In a survey of flare and CME events observed with the SECCHI/EUVI telescope during the first two years of the mission, at least 10 events were identified that contain loop oscillations and/or propagating waves (Aschwanden et al., 2009b), which we list in Table 2 (Movies and quicklook plots of these oscillation events are also available at http://secchi.lmsal.com/EUVI/). This list of events may not be complete, because oscillating loops and propagating waves were mostly identified by visual inspection of EUVI 171 Å movies (either by some periodic motion over at least two periods or by some global wave propagation), rather than by automated detection algorithms that scan the entire EUVI database. Inspecting the spacecraft separation angle in Table 2 we see that 9 events have been observed at separation angles of and are thus suitable for stereoscopic 3D reconstruction.
|8||07/01/12||01:00 – 03:00||N00W87||0.2||C1.5||12||34||31.2||...||IPEW||L|
|35||07/05/02||23:20 – 23:59||S09W16||6.3||C8.5||12||30||23.0||17.3||IPW||...|
|43||07/05/16||17:10 – 18:10||N03E34||8.2||C2.9||12||26||12.7||9.9||IPDW||LS|
|46||07/05/19||12:40 – 13:20||N03W03||8.6||B1.3||12||46||17.4||13.9||IPEDW||LS|
|100||07/06/08||12:30 – 13:30||S08W08||11.9||B7.6||12||28||7.9||5.9||IPDW||LS|
|104||07/06/09||13:20 – 14:40||S10W23||12.1||M1.0||12||184||69.4||45.8||IW||L|
|109||07/06/27||17:30 – 18:30||S20E89||15.4||C1.3||3||34||2.9||2.4||IDOW||...|
|133||07/08/06||15:20 – 15:50||S12E38||23.3||C1.1||12||32||7.8||25.2||IPW||LS|
|175||07/12/31||00:30 – 01:40||S15E87||44.0||C8.3||25||288||7.5||39.3||IPDOW||LS|
|183||08/03/25||18:30 – 19:30||S25E90||47.2||M1.7||12||944||17.8||192.2||IPDEW||LS|
One loop oscillation event occurred during the 2007 Jun 27, 17:30 UT, flare and has been analyzed in several studies (Verwichte et al., 2009; Aschwanden et al., 2009b; Aschwanden, 2009c). No stereoscopic 3D reconstruction with a triangulation method has been attempted in the first study on this loop, because the loop footpoints are not visible in one spacecraft (STEREO/A) and cannot easily be located in the image of the other spacecraft (STEREO/B), as well as corresponding features of the upper loop segment are difficult to verify in both images (Verwichte et al., 2009). Instead, a semi-circular loop geometry was fitted in projection to both stereoscopic images by varying the inclination angle of the loop plane, leading to a loop radius of , an azimuth angle (of the loop baseline) of (anti-clockwise from the heliographic east-west direction), and an inclination angle of . The 2D projection of this 3D geometry in the LOS directions of STEREO/A and B is shown in Figure 31. The time behavior of the oscillating loop is shown in a sequence of running-difference images in Figure 32, which displays clear kink-mode displacements (black/white loop rims) for the considered loop. A time-slice plot obtained along a cross-sectional slice reveals the damped sinusoidal oscillation (Figure 33), whose amplitude could be fitted byet al. (2009). Note that the EUVI cadence is 150 s (2.5 min).
In a subsequent study (Aschwanden, 2009c), stereoscopic triangulation has been applied to the oscillating loop and the reconstructed 3D geometry is shown in Figure 34: The XY-projection in the image plane of STEREO/A and B is rendered in the left-hand panels, and the YZ-projections as viewed from the east direction at the east limb are shown in the right-hand panels. The spacecraft separation angle at that time was = 8.26°. The triangulation has been repeated three times with independent manual tracings and the three solutions are shown in Figure 35, projected parallel and perpendicular to the average loop plane. Surprisingly, the triangulated loop reveals an S-shaped geometry in the vertical projection top-down (Figure 35, right panels), and a heavily deformed asymmetry in the side-on projection (Figure 35, middle panels). Thus, the oscillating loop seems to be neither circular nor coplanar. This is an intriguing new result that could not have been obtained without STEREO observations.
If we fit a circular geometry to the same 2D loop tracings (dashed yellow curves in Figure 34), we obtain from the average and standard deviations of 3 independent tracings the following parameters: a baseline azimuth angle of , a loop plane inclination angle of , a loop radius of , and a full loop length of . The full 3D loop length of the triangulated loop is slightly shorter than the circular model, i.e., . This compares favorably with the semi-circular forward-fitting of Verwichte et al. (2009), who obtained values of , , , and . Thus, we conclude that the circular forward-fitting model yields values that are very close to those of the stereoscopic method, differing by for the loop plane inclination angle and for the loop length, which is the most important parameter for coronal seismology. However, the forward-fitting model makes the assumption of circularity and coplanarity and, thus, cannot reveal asymmetric and non-planar shapes of the oscillating loop.
In Figure 35, we transformed the loop coordinates from the image coordinate system into the loop coordinate system , which is defined in the following way: the horizontal -axis is aligned with the loop baseline between the two loop footpoints, with the midpoint as center . The vertical -axis intersects the baseline midpoint and the apex midpoint of the loop, while the -axis is perpendicular to the plane. The coordinate transformation is accomplished by 3 subsequent rotations (i.e., by the azimuth angle , the loop plane inclination angle , and the longitude angle , see Figure 23). The oscillating loop shown in Figure 35 is clearly heavily deformed and deviates significantly from a coplanar and circular model. The maximum deviations from the average loop radius are , and the non-planarity reaches up to of the loop radius, which is much larger than for typical active region loops, which have radial variations of and non-planarity deviations of . Obviously, this loop is highly non-circular and non-planar, possibly affected by the dynamic magnetic forces associated with the launch of a CME that usually is responsible for triggering loop oscillations.
Using the method of stereoscopic 3D triangulation, as shown for a single time frame at 2007 Jun 27, 18:18:30 UT in Figure 34, we repeat now the same procedure for 12 (epipolar-coaligned) stereoscopic image pairs in the time interval of 17:58 – 18:26 UT. The same time sequence is shown in form of running-time difference images in Figure 32, yielding an oscillation period of and an exponential damping time of . The triangulated 3D geometry of the oscillating loop is shown in Figure 36, which has a consistent asymmetric S-shape throughout the entire observed time interval ( 35 min) as shown in Figure 34, while the oscillation amplitude is much smaller than the deviations of the loop geometry from a circular model. We display the average amplitude of loop motions in x-direction (east-west amplitude in Figure 36 top right panel), and in z-direction (line-of-sight amplitude in Figure 36 middle right panel). Both amplitudes show a correlated oscillation with similar periods and amplitudes, i.e., for and for , and for and for , respectively. The amplitude corresponds to an oscillation in the vertical plane (with respect to the solar surface), and to an oscillation in the horizontal plane, but the two oscillations are almost in phase ( vs. ). The fact that the two oscillation directions have a similar amplitude implies that the polarization is a combination of horizontal and vertical planes with a polarization angle near 45°. However, since the average 3D loop geometry corresponds to a non-planar, helically-twisted shape, the 3D motion can also be described in terms of circular polarization or a torsional mode. It is instructive to inspect a movie visualization of Figure 36.
In Figure 37 we show the triangulated loop motion projected into the 3 orthogonal directions of the loop coordinate system. In order to illustrate the plausibility of circular polarized kink motion we simulate a helically twisted loop (with a twist of 0.75 turns and geometric tapering of the toroidal radius towards the footpoints) that undergoes a periodical change in the twist angle, where the displacement is highest at the loop apex and falls off towards the footpoints. This simple simulation shown in Figure 37 (bottom half) demonstrates qualitatively how the observed loop shapes and motions (Figure 37 top half) can be explained by a circular polarization. Some further modeling studies are required to decide whether we deal with a circularly polarized (helical) kink mode or with a torsional wave mode. Torsional wave modes and helical loop geometries are of particular interest for triggering mechanisms of flares and CMEs by the kink instability. A large twist angle of was recently observed to trigger a flare (Srivastava et al., 2010). In addition, numerical MHD simulations with realistic initial conditions for the excitation mechanisms may shed some light on the coupling of various known MHD wave modes, i.e., kink-modes, sausage-modes, and torsional modes (Ofman, 2009).
Living Rev. Solar Phys. 8, (2011), 5
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