Solar Physics

, Volume 291, Issue 12, pp 3659–3683 | Cite as

Improved Determination of the Location of the Temperature Maximum in the Corona

Article

Abstract

The most used method to calculate the coronal electron temperature [\(T_{\mathrm{e}} (r)\)] from a coronal density distribution [\(n_{\mathrm{e}} (r)\)] is the scale-height method (SHM). We introduce a novel method that is a generalization of a method introduced by Alfvén (Ark. Mat. Astron. Fys.27, 1, 1941) to calculate \(T_{\mathrm{e}}(r)\) for a corona in hydrostatic equilibrium: the “HST” method. All of the methods discussed here require given electron-density distributions [\(n_{\mathrm{e}} (r)\)] which can be derived from white-light (WL) eclipse observations. The new “DYN” method determines the unique solution of \(T_{\mathrm{e}}(r)\) for which \(T_{\mathrm{e}}(r \rightarrow \infty) \rightarrow 0\) when the solar corona expands radially as realized in hydrodynamical solar-wind models. The applications of the SHM method and DYN method give comparable distributions for \(T_{\mathrm{e}}(r)\). Both have a maximum [\(T_{\max}\)] whose value ranges between 1 – 3 MK. However, the peak of temperature is located at a different altitude in both cases. Close to the Sun where the expansion velocity is subsonic (\(r < 1.3\,\mathrm{R}_{\odot}\)) the DYN method gives the same results as the HST method. The effects of the other free parameters on the DYN temperature distribution are presented in the last part of this study. Our DYN method is a new tool to evaluate the range of altitudes where the heating rate is maximum in the solar corona when the electron-density distribution is obtained from WL coronal observations.

Keywords

Solar corona Coronal electron temperature Solar wind 

Notes

Acknowledgements

The authors wish to acknowledge Clément Botquin for his efficient assistance in the early work of programming. The open-source computer codes to compute and plot DYN temperature distributions are in FORTRAN and IDL. Copies are available through koen.stegen@oma.be. We wish to thank the Royal Belgian Institute for Space Aeronomy (BIRA-IASB), the Royal Observatory of Belgium (ROB), and BELSPO (Federal Public Planning Service Science Policy) for their support. We acknowledge discussions with Viviane Pierrard (BIRA-IASB), Marius Echim (BIRA-IASB), Hervé Lamy (BIRA-IASB), and Yuriy Voitenko (BIRA-IASB). We are grateful to Jack Scudder (University of Iowa) for his constructive remarks and suggestions concerning the first version of this work, which had been posted 16 December 2011 at arXiv. He encouraged us to submit this work to a refereed international Journal. We appreciate his interest in our work.

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 Dordrecht 2016

Authors and Affiliations

  1. 1.Royal Belgian Institute for Space AeronomyBrusselsBelgium
  2. 2.Royal Observatory of BelgiumBrusselsBelgium

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