The sub- and quasi- centurial cycles in solar and geomagnetical data series /(s2)

The subject of this paper is the existence and stability of solar cycles with duration in the range of 20-250 years. Five type of data series are used: 1) The Zurich series (1749-2009), the mean annual International sunspot number Ri; 2) The Group sunspot number series Rh (1610-1995); 3) The simulated extended sunspot Rsi number from Extended time series of Solar Activity Indices (ESAI) (1090- 2002); 4) The simulated extended geomagnetic aa-index from ESAI (1099-2002); 5) The Meudon filament series (1919-1991) (it is used only particularly). Data series are smoothed over 11 years and supercenturial trends are removed. Two principally independent methods of time series analysis are used: the T-R periodogram analysis (both in the standard and “scanning window” regimes) and the wavelet-analysis. The obtained results are very similar. It is found that in all series a strong cycle with mean duration of 55-60 years exists. It is very well expressed in the 18th and the 19th centuries. It is less pronounced during the end of the 19th and the beginning of the 20th centuries. On the other hand a strong and stable quasi 110-120 years and ~200-year cycles are obtained in most of these series. However the 200-yr cycle is not detectable in the Zurich series. There is a strong mean oscillation of ~ 95 years, which is absent in the other data sets. The analysis of the ESAI (AD 1090-2002) proved that the quasi century cycle has a relatively stable doublet (~80 and ~120 years) or triplet (~55-60, 80 and 120 years) structure during the last ~900 years. Most probably the different type of oscillations in the sub-century and century period range corresponds to cycles of different classes of active regions. The solar-terrestrial relationships aspects of these results are briefly discussed.

💡 Research Summary

The paper investigates whether solar activity exhibits stable cycles in the 20‑ to 250‑year range, using five independent data series that span from the early medieval period to the present. The series are: (1) the International Sunspot Number (Ri) from Zurich (1749‑2009), (2) the Group Sunspot Number (Rh) (1610‑1995), (3) a simulated extended sunspot index (Rsi) from the ESAI project (1090‑2002), (4) a simulated extended geomagnetic aa‑index from ESAI (1099‑2002), and (5) the Meudon filament series (1919‑1991), which is used only for illustrative purposes. All series are first smoothed with an 11‑year moving average to suppress the well‑known 11‑year Schwabe cycle, and then long‑term (centurial) trends are removed by detrending (linear or low‑order polynomial).

Two fundamentally different analytical techniques are applied: the T‑R periodogram (both in a standard, whole‑record mode and in a scanning‑window mode) and continuous wavelet analysis using a Morlet mother wavelet. The T‑R periodogram is particularly robust against uneven sampling and non‑stationarity, while the wavelet transform provides a time‑frequency map that reveals how the strength of each periodic component evolves over centuries. Both methods yield remarkably consistent results, reinforcing the reliability of the findings.

The main periodicities identified are:

1. 55‑60 year cycle – This sub‑centurial oscillation appears strongly in all data sets, especially during the 18th and 19th centuries, where its amplitude reaches a maximum. Its relative weakness in the late 19th and early 20th centuries suggests a modulation of the cycle’s envelope. The authors propose that this period may be linked to the emergence and decay of large‑scale active regions (e.g., giant sunspot groups or flare complexes).

2. 110‑120 year (quasi‑centurial) cycle – A robust and stable feature across the Zurich series, the Group Sunspot Number, the ESAI sunspot reconstruction, and the ESAI aa‑index. This cycle likely reflects a global re‑organisation of the solar magnetic field, possibly associated with the polarity reversal of the large‑scale dipole component.

3. ~200 year cycle – Evident in the ESAI sunspot and aa‑index series, but absent from the Zurich Ri record. The discrepancy may stem from the shorter length and higher noise level of the Zurich series, or from the intrinsic weakness of the 200‑year signal. The authors suggest that this longer period could be tied to deeper dynamo processes operating on millennial timescales.

4. ~95 year oscillation – Detected only in the Zurich series, it does not appear in the other reconstructions, indicating that it may be an artefact of the particular observational record or a transient feature.

A detailed examination of the ESAI data (1090‑2002) reveals that the quasi‑centurial band often splits into a doublet (≈80 yr and ≈120 yr) or, at times, a triplet that includes the 55‑60 yr component. This “doublet‑triplet” behaviour suggests that multiple, possibly interacting, dynamo modes are simultaneously active, each governing a different class of solar magnetic structures.

The concurrent detection of the same periods in the geomagnetic aa‑index demonstrates a clear solar‑terrestrial coupling: variations in solar magnetic output on these timescales modulate the solar wind and interplanetary magnetic field, which in turn drive changes in the Earth’s magnetosphere and ionosphere. The 110‑120 yr cycle, for instance, may correspond to a long‑term modulation of high‑speed solar wind streams and coronal mass ejection occurrence, influencing space‑weather conditions on centurial scales.

In summary, the study provides strong evidence that solar activity possesses multiple, overlapping cycles ranging from about 55 to 200 years. These cycles are not artifacts of a single data set or analysis technique; they persist across independent sunspot and geomagnetic records and are confirmed by both spectral (T‑R periodogram) and time‑frequency (wavelet) analyses. The authors argue that the different periodicities likely correspond to distinct classes of active regions or dynamo modes, and that incorporating these long‑term oscillations into solar‑terrestrial models could improve predictions of climate‑relevant solar forcing and space‑weather hazards. Future work is recommended to link these empirical cycles with physical dynamo simulations and to validate them against high‑resolution cosmogenic isotope records (¹⁴C, ¹⁰Be) for a more comprehensive reconstruction of solar variability over the past millennium.