On hydrodynamic mechanism of phase change of the Sun's dynamo-cycle

1Loginov, AA, 1Tkachenko, VA, 1Cheremnykh, OK
1Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
Kosm. nauka tehnol. 2007, 13 ;(Supplement1):093-098
https://doi.org/10.15407/knit2007.01s.093
Publication Language: Russian
Abstract: 
The model of phase change for the Sun's magnetic field generation is proposed. The mechanism of the change is as follows. Due to stability loss of toroidal differential rotation of the Sun at the threshold value of the relationship between the angular velocity and radius and latitude Ω (r, θ) poloidal flows arise and the dynamo-process associated with them and generating the Sun's variable magnetic field occurs. Influence of the Coriolis force on the poloidal flows brakes the differential rotation, which causes a change in structure of Ω (r, θ) and violation of the instability condition. This results in the disappearance of the poloidal flows and in the interruption of the dynamo-process. Then the differential rotation and dynamo-cycle are regained and when the angular velocity reaches the threshold value the Sun's variable magnetic field is generated again.
Keywords: angular velocity, differential rotation, dynamo-cycle
References: 
1. Braginskiy S. I. Kinematic Models of the Earth's Hydromagnetic Dynamo. Geomagnetizm i Aeronomiia, 4, 572—583 (1964) [in Russian].
2. Braginskiy S. I. Geomagnetic Eccentric Dipole. Geomagnetizm i Aeronomiia, 4, 698—711 (1964) [in Russian].
3. Braginskii S. I. Self-excitation of a magnetic field during the motion of a highly conducting fluid. ZhETF, 48, 1084 (1964) [in Russian].
4. Braginskii S. I. Theory of the hydromagnetic dynamo. ZhETF, 48, 2178 (1964) [in Russian].
5. Vorontsov S. V., Zharkov V. N. In: Itogi Nauki Tekh., Ser. Astron., Vol. 38, 253 p. (VINITI, Moscow, 1988) [in Russian].
6. Zeldovich Ya. B. The magnetic field in the two-dimensional motion of a conducting turbulent fluid. ZhETF, 31, 154—156 (1956) [in Russian].
7. Cowling T. G. Magnetohydrodynamics. (Izd-vo inostr. lit., Moscow, 1959) [in Russian].
8. Kichatinov L. L. The differential rotation of stars. Uspekhi Fizicheskikh Nauk, 175 (5), 475—494 (2005) [in Russian].
https://doi.org/10.3367/UFNr.0175.200505b.0475 
9. Landau L. D., Lifshits E. M. Gidrodynamics, 733 p. (Nauka, Moscow, 1986) [in Russian].
10. Lebedinsky A. I. Rotation of the Sun. Astron. Zhurn., 18 (1), 10—25 (1941) [in Russian].
11. Loginov A. A., Samoilenko Yu. I., Tkachenko V. A. Excitation of meridional flow by differential rotation in Earth's liquid core. Kosm. nauka tehnol., 6 (2-3), 53—68 (2000) [in Russian].
12. Moffatt H. K. Magnetic field generation in electrically conducting fluids, 340 p. (Mir, Moscow, 1980) [in Russian].
13. Alfven H. On the existence of electromagnetic-hydrodinamic waves. Arkiv. F. Mat. Astron. Fysik, 29B (2), 7 p. (1942).
14. Cowling T. G. The magnetic field of sunspots. Mon. Notic. Roy. Astron. Soc., 94, 39—48 (1934).
https://doi.org/10.1093/mnras/94.1.39 
15. Howard R. E., LaBonte B. J. The sun is observed to be a torsional oscillator with a period of 11 years. Astrophys. J. Lett., 239, L33—L36 (1980).
https://doi.org/10.1086/183286 
16. Kipenhahn R. Differential rotation in stars with convective envelopes. Astrophys. J., 137, 664—678 (1963).
https://doi.org/10.1086/147539
17. Kitchatinov L. L., Rudiger G. Differential rotation in solar-type stars: revisiting the Taylor-number puzzle. Astron. and Astrophys., 299, 446 (1995).
18. Kitchatinov L. L., Rudiger G. Differential rotation models for late-type dwarfs and giants. Astron. and Astrophys., 344, 911—917 (1999).
19. Komm R. W., Howard R. E., Harvey J. W. Meridional flow of small photospheric magnetic features. Solar. Phys., 147 (2), 207—223 (1993).
https://doi.org/10.1007/BF00690713 
20. LaBonte B. J., Howard R. Torsional waves on the Sun and the activity cycle. Solar Phys., 75, 161 — 178 (1982).
https://doi.org/10.1007/BF00153469 
21. Larmor I. How could a rotation body such as the Sun become a magnet. Rep. Brit. Assoc. Adv. Sci., 159—160 (1919).
22. Parker E. N. Hydromagnetic dynamo models. Astrophys. J., 122, 293—314 (1955).
https://doi.org/10.1086/146087 
23. Rudiger G. Reynolds stresses and differential rotation. I. On recent calculations of zonal fluxes in slowly rotating stars. Geophys. and Astrophys. Fluid Dynamics, 16 (1), 239—261 (1980).
https://doi.org/10.1080/03091928008243659 
24. Sehou J., et al. Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler imager. Astrophys. J., 505 (1), 390—417 (1998).
https://doi.org/10.1086/306146 
25. Sokoloff D. D. The Maunder minimum and the solar dynamo. Solar Phys., 224, 145—152 (2004).
https://doi.org/10.1007/s11207-005-4176-6 
26. Steenbeck M., Krause F. The generation of stellar and planetary magnetic fields by turbulent dynamo action. Z. Naturforch., 21a, 1285—1296 (1966).
27. Steenbeck M., Krause F., Radler K. A colculation of the mean electromotive force in an electrically conducting fluid in turbulent motion under the influence of Coriolis forses. Z. Naturforch., 21a, 369—376 (1966).
28. Wilson P. R., Burtonclay D., Li Y. The rotational structure of the region below the solar convection zone. Astrophys. J., 489, 395—402 (1997).
https://doi.org/10.1086/304770 
29. Zhao J., Kosovichev A. G. Torsional oscillation, meridional flows, and vorticity inferred in the upper convection zone of the Sun by time-distance helioseismology. Astrophys. J., 603 (2), 776—784 (2004).