List of Figures

View Image Figure 1:
Left: Artists concept of the STEREO twin spacecraft 3D perspective on a coronal mass ejection launched from the Sun. Right: Orbits of STEREO-A (red) and STEREO-B (blue) with respect to the Earth’s annual orbit (green) (credit: NASA).
View Image Figure 2:
The principle of solar-rotation stereoscopy is illustrated with this example of radio brightness maps observed with the Very Large Array (VLA) at two different days (middle panels), where partial maps covering sources A or B (from day 1) are rotated to the locations A’ and B’ expected at day 2 as a function of the distance R + h ⊙ from Sun center (top), which are then cross-correlated with the actually observed maps A” and B” at day 2 (bottom), which yields a direct altitude measurement hA and hB of the source centroids (from Aschwanden and Bastian, 1994b).
View Image Figure 3:
The principle of dynamic solar-rotation stereoscopy is illustrated for an example of two adjacent loops (top). The only free parameter in the 3D reconstruction is the loop inclination plane, which yields different 2D projections at 3 consecutive days (middle). The best-fitting inclination angle can be determined by optimizing the (parallel) co-alignment between the observed and model loop stripe as a function of the inclination angle (bottom) (from Aschwanden et al., 1999).
View Image Figure 4:
The principle of the backprojection method used in medical tomography is visualized for the case of two 1-D projections observed from two arbitrary directions (angle 𝜃), from which the unknown true 2-D brightness distribution is reconstructed (from Davila and Thompson, 1992).
View Image Figure 5:
Generalized Thompson scattering geometry: The spherical Thompson surface represents the source locations of the maximum (90°) scattering angle with respect to an observer at distance R. The white-light brightness has to be integrated over all scattering positions P along a given line-of-sight (from Vourlidas and Howard, 2006).
View Image Figure 6:
Quiet-Sun brightness temperature spectrum for an isothermal corona with T = 1.0 MK e (solid line) or Te = 5.0 MK (dashed line) with a base density of 9 −3 n0 = 10 cm and gravitational stratification (with a density scale height of λ ≈ 50 (Te ∕1 MK ) Mm) (from Aschwanden et al., 2004).
View Image Figure 7:
Triangulation of point-like 1D (top), curvi-linear 2D (middle), and voluminous 3D (bottom) structures. The triangulation and back-projection of point-like and curvi-linear structures is unique for two stereoscopic viewpoints, while two projections of a voluminous structure do not unambiguously define the 3D surface or volume (from Inhester, 2006).
View Image Figure 8:
Orientation of epipolar planes in space and the respective epipolar lines in the images for two observers (e.g., STEREO spacecraft A and B) looking at the Sun (from Inhester, 2006).
View Image Figure 9:
The geometry of triangulating or projecting a point P from spacecraft A and B is shown, where the (epipolar) XZ plane is coincident with the Sun center position O and the two spacecraft positions A and B (left panel), while the vertical YZ plane is perpendicular (right panel). The distances of the spacecraft from the Sun are dA and dB, the observed angles of point P with respect to the Sun center O are αA and αB, intersecting the X-axis at positions xA and xB with the angles γA and γB. The spacecraft separation angle is αsep. The point P has the 3D coordinates (x,y,z) and heliographic longitude l and latitude b (from Aschwanden et al., 2008b).
View Image Figure 10:
A 3D magnetic field representation is rendered from photospheric magnetograms (optical image in orange), from extrapolated magnetic field lines (black lines), and the iso-Gauss contours for three gyroresonant layers that correspond to gyrofrequencies of 5 GHz (green), 8 GHz (blue), and 11 GHz (yellow). The outer contours of each iso-Gauss surface demarcate the extent of radio emission at each frequency (courtesy of Stephen White and Jeong Woo Lee).
View Image Figure 11:
SOHO/MDI magnetogram observed on 2007 Apr 30, 22:42 UT, with overlayed stereoscopically triangulated loop tracings (purple) and calculated NLFFF magnetic field model (colors in central box), where the colors indicate an increasing degree of misalignment from αmis < 5° (yellow) to αmis > 45° (red) (from DeRosa et al., 2009).
View Image Figure 12:
Left: A potential dipole field is calculated with two unipolar magnetic charges buried in equal depth and equal magnetic field strength, but opposite magnetic polarity (B1 = − 0.1, B2 = +0.1). An asymmetric EUV loop is observed at the same location (grey torus) with a misalignment of αmis = 20° at the top of the loop. Right: The magnetic field strength of the right-hand side unipolar charge is adjusted (to B = +0.08 2) so that the misalignment of the loop reaches a minimum (αmis = 0°) (from Aschwanden and Sandman, 2010).
View Image Figure 13:
The basic tomography concept of solar tomography is visualized for multiple spacecraft located at different aspect angles from the Sun, which can reconstruct the 2D density distribution in the solar corona (for instance, in the ecliptic plane) by synthesizing the 1D brightness distributions observed from each spacecraft (from Davila, 1994).
View Image Figure 14:
Rendering of solid flux tubes computed with a potential magnetic field model and hydrodynamic 1D models for each loop. The rendering displays a 3D view by shading, but can be scaled to electron densities, temperatures, or brightness in a particular temperature filter (from Gary, 1997).
View Image Figure 15:
Examples of tomographic reconstructions of the solar corona, visualized as synoptic density maps at a specific height level. Top left: Synoptic map of coronal density at a height of r = 2.55 R⊙, reconstructed with 87 pB images from LASCO C-2 (Frazin et al., 2007); Bottom left: Synoptic electron density map at a heigth of r = 1.075 R ⊙, reconstructed with a DEM method and STEREO/A and B observations (Frazin et al., 2009b); Right: Density reconstruction ne(l,b) at r = 2.5 R⊙ from LASCO C-2 total brightness images B (top right) and density difference Δne (l,b) after subtraction of polarized brightness images, B − pB, at the same height level (bottom right) (from Frazin et al., 2010).
View Image Figure 16:
3D isosurfaces of electron-density reconstructions of the solar corona using STEREO COR-1 data with a static (left) and a dynamic (right) tomographic reconstruction method (from Butala et al., 2010).
View Image Figure 17:
Synoptic maps of solar minimum corona tomographically reconstructed using solar rotation and the dual STEREO/A and B spacecraft, at a height of r = 1.075 R ⊙, showing the electron density ne (top), the (emission measure weighted) temperature Tm (middle), and the temperature spread wT (bottom), overlaid with iso-Gauss magnetic field contours B obtained from PFSS models at the same height. The boundaries between open and closed magnetic field domains are marked with black curves (from Vásquez et al., 2010).
View Image Figure 18:
A 3D view of a coronal density and magnetic field reconstruction, showing PFSS magnetic field lines (white), temperature iso-Gauss surfaces (red for Tm = 2.0 MK and orange for Tm = 1.0 MK), and density iso-surfaces (see color scale at bottom right) (from Vásquez et al., 2011).
View Image Figure 19:
Examples of tomographic streamer belt reconstructions. Top left: Streamer belt density reconstruction with LASCO C-2 at r = 2.5R ⊙ (Saez et al., 2005); Bottom left: Electron density at height r = 2.0R ⊙ reconstructed from STEREO COR-1, overlaid with magnetic field contours from NSO/GONG (Kramar et al., 2009); Right: Qualitative density maps at r = 4.0 R⊙ reconstructed from LASCO C-2 data (Morgan et al., 2009) (top), (Morgan and Habbal, 2010) (bottom).
View Image Figure 20:
Density map (top) and temperature map (bottom) of active region NOAA AR 10955 observed on 2007 May 9 with STEREO/EUVI and reconstructed with the ISTAR method (Instant Stereoscopic Tomography of Active Regions). The model contains some 8000 loop components, of which a skeleton of 70 loops has been stereoscopically triangulated (from Aschwanden et al., 2009c).
View Image Figure 21:
The differential emission measure distribution dEM(T)/dT is computed from the ISTAR tomographic model and is compared with two active regions and two quiet-Sun regions from Brosius et al. (1996). Note that the primary temperature sensitivity range of EUVI is log (T ) ≈ 5.8– 6.3 (grey range), but the DEM could be constrained in the range of log(T ) ≈ 5– 7, based on the parameterized temperature profiles used in the stereoscopic tomography code. A canopy correction is applied in the temperature range of log(T ) = 5.7 –6.0, with a quadratic area expansion from 10% to 100% of the coronal flux tube area (histogram with thick linestyle). The uncorrected DEM is also shown (upper histogram) (from Aschwanden et al., 2009c).
View Image Figure 22:
Average pressure scale heights λn as a function of the loop apex temperature Tm. The error bars indicate the error of the mean value ∘ ---- em = σ∕ (N ), with σ being the standard deviation. For comparison, the linear relationship between the pressure scale height and temperature for hydrostatic equilibrium is also shown (thick line), i.e., λT = 47 (T/1 MK) Mm. Note that EUV loops with apex temperatures of Tm <∼ 3 MK show a trend to be super-hydrostatic, while the soft X-ray loops with Tm ≈ 3 − 6 Mm approximately follow the hydrostatic equilibrium (from Aschwanden et al., 2009c).
View Image Figure 23:
Definition of loop parameters: loop point positions (xi,yi),i = 1,...,n starting at the primary footpoint at height h = h 1 foot, the azimuth angle α between the loop footpoint baseline and heliographic east-west direction, and the inclination angle 𝜃 between the loop plane and the vertical to the solar surface.
View Image Figure 24:
Vertical and apparent density scale heights in coronal loops (right) and analogy with communicating water tubes (left) (from Aschwanden, 2005).
View Image Figure 25:
Orthogonal projections of the stereoscopically triangulated 70 coronal loops in AR 10955 observed on 2007 May 9 in three filters (171 Å = blue; 195 Å = red; 284 Å = yellow). The observed projection in the x-y image plane seen from spacecraft A is shown in the bottom panel left, the projection into the x-z plane in the top panel left, and the projection into the y-z plane in the bottom panel right. The three orthogonal projections correspond to rotations by 90° to the north or west (to positions indicated on the solar sphere in the top right panel) (from Aschwanden et al., 2009c).
View Image Figure 26:
Left panel: the effect of the variable column depth w (s) z measured parallel to the line-of-sight z is illustrated as a function of the loop length parameter s, for a loop with a constant diameter w. Right panel: the effect of the inclination angle 𝜃 of the loop plane on the inferred density scale height λ(𝜃) is shown. Both effects have to be accounted for when determining the electron density ne(s) along the loop (from Aschwanden, 2005).
View Image Figure 27:
Self-consistency of mean loop temperatures TA, TB (top left), base electron densities n ,n A B (middle left), and mean loop widths w ,w A B (bottom left) measured with spacecraft STEREO/A vs. STEREO/B. These loop parameters are inferred from the background-subtracted loop-associated flux (top right), based on independent background subtractions for the different line-of-sights of both spacecraf A and B (bottom right) (from Aschwanden et al., 2008b).
View Image Figure 28:
The loop overpressure factor qp = p ∕pRTV (normalized by Rosner-Tucker-Vaiana scaling law with uniform heating) is shown versus the loop half length L. Datapoints are given for the complete 7 loops detected along their full length, measured with STEREO-A (large diamonds) and with STEREO-B (small diamonds) (from Aschwanden et al., 2008b).
View Image Figure 29:
The mean misalignment angle for four active regions as a function of the GOES soft X-ray flux: for the potential field source surface model (PFSS: diamonds), for the unipolar potential field model bootstrapped with observed STEREO loops (PFU: triangles), and contributions from stereoscopic measurement errors (SE; crosses). The difference between the best-fit potential field model (triangles) and stereoscopic errors (crosses) can be considered as a measure of the non-potentiality of the active region (hatched area) (from Aschwanden and Sandman, 2010).
View Image Figure 30:
Best-fit potential field model of AR observed on 2007 Apr 30. The stereoscopically triangulated loops are shown in blue color, while field lines starting at identical footpoints as the STEREO loop extrapolated with the best-fit potential field (composed of nc = 200 unipolar magnetic charges) are shown in red. Side views are shown in the top and right panels. A histogram of misalignment angles measured between the two sets of field lines is displayed in the bottom panel. The distribution is fitted with a Gaussian, where the vertical solid line indicates the peak of the Gaussian (or most probable value), while the vertical dashed line indicates the median value (from Aschwanden and Sandman, 2010).
View Image Figure 31:
3D reconstruction of an oscillating loop observed during the flare of 2007 Jun 27, ≈ 18:19 UT, superimposed on the STEREO/A (left) and STEREO/B images (right), obtained by stereoscopic fitting of a circular loop geometry (from Verwichte et al., 2009).
View Image Figure 32:
Sequence of running-difference EUVI/B images in the area of the oscillating loop during the time period of 2007 Jun 26, 17:56:00 UT and 18:26:00 UT. The amplitude measurement of the oscillating loop is carried out along the cross-sectional slit marked with a diagonal bar (from Aschwanden et al., 2009b).
View Image Figure 33:
Time-slice plots (color) and amplitude of kink mode as a function of time with fitted damped sine function (graphs) for both STEREO/A and B spacecraft, for the loop oscillation event of 2007 Jun 27, 17:30 UT (from Verwichte et al., 2009).
Watch/download Movie Figure 34: (mov-Movie; 1131 KB)
Movie: 3D reconstruction of the same oscillating loop as Figure 32, observed on 2007 Jun 27, 18:19 UT, superimposed on a highpass-filtered image of STEREO/A (bottom) and STEREO/B image (top), using the stereoscopic triangulation method. The loop shape is traced with 9 points (red crosses), interpolated with a 2D spline (red curve), and fitted with an elliptical geometry (yellow curve). The circular model (yellow curve) and the solution of the 3D reconstruction (red curve) is also projected into the (z,y) plane (right panels), with z being the LOS (from Aschwanden, 2009c).
View Image Figure 35:
Projections of the reconstructed 3D loop geometry (see Figure 34) into the 3 orthogonal planes of the loop coordinate system: edge-on (left), side-on (middle), and top-down (right). The three rows present 3 independent trials of manual loop tracings.
Watch/download Movie Figure 36: (mov-Movie; 856 KB)
Movie: 3D reconstruction of loop oscillations for a sequence of 16 EUVI/A+B 171 Å images in the time interval of 2007 Jun 27, 17:58 – 18:26 UT, using the stereoscopic triangulation method. The loop tracings in EUVI/A are rendered in the x-y plane (bottom left panel), while the orthogonal reconstruction are shown in the x-z plane (top left panel) and in the z-y plane (bottom right panel). The loop tracings are rendered with grey curves, the semi-circular fit with a dashed curve, and the curvature radius maximization method with a thin black curve. The oscillation amplitudes averaged in the loop segments 0.3 < s ∕L < 0.6 (marked with thick black curves) are shown in x-direction (east-west amplitude dx(t) in top right panel) and in the z direction (line-of-sight amplitude dz(t) in middle right panel).
Watch/download Movie Figure 37: (mov-Movie; 831 KB)
Movie: Orthogonal projections of a triangulated oscillating loop (frames in top half) during the same time interval as shown in Figure 13 (with the time marked by colors, progressing in order of brown-red-orange-yellow). The bottom panels visualize the same projections of a helically twisted model loop (see model parameters in text).
View Image Figure 38:
Derived 3D geometry of the wave propagation along the coronal (fan) loop, observed on 2008 Jan 10 with STEREO/A and B (bottom panels) The top panels show the projected geometry of the propagation vector with the view rotated by 90° seen from solar north (from Marsh et al., 2009).
View Image Figure 39:
Time-slice plots of the integrated intensity along the (fan) loops for STEREO/B (left) and A (right). The abscissa indicates the observed distance long the loop, perpendicular to the line-of-sight from each spacecraft (from Marsh et al., 2009).
View Image Figure 40:
Two views of 3D reconstruction of the 2007 May 19 erupting filament during 11 time intervals, each one rendered with a different color. The filament erupts with the south-west end rising fastest, performing some counter-clockwise rotation (from Liewer et al., 2009).
View Image Figure 41:
3D reconstruction of the gradual filament eruption observed on 2009 Sept 26, shown from STEREO/A (left) and reconstructed in 3D (with the z-coordinate in the range of 1.0 –1.9 R⊙ indicated with colors) (from Li et al., 2010a).
View Image Figure 42:
Schematic depiction of tripolar reconnection between a closed-field loop and an open-field line (left), which channels the heated plasma after reconnection (marked with X) upward along the open field line (red line). This tripolar configuration became the standard scenario for coronal jets (from Moore et al., 2010).
View Image Figure 43:
Schematic depiction of the topology, eruption, and reconnection of the magnetic field for a blowout jet. The red field lines demarcate the already reconnected field that contains hot plasma, while the blue field lines indicate the pre-reconnection of not-reconnecting field (from Moore et al., 2010).
View Image Figure 44:
Side view (left) and perspective view (right) of the formation of the current sheet before onset of the first jet (at three different times). The field lines map out the fan surface and fan separatrix (from Pariat et al., 2010).
View Image Figure 45:
3D reconstruction of postflare loops of the 2007 Jun 3, 07:50 UT, flare with STEREO/A and B (left), and of the central flaring, non-eruptive filament in the 2007 Jun 10, 11:11 UT, flare (right). Note the difference in altitude for the eruptive flare with post-flare arcade (left) and the non-eruptive flare filament (right) (from Aschwanden et al., 2009b).
View Image Figure 46:
STEREO/EUVI/A and B observations of a twisted helical filament with approximately two turns (red helical line) observed shortly before the M8.9 flare on 2007 Jun 4, 05:08 UT (from Kumar et al., 2010).
View Image Figure 47:
Soft X-ray (GOES/Lo 0.5-4 Å and 1-8 Å, thin curves) and EUV (EUVI/A, diamonds) light curves, time derivative, dI (t)∕dt), of the harder soft X-ray light curve (thick solid line) are shown for the flare/CME event of 2008 Mar 25, 18:30 UT (top panel). Four EUVI/A images (second row) and running difference images (bottom row). Note the strong dimming in the EUV light curve. The diamond symbols mark the times of the EUV images, while the selected images shown below are marked with vertical lines. The peak EUV flux is F = 5.6 × 106 DN s− 1 (or 7.8% of the total flux). The FOV of the images is 512 EUVI pixels (≈ 600 Mm) (from Aschwanden et al., 2009b).
View Image Figure 48:
A numerical simulation of adiabatic CME expansion and resulting EUV dimming is shown in the x-z plane for three different times, with x the direction of the CME trajectory and z the line-of-sight direction of the observer. The relative EUV dimming qdimm(x, t) (normalized to the preflare value) resulting from the LOS-integrated emission measure is shown in the lower panels (from Aschwanden et al., 2009b).
View Image Figure 49:
Comparison of observed and simulated EUVI base-difference images at 5 times for the observations of STEREO/A 171 Å (left two columns) and STEREO/B 171 Å (right two columns). The pre-CME image at 18:36 UT was subtracted in these base-difference images (from Aschwanden et al., 2009b).
View Image Figure 50:
Sequence of median-filtered running difference images recorded in the EUVI 195 Å channel with a cadence of 10 minutes. The coronal wave (outlined by arrows) is observed on-disk in STEREO/B (top) and on the limb in STEREO/A (bottom) (from Kienreich et al., 2009).
View Image Figure 51:
Running difference images (in 5-min intervals) of the dome-shaped EUV wave front as observed with the EUVI/B channels in the 171, 195, 284, and 304 Å wavelengths. Arrows outline the wave dome, crosses indicate the erupting CME loops inside the dome (from Veronig et al., 2010).