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 16), applied to STEREO COR-1 data at heights of over a 4-week period, which yielded a better fit than static solutions.
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 ; (ii) axis-symmetry, which yields in addition the latitudinal variation (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 15, right-hand panels). The radial density profile , 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 (Zidowitz, 1999), 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 was found to agree with the effective temperature scale height for most locations, except for streamers where the ratio was found to increase up to , which corresponds to a super-hydrostatic dynamic state (Aschwanden and Acton, 2001). Integrating differential emission measure (DEM) modeling into solar-rotation based tomography, aided by multiple spacecraft (STEREO/A and B) observations, produced density maps at temperatures of and in altitude ranges of (Frazin et al., 2009b) (Figure 15, bottom left) and (Vásquez et al., 2010) (Figure 17), (Vásquez et al., 2011) (Figure 18), including polar crown filaments, coronal cavities, and streamers (Vásquez et al., 2009).
Living Rev. Solar Phys. 8, (2011), 5
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