Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in Coronal Loops with and Without Heating–Cooling Imbalance

Abstract

In the present article, we derive a new dispersion relation for slow magnetoacoustic waves invoking the effect of thermal conductivity, compressive viscosity, radiation, and an unknown heating term along with the consideration of heating–cooling imbalance from linearized MHD equations. We solve the general dispersion relation to understand the role of compressive viscosity and thermal conductivity in the damping of slow waves in coronal loops with and without heating–cooling imbalance. We have analyzed the wave damping for the range of loop length \(L=50\,\text{--}\,500~\text{Mm}\), temperature \(T=5\,\text{--}\,30~\text{MK}\), and density \(\rho=10^{-11}\,\text{--}\,10^{-9}~\text{kg}\,\text{m}^{-3}\). It was found that the inclusion of compressive viscosity along with thermal conductivity significantly enhances the damping of the fundamental mode oscillations in shorter (e.g. \(L=50~\text{Mm}\)) and super-hot (\(T>10~\text{MK}\)) loops. However, the role of viscosity in the damping is insignificant in longer (e.g. \(L=500~\text{Mm}\)) and hot loops (\(T\leq 10~\text{MK}\)) where, instead, thermal conductivity along with the presence of heating–cooling imbalance plays a dominant role. For shorter loops at a super-hot regime of temperature, the increment in the loop density substantially enhances the damping of the fundamental modes due to thermal conductivity when viscosity is absent, however, when the compressive viscosity is added the increase in density substantially weakens the damping. Thermal conductivity alone is found to play a dominant role in longer loops at lower temperatures (\(T\leq10~\text{MK}\)), while compressive viscosity dominates the damping at super-hot temperatures (\(T>10~\text{MK}\)) in shorter loops. The predicted scaling law between damping time (\(\tau \)) and wave period (\(P\)) is found to better match the observed SUMER (Solar Ultraviolet Measurements of Emitted Radiation) oscillations when the heating–cooling imbalance is taken into account in addition to thermal conductivity and compressive viscosity for the damping of the fundamental slow mode oscillations.

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

References

  1. Aschwanden, M.J.: 2004, Physics of the Solar Corona.

    Google Scholar 

  2. Abedini, A., Safari, H., Nasiri, S.: 2012, Solar Phys. 280, 137. DOI.

    ADS  Article  Google Scholar 

  3. Al-Ghafri, K.S., Erdélyi, R.: 2013, Solar Phys. 283, 413. DOI.

    ADS  Article  Google Scholar 

  4. Braginskii, S.I.: 1965, Rev. Plasma Phys. 1, 205.

    ADS  Google Scholar 

  5. Bradshaw, S.J., Erdélyi, R.: 2008, Astron. Astrophys. 483, 301. DOI.

    ADS  Article  Google Scholar 

  6. Caspi, A., Krucker, S., Lin, R.P.: 2014, Astrophys. J. 781, 43. DOI.

    ADS  Article  Google Scholar 

  7. Cho, I.-H., Cho, K.-S., Nakariakov, V.M., Kim, S., Kumar, P.: 2016, Astrophys. J. 830, 110. DOI.

    ADS  Article  Google Scholar 

  8. De Moortel, I., Hood, A.W.: 2003, Astron. Astrophys. 408, 755. DOI.

    ADS  Article  Google Scholar 

  9. De Moortel, I., Hood, A.W.: 2004, Astron. Astrophys. 415, 705. DOI.

    ADS  Article  Google Scholar 

  10. Erdélyi, R., Taroyan, Y.: 2008, Astron. Astrophys. 489, L49. DOI.

    ADS  Article  Google Scholar 

  11. Erdélyi, R., Luna-Cardozo, M., Mendoza-Briceño, C.A.: 2008, Solar Phys. 252, 305. DOI.

    ADS  Article  Google Scholar 

  12. Haynes, M., Arber, T.D., Verwichte, E.: 2008, Astron. Astrophys. 479, 235. DOI.

    ADS  Article  Google Scholar 

  13. Kumar, S., Nakariakov, V.M., Moon, Y.-J.: 2016, Astrophys. J. 824, 8. DOI.

    ADS  Article  Google Scholar 

  14. Kolotkov, D.Y., Nakariakov, V.M., Zavershinskii, D.I.: 2019, Astron. Astrophys. 628, A133. DOI.

    ADS  Article  Google Scholar 

  15. Ofman, L., Wang, T.: 2002, Astrophys. J. 580, L85. DOI.

    ADS  Article  Google Scholar 

  16. Parnell, C.E., De Moortel, I.: 2012, Phil. Trans. Roy. Soc. London Ser. A 370, 3217. DOI.

    ADS  Article  Google Scholar 

  17. Pandey, V.S., Dwivedi, B.N.: 2006, Solar Phys. 236, 127. DOI.

    ADS  Article  Google Scholar 

  18. Patsourakos, S., Klimchuk, J.A.: 2006, Astrophys. J. 647, 1452. DOI.

    ADS  Article  Google Scholar 

  19. Lionello, R., Linker, J.A., Mikic’, Z.: 2009, Astrophys. J. 690, 902. DOI.

    ADS  Article  Google Scholar 

  20. Mariska, J.T., Warren, H.P., Williams, D.R., Watanabe, T.: 2008, Astrophys. J. 681, L41. DOI.

    ADS  Article  Google Scholar 

  21. Mendoza-Briceño, C.A., Erdélyi, R., Sigalotti, L.D.G.: 2004, Astrophys. J. 605, 493. DOI.

    ADS  Article  Google Scholar 

  22. Mitra-Kraev, U., Harra, L.K., Williams, D.R., Kraev, E.: 2005, Astron. Astrophys. 436, 1041. DOI.

    ADS  Article  Google Scholar 

  23. Nakariakov, V.M., Afanasyev, A.N., Kumar, S., Moon, Y.-J.: 2017, Astrophys. J. 849, 62. DOI.

    ADS  Article  Google Scholar 

  24. Nakariakov, V.M., Kosak, M.K., Kolotkov, D.Y., Anfinogentov, S.A., Kumar, P., Moon, Y.-J.: 2019, Astrophys. J. 874, L1. DOI.

    ADS  Article  Google Scholar 

  25. Priest, E.: 2014, Magnetohydrodynamics of the Sun.

    Google Scholar 

  26. Reale, F.: 2014, Living Rev. Solar Phys. 11, 4. DOI.

    ADS  Article  Google Scholar 

  27. Reale, F.: 2016, Astrophys. J. 826, L20. DOI.

    ADS  Article  Google Scholar 

  28. Rosner, R., Tucker, W.H., Vaiana, G.S.: 1978, Astrophys. J. 220, 643. DOI.

    ADS  Article  Google Scholar 

  29. Ryan, D.F., O’Flannagain, A.M., Aschwanden, M.J., Gallagher, P.T.: 2014, Solar Phys. 289, 2547. DOI.

    ADS  Article  Google Scholar 

  30. Selwa, M., Murawski, K., Solanki, S.K.: 2005, Astron. Astrophys. 436, 701. DOI.

    ADS  Article  Google Scholar 

  31. Selwa, M., Ofman, L., Murawski, K.: 2007, Astrophys. J. 668, L83. DOI.

    ADS  Article  Google Scholar 

  32. Sigalotti, L.D.G., Mendoza-Briceño, C.A., Luna-Cardozo, M.: 2007, Solar Phys. 246, 187. DOI.

    ADS  Article  Google Scholar 

  33. Sharykin, I.N., Kosovichev, A.G.: 2015, Astrophys. J. 808, 72. DOI.

    ADS  Article  Google Scholar 

  34. Srivastava, A.K., Dwivedi, B.N.: 2010, New Astron. 15, 8. DOI.

    ADS  Article  Google Scholar 

  35. Srivastava, A.K., Lalitha, S., Pandey, J.C.: 2013, Astrophys. J. 778, L28. DOI.

    ADS  Article  Google Scholar 

  36. Taroyan, Y., Erdélyi, R., Wang, T.J., Bradshaw, S.J.: 2007, Astrophys. J. 659, L173. DOI.

    ADS  Article  Google Scholar 

  37. Taroyan, Y., Bradshaw, S.: 2008, Astron. Astrophys. 481, 247. DOI.

    ADS  Article  Google Scholar 

  38. Taroyan, Y., Erdélyi, R., Doyle, J.G., Bradshaw, S.J.: 2005, Astron. Astrophys. 438, 713. DOI.

    ADS  Article  Google Scholar 

  39. Verwichte, E., Haynes, M., Arber, T.D., Brady, C.S.: 2008, Astrophys. J. 685, 1286. DOI.

    ADS  Article  Google Scholar 

  40. Wang, T.J.: 2011, Space Sci. Rev. 158, 397. DOI.

    ADS  Article  Google Scholar 

  41. Wang, T.J., Ofman, L.: 2019, Astrophys. J. 886, 2. DOI.

    ADS  Article  Google Scholar 

  42. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W.: 2005, Astron. Astrophys. 435, 753. DOI.

    ADS  Article  Google Scholar 

  43. Wang, T.J., Ofman, L., Sun, X., Provornikova, E., Davila, J.M.: 2015, Astrophys. J. 811, L13. DOI.

    ADS  Article  Google Scholar 

  44. Wang, T.J., Ofman, L., Sun, X., Solanki, S.K., Davila, J.M.: 2018, Astrophys. J. 860, 107. DOI.

    ADS  Article  Google Scholar 

  45. Wang, T.J., Solanki, S.K., Curdt, W., Innes, D.E., Dammasch, I.E.: 2002, Astrophys. J. 574, L101. DOI.

    ADS  Article  Google Scholar 

  46. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W., Marsch, E.: 2003a, Astron. Astrophys. 402, L17. DOI.

    ADS  Article  Google Scholar 

  47. Wang, T.J., Solanki, S.K., Curdt, W., Innes, D.E., Dammasch, I.E., Kliem, B.: 2003b, Astron. Astrophys. 406, 1105. DOI.

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank the reviewer for his/her constructive comments that improved our manuscript. AP thanks IIT (BHU) for the computational facility, and AKS acknowledges the support of UKIERI (Indo-UK) research grant for the present research. The work of TW was supported by NASA grants 80NSSC18K1131 and 80NSSC18K0668 as well as the NASA Cooperative Agreement NNG11PL10A to CUA. AKS also acknowledges the ISSI-BJ regarding the science team project on “Oscillatory Processes in Solar and Stellar Coronae”. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA), University of Cambridge (UK) and NASA Goddard Space Flight Center (USA).

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. K. Srivastava.

Ethics declarations

Disclosure of Potential Conflicts of Interest

The authors declare that there are no conflicts of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Prasad, A., Srivastava, A.K. & Wang, T.J. Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in Coronal Loops with and Without Heating–Cooling Imbalance. Sol Phys 296, 20 (2021). https://doi.org/10.1007/s11207-021-01764-x

Download citation

Keywords

  • Flares, dynamics
  • Oscillations and waves, MHD
  • Magnetic fields, corona