169 research outputs found
Comment on "Resolving the 180-deg Ambiguity in Solar Vector Magnetic Field Data: Evaluating the Effects of Noise, Spatial Resolution, and Method Assumptions"
In a recent paper, Leka at al. (Solar Phys. 260, 83, 2009)constructed a
synthetic vector magnetogram representing a three-dimensional magnetic
structure defined only within a fraction of an arcsec in height. They rebinned
the magnetogram to simulate conditions of limited spatial resolution and then
compared the results of various azimuth disambiguation methods on the resampled
data. Methods relying on the physical calculation of potential and/or
non-potential magnetic fields failed in nearly the same, extended parts of the
field of view and Leka et al. (2009) attributed these failures to the limited
spatial resolution. This study shows that the failure of these methods is not
due to the limited spatial resolution but due to the narrowly defined test
data. Such narrow magnetic structures are not realistic in the real Sun.
Physics-based disambiguation methods, adapted for solar magnetic fields
extending to infinity, are not designed to handle such data; hence, they could
only fail this test. I demonstrate how an appropriate limited-resolution
disambiguation test can be performed by constructing a synthetic vector
magnetogram very similar to that of Leka et al. (2009) but representing a
structure defined in the semi-infinite space above the solar photosphere. For
this magnetogram I find that even a simple potential-field disambiguation
method manages to resolve the ambiguity very successfully, regardless of
limited spatial resolution. Therefore, despite the conclusions of Leka et al.
(2009), a proper limited-spatial-resolution test of azimuth disambiguation
methods is yet to be performed in order to identify the best ideas and
algorithms.Comment: Solar Physics, in press (19 pp., 5 figures, 2 tables
Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data
We investigate how the divergence-free property of magnetic fields can be
exploited to resolve the azimuthal ambiguity present in solar vector
magnetogram data, by using line-of-sight and horizontal heliographic derivative
information as approximated from discrete measurements. Using synthetic data we
test several methods that each make different assumptions about how the
divergence-free property can be used to resolve the ambiguity. We find that the
most robust algorithm involves the minimisation of the absolute value of the
divergence summed over the entire field of view. Away from disk centre this
method requires the sign and magnitude of the line-of-sight derivatives of all
three components of the magnetic field vector.Comment: Solar Physics, in press, 20 pages, 11 figure
A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests
Based on a second-order approximation of nonlinear force-free magnetic field
solutions in terms of uniformly twisted field lines derived in Paper I, we
develop here a numeric code that is capable to forward-fit such analytical
solutions to arbitrary magnetogram (or vector magnetograph) data combined with
(stereoscopically triangulated) coronal loop 3D coordinates. We test the code
here by forward-fitting to six potential field and six nonpotential field cases
simulated with our analytical model, as well as by forward-fitting to an
exactly force-free solution of the Low and Lou (1990) model. The
forward-fitting tests demonstrate: (i) a satisfactory convergence behavior
(with typical misalignment angles of ), (ii)
relatively fast computation times (from seconds to a few minutes), and (iii)
the high fidelity of retrieved force-free -parameters ( for simulations and for the Low and Lou model). The
salient feature of this numeric code is the relatively fast computation of a
quasi-forcefree magnetic field, which closely matches the geometry of coronal
loops in active regions, and complements the existing {\sl nonlinear force-free
field (NLFFF)} codes based on photospheric magnetograms without coronal
constraints.Comment: Solar PHysics, (in press), 25 pages, 11 figure
How to 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
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
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
The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare
Solar flares occur due to the sudden release of energy stored in
active-region magnetic fields. To date, the pre-cursors to flaring are still
not fully understood, although there is evidence that flaring is related to
changes in the topology or complexity of an active region's magnetic field.
Here, the evolution of the magnetic field in active region NOAA 10953 was
examined using Hinode/SOT-SP data, over a period of 12 hours leading up to and
after a GOES B1.0 flare. A number of magnetic-field properties and low-order
aspects of magnetic-field topology were extracted from two flux regions that
exhibited increased Ca II H emission during the flare. Pre-flare increases in
vertical field strength, vertical current density, and inclination angle of ~
8degrees towards the vertical were observed in flux elements surrounding the
primary sunspot. The vertical field strength and current density subsequently
decreased in the post-flare state, with the inclination becoming more
horizontal by ~7degrees. This behaviour of the field vector may provide a
physical basis for future flare forecasting efforts.Comment: Accepted for Publication in Solar Physics. 16 pages, 4 figure
Eruptions of Magnetic Ropes in Two Homologous Solar Events on 2002 June 1 and 2: a Key to Understanding of an Enigmatic Flare
The goal of this paper is to understand the drivers, configurations, and
scenarios of two similar eruptive events, which occurred in the same solar
active region 9973 on 2002 June 1 and 2. The June 2 event was previously
studied by Sui, Holman, and Dennis (2006, 2008), who concluded that it was
challenging for popular flare models. Using multi-spectral data, we analyze a
combination of the two events. Each of the events exhibited an evolving
cusp-like feature. We have revealed that these apparent ``cusps'' were most
likely mimicked by twisted magnetic flux ropes, but unlikely to be related to
the inverted Y-like magnetic configuration in the standard flare model. The
ropes originated inside a funnel-like magnetic domain whose base was bounded by
an EUV ring structure, and the top was associated with a coronal null point.
The ropes appear to be the major drivers for the events, but their rise was not
triggered by reconnection in the coronal null point. We propose a scenario and
a three-dimensional scheme for these events in which the filament eruptions and
flares were caused by interaction of the ropes.Comment: 22 pages, 11 figure
The clustering of ultra-high energy cosmic rays and their sources
The sky distribution of cosmic rays with energies above the 'GZK cutoff'
holds important clues to their origin. The AGASA data, although consistent with
isotropy, shows evidence for small-angle clustering, and it has been argued
that such clusters are aligned with BL Lacertae objects, implicating these as
sources. It has also been suggested that clusters can arise if the cosmic rays
come from the decays of very massive relic particles in the Galactic halo, due
to the expected clumping of cold dark matter. We examine these claims and show
that both are in fact not justified.Comment: 13 pages, 8 figures, version in press at Phys. Rev.
The free energy of NOAA active region AR 11029
The NOAA active region AR 11029 was a small but highly active sunspot region
which produced 73 GOES soft X-ray flares. The flares appear to show a departure
from the well known power-law frequency-size distribution. Specifically, too
few GOES C-class and no M-class flares were observed by comparison with a
power-law distribution (Wheatland in Astrophys. J. 710, 1324, 2010). This was
conjectured to be due to the region having insufficient magnetic energy to
power large events. We construct nonlinear force-free extrapolations of the
coronal magnetic field of active region AR 11029 using data taken on 24 October
by the SOLIS Vector-SpectroMagnetograph (SOLIS/VSM), and data taken on 27
October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP).
Force-free modeling with photospheric magnetogram data encounters problems
because the magnetogram data are inconsistent with a force-free model, and we
employ a recently developed `self-consistency' procedure which addresses this
and accommodates uncertainties in the boundary data (Wheatland and Regnier in
Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of
the self-consistent solution and find that the free energy was 4x10^29 erg on
24 October, and 7x10^31 erg on 27 October. An order of magnitude scaling
between RHESSI non-thermal energy and GOES peak X-ray flux is established from
a sample of flares from the literature and is used to estimate flare energies
from observed GOES peak X-ray flux. Based on the scaling, we conclude that the
estimated free energy of AR 11029 on 27 October when the flaring rate peaked is
sufficient to power M-class or X-class flares, and hence the modeling does not
appear to support the hypothesis that the absence of large flares is due to the
region having limited energy.Comment: Accepted for publication in Solar Physic
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