Simulation of the generation of the toroidal magnetic field of the Sun by differential rotation
Heading:
| 1Loginov, AA, 2Kryvodubskyj, VN, 1Salnikov, NN, 1Prutsko, YV 1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine 2Astronomical Observatory, Taras Shevchenko National University of Kyiv, 04053, Kyiv, Ukraine |
| Kinemat. fiz. nebesnyh tel (Online) 2017, 33(6):17-33 |
| https://doi.org/10.15407/kfnt2017.06.017 |
| Start Page: Solar Physics |
| Language: Russian |
Abstract: Within the framework of the kinematic dynamo theory, we constructed a mathematical model for the evolution of the toroidal magnetic field of the Sun, excited by the differential rotation of the convective zone in the presence of the poloidal field of relic origin. We used the velocity profile obtained as a result of decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculated the latitudinal profiles of a toroidal field that increases in time for different depths in the solar convection zone. It is found that in the region of differential rotation, the exciting toroidal field is characterized by substantial fluctuations in its magnitude depend on the depth. On the basis of our simulations results, we proposed an explanation for the «incorrect polarity» of magnetic bipolar groups of spots in solar cycles. |
| Keywords: helioseismology, the Sun, toroidal magnetic field |
References:
1.S. I. Vainshtein, Ya. B. Zel’dovich, and A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980) [in Russian].
2.M. N. Gnevyshev and A. I. Ol’, “On the 22 year cycle of solar activity,” Astron. Zh. 25 (1), 18–20 (1948).
3.A. G. Zagorodnyi and O. K. Cheremnykh, Introduction to Plasma Physics (Naukova Dumka, Kyiv, 2014) [in Russian].
4.I. O. Kremenets’kii and O. K. Cheremnikh, Space Weather: Mechanisms and Manifestations (Naukova Dumka, Kyiv, 2009) [in Ukrainian].
5.V. N. Krivodubskii, “On turbulent conductivity and magnetic permeability of solar plasma,” Soln. Dannye, No. 7, 99–109 (1982).
6.Yu. P. Ladikov-Roev and O. K. Cheremnykh, Mathematical Models of Continuous Media (Naukova Dumka, Kyiv, 2010) [in Russian].
7.A. A. Loginov, V. N. Krivodubskii, O. K. Cheremnykh, and N. N. Sal’nikov, “On spatial-temporal structure of the Sun global flows,” Visn. Kyiv. Nats. Univ. im. T. Shevchenka. Astron. 48, 54–57 (2012).
8.A. A. Loginov, N. N. Sal’nikov, O. K. Cheremnykh, V. N. Krivodubskii, and N. V. Maslova, “Hydrodynamic model for generation of global poloidal flow of the Sun,” Kosm. Nauka Tekhnol. 17 (1), 29–35 (2011).
9.A. A. Loginov, O. K. Cheremnykh, V. N. Krivodubskii, and N. N. Sal’nikov, “Hydrodynamic model of torsional oscillations of the Sun,” Kosm. Nauka Tekhnol. 18 (1), 74–81 (2012).
https://doi.org/10.15407/knit2012.01.074
10.V. I. Makarov and M. V. Kushnir, “On the low l-modes of the large-scale solar magnetic field,” Soln. Dannye, No. 7, 64–69 (1987).
11.A. I. Khlystova and D. D. Sokolov, “Toroidal magnetic field of the Sun from data on Hale-rule-violating sunspot groups,” in Solar and Solar-Terrestrial Physics–2008, St. Petersburg, Russia, July 7–12, 2008 (Gl. Astron. Obs. Ross. Akad. Nauk, St. Petersburg, 2008), pp. 373–374.
12.M. D. Altschuler, D. F. Trotter, G. Newkirk, and R. Howard, “The large-scale solar magnetic field,” Sol. Phys. 39, 3–17 (1974).
https://doi.org/10.1007/BF00154967
13.S. Basu and H. M. Antia, “Characteristics of solar meridional flows during solar cycle 23,” Astrophys. J. 717, 488–495 (2010).
https://doi.org/10.1088/0004-637X/717/1/488
14.D. W. Boyer and E. H. Levy, “Oscillating dynamo magnetic field in the presence of an external nondynamo field–The influence of a solar primordial field,” Astrophys. J. 277, 848–861 (1984).
https://doi.org/10.1086/161755
15.D. C. Braun and A. C. Birch, “Prospects for the detection of the deep solar meridional circulation,” Astrophys. J., Lett. 689, L161–L165 (2008).
https://doi.org/10.1086/595884
16.A. S. Brum, M. K. Browning, M. Dikpati, H. Hotta, and A. Strugarek, “Recent advances on solar global magnetism and variability,” Space Sci. Rev. 196, 101–136 (2015).
https://doi.org/10.1007/s11214-013-0028-0
17.F. H. Busse, “Magnetohydrodynamics of the Earth’s dynamo,” Annu. Rev. Fluid Mech. 10, 435–462 (1978).
https://doi.org/10.1146/annurev.fl.10.010178.002251
18.P. Charbonneau, “Dynamo models of the solar cycle,” Living Rev. Sol. Phys. 7, 3 (2010).
https://doi.org/10.12942/lrsp-2010-3
19.O. K. Cheremnykh, V. O. Yatsenko, O. V. Semeniv, and Yu. V. Shatokhina, “Nonlinear dynamical model for space weather prediction,” Ukr. J. Phys. 53, 504–507 (2008).
20.A. R. Choudhuri, M. Schussler, and M. Dikpati, “The solar dynamo with meridional circulation,” Astron. Astrophys. 303, L29 (1995).
21.M. Couette, “Etudes sur le frottement des liquides,” Ann. Chem. Phis. 21, 433 (1890).
22.D. R. Durran, “Improving the anelactic approximation,” J. Atmos. Sci. 46, 1453–1461 (1989).
https://doi.org/10.1175/1520-0469(1989)0462.0.CO;2
23.P. M. Giles, T. L. Duval Jr., P. H. Scherrer, and R. S. I. Bogart, “A subsurface flow of material from the Sun’s equator to its poles,” Nature 390, 52–54 (1997).
https://doi.org/10.1038/36294
24.G. E. Hale and S. B. Nicholson, “The law of sun-spot polarity,” Astrophys. J. 62, 270 (1925).
https://doi.org/10.1086/142933
25.D. H. Hathaway, “Doppler measurements of the Sun’s meridional flow,” Astrophys. J. 460, 1027–1033 (1996).
https://doi.org/10.1086/177029
26.D. H. Hathaway, “The solar cycle,” Living Rev. Sol. Phys. 12, 4 (2015).
https://doi.org/10.1007/lrsp-2015-4
27.G. Hazra, B. B. Karak, and A. R. Choudhuri, “Is a deep one-cell meridional circulation essential for the flux transport solar dynamo?,” Astrophys. J. 782, 93 (2014).
https://doi.org/10.1088/0004-637X/782/2/93
28.R. Howard, “Studies of solar magnetic fields. I: The average field strengths,” Sol. Phys. 38, 283–299 (1974).
https://doi.org/10.1007/BF00155067
29.R. Howard and B. J. LaBonte, “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
30.R. Howe, J. Christensen-Dalsgaard, F. Hill, R. W. Komm, R. M. Larsen, J. Schou, M. J. Thompson, and J. Toomre, “Deeply penetrating banded zonal flows in the solar convection zone,” Astrophys. J., Lett. 533, L163–L166 (2000).
https://doi.org/10.1086/312623
31.R. Howe, J. Christensen-Dalsgaard, F. Hill, R. W. Komm, R. M. Larsen, J. Schou, M. J. Thompson, and J. Toomre, “Dynamic variations at the base of the solar convection zone,” Science 287, 2456–2460 (2000).
32.R. Howe, J. Christensen-Dalsgaard, F. Hill, R. Komm, J. Schou, and M. J. Thompson, “Solar convection-zone dynamics, 1995–2004,” Astrophys. J. 634, 1405–1415 (2005).
https://doi.org/10.1086/497107
33.L. L. Kitchatinov, “The solar dynamo: Inferences from observations and modeling,” Geomagn. Aeron. 54, 867–876 (2014).
https://doi.org/10.1134/S0016793214070056
34.A. G. Kosovichev, “Probing solar and stellar interior dynamics and dynamo,” Adv. Space Res. 41, 830–837 (2008).
https://doi.org/10.1016/j.asr.2007.05.023
35.F. Krause and K.-H. Rädler, Mean Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).
36.V. N. Krivodubskii, “Rotational anisotropy and magnetic quenching of gyrotropic turbulence in the solar convective zone,” Astron. Rep. 42, 122–126 (1998).
37.V. N. Krivodubskii, “The structure of the global solar magnetic field excited by the turbulent dynamo mechanism,” Astron. Rep. 45, 738–745 (2001).
https://doi.org/10.1134/1.1398923
38.V. N. Krivodubskij, “Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone,” Astron. Nachr. 326, 61–74 (2005).
https://doi.org/10.1002/asna.200310340
39.V. N. Kryvodubskyj, “Dynamo parameters of the solar convection zone,” Kinematics Phys. Celestial Bodies 22, 1–20 (2006).
40.V. N. Krivodubskij, “Turbulent effects of sunspot magnetic field reconstruction,” Kinematics Phys. Celestial Bodies 28, 232–238 (2012).
https://doi.org/10.3103/S0884591312050054
41.V. N. Krivodubskij, “Small scale alpha-squared effect in the solar convection zone,” Kinematics Phys. Celestial Bodies 31, 55–64 (2015).
https://doi.org/10.3103/S0884591315020038
42.V. N. Krivodubskij, “Double maxima of 11-year solar cycles,” Kinematics Phys. Celestial Bodies 33, 24–38 (2017).
https://doi.org/10.3103/S0884591317010044
43.Yu. P. Ladikov-Roev, A. A. Loginov, and O. K. Cheremnykh, “Nonstationary model of solar spicule,” J. Autom. Inform. Sci. 46 (10), 20–29 (2014).
https://doi.org/10.1615/JAutomatInfScien.v46.i10.30
44.A. A. Loginov, O. K. Cheremnykh, V. N. Krivodubskij, and N. N. Salnikov, “Hydrodynamic model of spatial and temporal variations of poloidal and toroidal components of three-dimensional solar flows,” Bull. Crimean Astrophys. Observatory 108, 58–63 (2012).
https://doi.org/10.3103/S0190271712010159
45.A. A. Loginov, N. N. Salnikov, O. K. Cheremnykh, Ya. I. Zyelyk, and N. V. Maslova, “On the hydrodynamic mechanism of the generation of the global poloidal flux on the Sun,” Kinematics Phys. Celestial Bodies 27, 217–223 (2011).
https://doi.org/10.3103/S0884591311050060
46.V. I. Makarov and K. R. Sivaraman, “On the epochs of polarity reversals of the polar magnetic field of the Sun during 1870–1982,” Bull. Astron. Soc. India 14, 163–167 (1986).
47.D. Nandy and A. R. Choudhuri, “Explaining the latitudinal distribution of sunspots with deep meridional flow,” Science 296, 1671–1673 (2002).
https://doi.org/10.1126/science.1070955
48.H. W. Newton and M. J. Nunn, “The Sun’s rotation derived from sunspots 1934–1944 and additional results,” Mon. Not. R. Astron. Soc. 111, 413 (1951).
https://doi.org/10.1093/mnras/111.4.413
49.M. I. Pudovkin and E. E. Behevolenskaya, “The quasisteady primordial magnetic field of the Sun and the intensity variations of the solar cycle,” Sov. Astron. Lett. 8 (8), 273–274 (1982).
50.L. Rayleigh, “On the dynamics of revolving fluids,” Sci. Pap. 6, 447–453 (1916); Proc. R. Soc. London A 93, 148 (1916).
51.G. Rüdiger and L. L. Kitchatinov, “Alpha-effect and alpha-quenching,” Astron. Astrophys. 269, 581–588 (1993).
52.R. Schwenn, “Space weather: The solar perspective,” Living Rev. Sol. Phys. 3 (2), 1–72 (2006).
https://doi.org/10.12942/lrsp-2006-2
53.O. V. Semeniv, V. I. Sidorenko, Y. V. Shatokhina, O. K. Cheremnykh, and V. A. Yatsenko, “Optimization approach to space weather prediction,” J. Autom. Inform. Sci. 40 (8), 41–56 (2008).
https://doi.org/10.1615/JAutomatInfScien.v40.i8.50
54.H. B. Snodgrass and S. B. Dailey, “Meridional motions of magnetic features in the solar photosphere,” Sol. Phys. 163, 21–42 (1996).
https://doi.org/10.1007/BF00165454
55.G. I. Taylor, “VIII. Stability of a viscous liquid contained between two rotating cylinders,” Philos. Trans. R. Soc., A 223, 289 (1923).
https://doi.org/10.1098/rsta.1923.0008
56.S. V. Vorontsov, J. Christensen-Dalsgaard, J. Schou, V. N. Strakhov, and M. J. Thompson, “Helioseismic measurement of solar torsional oscillations,” Science 296, 101–103 (2002).
https://doi.org/10.1126/science.1069190
57.Y.-M. Wang, N. R. Sheeley Jr., and A. G. Nash, “A new solar cycle model including meridional circulation,” Astrophys. J. 383, 431–442 (1991).
https://doi.org/10.1086/170800
58.Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983).