Abstract
This article reviews some of the leading results obtained in solar dynamo physics by using temporal oscillator models as a tool to interpret observational data and dynamo model predictions. We discuss how solar observational data such as the sunspot number is used to infer the leading quantities responsible for the solar variability during the last few centuries. Moreover, we discuss the advantages and difficulties of using inversion methods (or backward methods) over forward methods to interpret the solar dynamo data. We argue that this approach could help us to have a better insight about the leading physical processes responsible for solar dynamo, in a similar manner as helioseismology has helped to achieve a better insight on the thermodynamic structure and flow dynamics in the Sun’s interior.
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S.L. Baliunas, R.A. Donahue, W.H. Soon, J.H. Horne, J. Frazer, L. Woodard-Eklund, M. Bradford, L.M. Rao, O.C. Wilson, Q. Zhang, W. Bennett, J. Briggs, S.M. Carroll, D.K. Duncan, D. Figueroa, H.H. Lanning, T. Misch, J. Mueller, R.W. Noyes, D. Poppe, A.C. Porter, C.R. Robinson, J. Russell, J.C. Shelton, T. Soyumer, A.H. Vaughan, J.H. Whitney, Chromospheric variations in main-sequence stars. Astrophys. J. 438, 269–287 (1995)
G. Basri, L.M. Walkowicz, N. Batalha, R.L. Gilliland, J. Jenkins, W.J. Borucki, D. Koch, D. Caldwell, A.K. Dupree, D.W. Latham, S. Meibom, S. Howell, T. Brown, Photometric variability in Kepler target stars: the Sun among stars a first look. Astrophys. J. Lett. 713, 155–159 (2010). doi:10.1088/2041-8205/713/2/L155
S. Basu, H.M. Antia, Characteristics of solar meridional flows during solar cycle 23. Astrophys. J. 717, 488–495 (2010). doi:10.1088/0004-637X/717/1/488
J. Beer, S. Tobias, N.O. Weiss, An active sun throughout the Maunder Minimum. Sol. Phys. 181, 237–249 (1998). doi:10.1023/A:1005026001784
R.N. Bracewell, Three-halves law in sunspot cycle shape. Mon. Not. R. Astron. Soc. 230, 535–550 (1988). Oscillator models of the solar cycle. http://adsabs.harvard.edu/abs/1988MNRAS.230..535B
B.P. Brown, M.S. Miesch, M.K. Browning, A.S. Brun, J. Toomre, Magnetic cycles in a convective dynamo simulation of a young solar-type star. Astrophys. J. 731, 69 (2011). doi:10.1088/0004-637X/731/1/69
P.J. Bushby, Zonal flows and grand minima in a solar dynamo model. Mon. Not. R. Astron. Soc. 371, 772–780 (2006). doi:10.1111/j.1365-2966.2006.10706.x
R. Cameron, M. Schüssler, A robust correlation between growth rate and amplitude of solar cycles: consequences for prediction methods. Astrophys. J. 685, 1291–1296 (2008). doi:10.1086/591079, http://adsabs.harvard.edu/abs/2008ApJ...685.1291C
E. Cardoso, I. Lopes, Impact of a realistic density stratification on a simple solar dynamo calculation. Astrophys. J. 757(1), 71 (2012). doi:10.1088/0004-637X/757/1/71
W.J. Chaplin, S. Basu, D. Huber, A. Serenelli, L. Casagrande, V. Silva Aguirre, W.H. Ball, O.L. Creevey, L. Gizon, R. Handberg, C. Karoff, R. Lutz, J.P. Marques, A. Miglio, D. Stello, M.D. Suran, D. Pricopi, T.S. Metcalfe, M.J.P.F.G. Monteiro, J. Molenda-Żakowicz, T. Appourchaux, J. Christensen-Dalsgaard, Y. Elsworth, R.A. García, G. Houdek, H. Kjeldsen, A. Bonanno, T.L. Campante, E. Corsaro, P. Gaulme, S. Hekker, S. Mathur, B. Mosser, C. Régulo, D. Salabert, Asteroseismic fundamental properties of solar-type stars observed by the NASA Kepler mission. Astrophys. J. Suppl. Ser. 210(1), 1 (2014)
P. Charbonneau, Dynamo models of the solar cycle. Living Rev. Sol. Phys. 7, 3 (2010)
P. Charbonneau, Where is the solar dynamo? J. Phys. Conf. Ser. 440(1), 012014 (2013). doi:10.1088/1742-6596/440/1/012014
P. Charbonneau, M. Dikpati, Stochastic fluctuations in a Babcock-Leighton model of the solar cycle. Astrophys. J. 543, 1027–1043 (2000). doi:10.1086/317142
P. Charbonneau, C. St-Jean, P. Zacharias, Fluctuations in Babcock-Leighton dynamos. I. Period doubling and transition to chaos. Astrophys. J. 619, 613–622 (2005). doi:10.1086/426385
A.R. Choudhuri, M. Schüssler, M. Dikpati, The solar dynamo with meridional circulation. Astron. Astrophys. 303, 29 (1995)
J.A. Eddy, The Maunder minimum. Science 192, 1189–1202 (1976). doi:10.1126/science.192.4245.1189
R.A. García, S. Mathur, D. Salabert, J. Ballot, C. Régulo, T.S. Metcalfe, A. Baglin, CoRoT reveals a magnetic activity cycle in a Sun-like star. arXiv:1008.4399 (2010)
M. Ghizaru, P. Charbonneau, P.K. Smolarkiewicz, Magnetic cycles in global large-eddy simulations of solar convection. Astrophys. J. Lett. 715, 133–137 (2010). doi:10.1088/2041-8205/715/2/L133
D.T. Gillespie, Exact numerical simulation of the Ornstein–Uhlenbeck process and its integral. Phys. Rev. E 54, 2084–2091 (1996)
D.H. Hathaway, L. Rightmire, Variations in the sun meridional flow over a solar cycle. Science 327, 1350 (2010). doi:10.1126/science.1181990
S. Hazra, D. Passos, D. Nandy, A stochastically forced time delay solar dynamo model: self-consistent recovery from a Maunder-like grand minimum necessitates a mean-field alpha effect. Astrophys. J. 789(1), 5 (2014)
K.M. Hiremath, The solar cycle as a forced and damped harmonic oscillator: long-term variations of the amplitudes, frequencies and phases. Astron. Astrophys. 452, 591–595 (2006). doi:10.1051/0004-6361:20042619, http://www.aanda.org/articles/aa/abs/2006/23/aa2619-04/aa2619-04.html
K.M. Hiremath, Prediction of solar cycle 24 and beyond. Astrophys. Space Sci. 314, 45–49 (2008). http://springerlink.bibliotecabuap.elogim.com/article/10.1007%2Fs10509-007-9728-9
R. Howe, Solar interior rotation and its variation. Living Rev. Sol. Phys. 6, 1 (2009)
P.J. Käpylä, M.J. Mantere, A. Brandenburg, Cyclic magnetic activity due to turbulent convection in spherical wedge geometry. Astrophys. J. Lett. 755, 22 (2012). doi:10.1088/2041-8205/755/1/L22
B.B. Karak, Importance of meridional circulation in flux transport dynamo: the possibility of a Maunder-like grand minimum. Astrophys. J. 724, 1021–1029 (2010). doi:10.1088/0004-637X/724/2/1021
B.B. Karak, A.R. Choudhuri, The Waldmeier effect and the flux transport solar dynamo. Mon. Not. R. Astron. Soc. 410, 1503–1512 (2011). doi:10.1111/j.1365-2966.2010.17531.x
F. Krause, K.-H. Raedler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980), 271 pp.
L. Lefevre, F. Clette, Survey and merging of sunspot catalogs. Sol. Phys. 289(2), 545–561 (2014)
I. Lopes, D. Passos, Solar variability induced in a dynamo code by realistic meridional circulation variations. Sol. Phys. 257(1), 1–12 (2009). doi:10.1007/s11207-009-9372-3
I. Lopes, E. Cardoso, H. Silva, Looking for periodicities in the sunspot time series. Astrophys. J. (2014 accepted)
A. McQuillan, S. Aigrain, S. Roberts, Statistics of stellar variability from Kepler. I. Revisiting quarter 1 with an astrophysically robust systematics correction. Astron. Astrophys. 539, 137 (2012). doi:10.1051/0004-6361/201016148
M.S. Miesch, J. Toomre, Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41(1), 317–345 (2009)
P.D. Mininni, D.O. Gómez, Study of stochastic fluctuations in a shell dynamo. Astrophys. J. 573, 454–463 (2002). doi:10.1086/340495
P.D. Mininni, D.O. Gomez, G.B. Mindlin, Stochastic relaxation oscillator model for the solar cycle. Phys. Rev. Lett. 85, 5476–5479 (2000). doi:10.1103/PhysRevLett.85.5476, http://adsabs.harvard.edu/abs/2000PhRvL..85.5476M
P.D. Mininni, D.O. Gomez, G.B. Mindlin, Simple model of a stochastically excited solar dynamo. Sol. Phys. 201, 203–223 (2001). doi:10.1023/A:1017515709106
H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978), 353 pp.
D. Moss, J. Brooke, Towards a model for the solar dynamo. Mon. Not. R. Astron. Soc. 315, 521–533 (2000). doi:10.1046/j.1365-8711.2000.03452.x
M. Nagy, K. Petrovay, Oscillator models of the solar cycle and the Waldmeier effect. Astron. Nachr. 334, 964 (2013). doi:10.1002/asna.201211971
D. Nandy, A. Muñoz-Jaramillo, P.C.H. Martens, The unusual minimum of sunspot cycle 23 caused by meridional plasma flow variations. Nature 471, 80–82 (2011). doi:10.1038/nature09786
B. Owens, Long-term research: slow science. Nature 495, 300 (2013)
E.N. Parker, The formation of sunspots from the solar toroidal field. Astrophys. J. 121, 491 (1955)
D. Passos, Modelling solar variability. PhD Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa (2010)
D. Passos, Evolution of solar parameters since 1750 based on a truncated dynamo model. Astrophys. J. 744(2), 172 (2012)
D. Passos, P. Charbonneau, Characteristics of magnetic solar-like cycles in a 3D MHD simulation of solar convection. Astron. Astrophys. (2014)
D. Passos, I. Lopes, Phase space analysis: the equilibrium of the solar magnetic cycle. Sol. Phys. 250(2), 403–410 (2008a)
D. Passos, I. Lopes, A low-order solar dynamo model: inferred meridional circulation variations since 1750. Astrophys. J. 686(2), 1420–1425 (2008b)
D. Passos, I. Lopes, Grand minima under the light of a low order dynamo model. J. Atmos. Sol.-Terr. Phys. 73(2), 191–197 (2011)
D. Passos, P. Charbonneau, P. Beaudoin, An exploration of non-kinematic effects in flux transport dynamos. Sol. Phys. 279(1), 1–22 (2012)
D. Passos, D. Nandy, S. Hazra, I. Lopes, A solar dynamo model driven by mean-field alpha and Babcock-Leighton sources: fluctuations, grand-minima-maxima, and hemispheric asymmetry in sunspot cycles. Astron. Astrophys. 563, 18 (2014). doi:10.1051/0004-6361/201322635
J.M. Polygiannakis, X. Moussas, A non-linear model for the solar cycle. Astrophys. Lett. Commun. 34, 35 (1996)
A. Pontieri, F. Lepreti, L. Sorriso-Valvo, A. Vecchio, V. Carbone, A simple model for the solar cycle. Sol. Phys. 213(1), 195–201 (2003)
M. Rempel, Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: saturation mechanism and torsional oscillations. Astrophys. J. 647, 662–675 (2006). doi:10.1086/505170
A. A. Ruzmaikin, The solar cycle as a strange attractor. Comments Astrophys. 9, 85–93 (1981).
E.A. Spiegel, Chaos and intermittency in the solar cycle. Space Sci. Rev. 144, 25–51 (2009). doi:10.1007/s11214-008-9470-9
M. Steenbeck F. Krause, Erklärung stellarer und planetarer Magnetfelder durch einen turbulenzbedingten Dynamomechanismus Z. Naturforsch. Teil A 21, 1285 (1966)
S.M. Tobias, Diffusivity quenching as a mechanism for Parker’s surface dynamo. Astrophys. J. 467, 870 (1996). doi:10.1086/177661
S.M. Tobias, N.O. Weiss, V. Kirk, Chaotically modulated stellar dynamos. Mon. Not. R. Astron. Soc. 273(4), 1150–1166 (1995)
A. Vecchio, V. Carbone, A simple model to describe solar cycle periodicities below 11 years. Sol. Phys. 249, 11–16 (2008). doi:10.1007/s11207-008-9180-1
M. Waldmeier, Neue Eigenschaften der Sonnenfleckenkurve. Astron. Mitt. Zür. 14(133), 105–130 (1935)
N.O. Weiss, Modulation of the sunspot cycle. Astron. Geophys. 51, 9–15 (2010). doi:10.1111/j.1468-4004.2010.51309.x
N.O. Weiss, C.A. Cattaneo, F. Jones, Periodic and aperiodic dynamo waves. Geophys. Astrophys. Fluid Dyn. 30, 305–341 (1984). doi:10.1080/03091928408219262
A.L. Wilmot-Smith, P.C.H. Martens, D. Nandy, E.R. Priest, S.M. Tobias, Low-order stellar dynamo models. Mon. Not. R. Astron. Soc. 363, 1167–1172 (2005). doi:10.1111/j.1365-2966.2005.09514.x
A.L. Wilmot-Smith, D. Nandy, G. Hornig, P.C.H. Martens, A time delay model for solar and stellar dynamos. Astrophys. J. 652, 696 (2006). doi:10.1086/508013, http://iopscience.iop.org/0004-637X/652/1/696/
R. Wolf, W. Brunner, Neue Eigenschaften der Sonnenfleckenkurve. Astron. Mitt. Eidgenöss. Sternwarte Zür. 14, 105–136 (1935)
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Lopes, I., Passos, D., Nagy, M., Petrovay, K. (2015). Oscillator Models of the Solar Cycle. In: Balogh, A., Hudson, H., Petrovay, K., von Steiger, R. (eds) The Solar Activity Cycle. Space Sciences Series of ISSI, vol 53. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2584-1_19
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