First Three‐Dimensional Reconstructions of Coronal Loops with the<i>STEREO A</i>and<i>B</i>Spacecraft. I. Geometry

Aschwanden, Markus J.; Wülser, J. P.; Nitta, N.; Lemen, J. R.

doi:10.1086/529542

Cited by 117 publications

(119 citation statements)

References 17 publications

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“…As discussed in Sect. 3.1, there is observational evidence that loops will not have such a high degree of ellipticity and the greatest value of ellipticity estimated for the seven loops observed by Aschwanden et al (2008) provides initial evidence for this claim.…”

Section: Discussionmentioning

confidence: 89%

“…Therefore, in this paper the typical values of h a /H will be taken from 0 to 4. Recent observations using STEREO (Aschwanden et al 2008), have provided an insight to the extent of the ellipticity of loops in the corona. Seven loops were reconstructed in threedimensions and a circle, with radius r fit , was fitted through the loop footpoints and the loop top above the midpoint.…”

Section: Elliptically Shaped Loops With Plasma Density Exponentially mentioning

confidence: 99%

“…The magnitude of the effect of ellipticity is then compared with the circle-arc model (Dymova & Ruderman 2006). Beside the theoretical justification given above, in this particular aspect, recent progress by Aschwanden et al (2008) in 3D reconstruction of loops using the Solar TErrestrial RElations Observatory (STEREO), has provided new and interesting information on the loop geometry. It was found that the majority of the loops studied were in fact non-circular in shape, with a deviation from circularity up to 30%.…”

Section: Introductionmentioning

confidence: 99%

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The effect of elliptic shape on the period ratioP${_{1}}$/P${_{2}}$ of emerging coronal loops

Morton

Erdélyi

2009

A&A

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Aims. We determine the effect of an elliptical shape on the period ratio for the standing transversal oscillations of a longitudinally stratified coronal loop throughout its emergence from the low solar atmosphere into the ubiquitously magnetised corona. Methods. Under the assumption that elliptical curvature has a negligible effect on eigenfrequencies, the equation that describes the projection of a density profile onto a magnetic flux tube with elliptical shape is obtained in a gravitationally stratified atmosphere. The effect of the elliptical shape on the period ratio of the fundamental mode to the first harmonic (P 1 /P 2 ) at various stages of emergence is determined, assuming that the oscillation periods are much shorter than the characteristic time scale of loop emergence. Results. We find that there are two separate cases of elliptical shape that occur, the minor ellipse and the major ellipse. It is then shown how the period ratio P 1 /P 2 is dependent upon the ellipticity ( ), the parameter characterising the stage of emergence (λ) and the density scale height (H). Ellipticity is found to make an important contribution to P 1 /P 2 for the minor ellipse when compared to its counterpart of standing oscillations of stratified loops with semi-circle or circle-arc shape. The major ellipse was found to have a lesser effect on the period ratio of standing oscillations. We also find the value of P 1 /P 2 is dependent upon the stage of emergence of the loop, where the greatest contribution from emergence to the ratio of P 1 /P 2 is when the loop is almost fully emerged. The important implication for magneto-seismological interpretations of the observations of oscillating coronal loops is that measurements of ellipticity and stage of emergence should supplement observations of oscillation periods and should be considered when applying observed frequencies of the fundamental mode and first harmonic to determine the diagnostic properties of these oscillating loops, e.g. the density scale height or strength of magnetic field. Neglecting the determination of ellipticity and stage of emergence may result in a 35% error in estimating density scale height.

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Section: Discussionmentioning

confidence: 89%

Section: Elliptically Shaped Loops With Plasma Density Exponentially mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of elliptic shape on the period ratioP${_{1}}$/P${_{2}}$ of emerging coronal loops

Morton

Erdélyi

2009

A&A

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“…Active region NOAA 10953, 2007 May 9 (B) was subject to the first 3D reconstruction with STEREO (Aschwanden et al, 2008a), stereoscopic electron density and temperature measurements (Aschwanden et al, 2008b), and instant stereoscopic tomography and DEM modeling ). This active region exhibits the simplest bipolar magnetic configuration among all four analyzed active regions and we find a nonpotential energy ratio of E N /E P = 1.023 (Table 3), i.e., a free energy ratio of ≈ 2.3%.…”

Section: Tests With Stereoscopic Observationsmentioning

confidence: 99%

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

Aschwanden

2012

Sol Phys

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An analytical approximation of a nonlinear force-free magnetic field (NLFFF) solution was developed in Paper I, while a numerical code that performs fast forward-fitting of this NLFFF approximation to a line-of-sight magnetogram and coronal 3D loops has been described and tested in Paper II. Here we calculate the free magnetic energy E free = E N − E P , i.e., the difference of the magnetic energies between the nonpotential field and the potential field. A second method to estimate the free energy is obtained from the mean misalignment angle change ∆µ = µ P − µ N between the potential and nonpotential field, which scales as E free /E P ≈ tan 2 (∆µ). For four active regions observed with STEREO in 2007 we find free energies in the range of q free = (E free /E P ) ≈ 1% − 10%, with an uncertainty of less than ±2% between the two methods, while the free energies obtained from 11 other NLFFF codes exhibit a larger scatter of order ≈ ±10%. We find also a correlation between the free magnetic energy and the GOES flux of the largest flare that occurred during the observing period, which can be quantified by an exponential relationship, F GOES ∝ exp (q free /0.015), implying an exponentiation of the dissipated currents.

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“…This, however, eventually requires that the surface curvature is taken into account. DeRosa et al (2009) compared several nonlinear force-free codes in cartesian geometry with stereoscopic reconstructed loops as produced by Aschwanden et al (2008). The codes used as input vector magnetograms from the Hinode-SOT-SP, which were unfortunately available for only a very small field of view (about 10 percent of the area spanned by STEREO-loops).…”

Section: Introductionmentioning

confidence: 99%

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

Tadesse

Wiegelmann

Inhester

2009

A&A

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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.

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First Three‐Dimensional Reconstructions of Coronal Loops with theSTEREO AandBSpacecraft. I. Geometry

Cited by 117 publications

References 17 publications

The effect of elliptic shape on the period ratioP${_{1}}$/P${_{2}}$ of emerging coronal loops

The effect of elliptic shape on the period ratioP${_{1}}$/P${_{2}}$ of emerging coronal loops

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

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

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