4.3 Active regions

Active regions have typical sizes in the range of 10 – 100 Mm and, thus, are barely resolved in the coarse-meshed tomographic reconstructions of the (large-scale) solar corona, which explains the lack of active region tomography in literature. However, 3D reconstructions of active regions were attempted with stereoscopic methods in radio wavelengths (Aschwanden and Bastian, 1994a,bJump To The Next Citation Point; Aschwanden, 1995Jump To The Next Citation Point) and EUV (Aschwanden et al., 1999Jump To The Next Citation Point, 2000Jump To The Next Citation Point, 2009cJump To The Next Citation Point). Imaging of active regions at a wavelength of λ = 20 cm (ν = 1.5 GHz) with the Very Large Array (VLA) was used over 6 different days and 66 Gaussian radio source components from 22 different active regions were stereoscopically triangulated. A height distribution of h = 25 ± 15 Mm was determined, as well as a systematic center-limb darkening as a function of the center-to-limb angle α was found,
[ ] TB(α ) = TB(0) 0.4 + 0.6cos2 (α ) , (24 )
which was interpreted as an opacity effect of thermal free-free absorption due to denser cool coronal plasma along the line-of-sight near the limb (Aschwanden and Bastian, 1994b; Aschwanden, 1995). Thus, radio stereoscopy can provide quantitative information on the 3D density and temperature distribution of active regions, but the stereoscopically triangulated altitude h(λ) of a radio source at a given wavelength localizes only the layer where free-free emission becomes optically thick, which requires an “onion shell-like” parameterization of 3D density and temperature models.

The 3D architecture of an active region can be assembled by modules, consisting of 1D coronal loops. Their 3D coordinates can be calculated by stereoscopic triangulation, either using a solar rotation based method (Section 3.1), as it was applied to SOHO/EIT images (Aschwanden et al., 1999Jump To The Next Citation Point, 2000Jump To The Next Citation Point), or using stereoscopic triangulation (Section 3.3) with the dual STEREO spacecraft (Aschwanden et al., 2009cJump To The Next Citation Point; Aschwanden and Wülser, 2011Jump To The Next Citation Point; Rodriguez et al., 2009Jump To The Next Citation Point). A review on the 3D reconstruction, the 3D geometry, and the 3D distributions of physical parameters in active regions is given in Aschwanden and Wülser (2011).

Active region NOAA 7986 was reconstructed this way from SOHO/EIT 171, 191, and 284 Å images, and it was found that (i) the loops in the temperature range of T ≈ 1.0– 2.5 MK e were in hydrostatic equilibrium (since the expected temperature scale height matched the observed density scale height), and (ii) radiative loss exceeded the conductive loss rate by two orders of magnitude, in contrast to the standard steady-state Rosner–Tucker–Vaiana (RTV) model (Aschwanden et al., 2000Jump To The Next Citation Point). This observation represented the first statistical evidence that EUV loops are dominated by radiative cooling, and that the energy balance postulated by the RTV law (with a constant uniform heating rate) is violated.

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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., 2009cJump To The Next Citation Point).

Active region NOAA 10955 was observed with STEREO on 2007 May 9 and reconstructed in detail, using stereoscopic triangulation with EUVI STEREO/A and B that provided the 3D geometry [x(s),y(s),z(s)] of some 70 loops in the three temperature filters 171, 191, and 284 Å (Aschwanden et al., 2008cJump To The Next Citation Point), density ne(s) and temperature Te(s) measurements of these loops (Aschwanden et al., 2008bJump To The Next Citation Point), which were then synthesized and interpolated into a space-filling 3D model of the density ne(x,y, z) and temperature Te(x,y,z) distribution of the active region (Aschwanden et al., 2009cJump To The Next Citation Point). A projection of the 3D density and temperature distributions is shown in Figure 20View Image. The density and temperature solutions for each of the 8000 modular loops are not unique, of course, but are constrained by a dual set of three temperature filter images and, thus, should at least closely represent the statistical distribution of the active region. Interestingly, the full-loop modeling includes also extrapolated temperatures to the loop footpoints (apexes) that are cooler (hotter) than the EUVI filter temperature range of Te ≈ 1.0 –2.5 MK, and this way the differential emission measure (DEM) distribution of the active region could be reconstructed in the full temperature range of log(T ) = 5.0– 7.0 (Figure 21View Image).

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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., 2009cJump To The Next Citation Point).
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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., 2009cJump To The Next Citation Point).

The forward-fitting of parameterized loop density ne(s) and temperature Te(s) profiles in this study yielded also statistics on the hydrostaticity of the active region loops. The statistical dependence of the pressure scale height λp(Tm ) on the loop apex temperature Tm revealed mostly super-hydrostatic scale heights for cool EUV loops (Tm ≈ 0.5– 3.0 MK), while the hotter (Tm ≈ 3– 6 MK) soft X-ray emitting loops were found to be slightly below the expected hydrostatic scale height (Figure 22View Image). This means that the heating rate approximately balances the conductive cooling rate in soft X-rays (as expected in the steady-state energy balance RTV model), while the radiative loss rate dominates the heating rate in the cooler EUV loops. In other words, soft X-ray loops are close to steady-state, while EUV loops are in non-equilibrium.

Extended temperature analysis of active regions with Hinode data (Noglik et al., 2009; Rodriguez et al., 2009) and AIA/SDO (Aschwanden and Boerner, 2011; Aschwanden et al., 2011) with a comprehensive set of temperature filters in the entire range of Te ≈ 0.5 –16 MK reveals the basic temperature structure of active regions quite clearly: The hottest loops are found in the compact core of the active region, which straddle the neutral line, have a relatively small length scale, and emit in soft X-rays, while the cooler loops overarch the active region, have relatively large length scales, and emit in EUV. This tells us also something about the heating rate, which is the lower per volume element, the longer the loops are. Thus, stereoscopic and tomographic 3D reconstruction of active regions provide important information on the hydrostaticity, the energy balance between heating and cooling, and this way offer a sensitive diagnostic of the coronal heating process.

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