4.1 3D reconstruction of the large-scale corona

Reconstructing the solar corona as a whole yields mostly information on the 3D density distribution ne(l,b,r) that varies horizontally (as a function of heliographic longitude l and latitude b) and vertically (as a function of height h = r − R⊙ in the lower corona, say within a few solar radii). The horizontal variations demarcate coronal holes (magnetic open-field regions), quiet-Sun regions (large-scale closed-field regions), active regions (medium-scale closed-field regions containing the strongest magnetic fields), or streamers (quasi-steady structures with bipolar feets and vertical outflows along open field lines, feeding the slow solar wind component). In the solar minimum corona, active regions may disappear completely. Some structures are extremely long-lived, such as coronal holes that survive from 7 up to 27 solar rotations (Abramenko et al., 2010). The vertical coronal structure is mostly governed by gravitational stratification, but tomographic reconstructions can quantify hydrostatic equilibrium versus super-hydrostatic dynamical states. Generally, the 3D density ne(l,b,r) and temperature distributions Te(l,b,r) obtained from tomographic reconstructions of the full corona contain valuable information on the hydrodynamic structure, heating requirement, magnetic structure, sources of the solar wind, and the heliospheric connectivity.
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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., 2010Jump To The Next Citation Point).
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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., 2010Jump To The Next Citation Point).

The most restricting constraint of coronal tomography is the static assumption. First attempts of dynamic tomography of the 3D density reconstruction in the solar corona (Frazin et al., 2005a), using a linear time-variability term (similar to Kalman filters), was carried out by Butala et al. (2010) (Figure 16View Image), applied to STEREO COR-1 data at heights of 1.3– 4R ⊙ over a 4-week period, which yielded a better fit than static solutions.

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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., 2011Jump To The Next Citation Point).

Because of the under-constraintness of 3D tomographic inversion, assumptions on the global geometry are usually made, such as: (i) spherical symmetry, which yields only the radial density function ne(r); (ii) axis-symmetry, which yields in addition the latitudinal variation ne (b,r) (Quémerais and Lamy, 2002), or (iii) local symmetry with respect to the neutral magnetic surface (e.g., heliospheric current sheet), which can be computed from PFSS magnetic fields (Saez et al., 2007). Polarized brightness (pB) images, such as from LASCO C-2, were initially preferred for tomographic reconstructions, but improved calibrations allowed also the use of total brightness (B) images, after correcting for the weighting function of Thompson scattering (Frazin et al., 2010) (Figure 15View Image, right-hand panels). The radial density profile n (h) e, reconstructed with tomographic inversion from Mark III K-coronagraph and LASCO C-1 data during the solar minimum, was found to correspond to scale-height temperatures of λ = 1.3 − 1.9 MK (Zidowitz, 1999Jump To The Next Citation Point), which could be, in the absence of temperature information, either hydrostatic or super-hydrostatic. Using temperature information from multiple soft X-ray filters of Yohkoh and an inversion based on axis-symmetry, the radial electron density scale height λ n was found to agree with the effective temperature scale height λT for most locations, except for streamers where the ratio was found to increase up to λn ∕λT <∼ 2.3, which corresponds to a super-hydrostatic dynamic state (Aschwanden and Acton, 2001). Integrating differential emission measure (DEM) dEM ∕dT modeling into solar-rotation based tomography, aided by multiple spacecraft (STEREO/A and B) observations, produced density n (l,b,h) e maps at temperatures of Te ≈ 0.5 –2.5 MK and in altitude ranges of r = 1.075 R ⊙ (Frazin et al., 2009b) (Figure 15View Image, bottom left) and r = 1.03 –1.23 R ⊙ (Vásquez et al., 2010) (Figure 17View Image), (Vásquez et al., 2011) (Figure 18View Image), including polar crown filaments, coronal cavities, and streamers (Vásquez et al., 2009).

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