Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Mayorov A. O., Romanov V. A., Romanov K. V., Romanov D. V. Numerical Modeling of the Physical Mechanism of Anomalous Heating of the Solar Atmosphere. Izvestiya of Saratov University. Physics , 2020, vol. 20, iss. 1, pp. 4-15. DOI: 10.18500/1817-3020-2020-20-1-4-15

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.03.2020
Full text:
download
(downloads: 304)
Language: 
Russian
Heading: 
Theoretical and mathematical physics
Article type: 
Article
UDC: 
533.951
DOI: 
10.18500/1817-3020-2020-20-1-4-15

Numerical Modeling of the Physical Mechanism of Anomalous Heating of the Solar Atmosphere

Autors: 
Mayorov Alexander Olegovich, Saratov State University
Romanov Valeriy Alexandrovich, Saratov State University
Romanov Konstantin Valeryevich, Krasnoyarsk State Pedagogical University named after V. P. Astafyev
Romanov Dmitriy Valeryevich, Krasnoyarsk State Pedagogical University named after V. P. Astafyev
Abstract: 

 Background and Objectives: Processing and analysis of observational data on the study of physical processes occurring in the Sun's atmosphere at various stages of the activity cycle requires a systematic identification of stable components for all physical parameters related to the stationary solar atmosphere. The first attempts at numerical calculation of the structure of the stationary atmosphere gave a sharp discrepancy with direct measurements of the distribution of the physical parameters of the solar atmosphere in height. In model calculations, the temperature decreases monotonically from 5700 K at the photosphere level as the altitude increases, and the energy flow is formed due to the radiant and kinetic thermal conductivity. In the observational data from the photospheric level to heights of about 500 km the temperature decreases (in agreement with theoretical calculations), passes through the temperature minimum, but then begins to grow. At the altitude of 28 000 km, the temperature reaches 1.5·106 K, and remains stable at this level at altitudes of the order of several radii of the Sun. So there was a problem of "abnormal warming" of the solar atmosphere . In this work the phenomenon of anomalous heating of the solar atmosphere due to the dissipation of the energy of weak shock waves generated in the upper layers of the convective zone is studied. Materials and Methods: The distributions of plasma characteristics are calculated based on the empirical model of the solar atmosphere and the convective zone of the Sun. It is shown that in the convective zone and the chromosphere of the Sun the model of single-liquid gas dynamics is used to describe the movement of gas. A system of equations for single-liquid gas dynamics is used. The model problem takes into account the effect of thermal conductivity and viscosity, which plays an important role in the formation of the resulting distribution of thermodynamic parameters of the solar atmosphere. On the basis of completely conservative difference schemes of gravitational gas dynamics the method of establishing calculated the distribution of thermodynamic parameters in height within the solar chromosphere. Results: The method of determination was used to calculate the anomalous heating during the generation of acoustic waves from the photospheric level, as well as in the upper layers of the convective zone. These calculations implement a direct test of the Schwarzschild-Birman hypothesis in the original formulation about the mechanism of excitation of acoustic waves by stochastic pulsations of convective flows near the photospheric level. Due to the influence of dissipative processes (viscosity, radiant heat conduction) the calculated distributions weakly depend on the frequency and depth of wave flow generation in the upper layers of the solar convective zone. Conclusion: The calculation results are in satisfactory agreement with the observational data. Keywords: atmosphere of the Sun, abnormal heating, shock wave, initial and boundary conditions of the problem.

Key words: 
atmosphere of the Sun
abnormal heating
shock wave
initial and boundary conditions of the problem
Reference: 
  1. Prist E. R. Solnechnaya magnitogidrodinamika [Solar magnetohydrodynamics]. Moscow, Mir Publ., 1985. 592 p. (in Russian). DOI: https://doi.org/10.1017/CBO9781139020732
  2. Zirin G. Solnechnaya atmosfera [Solar atmosphere]. Moscow, Mir Publ., 1969. 504 p. (in Russian).
  3. Vernazza J. E., Avertt E. H., Loeser R. Structure of the Solar chromosphere. I. Basic computation and summary of the results. Astrophys. J., 1973, vol. 184, pp. 605–631. DOI: https://doi.org/10.1007/978-94-011-4820-7_24
  4. Nakada M. P. A Study of the Composition of the Solar Corona and Solar Wind. Solar Phys., 1970, vol. 14, pp. 457–479. DOI: https://doi.org/10.1007/BF00221331
  5. Alissandrakis C. E., Valentino A. Structure of the Transition Region and the Low Corona from TRACE and SDO Observations Near the Limb. Solar Phys., 2019, vol. 294, pp. 96. DOI: https://doi.org/10.1007/s11207-019-1486-7
  6. Hamada A., Asikainen T., Mursula K. New Homogeneous Dataset of Solar EUV Synoptic Maps from SOHO/EIT and SDO/AIA. Solar Phys., 2020, vol. 295, pp. 2. DOI: https://doi.org/10.1007/s11207-019-1563-y
  7. Kontogiannis I., Gontikakis C., Tsiropoula G., Tziotziou K. Probing the Quiet Solar Atmosphere from the Photosphere to the Corona. Solar Phys., 2018, vol. 293, pp. 56. DOI: https://doi.org/10.1007/s11207-018-1275-8
  8. Reeves E. M., Noyes R. W., Withbroe G. L. Observing Programs in Solar Physics during the 1973 ATM Skylab Program. Solar Phys., 1972, vol. 27, pp. 251–270. DOI: https://doi.org/10.1007/BF00153096
  9. Bierman L. Z. Inhomogeneous stellar atmosphere models. Naturwissenschaften, 1946, Bd. 33, S. 118.
  10. Schwarzschild M. Stability of the Sun against spherical thermal perturbations. Astrophys. J., 1948, vol. 107, pp. 1.
  11. Piddington J. H. A Model of the Quiet Solar Atmosphere. Solar Phys., 1972, vol. 27, pp. 402–418.
  12. Vásquez A. M., Frazin R. A., Vourlidas A., Ward B., Bart van der Holst, Russell A., Philippe L. Tomography of the Solar Corona with the Wide-Field Imager for the Parker Solar Probe. Solar Phys., 2019, vol. 294, pp. 81. DOI: https://doi.org/10.1007/s11207-019-1471-1
  13. McCauley P. I., Cairns I. H., White S. M., Mondal S., Lenc E., Morgan J., Oberoi D. The Low-Frequency Solar Corona in Circular Polarization. Solar Phys., 2019, vol. 294, pp. 106. DOI: https://doi.org/10.1007/s11207-019-1502-y
  14. Zeldovich Ya. B., Raizer Yu. P. Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavleniy [Physics of shock waves and high-temperature hydrodynamic phenomena]. Moscow, Nauka Publ., 1966. 670 p. (in Russian).
  15. Piddington J. H. Solar Atmospheric Heating. Solar Phys., 1973, vol. 33, pp. 363–374. DOI: https://doi.org/10.1007/BF00152424
  16. Mariska J. T., Kjeldseth-Moe O. Book-Review - the Solar Transition Region. Solar Phys., 1994, vol. 149, pp. 421. DOI: https://doi.org/10.1023/A:1005138131541
  17. Stix M. Modulation of Acoustic Waves by Solar Convection. Solar Phys., 2000, vol. 196, pp. 19–28. DOI: https://doi.org/10.1023/A:1005275115455
  18. Wentzel D. G. Wave reflection and wave disorder in the solar transition zone and corona. Solar Phys., 1978, vol. 58, pp. 307–318. DOI: https://doi.org/10.1007/BF00157276
  19. Whitham G. B. Linear and Nonlinear Waves. New York, Wiley Interscience, 1974. 394 p.
  20. Ulmschneider P., Schmitz F., Kalkofen W., Bohn H. U. Acoustic Waves in the Solar Atmosphere. V. On the chromosphere temperature rise. Astron. Astrophys., 1978, vol. 70, pp. 487–500.
  21. Ulmschneider P. On Frequency and Strength of Shock Waves in the Solar Atmosphere. Solar Phys., 1970, vol. 12, pp. 403–415. DOI: https://doi.org/10.1007/BF00148023
  22. Ulmschneider P. Radiation loss and mechanical heating in the solar chromosphere. Solar Phys., 1974, vol. 39, pp. 327–336. DOI: https://doi.org/10.1007/BF00162426
  23. Jeffrey A., Taniuti T. Nonlinear wave propagation. New York, Academic Press, 1964. 472 p.
  24. Schatzman E. Solar neutrinos and turbulent diffusion. Ann. Astrophys., 1949, vol. 12, pp. 203.
  25. Osterbrock D. E. Solar irradiance variation. I. Analysis of modeling techniques and inter comparison of groundbases data. Astrophys. J., 1961, vol. 134, pp. 347–388.
  26. Kuperus M. The coronal and transition region temperature structure of a Solar active region. Rech. Astron. Observ. Utrecht., 1965, vol. 17, pp. 1–24.
  27. Klein R. I., Stein R. F., Kalkofen W. Solar pulsations and angular coherence of atmospheric temperature fl uctuations. Astrophys. J., 1975, vol. 205, pp. 499.
  28. Deubner F.-L. Astronomical observation of low wavenumber nonradial eigenmodes of the Sun. Astrophys. J., 1976, vol. 51, pp. 189.
  29. Deubner Franz-Ludwig. On the Powerspectrum of the Photospheric Resonance Oscillations. Solar Phys., 1972, vol. 23, pp. 304–308. DOI: https://doi.org/10.1007/BF00148095
  30. Samarsky A. A., Popov Yu. P. Raznostnyye skhemy gazovoy dinamiki [Difference schemes of gas dynamics]. Moscow, Nauka Publ., 1973. 351 p. (in Russian).
  31. Romanov D. V. Matematicheskoye modelirovaniye vliyaniya mnogomernosti na evolyutsiyu magnitnykh poley i strukturu anomal’nogo progreva solnechnoy atmosfery [Mathematical modeling of the infl uence of multidimensionality on the evolution of magnetic fi elds and the structure of anomalous heating of the solar atmosphere]. Thesis Diss. Cand. Sci. (Phys.). Krasnoyarsk, 2003. 128 p. (in Russian).
  32. Christensen-Dalsgaard J., Dappen W., Ajukov S. V., Anderson E. R., Oberoi D. The current state of Solar modeling. Science, 1996, vol. 272, pp. 1286.
  33. Braginsky S. I. Voprosy teorii plazmy [Issues of the theory of plasma]. Moscow, Atomizdat Publ., 1963, iss. 1. 183 p. (in Russian).
  34. McWhirter R. W. P., Thonemann P. C., Wilson R. The heating of the Solar Corona: a model based on energy balance. Astron. Astrophys., 1975, vol. 40, pp. 63–73.
  35. Landau L. D., Lifshitz E. M. Gidrodinamika [Hydrodynamics]. Moscow, Nauka Publ., 1986. 736 p. (in Russian).
  36. Stix M. Modulation of Acoustic Waves by Solar Convection. Solar Phys., 2000, vol. 196, pp. 19–28. DOI: https://doi.org/10.1023/A:1005275115455
  37. Unno W., Spiegel E. A. The Eddington approximation in the radiative heat equation. Publication of the astronomical society of Japan, 1966, vol. 18, no. 2, pp. 85–95.
  38. Kotelnikov I. A., Stupakov G. V. Lektsii po fi zike plazmy [Lectures on plasma physics]. Novosibirsk, Novosibirskiy gosudarstvennyi universitet, 1996. 128 p. (in Russian).
  39. Romanov K. V. Matematicheskoye modelirovaniye fi zicheskikh protsessov anomal’nogo progreva solnechnoy atmosfery [Mathematical modeling of the physical processes of anomalous heating of the solar atmosphere]. Thesis Diss. Cand. Sci. (Phys.). Novosibirsk, 2003. 145 p. (in Russian).
Received: 
13.10.2019
Accepted: 
14.01.2020
Published: 
02.03.2020
  • 1456 reads