Abstract
We have studied solar activity by analyzing naked-eye sunspot observations and aurorae borealis observed at latitudes below \(45^{\circ}\). We focused on the medieval epoch by considering the non-telescopic observations of sunspots from AD 974 to 1278 and aurorae borealis from AD 965 to 1273 that are reported in several Far East historical sources, primarily in China and Korea. After setting selection rules, we analyzed the distribution of these individual events following the months of the Gregorian calendar. In December, an unusual peak is observed with data recorded in both China and Japan, but not within Korean data.
In extreme conditions, where the collection of events is reduced and discontinuous in some temporal intervals, we used the non-parametric kernel method. We opted for the plug-in approach of Sheather and Jones instead of cross-validation techniques to estimate the probability density functions (pdf) of the events. We obtained optimized bandwidths of 13.29 years for sunspots and 9.06 years for auroras, and 95% confidence intervals. The pdf curves exhibit multiple peaks occurring at quasi-periodic times with a very high positive correlation, \(r_{\mathrm{tt}} = 0.9958\), between the dates of occurrence of the nine extrema of sunspots and auroras. Furthermore, these extrema enabled us to evaluate mean periods at two standard deviations, \(66.77 \pm 7.25~\mbox{years}\) for sunspots and \(65.06 \pm 9.36~\mbox{years}\) for auroras. The accuracy of the average periods, 62.00 years for sunspots and 61.80 years for auroras, was improved by the use of the power spectrum method. The percentage of the total number of non-observed sunspots, using redundant data, from AD 1151 to 1275 was estimated to be greater than or equal to 78%.
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Notes
All dates in this article are given in decimal notation.
Start of the campaign in China in AD 1211.
Start of the campaign in Korea in AD 1231.
\(|t ^{(\mathrm{a})}-t^{(\mathrm{s})}|/(1273-974)\).
In fact, due to the rotation of the Sun, an observer on Earth could never continuously observe a sunspot during a period greater than \(\tau_{\mathrm{max}}=1.5\,T_{\mathrm{s}}\approx40~\mbox{days}\), where \(T_{s}\) is the synodic solar rotation period (Nagovitsyn, 2001).
In principle, we have \(\overline{n}_{0}=\widetilde{n}-N\), where \(\widetilde{n}\) would be the number of observed sunspots in days without a cloud cover, measured for example with a telescope attached to a satellite away from the Earth atmosphere; throughout a year, this number is not necessarily constant \(\widetilde{n}=\widetilde{n}(t)\).
As determined with more observations, the mean period of auroras is more significant than that estimated for sunspots. Thus, the relative error used is \(|\overline{T}_{2}-\overline{T}_{1}|/ \overline{T}_{1}\).
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Acknowledgements
The authors would like to thank the anonymous referee for valuable comments. We are grateful to Imad Belabbas for fruitful discussions and pertinent remarks that have substantially improved this article. We thank Célestin Kokonendji for valuable discussions and Nadia Haffaf for useful remarks.
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Bekli, M.R., Zougab, N., Belabbas, A. et al. Non-parametric Data Analysis of Low-latitude Auroras and Naked-eye Sunspots in the Medieval Epoch. Sol Phys 292, 52 (2017). https://doi.org/10.1007/s11207-017-1084-5
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DOI: https://doi.org/10.1007/s11207-017-1084-5