[Paper Review] Long-term Variability in the Length of the Solar Cycle

Michael L. Rogers, Mercedes T. Richards+1 more|arXiv (Cornell University)|Jun 17, 2006

Solar and Space Plasma Dynamics4 citations

TL;DR

This study investigates long-term variability in the length of the solar cycle using sunspot number and area data from 1700–2005 and reconstructed data back to 1610. Employing power spectrum and phase dispersion minimization analyses, it identifies a dominant 188 ± 38-year cycle in cycle length that correlates with historical minima, suggesting a secular modulation of the 11-year Schwabe cycle linked to solar activity levels.

ABSTRACT

Detailed models of the solar cycle require information about the starting time and rise time as well as the shape and amplitude of the cycle. However, none of these models includes a discussion of the variations in the length of the cycle, which has been known to vary from $\sim$7 to 17 years. The focus of our study was to investigate whether this range was associated with a secular pattern in the length of the sunspot cycle. To provide a basis for the analysis of the long-term behavior of the Sun, we analyzed archival data of sunspot numbers from 1700 - 2005 and sunspot areas from 1874 - 2005. The independent techniques of power spectrum analysis and phase dispersion minimization were used to confirm the $\sim$11-year Schwabe Cycle, and to illustrate the large range in the length of this cycle. Long-term cycles were identified in archival data from 1610 -- 2000 using median trace analyses of the length of the cycle, and from power spectrum analyses of the (O-C) residuals of the dates of sunspot minima and maxima. The median trace analysis suggested that the cycle length had a period of 183 - 243 years, while the more precise power spectrum analysis identified a period of 188 $\pm$ 38 years. We found that the 188-year cycle was consistent with the variation of sunspot numbers and seems to be related to the Schwabe Cycle. We found a correlation between the times of historic minima and the length of the sunspot cycle such that the length of the cycle was usually highest when the actual number of sunspots was lowest. The cycle length was growing during the Maunder Minimum when there were almost no sunspots visible on the Sun. This information can now be used to improve the accuracy of the current solar cycle models, to better predict the starting time of a given cycle.

Motivation & Objective

• To investigate long-term variability in the length of the solar cycle, which ranges from 7 to 17 years.
• To determine whether this variability exhibits a secular pattern over centuries.
• To link variations in cycle length to historical epochs of low solar activity, such as the Maunder Minimum.
• To improve solar cycle models by incorporating long-term cycle length modulation.
• To validate the existence of a 188-year cycle in cycle length using independent statistical techniques.

Proposed method

• Analyzed archival sunspot number data (1700–2005) and sunspot area data (1874–2005) using power spectrum analysis and phase dispersion minimization (PDM).
• Applied median trace analysis to the length of the sunspot cycle to detect long-term cycles in cycle duration.
• Performed power spectrum analysis on the (O-C) residuals of sunspot minima and maxima dates to identify periodicities.
• Compared derived cycles with historical solar minima (Oort, Wolf, Spörer, Maunder, Dalton) using reconstructed sunspot data from 1610–2000.
• Used reconstructed sunspot numbers based on radiocarbon concentrations from tree rings (Solanki et al., 2004) to extend data coverage.
• Evaluated model fits using phase alignment and amplitude consistency across different data sets and cycle periods.

Experimental results

Research questions

• RQ1 Is there a long-term secular cycle in the length of the solar cycle, and if so, what is its period?
• RQ2 How does the length of the sunspot cycle correlate with the amplitude of solar activity, particularly during historical minima?
• RQ3 Can the 188-year cycle in cycle length be independently confirmed using multiple statistical techniques?
• RQ4 Is the 188-year cycle related to the fundamental 11-year Schwabe cycle, and how does it modulate solar activity?
• RQ5 Can this cycle be used to improve predictions of solar cycle onset and amplitude?

Key findings

• A dominant long-term cycle of 188 ± 38 years was identified in the (O-C) residuals of sunspot minima and maxima dates using power spectrum analysis.
• The 188-year cycle is consistent with historical solar minima, with all four major minima (Wolf, Spörer, Maunder, Dalton) occurring during the rising phase of the cycle.
• Cycle length was found to be highest during periods of low sunspot activity, particularly during the Maunder Minimum, when cycle length increased despite near-zero sunspot counts.
• The 188-year cycle correlates strongly with the Schwabe cycle, suggesting a fundamental modulation of the 11-year cycle by a longer-term dynamical process.
• Median trace analysis identified additional cycles of 183–243 years, but the 188-year cycle from power spectrum analysis showed superior phase alignment and consistency with observed data.
• The model predicts a continued increase in cycle length over the next ~75 years, accompanied by a decline in sunspot numbers, supporting improved long-term solar cycle forecasting.