available to test
the extrapolations. We compare the observations with potential fields,
linear force-free fields and non-linear force-free fields. This
comparison reveals that a potential field extrapolation is not
suitable for a reconstruction of the magnetic field in this young,
developing active region. The inclusion of field-line-parallel
electric currents, the so called force-free approach, gives much better
results. Furthermore, a non-linear force-free computation reproduces
the observations better than the linear force-free approximation,
although no free parameters are available in the former case.

---------------------------------------------------------
Title: Links between magnetic fields and plasma flows in a coronal
hole
Authors: Wiegelmann, T.; Xia, L. D.; Marsch, E.
2005A&A...432L...1W Altcode: 2008arXiv0801.4724W
We compare the small-scale features visible in the Ne viii Doppler-shift
map of an equatorial coronal hole (CH) as observed by SUMER with the
small-scale structures of the magnetic field as constructed from a
simultaneous photospheric magnetogram by a potential magnetic-field
extrapolation. The combined data set is analysed with respect to
the small-scale flows of coronal matter, which means that the Ne viii
Doppler-shift used as tracer of the plasma flow is investigated in close
connection with the ambient magnetic field. Some small closed-field
regions in this largely open CH are also found in the coronal volume
considered. The Doppler-shift patterns are found to be clearly linked
with the field topology.

---------------------------------------------------------
Title: Why are Coronal Holes Indistinguishable from the Quiet Sun
in Transition Region Radiation?
Authors: Wiegelmann, T.; Solanki, S. K.
2004ESASP.575...35W Altcode: 2004soho...15...35W
No abstract at ADS

---------------------------------------------------------
Title: Coronal plasma flows and magnetic fields in solar active
regions. Combined observations from SOHO and NSO/Kitt Peak
Authors: Marsch, E.; Wiegelmann, T.; Xia, L. D.
2004A&A...428..629M Altcode:
During the early days of the SOHO mission, SUMER observed a few
active regions (ARs) connected with sunspots on the Sun and took their
images and spectra in various EUV emission lines. In addition to these
spectroscopic data magnetograms of the photospheric footpoint regions
of the AR loops were available from the MDI on SOHO and the National
Solar Observatory/Kitt Peak (NSO/KP), data which here are used to
construct the coronal magnetic field of the ARs by force-free-field
extrapolation. The combined data set is analysed with respect to
the large-scale circulation of coronal matter, which means that the
Dopplershifts of various lines used as tracers of the plasma flow are
investigated in close connection with the ambient magnetic field,
which is found to be either closed or open in the coronal volume
considered. The Dopplershift pattern is found to be clearly linked
with the field topology, and several regions of strong velocity shear
are identified. We also estimate the coronal currents. We discuss
the results of this mainly phenomenological correlative study with
the perspective to understand coronal heating and mass supply to the
extended corona, and with respect to the role played by the field in
guiding and constraining plasma flows.

---------------------------------------------------------
Title: Similarities and Differences between Coronal Holes and the
Quiet Sun: Are Loop Statistics the Key?
Authors: Wiegelmann, T.; Solanki, S. K.
2004SoPh..225..227W Altcode: 2008arXiv0802.0120W
Coronal holes (CH) emit significantly less at coronal temperatures
than quiet-Sun regions (QS), but can hardly be distinguished in most
chromospheric and lower transition region lines. A key quantity for the
understanding of this phenomenon is the magnetic field. We use data from
SOHO/MDI to reconstruct the magnetic field in coronal holes and the
quiet Sun with the help of a potential magnetic model. Starting from
a regular grid on the solar surface we then trace field lines, which
provide the overall geometry of the 3D magnetic field structure. We
distinguish between open and closed field lines, with the closed field
lines being assumed to represent magnetic loops. We then try to compute
some properties of coronal loops. The loops in the coronal holes (CH)
are found to be on average flatter than in the QS. High and long closed
loops are extremely rare, whereas short and low-lying loops are almost
as abundant in coronal holes as in the quiet Sun. When interpreted in
the light of loop scaling laws this result suggests an explanation for
the relatively strong chromospheric and transition region emission
(many low-lying, short loops), but the weak coronal emission (few
high and long loops) in coronal holes. In spite of this contrast
our calculations also suggest that a significant fraction of the cool
emission in CHs comes from the open flux regions. Despite these insights
provided by the magnetic field line statistics further work is needed
to obtain a definite answer to the question if loop statistics explain
the differences between coronal holes and the quiet Sun.

---------------------------------------------------------
Title: Optimization code with weighting function for the
reconstruction of coronal magnetic fields
Authors: Wiegelmann, T.
2004SoPh..219...87W Altcode: 2008arXiv0802.0124W
We developed a code for the reconstruction of nonlinear force-free
and non-force-free coronal magnetic fields. The 3D magnetic field is
computed numerically with the help of an optimization principle. The
force-free and non-force-free codes are compiled in one program. The
force-free approach needs photospheric vector magnetograms as input. The
non-force-free code additionally requires the line-of-sight integrated
coronal density distribution in combination with a tomographic inversion
code. Previously the optimization approach has been used to compute
magnetic fields using all six boundaries of a computational box. Here
we extend this method and show how the coronal magnetic field can
be reconstructed only from the bottom boundary, where the boundary
conditions are measured with vector magnetographs. The program is
planed for use within the Stereo mission.

---------------------------------------------------------
Title: A Quantitative Method to Optimise Magnetic Field Line Fitting
of Observed Coronal Loops
Authors: Carcedo, L.; Brown, D. S.; Hood, A. W.; Neukirch, T.;
Wiegelmann, T.
2003SoPh..218...29C Altcode:
Many authors use magnetic-field models to extrapolate the field in
the solar corona from magnetic data in the photosphere. The accuracy
of such extrapolations is usually judged qualitatively by eye, where
a less judgemental quantitative approach would be more desirable. In
this paper, a robust method for obtaining the best fit between a
theoretical magnetic field and intensity observations of coronal loops
on the solar disk will be presented. The method will be applied to
Yohkoh data using a linear force-free field as an illustration. Any
other theoretical model for the magnetic field can be used, provided
there is enough freedom in the model to optimize the fit.

---------------------------------------------------------
Title: Magnetic modeling and tomography: First steps towards a
consistent reconstruction of the solar corona
Authors: Wiegelmann, T.; Inhester, B.
2003SoPh..214..287W Altcode: 2008arXiv0802.0687W
We undertake a first attempt towards a consistent reconstruction
of the coronal magnetic field and the coronal density structure. We
consider a stationary solar corona which has to obey the equations of
magnetohydrostatics. We solve these equations with help of a newly
developed optimization scheme. As a first step we illustrate how
tomographic information can be included into the reconstruction of
coronal magnetic fields. In a second step we use coronal magnetic field
information to improve the tomographic inversion process. As input
the scheme requires magnetic field measurements on the photosphere
from vector-magnetographs and the line-of-sight integrated density
distribution from coronagraphs. We test our codes with well-known
analytic magnetohydrostatic equilibria and models. The program is
planned for use within the STEREO mission.

---------------------------------------------------------
Title: Computing nonlinear force free coronal magnetic fields
Authors: Wiegelmann, T.; Neukirch, T.
2003NPGeo..10..313W Altcode: 2008arXiv0801.3215W
Knowledge of the structure of the coronal magnetic field is important
for our understanding of many solar activity phenomena, e.g. flares
and CMEs. However, the direct measurement of coronal magnetic fields
is not possible with present methods, and therefore the coronal field
has to be extrapolated from photospheric measurements. Due to the low
plasma beta the coronal magnetic field can usually be assumed to be
approximately force free, with electric currents flowing along the
magnetic field lines. There are both observational and theoretical
reasons which suggest that at least prior to an eruption the coronal
magnetic field is in a nonlinear force free state. Unfortunately the
computation of nonlinear force free fields is way more difficult than
potential or linear force free fields and analytic solutions are not
generally available. We discuss several methods which have been proposed
to compute nonlinear force free fields and focus particularly on an
optimization method which has been suggested recently. We compare the
numerical performance of a newly developed numerical code based on the
optimization method with the performance of another code based on an
MHD relaxation method if both codes are applied to the reconstruction of
a semi-analytic nonlinear force-free solution. The optimization method
has also been tested for cases where we add random noise to the perfect
boundary conditions of the analytic solution, in this way mimicking
the more realistic case where the boundary conditions are given by
vector magnetogram data. We find that the convergence properties of
the optimization method are affected by adding noise to the boundary
data and we discuss possibilities to overcome this difficulty.

---------------------------------------------------------
Title: Including stereoscopic information in the reconstruction of
coronal magnetic fields
Authors: Wiegelmann, T.; Neukirch, T.
2002SoPh..208..233W Altcode: 2008arXiv0801.3234W
We present a method to include stereoscopic information about the
three-dimensional structure of flux tubes into the reconstruction of the
coronal magnetic field. Due to the low plasma beta in the corona we can
assume a force-free magnetic field, with the current density parallel
to the magnetic field lines. Here we use linear force-free fields for
simplicity. The method uses the line-of-sight magnetic field on the
photosphere as observational input. The value of α is determined
iteratively by comparing the reconstructed magnetic field with the
observed structures. The final configuration is the optimal linear
force-free solution constrained by both the photospheric magnetogram
and the observed plasma structures. As an example we apply our method
to SOHO MDI/EIT data of an active region. In the future it is planned
to apply the method to analyse data from the SECCHI instrument aboard
the STEREO mission.

---------------------------------------------------------
Title: Tests and limits of Vlasov code simulations and its application
to null-helicity and co-helicity reconnection
Authors: Wiegelmann, T.; Neukirch, T.; Büchner, J.
2001sps..proc...58W Altcode:
Magnetic reconnection is an important process in many space plasmas
(e.g. geomagnetic substorms, coronal mass ejections). The large
scale structure of these phenomena is usually described within
MHD. Reconnection requires a non ideal region (resistivity) in the
plasma. The cause of a non ideal behaviour in localized regions could
for example be anomalous resistivity in thin current sheets. The
formation of these thin current sheets can be understand within the
framework of MHD. The further evolution of the current sheets cannot
be investigated with MHD, because the sheet width becomes comparable
with kinetic scales like the ion gyro radius and kinetic effects
have to be taken into account. For many space plasmas, the kinetic
processes are collisionless and can thus be described by the Vlasov
equation. A code to solve the Vlasov equation has been developed and
we report first results obtained with the code. To test the accuracy
and limits of our code we carry out several consistency checks, which
can be compared with analytic results, in particular phase mixing and
Landau damping. We also apply our Vlasov code to collisionless magnetic
reconnection in the magnetospheric plasma sheet and at the magnetopause.

---------------------------------------------------------
Title: Helmet Streamers with Triple Structures: Simulations of
resistive dynamics
Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas
2000SoPh..191..391W Altcode: 2008arXiv0801.3187W
Recent observations of the solar corona with the LASCO coronagraph on
board of the SOHO spacecraft have revealed the occurrence of triple
helmet streamers even during solar minimum, which occasionally go
unstable and give rise to large coronal mass ejections. There are
also indications that the slow solar wind is either a combination of a
quasi-stationary flow and a highly fluctuating component or may even
be caused completely by many small eruptions or instabilities. As a
first step we recently presented an analytical method to calculate
simple two-dimensional stationary models of triple helmet streamer
configurations. In the present contribution we use the equations of
time-dependent resistive magnetohydrodynamics to investigate the
stability and the dynamical behaviour of these configurations. We
particularly focus on the possible differences between the dynamics
of single isolated streamers and triple streamers and on the way
in which magnetic reconnection initiates both small scale and large
scale dynamical behaviour of the streamers. Our results indicate that
small eruptions at the helmet streamer cusp may incessantly accelerate
small amounts of plasma without significant changes of the equilibrium
configuration and might thus contribute to the non-stationary slow
solar wind. On larger time and length scales, large coronal eruptions
can occur as a consequence of large scale magnetic reconnection events
inside the streamer configuration. Our results also show that triple
streamers are usually more stable than a single streamer.

---------------------------------------------------------
Title: A Self-consistent Model for Coronal Streamers and their
Relevance for coronal mass ejections and the slow Solar wind
Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas
1999AGAb...15...78W Altcode: 1999AGM....15..J23W
Coronal helmet streamers are large scale magnetic field structures in
the solar corona. The coronal magnetic field is approximately frozen
into the plasma. Observations with the LASCO coronagraph on board of
SOHO have shown that these helmet streamers show a triple structure
during the solar activity minimum. The streamer regions have been
identified as the source regions for the slow solar wind and new
observations provide evidence that a stationary slow solar wind may
not exist, but that the slow solar wind is produced by many little
eruptions near the helmet streamer cusp leading to an approximately
stationary plasma flow on large scales. The observations further show,
that the streamer structures occasionally go unstable, leading tohuge
coronal mass ejections. We present a method to calculate analytically
self-consistent stationary helmet streamer configurations with triple
structures. We then use these stationary configurations as input for
time-dependent MHD simulations. Our simulations give evidence, that
magnetic reconnection plays an important role for both the acceleration
of the slow solar wind and huge coronal eruptions.

---------------------------------------------------------
Title: Numerical Simulations of Kinetic Instabilities in Space Plasmas
Authors: Wiegelmann, Thomas; Büchner, Jörg
1999AGAb...15...83W Altcode: 1999AGM....15..L01W
Spontaneous formation of structures plays an important role for
the dynamics of space plasmas. Small scale turbulence may cause
configuration instabilities on larger scales. Of major interest
are nonlinear processes which lead to changes in the large scale
struc ture of magnetic field topology as a consequence of magnetic
reconnection. Magnetic reconnection is a generic process for efficient
transformation of magnetic field energy in plasma. Examples of
astrophysical processes where magnetic reconnection is assumed to play
an important role are magnetic storms and coronal mass ejections. Recent
research showed that thin current sheets play an important role for
the occurrence of reconnection. To investigate the stability of these
very thin current sheets we have carried out three dimensional kinetic
plasma simulations with the Particle in Cell Code GISMO. We observe
kinetic instabilities in the current direction (sausage instability)
and perpendicular to the current direction (tearing). We investigate
the growth rates and spatial scale length of these instabilities with
the help of Fourier analysis.

---------------------------------------------------------
Title: Closely-spaced multi-satellite project ROY to study small-scale
structures during magnetic field annihilation and strong turbulence
in critical magnetospheric regions: Results of Phase A
Authors: Galperin, Yu. I.; Zelenyi, L. M.; Veselov, M. V.; Savin,
S. P.; Mogilevsky, M. M.; Yanovsky, M. I.; Prokhorenko, V. I.;
Eismont, N. A.; Kunitsyn, V. E.; Silin, I. V.; Sosnovets, E. N.;
Bûchner, J.; Nikutowski, B.; Wiegelmann, T.
1999ASIC..537...55G Altcode: 1999iip..conf...55G
No abstract at ADS

---------------------------------------------------------
Title: Helmet Streamers with Triple Structures: Weakly Two-Dimensional
Stationary States
Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas
1998SoPh..180..439W Altcode: 1997astro.ph.12012W
Recent observations of the solar corona with the LASCO coronagraph on
board the SOHO spacecraft have revealed the occurrence of triple helmet
streamers even during solar minimum, which occasionally go unstable
and give rise to particularly huge coronal mass ejections. We present
a method to calculate (semi-)analytically self-consistent stationary
configurations of triple helmet streamers which can serve as input
for stability considerations and dynamical calculations. The method is
based on an asymptotic expansion procedure using the elongated structure
of the streamers. The method is very flexible and can be used in both
Cartesian and spherical geometry. We discuss the effects of magnetic
shear, gravity and field-aligned flow on open field lines. Example
solutions illustrating the influence of each of these features on the
solution structure are presented.

---------------------------------------------------------
Title: Solar magnetic fields: triple arcade structures
Authors: Wiegelmann, Thomas
1998PhST...74...77W Altcode:
Recent observation with the LASCO coronagraph on board the SOHO
spacecraft have shown that helmet streamers may have an internal
triple arcade structure. The observations suggest that this triple
structure might be important for the initiation of coronal mass
ejections (CME's). In this paper we undertake a first step towards
the theoretical description of such triple structures by calculating
self-consistent solutions of the magnetohydrostatic equations in
two dimensions. For simplicity, we start with the investigations of
current-free structures, leading to potential magnetic fields. We then
go on to investigate the case of linear currents. These two cases have
the disadvantage of being linearly stable in the framework of MHD,
which makes it difficult to take them as starting-points for further
investigations. Therefore, we also investigate special exact solutions
of a nonlinear case and apply the method of asymptotic expansion to
another nonlinear problem to obtain approximate elongated solutions,
which might be useful for linear or nonlinear stability checks.

---------------------------------------------------------
Title: Helmet streamers with triple structures.
Authors: Wiegelmann, T.
1997AGAb...13..101W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Formation of thin current sheets in a quasistatic magnetotail
model
Authors: Wiegelmann, T.; Schindler, K.
1995GeoRL..22.2057W Altcode:
Observations suggest that thin current sheets forming in the near-Earth
magnetotail late in substorm growth phases may be a crucial part of
substorm evolution. In a simple theoretical model the current density
was shown to become singular for suitable external perturbations. Here,
we address the same problem in a more realistic model based on the
adiabatic MHD - theory developed by Schindler and Birn [1982]. We show
that under suitable conditions the formation of a thin current sheet
in the near-Earth tail is an intrinsic aspect of flux transfer to the
magnetotail. The mechanism is based on the strong variation of flux
tube volume with the magnetic flux function.