Abstract
In this review, we explain recent progress made in the Babcock–Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are two-dimensional (2D) axisymmetric and the mean-field dynamo equations are solved in the meridional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock–Leighton mechanism) involved in these models are inherently three-dimensional (3D) processes and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., mean-field Babcock–Leighton dynamo models and surface flux transport models), we describe recently developed next-generation 3D dynamo models that implement a more sophisticated flux emergence algorithm of buoyant flux tube rise through the convection zone and capture the Babcock–Leighton process more realistically than previous 2D models. The detailed results from these 3D dynamo models including surface flux transport counterparts are presented. We explain the cycle irregularities that are reproduced in 3D dynamo models by introducing scattering around the tilt angle only. Some results by assimilating observed photospheric convective velocity fields into the 3D models are also discussed, pointing out the wide opportunity that these 3D models hold to deliver.
Similar content being viewed by others
References
Antia H. M., Basu S., Chitre S. M. 1998, Mon. Not. R. Astron. Soc., 298, 543, https://doi.org/10.1046/j.1365-8711.1998.01635.x
Antia H. M., Basu S. 2000, Astrophys. J., 541, 442, https://doi.org/10.1086/309421
Antia H. M., Basu S., Chitre S. M., 2008, Astrophys. J., 681, 680, https://doi.org/10.1086/588523
Babcock H. W. 1961, Astrophys. J., 133, 572, https://doi.org/10.1086/147060
Baumann I., Schmitt D., Schüssler M., Solanki S. K. 2004, Astron. Astrophys., 426, 1075, https://doi.org/10.1051/0004-6361:20048024
Baumann I., Schmitt D., Schüssler M. 2006, Astron. Astrophys., 446, 307, https://doi.org/10.1051/0004-6361:20053488
Berdyugina S. V. 2005, Living Rev. Solar Phys., 2, 8, https://doi.org/10.12942/lrsp-2005-8
Chakraborty S., Choudhuri A. R., Chatterjee P. 2009, Phys. Rev. Lett., 102, 041102, https://doi.org/10.1103/PhysRevLett.102.041102
Charbonneau P., Dikpati M. 2000, Astrophys. J., 543, 1027, https://doi.org/10.1086/317142
Charbonneau P. 2014, Ann. Rev. Astron. Astrophys., 52, 251, https://doi.org/10.1146/annurev-astro-081913-040012
Chatterjee P., Nandy D., Choudhuri A. R., 2004, Astron. Astrophys., 427, 1019, https://doi.org/10.1051/0004-6361:20041199
Chatterjee P., Choudhuri A. R., 2006, Solar Phys., 239, 29, https://doi.org/10.1007/s11207-006-0201-6
Choudhuri A. R. 1992, Astron. Astrophys., 253, 277
Choudhuri A. R., Schüssler M., Dikpati M. 1995, Astron. Astrophys., 303, L29
Choudhuri A. R. 1998, The Physics of Fluids and Plasmas: An Introduction for Astrophysicists. Cambridge University Press, Cambridge
Choudhuri A. R., Dikpati M. 1999, Solar Phys., 184, 61, https://doi.org/10.1023/A:1005092601436
Choudhuri A. R., Chatterjee P., Jiang J. 2007, Phys. Rev. Lett., 98, 131103, https://doi.org/10.1103/PhysRevLett.98.131103
Choudhuri A. R., Karak B. B. 2009, Res. Astron. Astrophys., 9, 953, https://doi.org/10.1088/1674-4527/9/9/001
Choudhuri A. R., Hazra G. 2016, Adv. Space Res. 58, 1560, https://doi.org/10.1016/j.asr.2016.03.015
Dasi-Espuig M., Solanki S. K., Krivova N. A., Cameron R., Peñuela T. 2010, Astron. Astrophys., 518, A7, https://doi.org/10.1051/0004-6361/201014301
Dikpati M., Choudhuri A. R. 1994, Astron. Astrophys., 291, 975
Dikpati M., Choudhuri A. R. 1995, Solar Phys., 161, 9, https://doi.org/10.1007/BF00732081
Dikpati M., Charbonneau P. 1999, Astrophys. J., 518, 508, https://doi.org/10.1086/307269
Dikpati M., Gilman P. A. 2005, Astrophys. J. Lett., 635, L193, https://doi.org/10.1086/499626
Dikpati M., McIntosh S. W., Bothun G., et al. 2018, Astrophys. J., 853, 144, https://doi.org/10.3847/1538-4357/aaa70d
Dikpati M., McIntosh S. W. 2020, Space Weather, 18, e02109, https://doi.org/10.1029/2019SW002109
D’Silva S., Choudhuri A. R. 1993, Astron. Astrophys., 272, 621
Durney B. R. 1995, Solar Phys., 160, 213, https://doi.org/10.1007/BF00732805
Durney B. R. 1997, Astrophys. J., 486, 1065
Gizon L., Cameron R. H., Pourabdian M., et al. 2020, Science, 368, 1469, https://doi.org/10.1126/science.aaz7119
Gopalswamy N., Yashiro S., Krucker S., Stenborg G., Howard R. A. 2004, J. Geophys. Res. (Space Phys.), 109, A12105, https://doi.org/10.1029/2004JA010602
Hale G. E., 1909 Pub. Astron. Soc. Pac., 21, 205, https://doi.org/10.1086/121926
Hale G. E., Ellerman F., Nicholson S. B., Joy A. H. 1919, Astrophys. J., 49, 153, https://doi.org/10.1086/142452
Hathaway D. H. 2012a, Astrophys. J. Lett., 749, L13, https://doi.org/10.1088/2041-8205/749/1/L13
Hathaway D. H. 2012b, Astrophys. J., 760, 84, https://doi.org/10.1088/0004-637X/760/1/84
Hazra G., Karak B. B., Choudhuri A. R. 2014, Astrophys. J., 782, 93, https://doi.org/10.1088/0004-637X/782/2/93
Hazra G., Karak B. B., Banerjee D., Choudhuri A. R. 2015, Solar Phys., 290, 1851, https://doi.org/10.1007/s11207-015-0718-8
Hazra G., Choudhuri A. R., Miesch M. S. 2017, Astrophys. J., 835, 39, https://doi.org/10.3847/1538-4357/835/1/39.
Hazra G., Miesch M. S., 2018, Astrophys. J., 864, 110, https://doi.org/10.3847/1538-4357/aad556
Hazra G., Choudhuri A. R. 2019, Astrophys. J., 880, 113, https://doi.org/10.3847/1538-4357/ab2718
Hazra G., Jiang J, Karak B. B., Kitchatinov L. 2019, Astrophys. J., 884, 35, https://doi.org/10.3847/1538-4357/ab4128
Hazra G., Vidotto A. A., D’Angelo C. V. 2020, Mon. Not. R. Astron. Soc., 496, 4017, https://doi.org/10.1093/mnras/staa1815
Howard R. F. 1991, Solar Phys., 136, 251, https://doi.org/10.1007/BF00146534
Jiang J., Chatterjee P., Choudhuri A. R. 2007, Mon. Not. R. Astron. Soc., 381, 1527, https://doi.org/10.1111/j.1365-2966.2007.12267.x
Jiang J., Cameron R. H., Schüssler M. 2014a, Astrophys. J., 791, 5, https://doi.org/10.1088/0004-637X/791/1/5
Jiang J., Hathaway D. H., Cameron R. H., Solanki S. K., Gizon L., Upton L. 2014b, Space Sci. Rev., 186, 491, https://doi.org/10.1007/s11214-014-0083-1
Jiang J., Cameron R. H., Schüssler M. 2015, Astrophys. J. Lett., 808, L28, https://doi.org/10.1088/2041-8205/808/1/L28
Karak B. B., Choudhuri A. R. 2011, Mon. Not. R. Astron. Soc., 410, 1503, https://doi.org/10.1111/j.1365-2966.2010.17531.x
Karak B. B., Choudhuri A. R. 2013, Res. Astron. Astrophys., 13, 1339, https://doi.org/10.1088/1674-4527/13/11/005
Karak B. B., Kitchatinov L. L., Choudhuri A. R., 2014a, Astrophys. J., 791, 59, https://doi.org/10.1088/0004-637X/791/1/59
Karak B. B., Rheinhardt M., Brandenburg A., Käpylä P. J., Käpylä M. J. 2014b, Astrophys. J., 795, 16, https://doi.org/10.1088/0004-637X/795/1/16
Karak B. B., Cameron R. 2016, Astrophys. J., 832, 94, https://doi.org/10.3847/0004-637X/832/1/94
Karak B. B., Miesch M. 2017, Astrophys. J., 847, 69, https://doi.org/10.3847/1538-4357/aa8636
Karak B. B., Miesch M. 2018, Astrophys. J. Lett., 860, L26, https://doi.org/10.3847/2041-8213/aaca97
Kitchatinov L. L., Pipin V. V., Ruediger G. 1994, Astron. Nachrichten, 315, 157, https://doi.org/10.1002/asna.2103150205
Kitchatinov L. L., Olemskoy S. V. 2011, Astron. Lett., 37, 656, https://doi.org/10.1134/S0320010811080031
Kumar R., Jouve L., Nandy D. 2019, Astron. Astrophys., 623, A54, https://doi.org/10.1051/0004-6361/201834705
Leighton R. B. 1969, Astrophys. J., 156, 1, https://doi.org/10.1086/149943
Lemerle A., Charbonneau P., 2017, Astrophys. J., 834, 133, https://doi.org/10.3847/1538-4357/834/2/133
Longcope D., Choudhuri A. R. 2002, Solar Phys., 205, 63, https://doi.org/10.1023/A:1013896013842
Mandal S., Chatterjee S., Banerjee D. 2017, Astrophys. J., 835, 62, https://doi.org/10.3847/1538-4357/835/1/62
Manoharan P. K., Gopalswamy N., Yashiro S., et al. 2004, J. Geophys. Res. (Space Phys.), 109, A06109, https://doi.org/10.1029/2003JA010300
McIntosh S. W., Leamon R. J., Krista L. D., et al. 2015, Nat. Commun., 6, 6491, https://doi.org/10.1038/ncomms7491
Miesch M. S., Dikpati M. 2014, Astrophys. J. Lett., 785, L8, https://doi.org/10.1088/2041-8205/785/1/L8
Miesch, M. S., Teweldebirhan K. 2016. Adv. Space Res., 58, 1571
Muñoz-Jaramillo A., Nandy D., Martens P. C. H., Yeates A. R. 2010, Astrophys. J. Lett., 720, L20, https://doi.org/10.1088/2041-8205/720/1/L20
Muñoz-Jaramillo A., Dasi-Espuig M., Balmaceda L. A., DeLuca E. E. 2013, Astrophys. J. Lett., 767, L25, https://doi.org/10.1088/2041-8205/767/2/L25
Nagy M., Lemerle A., Labonville F., Petrovay K., Charbonneau P. 2017, Solar Phys., 292, 167, https://doi.org/10.1007/s11207-017-1194-0
Parker E. N. 1955, Astrophys. J., 122, 293, https://doi.org/10.1086/146087.
Passos D., Charbonneau P., Miesch M. 2015, Astrophys. J. Lett., 800, L18, https://doi.org/10.1088/2041-8205/800/1/L18
Priyal M., Banerjee D., Karak B. B., et al. 2014, Astrophys. J. Lett., 793, L4, https://doi.org/10.1088/2041-8205/793/1/L4
Rempel M. 2005, Astrophys. J., 622, 1320, https://doi.org/10.1086/428282
Robbrecht E., Berghmans D., Van der Linden R. A. M. 2009, Astrophys. J., 691, 1222, https://doi.org/10.1088/0004-637X/691/2/1222
Schou J., Antia H. M., Basu S., et al. 1998, Astrophys. J., 505, 390, https://doi.org/10.1086/306146
Stenflo J. O., Kosovichev A. G. 2012, Astrophys. J., 745, 129, https://doi.org/10.1088/0004-637X/745/2/129
Svalgaard L., Cliver E. W., Kamide Y. 2005, Geophys. Res. Lett., 32, L01104, https://doi.org/10.1029/2004GL021664
Thompson M. J., Toomre J., Anderson E. R., et al. 1996, Science, 272, 1300, https://doi.org/10.1126/science.272.5266.1300
Tokumaru M., Kojima M., Fujiki K. 2010, J. Geophys. Res. (Space Phys.), 115, A04102, https://doi.org/10.1029/2009JA014628
Usoskin I. G., Berdyugina S. V., Poutanen J. 2005, Astron. Astrophys., 441, 347, https://doi.org/10.1051/0004-6361:20053201
Wang Y.-M., Nash A. G., Sheeley Jr. N. R. 1989a, Science, 245, 712, https://doi.org/10.1126/science.245.4919.712
Wang Y. M., Nash Jr. A. G., Sheeley, N. R. 1989b, Astrophys. J., 347, 529, https://doi.org/10.1086/168143
Wang Y. M., Robbrecht Jr. E., Sheeley, N. R. 2009, Astrophys. J., 707, 1372, https://doi.org/10.1088/0004-637X/707/2/1372
Wang Y.-M., Colaninno R. C., Baranyi T., Li J. 2015, Astrophys. J., 798, 50, https://doi.org/10.1088/0004-637X/798/1/50
Weber M. A., Fan Y., Miesch M. S., 2011, Astrophys. J., 741, 11, https://doi.org/10.1088/0004-637X/741/1/11
Whitbread T., Yeates A. R., Muñoz-Jaramillo A. 2019, Astron. Astrophys., 627, A168, https://doi.org/10.1051/0004-6361/201935986.
Winter L. M., Pernak R. L., Balasubramaniam K. S. 2016, Solar Phys., 291, 3011, https://doi.org/10.1007/s11207-016-0901-6
Wu C. J., Krivova N. A., Solanki S. K., Usoskin I. G. 2018, Astron. Astrophys., 620, A120, https://doi.org/10.1051/0004-6361/201832956
Yashiro S., Gopalswamy N., Michalek G., et al. 2004, J. Geophys. Res. (Space Phys.), 109, A07105, https://doi.org/10.1029/2003JA010282
Yeates A. R., Muñoz-Jaramillo A. 2013, Mon. Not. R. Astron. Soc., 436, 3366, https://doi.org/10.1093/mnras/stt1818
Yoshimura H. 1975, Astrophys. J., 201, 740, https://doi.org/10.1086/153940
Acknowledgements
The author thanks an anonymous referee for her/his insightful comments which helped to improve the manuscript. The author also would like to thank Prof. Arnab Rai Choudhuri for thoroughly going through the manuscript and giving many useful suggestions that help a lot to improve the review. The author also acknowledges the funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 817540, ASTROFLOW).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hazra, G. Recent advances in the 3D kinematic Babcock–Leighton solar dynamo modeling. J Astrophys Astron 42, 22 (2021). https://doi.org/10.1007/s12036-021-09738-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12036-021-09738-y