The aim of this work is to diagnose pre-flare dynamics of magnetic fields in the active regions of the Sun on the HMI SDO magnetograms. We use a tool based on the methods of the geometry of random fields and computational topology. The results show that the proposed formalism allows one to find some precursors of major flares for practically significant time slots.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
R. J. Adler, The Geometry of Random Fields, Wiley, New York (1981).
R. J. Adler and J. E. Taylor, Random Fields and Geometry, Springer Monogr. Math., Springer, New York (2007).
O. Bobrowski, Algebraic Topology of Random Fields and Complexes, PhD Thesis (2012).
J. M. Borrero and K. Ichimoto, “Magnetic structure of sunspots,” Living Rev. Sol. Phys., 8, 4 (2011).
Y. Cui, R. Li, L. Zhang, Y. He, and H. Wang, “Correlation between solar flare productivity and photospheric magnetic field properties,” Sol. Phys., 237, 45–59 (2006).
H. Edelsbrunner and J. Harer, Computational Topology. An Introduction, Amer. Math. Soc., Providence (2010).
D. A. Falconer, A. F. Barghouty, I. Khazanov, and R. L. Moore, “A tool for empirical forecasting of major flares, coronal mass ejections, and solar particle events from a proxy of active region free magnetic energy,” Space Weather, 9, S04003 (2011).
R. Ghrist, “Barcodes: The persistent topology of data,” Bull. Am. Math. Soc., 45, No. 1, 61–75 (2008).
S. Gu, Y. Zheng, and C. Tomasi, “Critical nets and beta-stable features for image matching,” in: Computer Vision — ECCV 2010, Lect. Notes Comput. Sci., Vol. 6313, Springer, Berlin (2010), pp. 663–676.
B. M. ter Haar Romeny, Front-End Vision and Multi-Scale Image Analysis, Springer, Berlin (2003).
L. M. Karimova, O. A. Kruglun, N. G. Makarenko, and N. V. Romanova, “Power law distribution in statistics of failures in operation of spacecraft onboard equipment,” Cosm. Res., 49, 458–463 (2011).
I. S. Knyazeva, N. G. Makarenko, and L. M. Karimova, “Topology of magnetic fields from MDI data: Background field,” Astron. Rep., 54, 747–755 (2010).
I. S. Knyazeva, N. G. Makarenko, and M. A. Livshits, “Detection of new emerging magnetic flux from the topology of SOHO/MDI magnetograms,” Astron. Rep., 55, 463–471 (2011).
J. Koenderink, “The structure of images,” Biol. Cybern., 50, 363–370 (1984).
T. Lindeberg, Scale-Space Theory in Computer Vision, Kluwer Academic, Dordrecht (1994).
B. W. Lites, “The topology and behavior of magnetic fields emerging at the solar photosphere,” Space Sci. Rev., 144, 197–212 (2009).
D. W. Longcope, “Topological methods for the analysis of solar magnetic fields,” Living Rev. Sol. Phys., 2, 7 (2005).
T. Magara, “Investigation into the subsurface magnetic structure in an emerging flux region on the Sun based on a comparison between Hinode’s observations and numerical simulation,” Astrophys. J., 685, L91 (2008).
N. G. Makarenko, I. S. Knyazeva, and L. M. Karimova, “Magnetic field topology by MDI data: Active region,” Astron. Lett., 38, 531–542 (2012).
J. P. Mason and J. T. Hoeksema, “Testing automated solar flare forecasting with 13 years of MDI synoptic magnetograms,” Astrophys. J., 723, 634–640 (2010).
Y. Matsumoto, An Introduction to Morse Theory, Amer. Math. Soc., Providence (2002).
T. Pulkkinen, “Space weather: terrestrial perspective,” Living Rev. Sol. Phys., 4, 1 (2007).
P. H. Scherrer, J. Schou, R. I. Bush, et al., “The Helioseismic and Magnetic Imager (HMI). Investigation for the Solar Dynamics Observatory (SDO),” Sol. Phys., 275, 207–227 (2012).
R. Schneider, Convex Bodies: The Brunn–Minkowski Theory, Cambridge Univ. Press, Cambridge (1993).
J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London (1988).
J. B. Smith, Jr., “Predicting activity levels for specific locations within solar active regions,” in: P. S. McIntosh and M. Dryer, eds., Solar Activity Observations and Predictions, MIT, Cambridge (1972).
X. Sun, J. T. Hoeksema, Y. Liu, T. Wiegelmann, K Hayashi, Q. Chen, and J. Thalmann, “Evolution of magnetic field and energy in a major eruptive active region based on SDO/HMI observation,” Astrophys. J., 74, No. 2, 1–15 (2012).
J. Weickert, Anisotropic Diffusion in Image Processing, Teubner, Stuttgart (1998).
A. P. Witkin, “Scale space filtering,” in: Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, Germany (1983 ), pp. 1019–1022.
K. J. Worsley, “The geometry of random images,” Chance, 9, 27 (1996).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 79–93, 2013.
About this article
Cite this article
Makarenko, N., Malkova, D., Machin, M. et al. Methods of Computational Topology for the Analysis of Dynamics of Active Regions of the Sun. J Math Sci 203, 806–815 (2014). https://doi.org/10.1007/s10958-014-2170-y
- Active Region
- Euler Characteristic
- Betti Number
- Solar Disk
- Mathematical Morphology