Solar Physics

, Volume 289, Issue 10, pp 3723–3745 | Cite as

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

  • Tongjiang WangEmail author
  • Joseph M. Davila


Determining 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 of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 R as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066). 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 smaller than about a factor of two; the former has the lower peak but extends more 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°. 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 the reconstruction by tomography for a period of low solar activity (CR 2066). 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.


Sun: corona Methods: data analysis STEREO COR1 



The work of TW was supported by the NASA Cooperative Agreement NNG11PL10A to the Catholic University of America and NASA grant NNX12AB34G. We very much appreciate the suggestions of Maxim Kramar, which led to an improved estimate of the angular resolution of the SSPA method in Appendix. We also thank the anonymous referee for his/her valuable comments that improved the manuscript.

Supplementary material

11207_2014_556_MOESM1_ESM.pdf (833 kb)
Figure 1. Electronic Supplementary material: a version of Figure 13 with continuous color scale. The ratio of tomographic density to the SSPA average density for COR1-A and -B at 1.6, 2.0, and 2.5 R in two cases. (a) – (c): The case for the SSPA 3D coronal density obtained using synthetic pB data based on the 3D density model. (d) – (f): The case for the SSPA 3D coronal density obtained using the real pB data observed by COR1-A and -B. The color scale represents the logarithm of ratio values, with white color for ratio value of one, blue colors for ratio values in the range 0.2 – 1, and red colors for ratio values in the range 1 – 5. (PDF 833 kB)


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhysicsCatholic University of AmericaWashingtonUSA
  2. 2.NASA Goddard Space Flight CenterGreenbeltUSA

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