Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 91312 10.12737/stp-112202504 Results of current research Results of current research Results of current research Hysteresis cycles and invariance of the Dst index form during geomagnetic storm development Hysteresis cycles and invariance of the Dst index form during geomagnetic storm development Куражковская Надежда Андреевна Kurazhkovskaya Nadezhda Andreevna knady@borok.yar.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Клайн Борис Ицикович Klain Boris Icikovich klain@borok.yar.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 Зотов Олег Дмитриевич Zotov Oleg Dmitrievich ozotov@inbox.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Куражковский Александр Юрьевич Kurazhkovskii Alexander Yur'evich ksasha@borok.yar.ru Геофизическая обсерватория «Борок» ИФЗ РАН Борок Россия Borok Geophysical Observatory of IPE RAS Borok Russian Federation Геофизическая обсерватория «Борок» ИФЗ РАН Борок Россия Borok Geophysical Observatory of IPE RAS Borok Russian Federation Геофизическая обсерватория «Борок» ИФЗ РАН Борок Россия Borok Geophysical Observatory of IPE RAS Borok Russian Federation Геофизическая обсерватория “Борок” – филиал Института физики Земли им. О.Ю. Шмидта РАН (ГО “Борок” ИФЗ РАН) Борок Россия Borok Geophysical Observatory, the Branch of Schmidt Institute of Physics of the Earth, Russian Academy of Sciences Borok Russian Federation 26 06 2025 26 06 2025 11 2 39 47 02 12 2024 23 01 2025 https://zh-szf.ru/en/nauka/article/91312/view

We have studied the relationship between the Dst index and heliospheric parameters during 933 isolated geomagnetic storms observed over the period from 1964 to 2010. The storms were classified by their onset type (sudden or gradual) and intensity (weak, moderate, and strong). We have analyzed the Dst index, solar wind, and interplanetary magnetic field (IMF) data accumulated using the epoch superposition method. It is shown that over the time interval of development of varying intensity storms with sudden and gradual onset the trajectory of Dst change depending on heliospheric parameters during the main phase of the storms does not coincide with its trajectory during the recovery phase, which is typical of the hysteresis phenomenon. During the storms, Dst forms hysteresis cycles with all analyzed solar wind and IMF parameters. The obtained dependences Dst(B), Dst(Bz), Dst(Ey), Dst(V), Dst(Pdyn), and Dst() have the shape of a hysteresis loop during the excitation of weak, moderate, and strong storms. The shape and area of hysteresis loops was found to change depending on heliospheric parameters and storm intensity. It is shown that the shape of the average Dst dynamics during the storms does not depend on their intensity, i.e. it is invariant. Invariant behavior is also characteristic of the shape of the average dynamics of heliospheric parameters during the magnetic storms of different intensities. Based on the nonlinear relationship of the Dst index with interplanetary parameters and the invariance of the shape of its dynamics, an integral equation of the Volterra type is proposed to describe the Dst dependence on solar wind and IMF parameters. The proposed model is suitable for interpreting the results obtained from the experimental study of hysteresis effects associated with phase shifts between changes in Dst and heliospheric parameters.

We have studied the relationship between the Dst index and heliospheric parameters during 933 isolated geomagnetic storms observed over the period from 1964 to 2010. The storms were classified by their onset type (sudden or gradual) and intensity (weak, moderate, and strong). We have analyzed the Dst index, solar wind, and interplanetary magnetic field (IMF) data accumulated using the epoch superposition method. It is shown that over the time interval of development of varying intensity storms with sudden and gradual onset the trajectory of Dst change depending on heliospheric parameters during the main phase of the storms does not coincide with its trajectory during the recovery phase, which is typical of the hysteresis phenomenon. During the storms, Dst forms hysteresis cycles with all analyzed solar wind and IMF parameters. The obtained dependences Dst(B), Dst(Bz), Dst(Ey), Dst(V), Dst(Pdyn), and Dst() have the shape of a hysteresis loop during the excitation of weak, moderate, and strong storms. The shape and area of hysteresis loops was found to change depending on heliospheric parameters and storm intensity. It is shown that the shape of the average Dst dynamics during the storms does not depend on their intensity, i.e. it is invariant. Invariant behavior is also characteristic of the shape of the average dynamics of heliospheric parameters during the magnetic storms of different intensities. Based on the nonlinear relationship of the Dst index with interplanetary parameters and the invariance of the shape of its dynamics, an integral equation of the Volterra type is proposed to describe the Dst dependence on solar wind and IMF parameters. The proposed model is suitable for interpreting the results obtained from the experimental study of hysteresis effects associated with phase shifts between changes in Dst and heliospheric parameters.

 geomagnetic storms solar wind heliospheric parameters Dst index hysteresis invariance geomagnetic storms solar wind heliospheric parameters Dst index hysteresis invariance The work was performed under government assignment of Borok Geophysical Observatory of IPE RAS The work was performed under government assignment of Borok Geophysical Observatory of IPE RAS

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