136 research outputs found
Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data
We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to
model the force-free coronal field above a solar active region, assuming
magnetic forces to dominate. We take measurement uncertainties caused by, e.g.,
noise and the particular inversion technique into account. After searching for
the optimum modeling parameters for the particular data sets, we compare the
resulting nonlinear force-free model fields. We show the degree of agreement of
the coronal field reconstructions from the different data sources by comparing
the relative free energy content, the vertical distribution of the magnetic
pressure and the vertically integrated current density. Though the longitudinal
and transverse magnetic flux measured by the VSM and HMI is clearly different,
we find considerable similarities in the modeled fields. This indicates the
robustness of the algorithm we use to calculate the nonlinear force-free fields
against differences and deficiencies of the photospheric vector maps used as an
input. We also depict how much the absolute values of the total force-free,
virial and the free magnetic energy differ and how the orientation of the
longitudinal and transverse components of the HMI- and VSM-based model volumes
compares to each other.Comment: 9 pages, 5 figure
Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?
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,
e.g., chromospheric H 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.Comment: 22 pages, 6 Figur
How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?
The SDO/HMI instruments provide photospheric vector magnetograms with a high
spatial and temporal resolution. Our intention is to model the coronal magnetic
field above active regions with the help of a nonlinear force-free
extrapolation code. Our code is based on an optimization principle and has been
tested extensively with semi-analytic and numeric equilibria and been applied
before to vector magnetograms from Hinode and ground based observations.
Recently we implemented a new version which takes measurement errors in
photospheric vector magnetograms into account. Photospheric field measurements
are often due to measurement errors and finite nonmagnetic forces inconsistent
as a boundary for a force-free field in the corona. In order to deal with these
uncertainties, we developed two improvements: 1.) Preprocessing of the surface
measurements in order to make them compatible with a force-free field 2.) The
new code keeps a balance between the force-free constraint and deviation from
the photospheric field measurements. Both methods contain free parameters,
which have to be optimized for use with data from SDO/HMI. Within this work we
describe the corresponding analysis method and evaluate the force-free
equilibria by means of how well force-freeness and solenoidal conditions are
fulfilled, the angle between magnetic field and electric current and by
comparing projections of magnetic field lines with coronal images from SDO/AIA.
We also compute the available free magnetic energy and discuss the potential
influence of control parameters.Comment: 17 Pages, 6 Figures, Sol. Phys., accepte
Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm
We compare the performance of two alternative algorithms which aim to
construct a force-free magnetic field given suitable boundary conditions. For
this comparison, we have implemented both algorithms on the same finite element
grid which uses Whitney forms to describe the fields within the grid cells. The
additional use of conjugate gradient and multigrid iterations result in quite
effective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithms
both perform well for the reconstruction of a known analytic force-free field.
For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotis
approach has some difficulties because it requires overdetermined boundary
information which may include inconsistencies. The Grad-Rubin code on the other
hand loses convergence for strong current densities. For the example we have
investigated, however, the maximum possible current density seems to be not far
from the limit beyond which a force free field cannot exist anymore for a given
normal magnetic field intensity on the boundary.Comment: 21 pages, 13 figure
A Statistical Study on Force-Freeness of Solar Magnetic Fields in the Photosphere
It is an indisputable fact that solar magnetic fields are force-free in the
corona, where force free fields means that current and magnetic fields are
parallel and there is no Lorentz force in the fields. While the force-free
extent of photospheric magnetic fields remains open. In this paper, the
statistical results about it is given. The vector magnetograms (namely,
, and in heliocentric coordinates) are employed, which
are deduced and calibrated from Stokes spectra, observed by Solar Magnetic
Field Telescope (SMFT) at Huairou Solar Observing Station (HSOS) are used. We
study and calibrated 925 magnetograms calibrated by two sets of calibration
coefficients, that indicate the relations between magnetic fields and the
strength of Stokes spectrum and can be calculated either theoretically or
empirically. The statistical results show that the majority of active region
magnetic fields are not consistent with the force-free model.Comment: 10 pages, 5 figures, has been accepted by PAS
Nonlinear force-free modeling of the solar coronal magnetic field
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, e.g. force-freeness. Force-free means that all non-magnetic
forces like pressure gradients and gravity are neglected. This approach is well
justified in the solar corona due to the low plasma beta. One has to take care,
however, about ambiguities, noise and non-magnetic 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.Comment: 33 pages, 3 figures, Review articl
Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation
Extrapolation codes for modelling the magnetic field in the corona in
cartesian geometry do not take the curvature of the Sun's surface into account
and can only be applied to relatively small areas, \textit{e.g.}, a single
active region. We apply a method for nonlinear force-free coronal magnetic
field modelling of photospheric vector magnetograms in spherical geometry which
allows us to study the connectivity between multi-active regions. We use vector
magnetograph data from the Synoptic Optical Long-term Investigations of the Sun
survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic
field, where we study three neighbouring magnetically connected active regions
(ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively.
We compare the magnetic field topologies and the magnetic energy densities and
study the connectivities between the active regions(ARs). We have studied the
time evolution of magnetic field over the period of three days and found no
major changes in topologies as there was no major eruption event. From this
study we have concluded that active regions are much more connected
magnetically than the electric current.Comment: Solar Physic
Analysis and interpretation of a fast limb CME with eruptive prominence, C-flare and EUV dimming
Coronal Mass ejections or CMEs are large dynamical solar-corona events. The
mass balance and kinematics of a fast limb CME, including its prominence
progenitor and the associated flare, will be compared with computed magnetic
structures to look for their origin and effect.
Multi-wavelength ground-based and space-borne observations are used to study
a fast W-limb CME event of December 2, 2003, taking into account both on and
off disk observations. Its erupting prominence is measured at high cadence with
the Pic du Midi full H-alpha line-flux imaging coronagraph. EUV images from
space instruments are processed including difference imaging. SOHO/LASCO images
are used to study the mass excess and motions. A fast bright expanding coronal
loop is identified in the region recorded slightly later by GOES as a C7.2
flare, followed by a brightening and an acceleration phase of the erupting
material with both cool and hot components. The total coronal radiative flux
dropped by 5 percent in the EUV channels, revealing a large dimming effect at
and above the limb. The typical 3-part structure observed 1 hour later shows a
core shaped similarly to the eruptive filament/prominence. The total measured
mass of the escaping CME (1.5x10to16 g from C2 LASCO observations) definitely
exceeds the estimated mass of the escaping cool prominence material although
assumptions made to analyse the Ha erupting prominence, as well as the
corresponding EUV darkening of the filament observed several days before, made
this evaluation uncertain by a factor of 2. From the current free extrapolation
we discuss the shape of the magnetic neutral surface and a possible scenario
leading to an instability, including the small scale dynamics inside and around
the filament.Comment: 11 pages, 9 figure
On the Force-Freeness of the Photospheric Sunspot Magnetic Fields as Observed from Hinode (SOT/SP)
A magnetic field is force-free if there is no interaction between the
magnetic field and plasma in surrounding atmosphere i.e., electric currents are
aligned with the magnetic field, giving rise to zero Lorentz force. Computation
of various magnetic parameters such as magnetic energy, gradient of twist of
sunspot fields and any kind of extrapolations, heavily hinge on the force-free
approximation of the photospheric sunspot magnetic fields. Thus it is important
to inspect the force-freeness of sunspot fields. The force-freeness of sunspot
magnetic fields has been examined earlier by some researchers ending with
incoherent results. Accurate photospheric vector field measurements with high
spatial resolution are required to inspect the force-free nature of sunspots.
We use several such vector magnetograms obtained from the Solar Optical
Telescope/Spectro-Polarimeter aboard the Hinode. Both necessary and sufficient
conditions for force-freeness are examined by checking global and local nature
of magnetic forces over sunspots. We find that the sunspot magnetic fields are
not much away from force-free configuration, although they are not completely
force-free on the photosphere. The umbral and inner penumbral fields are more
force-free than the middle and the outer penumbral fields. During their
evolution, sunspot magnetic fields are found to maintain their proximity to
force-free behaviour. Although a dependence of net Lorentz force components is
seen on the evolutionary stages of the sunspots, we don't find a systematic
relationship between the nature of sunspot fields and associated flare
activity. Further, we examine whether the fields at photosphere follow linear
or non-linear force free conditions. After examining this in various complex
and simple sunspots we conclude that,in either case,the photospheric sunspot
fields are closer to satisfy non linear force-free field approximation.Comment: 34 pages, 4 figures, 2 tables; accepted for publication in the
Astrophysical Journa
Using models of the ocean's mean dynamic topography to identify errors in coastal geodetic levelling
Identifying errors (blunders and systematic errors) in coastal geodetic levelling networks has often been problematic. This is because (1) mean sea level (MSL) at tide gauges cannot be directly compared to height differences from levelling because the geoid/quasigeoid and MSL are not parallel, being separated by the ocean’s mean dynamic topography (MDT) and (2) the lack of redundancy at the edge of the levelling network. This paper sets out a methodology to independently identify blunders and/or systematic errors (over long distances) in geodetic levelling using MDT models to account for the separation between the geoid/quasigeoid and MSL at tide gauges. This method is then tested in a case study using an oceanographic MDT model, MSL observations, GNSS data and a quasigeoid model. The results are significant because the errors found could not be detected by standard levelling misclosure checks alone, with supplementary data from an MDT model, with cross-validation from GNSS-quasigeoid allowing their detection. In addition, it appears that an oceanographic-only MDT is as effective as GNSS and a quasigeoid model for detecting levelling errors, which could be particularly useful for countries with coastal levelling errors in their levelling networks that cannot be identified by conventional levelling closure checks
- …