Validation of Spherically Symmetric Inversion by Use of a Tomographic   Reconstructed Three-Dimensional Electron Density of the Solar Corona
  Determination of the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (Spherically Symmetric Inversion, SSI) was developed in the 1950s, and has been widely applied to interpret various observations. However, to date there is no study about uncertainty estimation of this method. In this study we present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 Rsun as a model, which is reconstructed by tomography method from STEREO/COR1 observations during solar minimum in February 2008. We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally less than a factor of two or so; the former has the lower peak but more spread in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 degrees. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt) as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with that by tomography for a period of low solar activity. We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort. 
Tongjiang Wang and Joseph M. Davila
astro-ph.SR