Solar Physics

, 293:74 | Cite as

Influence of the Atmospheric Model on Hanle Diagnostics

  • Ryohko Ishikawa
  • Han Uitenbroek
  • Motoshi Goto
  • Yusuke Iida
  • Saku Tsuneta


We clarify the uncertainty in the inferred magnetic field vector via the Hanle diagnostics of the hydrogen Lyman-\(\upalpha\) line when the stratification of the underlying atmosphere is unknown. We calculate the anisotropy of the radiation field with plane-parallel semi-empirical models under the nonlocal thermal equilibrium condition and derive linear polarization signals for all possible parameters of magnetic field vectors based on an analytical solution of the atomic polarization and Hanle effect. We find that the semi-empirical models of the inter-network region (FAL-A) and network region (FAL-F) show similar degrees of anisotropy in the radiation field, and this similarity results in an acceptable inversion error (e.g., \({\sim}\, 40~\mbox{G}\) instead of 50 G in field strength and \({\sim}\,100^{\circ}\) instead of \(90^{\circ}\) in inclination) when FAL-A and FAL-F are swapped. However, the semi-empirical models of FAL-C (averaged quiet-Sun model including both inter-network and network regions) and FAL-P (plage regions) yield an atomic polarization that deviates from all other models, which makes it difficult to precisely determine the magnetic field vector if the correct atmospheric model is not known (e.g., the inversion error is much larger than 40% of the field strength; \({>}\,70~\mbox{G}\) instead of \(50~\mbox{G}\)). These results clearly demonstrate that the choice of model atmosphere is important for Hanle diagnostics. As is well known, one way to constrain the average atmospheric stratification is to measure the center-to-limb variation of the linear polarization signals. The dependence of the center-to-limb variations on the atmospheric model is also presented in this paper.


Polarization, magnetic Magnetic fields, chromosphere 



This work was initiated while Han Uitenbroek visited NAOJ as a visiting professor. We are grateful to J. Trujillo Bueno, J. Štěpán, L. Belluzzi, A. Asensio Ramos, R. Manso Sainz, and B. De Pontieu. This work was inspired by our exciting discussions with them. We also acknowledge other team members of the CLASP sounding rocket experiment. This work was supported by JSPS KAKENHI Grant No. 25887051.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Ryohko Ishikawa
    • 1
  • Han Uitenbroek
    • 2
  • Motoshi Goto
    • 3
  • Yusuke Iida
    • 4
  • Saku Tsuneta
    • 1
  1. 1.National Astronomical Observatory of JapanMitaka, TokyoJapan
  2. 2.National Solar ObservatoryBoulderUSA
  3. 3.National Institute for Fusion ScienceTokiJapan
  4. 4.Kwansei Gakuin UniversityHyogoJapan

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