Scientists have discovered that fluctuations in the magnetic field at the Sun’s poles obey a fundamental law of turbulence, which was first discovered by the Soviet mathematician Andrei Kolmogorov back in 1941. Using 50 years’ worth of direct magnetic field measurements from the Wilcox Observatory (USA) and an advanced data processing method — wavelet analysis — they discovered that the energy of these oscillations is distributed according to a mathematical law with an exponent close to –5/3; in other words, it is distributed between large and small oscillations in accordance with the universal law of turbulence. The authors of the paper believe that this discovery allows for a new way of testing and refining physical models of the Sun’s convective zone — the very region where its magnetic field originates. The article has been published in the journal Monthly Notices of the Royal Astronomical Society. The work was carried out with the support of the Russian Science Foundation (grant No. 21-72-20067).
Solar activity, including the well-known 11-year sunspot cycle, originates in the star’s interior — in its convective zone. This is a region approximately 200,000 kilometres thick, where superheated, turbulent plasma is in constant motion: hot currents rise from the depths to the surface, whilst cooler ones sink back down.
It is precisely this chaotic motion that generates the Sun’s magnetic field, which then manifests itself in the form of sunspots, solar flares and coronal mass ejections. It is impossible to observe the convective zone directly, either with telescopes or probes, as it is opaque to electromagnetic radiation. Therefore, solar turbulence is currently studied only through indirect evidence, primarily through statistics on the appearance of sunspots associated with the toroidal component of the magnetic field (horizontal field lines ‘encircling’ the Sun).
However, scientists from Perm Polytechnic University, the Institute of Mechanics of Continuous Media at the Ural Branch of the Russian Academy of Sciences, and IZMIRAN proposed turning to direct measurements of the magnetic field near the Sun’s poles — a region that had long remained unexplored. To this end, the researchers utilised unique data collected since May 1976 by the oldest operational magnetograph telescope at the Wilcox Observatory (USA). This 50-year-old dataset spans four and a half solar cycles.
Unlike the usual observations of sunspots, the focus here is specifically on the poles. The Sun’s structure is such that it is precisely in this region that the magnetic field bursts through to the surface in the form of vertical rays — this is the so-called poloidal component. It is this component that determines the star’s magnetic poles, which swap places every 11 years, as if resetting the entire solar mechanism.
To analyse the time series (50 years of regular measurements taken at equal intervals), the scientists applied an advanced mathematical method — the wavelet transform. This method allows them, much like analysing musical notation, to separate oscillations of different periods and see how they change over time.
As a result, for the first time in direct observations of the Sun’s magnetic field, scientists have detected a power-law spectrum spanning a range of scales of almost two orders of magnitude. In other words, they have identified a mathematical pattern covering a time span ranging from one month to 6,5 years.
It was precisely during this period that the spectral slope index — a measure of how rapidly oscillations decay as their frequency increases — proved to be close to the famous «-5/3» law, proposed by Academician Andrei Kolmogorov as far back as 1941 to describe developed turbulence.
«The spectral characteristics obtained are not merely confirmation of the universality of Kolmogorov turbulence. Now, any realistic computer model of the solar dynamo must reproduce not only the 11-year cycle, but also a complete spectrum of oscillations with an index close to –5/3,» — explained Rodion Stepanov, project leader of the project supported by an RSF grant, Professor in the Department of Mathematical Modelling of Systems and Processes at PNRPU, leading research fellow at the ICMM UB RAS, and Doctor of Physical and Mathematical Sciences.
Understanding this mechanism is the key to accurately predicting the Sun’s behaviour. This is because the current 25th solar activity cycle, which began in 2019, has turned out to be significantly stronger than predicted by models based on ‘precursors’ derived from polar field values at the solar minimum. In other words, scientists thought that by examining the state of the polar field during a lull (at the solar minimum, when there are almost no sunspots), they could predict what the next cycle would be like — but this method did not work for the current cycle.
«This means that the models need to be refined, including through the use of artificial intelligence. Our results show that the variability of the polar field is particularly valuable for machine learning, as it contains a wide range of fluctuations associated with non-linear processes in the convective zone,» added Rodion Stepanov.
In the future, new space missions will help to verify these findings: the European Solar Orbiter, as well as planned polar observatories, including the Chinese SPO and the Russian «Intergeliosond» project, which will provide even more detailed data on the fine structure of the Sun’s magnetic poles.