arXiv subjects

T. Wiegelmann

Publications and source records attributed to T. Wiegelmann.

At least 55 records · Page 3Linked to original sources

arXiv2009

Nonlinear force-free coronal magnetic field modelling and preprocessing of vector magnetograms in spherical geometry

Context: Knowledge about the coronal magnetic field is important to the understanding the structure of the solar corona. 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. Aims: 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.

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arXiv2009

Solar stereoscopy - where are we and what developments do we require to progress?

Observations from the two STEREO-spacecraft give us for the first time the possibility to use stereoscopic methods to reconstruct the 3D 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. 3.) Within the reconstruction problem stereoscopic methods are used to compute the 3D-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 3D-structure, which depends on the accuracy of the identified structures in 2D, 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 3D-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.

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arXiv2009

Stereoscopic Polar Plume Reconstructions from Stereo/Secchi Images

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 \emph{STEREO (Solar TErrestrial RElations Observatory)} spacecraft. The ten plumes investigated show a superradial expansion in the coronal hole in 3D which is consistent with the 2D results. Their deviations from the local meridian planes are rather small with an average of $6.47^{\circ}$. 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/\emph{SOHO} Si {\sc 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 to 1.8 times larger than the temperature obtained from Mg {\sc 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 {\sc 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 $\mathrm{km s^{-1}}$. It is unlikely that plumes are a dominant contributor to the fast solar wind.

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arXiv2009

Coronal hole boundaries evolution at small scales: I. EIT 195 A and TRACE 171 A view

We aim at studying the small-scale evolution at the boundaries of an equatorial coronal hole connected with a channel of open magnetic flux with the polar region and an `isolated' one in the extreme-ultraviolet spectral range. We intend to determine the spatial and temporal scale of these changes. Imager data from TRACE in the Fe IX/X 171 A passband and EIT on-board Solar and Heliospheric Observatory in the Fe XII 195 A passband were analysed. We found that small-scale loops known as bright points play an essential role in coronal holes boundaries 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 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. 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 a significant dynamics. The small-scale loops (10" - 40" and smaller) which are abundant along coronal hole boundaries have a contribution 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.

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arXiv2009

Formation Heights of Extreme Ultraviolet Lines in an Active Region Derived by Correlation of Doppler Velocity and Magnetic Field

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 (EIS) and Solar Optical Telescope (SOT) on board \emph{Hinode}. The nonlinear force-free field (NLFFF) optimization method is adopted to extrapolate the 3D 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 {\sc \romannumeral 2} 256.32 Åand Si {\sc \romannumeral 10} 256.37 Ålines by the double Gaussian curve fitting, we find that the transition region lies higher in a strong magnetic area. In a pre-flare heating area there possibly exist multithermal loops as implied by comparing the Doppler velocity and the magnetic field on the solar disk.

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arXiv2008

Source region of the 2003 November 18 CME that led to the strongest magnetic storm of cycle 23

The super-storm of November 20, 2003 was associated with a high speed coronal mass ejection which originated in the NOAA AR 10501 on November 18. 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 November 18. 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 MDI line-of-sight magnetograms and vector magnetograms from Solar Flare Telescope, Mitaka, obtained during November, 17-19, 2003 were analysed. 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 pre-flare configuration leading up to the moderate flare which was associated with the geo-effective coronal mass ejection. We also examined the chromospheric images recorded in H-alpha 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.

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arXiv2008

First nonlinear force-free field extrapolations of SOLIS/VSM data

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. 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 minutes and six snapshots during a quiet period. The total magnetic energy in the active region was approximately $3 \times 10^{25}$ 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. 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.

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arXiv2008

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$α$ 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.

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arXiv2008

First Stereoscopic Coronal Loop Reconstructions from Stereo Secchi Images

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 onboard the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12 degrees. We demostrate that these data allow 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.

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arXiv2008

Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona

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 planed for use within the STEREO mission.

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arXiv2008

Similarities and Differences between Coronal Holes and the Quiet Sun: Are Loop Statistics the Key?

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.

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arXiv2008

Optimization code with weighting function for the reconstruction of coronal magnetic fields

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.

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arXiv2008

How to use magnetic field information for coronal loop identification?

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.

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arXiv2008

Links between magnetic fields and plasma flows in a coronal hole

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.

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arXiv2008

Comparing magnetic field extrapolations with measurements of magnetic loops

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.

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arXiv2008

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.

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arXiv2008

Including stereoscopic information in the reconstruction of coronal magnetic fields

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 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.

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arXiv2008

Segmentation of Loops from Coronal EUV Images

We present a procedure which extracts 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 ``ridgels'' which 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 which fit the observed loops. Finally, a half-automated user interface allows one to merge or split, eliminate or select loop fits obtained form the above 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 almost-simultaneously-taken magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated 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.

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