Solar-Terrestrial Physics Solar-Terrestrial Physics Солнечно-земная физика 2712-9640 122578 10.12737/szf-122202601 ilwjso Результаты исследований Results of current research Результаты исследований Waldmeier law for sunspot cycles: Statistical significance and implications for dynamo Правило Вальдмайера для солнечных циклов: статистическая достоверность и значение для динамо Кичатинов Леонид Леонидович Kitchatinov Leonid Leonidovich kit@iszf.irk.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar-Terrestrial Physics SB RAS Irkutsk Russian Federation 12 2 5 9 25 02 2026 06 04 2026 https://naukaru.ru/en/nauka/article/122578/view

Правило Вальдмайера для соотношения длительности фазы роста и амплитуды солнечных циклов является индикатором степени нелинейности механизма динамо. В работе проведено сравнение параметров правила Вальдмайера для чисел и площадей солнечных пятен в циклах активности с 12 по 25. Неоднозначность в датах минимумов и максимумов циклов устранена сглаживанием гауссовым фильтром. Показано, что соотношения чисел и площадей пятен существенно отличаются для фаз роста и спада активности. При этом высокая корреляция для правила Вальдмайера в числах пятен является артефактом определения чисел Вольфа и не означает высокой степени нелинейности механизма динамо. Относительно низкая корреляция и уровень достоверности ~70 % для правила Вальдмайера, определяемого по площадям пятен, указывает на слабую нелинейность в солнечном динамо и согласуется со свидетельcтвами, следующими из наблюдений вращения звезд.

Waldmeier law for the relation between the rise phase duration and amplitude of solar cycles is an indicator for strength of nonlinearity in the solar dynamo. The paper compares the Waldmeier law parameters for sunspot number and area in solar cycles 12–25. Uncertainty in dates of cycles’ maxima and minima is fixed by smoothing with the Gaussian filter. The ratio of sunspot number to area is shown to differ significantly between rise and decline phases of solar activity. The high correlation for Waldmeier law in sunspot number is an artifact of the Wolf number definition and does not imply any strong nonlinearity in the dynamo mechanism. The relative low correlation and significance level of about 70 % in Waldmeier law for sunspot area indicates a weak nonlinearity in the solar dynamo and agrees with evidences from observations of stellar rotation.

 cолнечная активность числа пятен площадь пятен динамо нелинейность solar activity sunspot number sunspot area dynamo nonlinearity Работа выполнена при финансовой поддержке Минобрнауки России This work is financially supported by the Ministry of Science and High Education of the Russian Federation

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