Иркутск, Россия
УДК 524.31.082 Карлики
УДК 524.3-17 Численная трактовка. Моделирование и т.д.
В рамках гидродинамики средних полей создана модель крупномасштабных течений в конвективных зонах Солнца и подобных Солнцу звезд, обобщающая предшествующие модели дифференциального вращения с учетом зависимости течения от времени и его отклонения от осевой симметрии. Модель реализована в виде программы численных расчетов, в которой применяется спектральный метод разложения по сферическим функциям в комбинации с конечно-разностным дифференцированием второго порядка точности по времени и радиусу. Первые расчеты показали близкое соответствие осесимметричной части течения данным гелиосейсмологии о дифференциальном вращении и меридиональной циркуляции. Картина затухающих во времени неосесимметричных течений, рассчитанных в модели, находится в качественном согласии с наблюдениями волн Россби на Солнце. Сформулирована задача дальнейшего развития теории крупномасштабных течений.
Солнце, звезды, вращение, конвекция, турбулентность, численное моделирование
1. Кичатинов Л.Л. Дифференциальное вращение звезд. УФН. 2005, т. 175, № 5, с. 475–494.
2. Кичатинов Л.Л. Происхождение приповерхностного слоя неоднородного вращения Солнца. Письма в АЖ. 2023, т. 49, № 11, с. 829–836. DOI:https://doi.org/10.31857/S0320010823110049.
3. Кичатинов Л.Л., Непомнящих А.А. Согласованная модель солнечного динамо и дифференциального вращения. Письма в АЖ. 2017, т. 43, № 5, с. 370–382. DOI:https://doi.org/10.7868/S0320010817040039.
4. Краузе Ф., Рэдлер К.-Х. Магнитная гидродинамика средних полей и теория динамо. М.: Мир, 1984.
5. Лебединский А.И. Вращение Солнца. Астрономический журнал. 1941, т. 18, № 1, с. 10–25.
6. Balona L.A., Abedigamba O.P. Differential rotation in K, G, F and A stars. Monthly Notices of the Royal Astronomical Society. 2016, vol. 461, iss. 1, pp. 497–506. DOI:https://doi.org/10.1093/mnras/stw1443.
7. Barnes J.R., Collier Cameron A., Donati J.-F., et al. The dependence of differential rotation on temperature and rotation. Monthly Notices of the Royal Astronomical Society. 2005, vol. 357, iss. 1, pp. L1–L5. DOI:https://doi.org/10.1111/j.1745-3933.2005.08587.x.
8. Brandenburg A., Elstner D., Masada Y., Pipin V. Turbulent processes and mean-field dynamo. Space Sci. Rev. 2023, vol. 219, iss. 7, id. 55. DOI:https://doi.org/10.1007/s11214-023-00999-3.
9. Chandrasekhar S. Hydrodynamic and hydromagnetic stability. Clarendon Press. Oxford. 1961.
10. Charbonneau P. Dynamo models of the solar cycle. Living Reviews in Solar Physics. 2020, vol. 17, iss. 1, id. 4. DOI:https://doi.org/10.1007/s41116-020-00025-6.
11. Charbonneau P., Sokoloff D. Evolution of solar and stellar dynamo theory. Space Sci. Rev. 2023, vol. 219, iss. 5, id. 35. DOI:https://doi.org/10.1007/s11214-023-00980-0.
12. Collier Cameron A., Donati J.-F. Doin’ the twist: secular changes in the surface differential rotation on AB Doradus. Monthly Notices of the Royal Astronomical Society. 2002, vol. 329, iss. 1, pp. L23–L27. DOI:https://doi.org/10.1046/j.1365-8711.2002.05147.x.
13. Durney B.R. On the behavior of the angular velocity in the lower part of the solar convection zone. Astrophys. J. 1989, vol. 338, p. 509. DOI:https://doi.org/10.1086/167214.
14. Gizon L., Cameron R., Pourabdian M., et al. Meridional flow in the Sun’s convection zone is a single cell in each hemisphere. Science. 2020, vol. 368, iss. 6498, p. 1469–1472. DOI:https://doi.org/10.1126/science.aaz7119.
15. Glatzmaier G.A., Gilman P.A. Compressible convection in a rotating spherical shell — Part two — a linear anelastic model. Astrophys. J. Suppl. 1981, vol. 45, pp. 351–380. DOI:https://doi.org/10.1086/190715.
16. Hazra G., Nandy D., Kitchatinov L., Choudhuri A.R. Mean field models of flux transport dynamo and meridional circulation in the Sun and stars. Space Sci. Rev. 2023, vol. 219, iss. 5, id. 39. DOI:https://doi.org/10.1007/s11214-023-00982-y.
17. Hotta H., Bekki Y., Gizon L., et al. Dynamics of large-scale solar flows. Space Sci. Rev. 2023, vol. 219, iss. 8, id. 77. DOI:https://doi.org/10.1007/s11214-023-01021-6.
18. Joyce M., Tayar J. A review of the mixing length theory of convection in 1D stellar modeling. Galaxies. 2023, vol. 11, iss. 3, id. 75. DOI:https://doi.org/10.3390/galaxies11030075.
19. Käpylä P.J., Browning M.K., Brun A.S., et al. Simulations of solar and stellar dynamos and their theoretical interpretation. Space Sci. Rev. 2023, vol. 219, iss. 7, id. 58. DOI:https://doi.org/10.1007/s11214-023-01005-6.
20. Karak B.B. Models for the long-term variations of solar activity. Living Reviews in Solar Physics. 2023, vol. 20, iss. 1, id. 3. DOI:https://doi.org/10.1007/s41116-023-00037-y.
21. Kichatinov L.L. Turbulent transport of angular momentum and differential rotation. Geophysical and Astrophysical Fluid Dynamics. 1986, vol. 35, iss. 1, pp. 93–110. DOI:https://doi.org/10.1080/03091928608245888.
22. Kichatinov L.L. A mechanism for differential rotation based on angular momentum transport by compressible convection. Geophysical and Astrophysical Fluid Dynamics. 1987, vol. 38, iss. 4, pp. 273–292. DOI:https://doi.org/10.1080/03091928708210111.
23. Kitchatinov L.L. The dependence of stellar activity cycles on effective temperature. Res. Astron. Astrophys. 2022, vol. 22, iss. 12, id. 125006. DOI:https://doi.org/10.1088/1674-4527/ac9780.
24. Kitchatinov L.L., Olemskoy S.V. Differential rotation of main-sequence dwarfs and its dynamo efficiency. Monthly Notices of the Royal Astronomical Society. 2011, vol. 411, iss. 2, pp. 1059–1066. DOI:https://doi.org/10.1111/j.1365-2966.2010.17737.x.
25. Kitchatinov L.L., Olemskoy S.V. Differential rotation of main-sequence dwarfs: predicting the dependence on surface temperature and rotation rate. Monthly Notices of the Royal Astronomical Society. 2012, vol. 423, iss. 4, pp. 3344–3351. DOI:https://doi.org/10.1111/j.1365-2966.2012.21126.x.
26. Kitchatinov L.L., Rüdiger G. Differential rotation and meridional flow in the solar convection zone and beneath. Astronomische Nachrichten. 2005, vol. 326, iss. pp. 379–385. DOI:https://doi.org/10.1002/asna.200510368.
27. Kitchatinov L.L., Pipin V.V., Ruediger G. Turbulent viscosity, magnetic diffusivity, and heat conductivity under the influence of rotation and magnetic field. Astronomische Nachrichten. 1994, vol. 315, no. 2, pp. 157–170. DOI:https://doi.org/10.1002/asna.2103150205.
28. Kitiashvili I.N., Kosovichev A.G., Wray A.A., et al. Leptocline as a shallow substructure of near-surface shear layer in 3D radiative hydrodynamic simulation. Monthly Notices of the royal astronomical society. 2023, vol. 518, iss. 1, pp. 504–512. DOI:https://doi.org/10.1093/mnras/stac2946.
29. Lantz S.R., Fan Y. Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. 1999, vol. 121, iss. 1, pp. 247–264. DOI:https://doi.org/10.1086/313187.
30. Löptien B., Gizon L., Birch A.C., et al. Global-scale equatorial Rossby waves as an essential component of solar internal dynamics. Nature Astronomy. 2018, vol. 2, pp. 568–573. DOI:https://doi.org/10.1038/s41550-018-0460-x.
31. Mandal K., Hanasoge S.M. Probing depth variations of solar inertial modes through normal mode coupling. Astrophys. J. 2024, vol. 967, iss. 1, id. 46. DOI:https://doi.org/10.3847/1538-4357/ad391b.
32. Mandal K., Hanasoge S.M., Gizon, L. Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling. Astron. Astrophys. 2021, vol. 652, id. A96. DOI:https://doi.org/10.1051/0004-6361/202141044.
33. Paxton B., Bildsten L., Dotter A., et al. Modules for experiments in stellar astrophysics (MESA). Astrophys. J. Suppl. 2011, vol. 192, iss. 1, id. 3. DOI:https://doi.org/10.1088/0067-0049/192/1/3.
34. Pipin V.V., Kosovichev A.G. On the origin of solar torsional oscillations and extended solar cycle. Astrophys. J. 2019, vol. 887, iss. 2, id. 215. DOI:https://doi.org/10.3847/1538-4357/ab5952.
35. Pipin V.V., Kosovichev A.G. Torsional oscillations in dynamo models with fluctuations and potential for helioseismic predictions of the solar cycles. Astrophys. J. 2020, vol. 900, iss. 1, id. 26. DOI:https://doi.org/10.3847/1538-4357/aba4ad.
36. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes. Cambridge University Press. 1992.
37. Rajaguru S.P., Antia H.M. Meridional circulation in the solar convection zone: time-distance helioseismic inferences from four years of HMI/SDO observations. Astrophys. J. 2015, vol. 813, iss. 2, id. 114. DOI:https://doi.org/10.1088/0004-637X/813/2/114.
38. Rüdiger G. Differential rotation and stellar convection. Sun and Solar-Type Stars. Akademie-Verlag, Berlin, 1989. 328 p.
39. Rüdiger G., Spahn F. On the stability of mean-field models of the solar convection zone. Solar. Phys. 1992, vol. 138, iss. 1, pp. 1–9. DOI:https://doi.org/10.1007/BF00146192.
40. Rüdiger G., Egorov P., Kitchatinov L.L., Küker M. The eddy heat-flux in rotating turbulent convection. Astron. Astrophys. 2005, vol. 431, pp. 345–352. DOI:https://doi.org/10.1051/0004-6361:20041670.
41. Saio H. R-mode oscillations in uniformly rotating stars. Astrophys. J. 1982, vol. 256, pp. 717–735. DOI:https://doi.org/10.1086/159945.
42. Schou J., Antia H.M., Basu S., et al. Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler Imager. Astrophys. J. 1998, vol. 505, iss. 1, pp. 390–417. DOI:https://doi.org/10.1086/306146.
43. Snodgrass H.B., Ulrich R.K. Rotation of Doppler features in the solar photosphere. Astrophys. J. 1990, vol. 351, pp. 309–316. DOI:https://doi.org/10.1086/168467.
44. Thompson M.J., Toomre J., Anderson E.R., et al. Differential rotation and dynamics of the solar interior. Science. 1996, vol. 272, iss. 5266, pp. 1300–1305.DOI:https://doi.org/10.1126/science.272.5266.1300.
45. Tuominen I., Brandenburg A., Moss D., Rieutord M. Does solar differential rotation ARISE from a large scale instability? Astron. Astrophys. 1994, vol. 284, pp. 259–264.
