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Determining the Statistical Significance of the North–South Asymmetry of Active Regions in Cycles 23 and 24 by Several Methods

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Abstract

To determine the statistical significance of the north–south (N–S) asymmetry of active regions (ARs) of different magneto-morphological classes (MMCs), 3553 ARs that appeared on the solar disk from June 1996 to December 2020 according to the MMC ARs CrAO catalog (http://sun.crao.ru/databases/catalog-mmc-ars) were studied. All ARs, except for unipolar sunspots, were distributed between two classes: the regular bipolar groups (following the Hale’s polarity law, Joy’s law, the leading spot dominance rule) and the irregular ARs (all the rest). The statistical significance of the N–S asymmetry was determined for each class of ARs for each of the two maxima of the 23rd and 24th solar cycles in several ways based on the use of a normal approximation of the binomial distribution and Pearson’s goodness-of-fit \({{\chi }^{2}}\)-test. The obtained simplified expressions can be used for some other astrophysical problems where objects are distributed between two classes. A high level of statistical significance of the observed N–S asymmetry (the probability of the observed deviations randomness is less than the significance level α = 0.01, i.e., 1%) was found for the regular ARs in both maxima of the 24th cycle and for the irregular ARs in the second maximum of each of the studied cycles. The temporal profiles of all AR subsets demonstrate the signs of the double-peak structure of the cycle; the peaks of ARs from different subsets occur sometimes in-phase and sometimes out-of-phase. The most pronounced manifestations of N–S asymmetry are observed for the irregular ARs in the second maximum of the cycle. In this time interval, characterized by the weakening of the global dynamo, the conditions for the manifestation of the turbulent component of the dynamo and distortion of the ARs magnetic tubes are created. The predominance of the irregular ARs in the S-hemisphere may be explained by an additional weakening of the toroidal field due to the interaction of the dipole and quadrupole components of the magnetic field.

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ACKNOWLEDGMENTS

The author is grateful to S.A. Korotin, V.I. Abramenko, A.I. Khlystova, D.D. Sokoloff for valuable comments, and also thanks the Internet resources https://statanaliz.info, https://www.scribbr.com for ideas on illustrating statistical methods.

Funding

This work was done due to funding Research work No. 1021051101548-7-1.3.8.

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  1. Crimean Astrophysical Observatory, Russian Academy of Sciences, Nauchny, Republic of Crimea, Russia

    A. V. Zhukova

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Zhukova, A.V. Determining the Statistical Significance of the North–South Asymmetry of Active Regions in Cycles 23 and 24 by Several Methods. Geomagn. Aeron. 63, 1224–1237 (2023). https://doi.org/10.1134/S0016793223080261

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