Skip to main content
Log in

Magnetohydrodynamic Spectroscopy of a Non-adiabatic Solar Atmosphere

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

The quantification of all possible waves and instabilities in any given system is of paramount importance, and knowledge of the full magnetohydrodynamic (MHD) spectrum allows one to predict the (in)stability of a given equilibrium state. This is highly relevant in many (astro)physical disciplines, and when applied to the solar atmosphere it may yield various new insights in processes such as prominence formation and coronal-loop oscillations. In this work we present a detailed, high-resolution spectroscopic study of the solar atmosphere, where we use our newly developed Legolas code to calculate the full spectrum with corresponding eigenfunctions of equilibrium configurations that are based on fully realistic solar atmospheric models, including gravity, optically thin radiative losses, and thermal conduction. Special attention is given to thermal instabilities, known to be responsible for the formation of prominences, together with a new outlook on the thermal and slow continua and how they behave in different chromospheric and coronal regions. We show that thermal instabilities are unavoidable in our solar atmospheric models and that there exist certain regions where the thermal, slow, and fast modes all have unstable wave-mode solutions. We also encounter regions where the slow and thermal continua become purely imaginary and merge on the imaginary axis. The spectra discussed in this work illustrate clearly that thermal instabilities (both discrete and continuum modes) and magneto-thermal overstable propagating modes are ubiquitous throughout the solar atmosphere, and they may well be responsible for much of the observed fine-structuring and multi-thermal dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12

Similar content being viewed by others

References

  • Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: 1999, LAPACK Users’ Guide, 3rd edn. Soc. Indust. App. Math., Philadelphia. 0-89871-447-8. DOI.

    Book  MATH  Google Scholar 

  • Avrett, E.H., Loeser, R.: 2008, Models of the solar chromosphere and transition region from SUMER and HRTS observations: formation of the extreme-ultraviolet spectrum of hydrogen, carbon, and oxygen. Astrophys. J. Suppl. 175, 229. DOI. ADS.

    Article  ADS  Google Scholar 

  • Berger, T.E., Liu, W., Low, B.C.: 2012, SDO/AIA detection of solar prominence formation within a coronal cavity. Astrophys. J. Lett. 758, L37. DOI. ADS.

    Article  ADS  Google Scholar 

  • Claes, N., De Jonghe, J., Keppens, R.: 2020, Legolas: a modern tool for magnetohydrodynamic spectroscopy. Astrophys. J. Suppl. 251, 25. DOI. ADS.

    Article  ADS  Google Scholar 

  • Claes, N., Keppens, R., Xia, C.: 2020, Thermal instabilities: fragmentation and field misalignment of filament fine structure. Astron. Astrophys. 636, A112. DOI. ADS.

    Article  ADS  Google Scholar 

  • Dalgarno, A., McCray, R.A.: 1972, Heating and ionization of HI regions. Annu. Rev. Astron. Astrophys. 10, 375. DOI. ADS.

    Article  ADS  Google Scholar 

  • Demaerel, T., Keppens, R.: 2016, Linear stability of ideal MHD configurations. II. Results for stationary equilibrium configurations. Phys. Plasmas 23, 122118. DOI. ADS.

    Article  ADS  Google Scholar 

  • Duckenfield, T.J., Kolotkov, D.Y., Nakariakov, V.M.: 2021, The effect of the magnetic field on the damping of slow waves in the solar corona. Astron. Astrophys. 646, A155. DOI. ADS.

    Article  ADS  Google Scholar 

  • Goedbloed, H., Keppens, R., Poedts, S.: 2019, Magnetohydrodynamics of Laboratory and Astrophysical Plasmas, Cambridge University Press, Cambridge. DOI.

    Book  MATH  Google Scholar 

  • Hermans, J., Keppens, R.: 2021, Effect of optically thin cooling curves on condensation formation: Case study using thermal instability. arXiv. DOI. ADS.

  • Jenkins, J.M., Keppens, R.: 2021, Prominence formation by levitation-condensation at extreme resolutions. Astron. Astrophys. 646, A134. DOI. ADS.

    Article  ADS  Google Scholar 

  • Keppens, R., van der Linden, R.A.M., Goossens, M.: 1993, Non-adiabatic discrete Alfvén waves in coronal loops and prominences. Solar Phys. 144, 267. DOI. ADS.

    Article  ADS  Google Scholar 

  • Ledentsov, L.: 2021, Thermal trigger for solar flares II: effect of the guide magnetic field. Solar Phys. 296, 93. DOI. ADS.

    Article  ADS  Google Scholar 

  • Lehoucq, R.B., Sorensen, D.C., Yang, C.: 1998, ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Soc. Indust. App. Math., Philadelphia. 978-0-89871-407-4. DOI.

    Book  MATH  Google Scholar 

  • Nye, A.H., Thomas, J.H.: 1976, Solar magneto-atmospheric waves. I. An exact solution for a horizontal magnetic field. Astrophys. J. 204, 573. DOI. ADS.

    Article  ADS  Google Scholar 

  • Parker, E.N.: 1953, Instability of thermal fields. Astrophys. J. 117, 431. DOI. ADS.

    Article  ADS  Google Scholar 

  • Priest, E.: 2014, Magnetohydrodynamics of the Sun, Cambridge University Press, Cambridge. DOI.

    Book  Google Scholar 

  • Ruan, W., Xia, C., Keppens, R.: 2020, A fully self-consistent model for solar flares. Astrophys. J. 896, 97. DOI. ADS.

    Article  ADS  Google Scholar 

  • Schure, K.M., Kosenko, D., Kaastra, J.S., Keppens, R., Vink, J.: 2009, A new radiative cooling curve based on an up-to-date plasma emission code. Astron. Astrophys. 508, 751. DOI. ADS.

    Article  ADS  Google Scholar 

  • van der Linden, R.A.M., Goossens, M.: 1991, The thermal continuum in coronal loops—instability criteria and the influence of perpendicular thermal conduction. Solar Phys. 134, 247. DOI. ADS.

    Article  ADS  Google Scholar 

  • Waters, T., Proga, D.: 2019, Non-isobaric thermal instability. Astrophys. J. 875, 158. DOI. ADS.

    Article  ADS  Google Scholar 

  • Xia, C., Keppens, R.: 2016, Formation and plasma circulation of solar prominences. Astrophys. J. 823, 22. DOI. ADS.

    Article  ADS  Google Scholar 

  • Zavershinskii, D.I., Kolotkov, D.Y., Nakariakov, V.M., Molevich, N.E., Ryashchikov, D.S.: 2019, Formation of quasi-periodic slow magnetoacoustic wave trains by the heating/cooling misbalance. Phys. Plasmas 26, 082113. DOI. ADS.

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme, Grant agreement No. 833251 PROMINENT ERC-ADG 2018; by the VSC (Flemish Supercomputer Center), funded by the Research Foundation – Flanders (FWO) and the Flemish Government – department EWI; and by internal funds KU Leuven, project C14/19/089 TRACESpace.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Niels Claes.

Ethics declarations

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection:

Magnetohydrodynamic (MHD) Waves and Oscillations in the Sun’s Corona and MHD Coronal Seismology

Guest Editors: Dmitrii Kolotkov and Bo Li

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Claes, N., Keppens, R. Magnetohydrodynamic Spectroscopy of a Non-adiabatic Solar Atmosphere. Sol Phys 296, 143 (2021). https://doi.org/10.1007/s11207-021-01894-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11207-021-01894-2

Keywords

Navigation