The processes of coronal plasma heating and cooling were previously shown to significantly affect the dynamics of slow magnetoacoustic (MA) waves, causing amplification or attenuation, and also dispersion. However, the entropy mode is also excited in such a thermodynamically active plasma and is affected by the heating/cooling misbalance too. This mode is usually associated with the phenomenon of coronal rain and formation of prominences. Unlike adiabatic plasmas, the properties and evolution of slow MA and entropy waves in continuously heated and cooling plasmas get mixed. Different regimes of the misbalance lead to a variety of scenarios for the initial perturbation to evolve. In order to describe properties and evolution of slow MA and entropy waves in various regimes of the misbalance, we obtained an exact analytical solution of the linear evolutionary equation. Using the characteristic timescales and the obtained exact solution, we identified regimes with qualitatively different behaviour of slow MA and entropy modes. For some of those regimes, the spatio-temporal evolution of the initial Gaussian pulse is shown. In particular, it is shown that slow MA modes may have a range of non-propagating harmonics. In this regime, perturbations caused by slow MA and entropy modes in a low-\(\beta \) plasma would look identical in observations, as non-propagating disturbances of the plasma density (and temperature) either growing or decaying with time. We also showed that the partition of the initial energy between slow MA and entropy modes depends on the properties of the heating and cooling processes involved. The exact analytical solution obtained could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona and the formation and evolution of coronal rain.
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De Moortel, I., Hood, A.W.: 2004, The damping of slow MHD waves in solar coronal magnetic fields. II. The effect of gravitational stratification and field line divergence. Astron. Astrophys. 415, 705. DOI. ADS.
Heyvaerts, J.: 1974, The thermal instability in a magnetohydrodynamic medium. Astron. Astrophys. 37, 65. ADS.
Kohutova, P., Antolin, P., Popovas, A., Szydlarski, M., Hansteen, V.H.: 2020, Self-consistent 3D radiative magnetohydrodynamic simulations of coronal rain formation and evolution. Astron. Astrophys. 639, A20. DOI. ADS.
Kolotkov, D.Y., Nakariakov, V.M., Zavershinskii, D.I.: 2019, Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona. Astron. Astrophys. 628, A133. DOI. ADS.
Krishna Prasad, S., Raes, J.O., Van Doorsselaere, T., Magyar, N., Jess, D.B.: 2018, The polytropic index of solar coronal plasma in sunspot fan loops and its temperature dependence. Astrophys. J. 868, 149. DOI. ADS.
Mandal, S., Magyar, N., Yuan, D., Van Doorsselaere, T., Banerjee, D.: 2016, Forward modeling of propagating slow waves in coronal loops and their frequency-dependent damping. Astrophys. J. 820, 13. DOI. ADS.
Molevich, N.E., Oraevskii, A.N.: 1988, Second viscosity in thermodynamically nonequilibrium media. Zh. Eksp. Teor. Fiz. 94, 128. [J. Exp. Theor. Phys. 67, 504 (1988)].
Molevich, N.E., Zavershinskiy, D.I., Ryashchikov, D.S.: 2016, Investigation of the mhd wave dynamics in thermally unstable plasma. Magnetohydrodynamics 52, 191. DOI.
Molevich, N.E., Zavershinsky, D.I., Galimov, R.N., Makaryan, V.G.: 2011, Traveling self-sustained structures in interstellar clouds with the isentropic instability. Astrophys. Space Sci. 334, 35. DOI. ADS.
Murawski, K., Zaqarashvili, T.V., Nakariakov, V.M.: 2011, Entropy mode at a magnetic null point as a possible tool for indirect observation of nanoflares in the solar corona. Astron. Astrophys. 533, A18. DOI. ADS.
Nakariakov, V.M., Kosak, M.K., Kolotkov, D.Y., Anfinogentov, S.A., Kumar, P., Moon, Y.-J.: 2019, Properties of slow magnetoacoustic oscillations of solar coronal loops by multi-instrumental observations. Astrophys. J. Lett. 874, L1. DOI. ADS.
Nisticò, G., Polito, V., Nakariakov, V.M., Del Zanna, G.: 2017, Multi-instrument observations of a failed flare eruption associated with MHD waves in a loop bundle. Astron. Astrophys. 600, A37. DOI. ADS.
Owen, N.R., De Moortel, I., Hood, A.W.: 2009, Forward modelling to determine the observational signatures of propagating slow waves for TRACE, SoHO/CDS, and Hinode/EIS. Astron. Astrophys. 494, 339. DOI. ADS.
Polyanin, A.D., Zaitsev, V.F.: 2002, Handbook of Exact Solutions for Ordinary Differential Equations, Chapman and Hall/CRC press. ADS.
Prasad, A., Srivastava, A.K., Wang, T.J.: 2021, Role of compressive viscosity and thermal conductivity on the damping of slow waves in coronal loops with and without heating-cooling imbalance. Solar Phys. 296, 20. DOI. ADS.
Reale, F., Lopez-Santiago, J., Flaccomio, E., Petralia, A., Sciortino, S.: 2018, X-ray flare oscillations track plasma sloshing along star-disk magnetic tubes in the Orion star-forming region. Astrophys. J. 856, 51. DOI. ADS.
Reale, F., Testa, P., Petralia, A., Kolotkov, D.Y.: 2019, Large-amplitude quasiperiodic pulsations as evidence of impulsive heating in hot transient loop systems detected in the EUV with SDO/AIA. Astrophys. J. 884, 131. DOI. ADS.
Ryashchikov, D.S., Molevich, N.E., Zavershinskii, D.I.: 2017, Characteristic times of acoustic and condensation instability in heat-releasing gas media. Proc. Eng. 176, 416. DOI.
Van Doorsselaere, T., Wardle, N., Del Zanna, G., Jansari, K., Verwichte, E., Nakariakov, V.M.: 2011, The first measurement of the adiabatic index in the solar corona using time-dependent spectroscopy of Hinode/EIS observations. Astrophys. J. Lett. 727, L32. DOI. ADS.
Wang, T.J.: 2016, Waves in solar coronal loops. In: Keiling, A., Lee, D.-H., Nakariakov, V. (eds.) Low-Frequency Waves in Space Plasmas, Geophys. Mono. Ser. 216, Am. Geophys. Union, Washington, 395. DOI. ADS.
Wang, T., Ofman, L.: 2019, Determination of transport coefficients by coronal seismology of flare-induced slow-mode waves: numerical parametric study of a 1D loop model. Astrophys. J. 886, 2. DOI. ADS.
Wang, T., Ofman, L., Sun, X., Provornikova, E., Davila, J.M.: 2015, Evidence of thermal conduction suppression in a solar flaring loop by coronal seismology of slow-mode waves. Astrophys. J. Lett. 811, L13. DOI. ADS.
Wang, T., Ofman, L., Sun, X., Solanki, S.K., Davila, J.M.: 2018, Effect of transport coefficients on excitation of flare-induced standing slow-mode waves in coronal loops. Astrophys. J. 860, 107. DOI. ADS.
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.
The work was supported in part by the Ministry of Science and Higher Education of the Russian Federation by State assignment to educational and research institutions under Projects No. FSSS-2020-0014, 0023-2019-0003, and by Subsidy No.075-GZ/C3569/278. D.Y. Kolotkov acknowledges support from the STFC consolidated grant ST/T000252/1.
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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
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Zavershinskii, D., Kolotkov, D., Riashchikov, D. et al. Mixed Properties of Slow Magnetoacoustic and Entropy Waves in a Plasma with Heating/Cooling Misbalance. Sol Phys 296, 96 (2021). https://doi.org/10.1007/s11207-021-01841-1
- Waves, modes
- Coronal seismology
- Oscillations, solar