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., 1999, 2000), or using stereoscopic triangulation (Section 3.3) with the dual STEREO spacecraft (Aschwanden et al., 2009c; Aschwanden and Wülser, 2011; Rodriguez et al., 2009). 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 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., 2000). 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.
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 of some 70 loops in the three temperature filters 171, 191, and 284 Å (Aschwanden et al., 2008c), density and temperature measurements of these loops (Aschwanden et al., 2008b), which were then synthesized and interpolated into a space-filling 3D model of the density and temperature distribution of the active region (Aschwanden et al., 2009c). A projection of the 3D density and temperature distributions is shown in Figure 20. 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 , and this way the differential emission measure (DEM) distribution of the active region could be reconstructed in the full temperature range of (Figure 21).
The forward-fitting of parameterized loop density and temperature profiles in this study yielded also statistics on the hydrostaticity of the active region loops. The statistical dependence of the pressure scale height on the loop apex temperature revealed mostly super-hydrostatic scale heights for cool EUV loops (), while the hotter () soft X-ray emitting loops were found to be slightly below the expected hydrostatic scale height (Figure 22). 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 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.
Living Rev. Solar Phys. 8, (2011), 5
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