517 research outputs found
Relationship between photospheric currents and coronal magnetic helicity for force-free bipolar fields
Aims.
The origin and evolution of the magnetic helicity in the solar corona are not well understood. For instance, the magnetic helicity of an active region is often about 1042 Mx2 (1026 Wb2), but the observed processes whereby it is thought to be injected into the corona do not yet provide an accurate estimate of the resulting magnetic helicity budget or time evolution. The variation in magnetic helicity is important for understanding the physics of flares, coronal mass ejections, and their associated magnetic clouds. To shed light on this topic, we investigate here the changes in magnetic helicity due to electric currents in the corona for a single twisted flux tube that may model characteristic coronal structures such as active region filaments, sigmoids, or coronal loops.
Methods.
For a bipolar photospheric magnetic field and several distributions of current, we extrapolated the coronal field as a nonlinear force-free field. We then computed the relative magnetic helicity, as well as the self and mutual helicities.
Results.
Starting from a magnetic configuration with a moderate amount of current, the amount of magnetic helicity can increase by 2 orders of magnitude when the maximum current strength is increased by a factor of 2. The high sensitivity of magnetic helicity to the current density can partially explain discrepancies between measured values on the photosphere, in the corona, and in magnetic clouds. Our conclusion is that the magnetic helicity strongly depends on both the strength of the current density and also on its distribution.
Conclusions.
Only improved measurements of current density at the photospheric level will advance our knowledge of the magnetic helicity content in the solar atmosphere
Nonlinear force-free models for the solar corona I. Two active regions with very different structure
With the development of new instrumentation providing measurements of solar
photospheric vector magnetic fields, we need to develop our understanding of
the effects of current density on coronal magnetic field configurations. The
object is to understand the diverse and complex nature of coronal magnetic
fields in active regions using a nonlinear force-free model. From the observed
photospheric magnetic field we derive the photospheric current density for two
active regions: one is a decaying active region with strong currents (AR8151),
and the other is a newly emerged active region with weak currents (AR8210). We
compare the three-dimensional structure of the magnetic fields for both active
region when they are assumed to be either potential or nonlinear force-free.
The latter is computed using a Grad-Rubin vector-potential-like numerical
scheme. A quantitative comparison is performed in terms of the geometry, the
connectivity of field lines, the magnetic energy and the magnetic helicity
content. For the old decaying active region the connectivity and geometry of
the nonlinear force-free model include strong twist and strong shear and are
very different from the potential model. The twisted flux bundles store
magnetic energy and magnetic helicity high in the corona (about 50 Mm). The
newly emerged active region has a complex topology and the departure from a
potential field is small, but the excess magnetic energy is stored in the low
corona and is enough to trigger powerful flares.Comment: 11 pages, 11 figure
A new look at a polar crown cavity as observed by SDO/AIA
Context.
The Solar Dynamics Observatory (SDO) was launched in February 2010 and is now providing an unprecedented view of the solar activity at high spatial resolution and high cadence covering a broad range of temperature layers of the atmosphere.
Aims.
We aim at defining the structure of a polar crown cavity and describing its evolution during the erupting process.
Methods.
We use the high-cadence time series of SDO/AIA observations at 304 Å (50 000 K) and 171 Å (0.6 MK) to determine the structure of the polar crown cavity and its associated plasma, as well as the evolution of the cavity during the different phases of the eruption. We report on the observations recorded on 13 June 2010 located on the north-west limb.
Results.
We observe coronal plasma shaped by magnetic field lines with a negative curvature (U-shape) sitting at the bottom of a cavity. The cavity is located just above the polar crown filament material. We thus observe the inner part of the cavity above the filament as depicted in the classical three part coronal mass ejection (CME) model composed of a filament, a cavity, and a CME front. The filament (in this case a polar crown filament) is part of the cavity, and it makes a continuous structuring from the filament to the CME front depicted by concentric ellipses (in a 2D cartoon).
Conclusions.
We propose to define a polar crown cavity as a density depletion sitting above denser polar crown filament plasma drained down the cavity by gravity. As part of the polar crown filament, plasma at different temperatures (ranging from 50 000 K to 0.6 MK) is observed at the same location on the cavity dips and sustained by a competition between the gravity and the curvature of magnetic field lines. The eruption of the polar crown cavity as a solid body can be decomposed into two phases: a slow rise at a speed of 0.6 km s-1 and an acceleration phase at a mean speed of 25 km s-1
The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
The nonlinear force-free field (NLFFF) model is often used to describe the
solar coronal magnetic field, however a series of earlier studies revealed
difficulties in the numerical solution of the model in application to
photospheric boundary data. We investigate the sensitivity of the modeling to
the spatial resolution of the boundary data, by applying multiple codes that
numerically solve the NLFFF model to a sequence of vector magnetogram data at
different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active
Region 10978 on 2007 December 13. We analyze the resulting energies and
relative magnetic helicities, employ a Helmholtz decomposition to characterize
divergence errors, and quantify changes made by the codes to the vector
magnetogram boundary data in order to be compatible with the force-free model.
This study shows that NLFFF modeling results depend quantitatively on the
spatial resolution of the input boundary data, and that using more highly
resolved boundary data yields more self-consistent results. The free energies
of the resulting solutions generally trend higher with increasing resolution,
while relative magnetic helicity values vary significantly between resolutions
for all methods. All methods require changing the horizontal components, and
for some methods also the vertical components, of the vector magnetogram
boundary field in excess of nominal uncertainties in the data. The solutions
produced by the various methods are significantly different at each resolution
level. We continue to recommend verifying agreement between the modeled field
lines and corresponding coronal loop images before any NLFFF model is used in a
scientific setting.Comment: Accepted to ApJ; comments/corrections to this article are welcome via
e-mail, even after publicatio
String Matching and 1d Lattice Gases
We calculate the probability distributions for the number of occurrences
of a given letter word in a random string of letters. Analytical
expressions for the distribution are known for the asymptotic regimes (i) (Gaussian) and such that is finite
(Compound Poisson). However, it is known that these distributions do now work
well in the intermediate regime . We show that the
problem of calculating the string matching probability can be cast into a
determining the configurational partition function of a 1d lattice gas with
interacting particles so that the matching probability becomes the
grand-partition sum of the lattice gas, with the number of particles
corresponding to the number of matches. We perform a virial expansion of the
effective equation of state and obtain the probability distribution. Our result
reproduces the behavior of the distribution in all regimes. We are also able to
show analytically how the limiting distributions arise. Our analysis builds on
the fact that the effective interactions between the particles consist of a
relatively strong core of size , the word length, followed by a weak,
exponentially decaying tail. We find that the asymptotic regimes correspond to
the case where the tail of the interactions can be neglected, while in the
intermediate regime they need to be kept in the analysis. Our results are
readily generalized to the case where the random strings are generated by more
complicated stochastic processes such as a non-uniform letter probability
distribution or Markov chains. We show that in these cases the tails of the
effective interactions can be made even more dominant rendering thus the
asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The
lattice gas analogy has been worked out in full, including virial expansion
and equation of state. This constitutes the main part of the paper now.
Connections with existing work is made and references should be up to date
now. To be submitted for publicatio
A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances
Spaced seeds have been recently shown to not only detect more alignments, but
also to give a more accurate measure of phylogenetic distances (Boden et al.,
2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower
misclassification rate when used with Support Vector Machines (SVMs) (On-odera
and Shibuya, 2013), We confirm by independent experiments these two results,
and propose in this article to use a coverage criterion (Benson and Mak, 2008,
Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both
cases in order to design better seed patterns. We show first how this coverage
criterion can be directly measured by a full automaton-based approach. We then
illustrate how this criterion performs when compared with two other criteria
frequently used, namely the single-hit and multiple-hit criteria, through
correlation coefficients with the correct classification/the true distance. At
the end, for alignment-free distances, we propose an extension by adopting the
coverage criterion, show how it performs, and indicate how it can be
efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017
Sparkling extreme-ultraviolet bright dots observed with Hi-C
Observing the Sun at high time and spatial scales is a step toward understanding the finest and fundamental scales of heating events in the solar corona. The high-resolution coronal (Hi-C) instrument has provided the highest spatial and temporal resolution images of the solar corona in the EUV wavelength range to date. Hi-C observed an active region on 2012 July 11 that exhibits several interesting features in the EUV line at 193 Å. One of them is the existence of short, small brightenings "sparkling" at the edge of the active region; we call these EUV bright dots (EBDs). Individual EBDs have a characteristic duration of 25 s with a characteristic length of 680 km. These brightenings are not fully resolved by the SDO/AIA instrument at the same wavelength; however, they can be identified with respect to the Hi-C location of the EBDs. In addition, EBDs are seen in other chromospheric/coronal channels of SDO/AIA, which suggests a temperature between 0.5 and 1.5 MK. Based on their frequency in the Hi-C time series, we define four different categories of EBDs: single peak, double peak, long duration, and bursty. Based on a potential field extrapolation from an SDO/HMI magnetogram, the EBDs appear at the footpoints of large-scale, trans-equatorial coronal loops. The Hi-C observations provide the first evidence of small-scale EUV heating events at the base of these coronal loops, which have a free magnetic energy of the order of 1026 erg. © 2014. The American Astronomical Society. All rights reserved
Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions
We examine the nonlinear magnetofrictional extrapolation scheme using the
solar active region model by Titov and D\'emoulin as test field. This model
consists of an arched, line-tied current channel held in force-free equilibrium
by the potential field of a bipolar flux distribution in the bottom boundary. A
modified version, having a parabolic current density profile, is employed here.
We find that the equilibrium is reconstructed with very high accuracy in a
representative range of parameter space, using only the vector field in the
bottom boundary as input. Structural features formed in the interface between
the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch
separatrix surface"-are reliably reproduced, as are the flux rope twist and the
energy and helicity of the configuration. This demonstrates that force-free
fields containing these basic structural elements of solar active regions can
be obtained by extrapolation. The influence of the chosen initial condition on
the accuracy of reconstruction is also addressed, confirming that the initial
field that best matches the external potential field of the model quite
naturally leads to the best reconstruction. Extrapolating the magnetogram of a
Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a
sequence of two opposing evolutionary phases which clearly indicate the
unstable nature of the configuration: a partial buildup of the flux rope with
rising free energy is followed by destruction of the rope, losing most of the
free energy.Comment: 14 pages, 10 figure
Chromospheric seismology above sunspot umbrae
The acoustic resonator is an important model for explaining the three-minute
oscillations in the chromosphere above sunspot umbrae. The steep temperature
gradients at the photosphere and transition region provide the cavity for the
acoustic resonator, which allows waves to be both partially transmitted and
partially reflected. In this paper, a new method of estimating the size and
temperature profile of the chromospheric cavity above a sunspot umbra is
developed. The magnetic field above umbrae is modelled numerically in 1.5D with
slow magnetoacoustic wave trains travelling along magnetic fieldlines.
Resonances are driven by applying the random noise of three different
colours---white, pink and brown---as small velocity perturbations to the upper
convection zone. Energy escapes the resonating cavity and generates wave trains
moving into the corona. Line of sight (LOS) integration is also performed to
determine the observable spectra through SDO/AIA. The numerical results show
that the gradient of the coronal spectra is directly correlated with the
chromosperic temperature configuration. As the chromospheric cavity size
increases, the spectral gradient becomes shallower. When LOS integrations is
performed, the resulting spectra demonstrate a broadband of excited frequencies
that is correlated with the chromospheric cavity size. The broadband of excited
frequencies becomes narrower as the chromospheric cavity size increases. These
two results provide a potentially useful diagnostic for the chromospheric
temperature profile by considering coronal velocity oscillations
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
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