The 27-Day Signal in Sunspot Number Series and the Solar Dynamo

We analyze the Wolf number daily series WN (1849 to present) as well as two other related series characterizing solar activity. Our analysis consists in computing the amplitude of a given Fourier component in a sliding time window and examining its long-term evolution. We start with the well-known 27.03- and 27.6-day periods and observe strong decadal variations of this amplitude as well as a sharp increase of the average value starting around 1905. We then consider a packet of 31 lines with periods from 25.743 to 28.453 days, which is shown to be a better representation of the synodic solar rotation. We first examine the temporal evolution of individual lines, then the energy of the packet. The energy of the packet increases sharply at the beginning of the 20th century, leading by more than two decades the well-known increase of the Wolf number. The nonaxisymmetry of sunspots increases before the total increase of activity and may be considered as a precursor. We discuss briefly and tentatively this observation in terms of solar dynamo theory.     

利用小波分析研究近地空间高能电子的周期变化特征

利用小波变换对GOES (Geostationary Operational Environmental Satellites)系列卫星(GOES 10/11) 1999年3月至2010年12月和风云2号系列卫星(FY 2C/2D) 2004年10月至2012年5月记录的2 MeV高能电子通量变化情况进行了相关研究,发现GOES卫星观测到的高能电子通量存在明显的13.9 d、 27.7 d、 187.0 d和342.9 d周期, FY卫星观测到的高能电子通量存在明显的13.9 d、27.7 d、222.3 d和374.0 d周期,在某些年份GOES和FY卫星均存在9 d的周期,与地磁Dst (赤道环电流指数)、 AE (极光电射流指数)指数周期高度相似.将高能电子通量和Dst、AE指数进行交叉小波分析,并利用该算法的多分辨率特点以及时域、频域局部化分析方法,将数据按不同频率进行分解,从低频系数重构图像和交叉小波谱图可以清楚看出高能电子通量和地磁指数的关系.基于FY和GOES卫星高能电子通量良好的相关性,对多卫星高能电子通量变化短周期相同、中长周期不同进一步研究,对比发现不同地磁扰动引起的GOES和FY卫星高能电子通量变化存在各向异性,小磁暴也可以对高能电子通量造成和强磁暴一样的效果,并且某些时候存在地方时一致的24 h周期.这一结果表明对地磁宁静期高能电子研究至关重要,同时对理解太阳活动,预报高能电子能谱和预警深层充电事件以及验证预测磁暴、亚暴等事件具有重要意义.     

Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.     

New Evidence for Long-Term Persistence in the Sun's Activity

Possible persistence of sunspot activity was studied using rescaled range and detrended fluctuation analyses. In addition to actual Wolf numbers (1700–2000 A.D.), two solar proxies were used in this research, viz., an annual sunspot proxy obtained for 1090–1700 A.D. and sunspot numbers reconstructed from the decadal radiocarbon series (8005 B.C. – 1895 A.D). The reconstruction was made using a five-box carbon exchange model. Analyses showed that in all cases the scaling exponent is significantly higher than 0.5 in the range of scales from 25 yr up to 3000 yr. This indicates the existence of a long-term memory in solar activity, in agreement with results obtained for other solar indices.     

Relative sunspot numbers in the first half of eighteenth century

We revised relative sunspot numbers in the time interval 1700–1748 for which Wolf derived their annual means. The frequency of daily observations, counting simultaneously the number of sunspots and the number of sunspot groups necessary for determinating Wolf's relative sunspot numbers, is in this time interval very low and covers, on average, 4.8% of the number of all days only. There also exist incomplete observations not convenient to determine relative sunspot numbers. To enlarge the number of daily relative sunspot numbers we used the nonlinear, two-step interpolation method derived earlier by Letfus (1996, 1999). After interpolation, the mean value increased to 13.8%. Waldmeier (1968) found that the scaling factor k can be derived directly from the observed number of spots f and from the number of sunspot groups g. From the observations made at Zürich (Wolf and his assistants, Wolfer), at Peckeloh, and at Moncalieri during the years 1861–1928, we derived a new, more correct empirical relation. The resulting annual relative sunspot numbers are given in Table II. However, only for 26 years (53.0%) from the total number of 49 years was it possible to derive annual relative sunspot numbers. The observations were missing for the other years. This corresponds with results of Wolf, which gives the annual relative sunspot numbers for all 49 years. For the years when the data were missing, he marked these values as interpolated or very uncertain ones. Most of the observations originate from two data series (Kirch, Plantade), for which Wolf derived a higher scaling factor (k=2.0) than followed from the newly derived relation (k=1.40). The investigated time interval covers four solar cycles. After our results, the height of the first cycle (No. –4), given by Wolf, should be lowered by about two-thirds, the following two cycles (Nos. –3 and –2) lowered by one-third, as given by Wolf, and only the height of the fourth one (No. –1) should be unchanged. The activity levels of the cycles, as represented by group sunspot numbers, are lower by about one-fourth and, in the case of the first one (No. –4) even by two-thirds of the levels derived by us. The group sunspot numbers, derived from a much greater number of observations, have also greater credibility than other estimates. The shapes of the cycles, as given by Wolf, can be considered only as their more or less idealized form.     

Group Sunspot Numbers: A New Solar Activity Reconstruction

In this paper, we construct a time series known as the Group Sunspot Number. The Group Sunspot Number is designed to be more internally self-consistent (i.e., less dependent upon seeing the tiniest spots) and less noisy than the Wolf Sunspot Number. It uses the number of sunspot groups observed, rather than groups and individual sunspots. Daily, monthly, and yearly means are derived from 1610 to the present. The Group Sunspot Numbers use 65941 observations from 117 observers active before 1874 that were not used by Wolf in constructing his time series. Hence, we have calculated daily values of solar activity on 111358 days for 1610–1995, compared to 66168 days for the Wolf Sunspot Numbers. The Group Sunspot Numbers also have estimates of their random and systematic errors tabulated. The generation and preliminary analysis of the Group Sunspot Numbers allow us to make several conclusions: (1) Solar activity before 1882 is lower than generally assumed and consequently solar activity in the last few decades is higher than it has been for several centuries. (2) There was a solar activity peak in 1801 and not 1805 so there is no long anomalous cycle of 17 years as reported in the Wolf Sunspot Numbers. The longest cycle now lasts no more than 15 years. (3) The Wolf Sunspot Numbers have many inhomogeneities in them arising from observer noise and this noise affects the daily, monthly, and yearly means. The Group Sunspot Numbers also have observer noise, but it is considerably less than the noise in the Wolf Sunspot Numbers. The Group Sunspot Number is designed to be similar to the Wolf Sunspot Number, but, even if both indices had perfect inputs, some differences are expected, primarily in the daily values.     

Group Sunspot Numbers: A New Solar Activity Reconstruction

In this paper, we construct a time series known as the Group Sunspot Number. The Group Sunspot Number is designed to be more internally self-consistent (i.e., less dependent upon seeing the tiniest spots) and less noisy than the Wolf Sunspot Number. It uses the number of sunspot groups observed, rather than groups and individual sunspots. Daily, monthly, and yearly means are derived from 1610 to the present. The Group Sunspot Numbers use 65941 observations from 117 observers active before 1874 that were not used by Wolf in constructing his time series. Hence, we have calculated daily values of solar activity on 111358 days for 1610–1995, compared to 66168 days for the Wolf Sunspot Numbers. The Group Sunspot Numbers also have estimates of their random and systematic errors tabulated. The generation and preliminary analysis of the Group Sunspot Numbers allow us to make several conclusions: (1) Solar activity before 1882 is lower than generally assumed and consequently solar activity in the last few decades is higher than it has been for several centuries. (2) There was a solar activity peak in 1801 and not 1805 so there is no long anomalous cycle of 17 years as reported in the Wolf Sunspot Numbers. The longest cycle now lasts no more than 15 years. (3) The Wolf Sunspot Numbers have many inhomogeneities in them arising from observer noise and this noise affects the daily, monthly, and yearly means. The Group Sunspot Numbers also have observer noise, but it is considerably less than the noise in the Wolf Sunspot Numbers. The Group Sunspot Number is designed to be similar to the Wolf Sunspot Number, but, even if both indices had perfect inputs, some differences are expected, primarily in the daily values.     

A Comparison of Wolf's Reconstructed Record of Annual Sunspot Number with Schwabe's Observed Record of ‘Clusters of Spots’ for the Interval of 1826–1868

Samuel Heinrich Schwabe, the discoverer of the sunspot cycle, observed the Sun routinely from Dessau, Germany during the interval of 1826–1868, averaging about 290 observing days per year. His yearly counts of ‘clusters of spots’ (or, more correctly, the yearly number of newly appearing sunspot groups) provided a simple means for describing the overt features of the sunspot cycle (i.e., the timing and relative strengths of cycle minimum and maximum). In 1848, Rudolf Wolf, a Swiss astronomer, having become aware of Schwabe's discovery, introduced his now familiar ‘relative sunspot number’ and established an international cadre of observers for monitoring the future behavior of the sunspot cycle and for reconstructing its past behavior (backwards in time to 1818, based on daily sunspot number estimates). While Wolf's reconstruction is complete (without gaps) only from 1849 (hence, the beginning of the modern era), the immediately preceding interval of 1818–1848 is incomplete, being based on an average of 260 observing days per year. In this investigation, Wolf's reconstructed record of annual sunspot number is compared against Schwabe's actual observing record of yearly counts of clusters of spots. The comparison suggests that Wolf may have misplaced (by about 1–2 yr) and underestimated (by about 16 units of sunspot number) the maximum amplitude for cycle 7. If true, then, cycle 7's ascent and descent durations should measure about 5 years each instead of 7 and 3 years, respectively, the extremes of the distributions, and its maximum amplitude should measure about 86 instead of 70. This study also indicates that cycle 9's maximum amplitude is more reliably determined than cycle 8's and that both appear to be of comparable size (about 130 units of sunspot number) rather than being significantly different. Therefore, caution is urged against the indiscriminate use of the pre-modern era sunspot numbers in long-term studies of the sunspot cycle, since such use may lead to specious results.     

地球物理现象和太阳活动中的高频振荡

本文用几种谱分析方法了从１９７６年７月－１９９２年９月期间的地球物理资料（日长变化，大气角动量）和太阳活动及１９７６年７月－１９８７年１２月的日冕指数。结果证实所有序列中呈现出４０－６０天的振荡，同时也表明：它们的振幅和周期是随时间变化的。本文研究了谱结构的时空分布和讨论地球物理象与太阳活动之间的可能联系。     

A revised listing of the number of sunspot groups made by Pastorff, 1819 to 1833

J. W. Pastorff of Drossen, Germany, made about 1477 observations of sunspots between 1819 and 1833. These observations were erroneously interpreted by A. C. Ranyard in 1874 and then used by Rudolf Wolf in his calculations of the Wolf Sunspot Numbers. The result is a noisier daily time series and overestimation of the monthly and yearly means for these years. Pastorff was actually a very good observer. In this paper, Pastorff's original observations are reexamined and more nearly correct values for the number of sunspot groups are tabulated. We show some examples of the problems created by Ranyard's interpretation and the consequences for the history of solar activity that a correct interpretation of Pastorff's observations will have. Pastorff's observations provide valuable information on the first strong cycle after the Dalton Minimum (1795–1823).     

Prediction of Solar Activity Based on Neuro-Fuzzy Modeling

This paper presents an application of the neuro-fuzzy modeling to analyze the time series of solar activity, as measured through the relative Wolf number. The neuro-fuzzy structure is optimized based on the linear adapted genetic algorithm with controlling population size (LAGA-POP). Initially, the dimension of the time series characteristic attractor is obtained based on the smallest regularity criterion (RC) and the neuro-fuzzy model. Then the performance of the proposed approach, in forecasting yearly sunspot numbers, is favorably compared to that of other published methods. Finally, a comparison predictions for the remaining part of the 22nd and the whole 23rd cycle of the solar activity are presented.     

Rieger quasi-periodicity in solar indices

Using wavelet analysis and Fourier analysis, the temporal behavior of ??156-day quasi-periodicity (Rieger quasi-periodicity, RQ) is investigated for series of daily solar indices: Wolf numbers W for 161 years (from 1849), the flux F_10.7 of the Sun??s radio emission at a frequency of 2800 MHz for 63 years (from 1947), the number of X-ray flares N _X for 29 years (from 1981), and the number of optical flares N _?? for 11 years in cycle 21. The N _?? series are studied for four quadrants of the solar disk. It is found for the W series that there is no stable dependence of the amplitude RQ on the cycle phase and the W value. It is associated with the fact that, corresponding to a period of around eight years, in the power spectrum changes in the amplitude of the Rieger quasiperiodicity of the index W are dominated by the peak. Moreover, the peaks corresponding to the 11-year cyclicity are also significant. The comparative study of the temporal behavior of the Rieger quasi-periodicity amplitude of the indices W, F_10.7, and N _X has shown that the quasi-periodicity covers the processes, occurring in active regions on the Sun at different altitudes, almost simultaneously. It is found that for N _??, the lag of variations of the Rieger quasi-periodicity amplitude for series of the Sun??s western hemisphere, relative to those for series of the eastern hemisphere, is on average less than for the flare series. Thus, if the flare occurrence is modulated by the Rieger quasi-periodicity process as a wave propagating over the Sun??s disc, then the wave is not a retrograde one. Different interpretations of the nature of the Rieger quasi-periodicity are discussed including the hypothesis of Rossby waves.     

Relative Sunspot Numbers in the First Half of the Seventeenth Century

We derived daily relative sunspot numbers and their monthly and annual means in the first half of the seventeenth century. The series of observations collected by Wolf were recorded in the years 1611–1613 and 1642–1644. We used a nonlinear two-step interpolation method derived earlier (Letfus, 1996, 1999) to enlarge the number of daily data. Before interpolation the relative monthly frequency of observations in 24 months of the first time interval 1611–1613 was 49.4% and in 22 months of the second interval 1642–1644 was 49.9%. After interpolation the relative frequency increased in the first time interval to 91.3%, in the second time interval to 82.6%. Most data series in the years 1611–1613 overlap one another and also overlap with a series, for which Wolf estimated a scaling factor converting relative sunspot numbers on the Zürich scale. We derived the scaling factors of all individual series of observations also from the ratios of observed numbers of sunspots to the numbers of sunspot groups (Letfus, 2000). The differences between almost all scaling factors derived in one and the other way are not substantial. All data series were homogenized by application of scaling factors and parallel data in the overlapping parts of data series were averaged. Resulting daily relative sunspot numbers and their monthly and annual means in the years l61l–1613 are given in Table I and those in the years 1642–1644 in Table II. The annual means of these data are compared with analogous data obtained otherwise.     

An analysis of the light changes of AR lacertae

An attempt has been made to bring photoelectric and dynamical properties of the system to a common focus. The photoelectric properties are exhibited by a series of light curves in the blue and infrared produced from a series of observations made by G. E. Kronet al. from 1938 to 1948. An analysis of these reveals a decrease of the period of the order of magnitude 10^–5.A Fourier analysis of the light curves is employed to estimate the elements for the period represented by each curve. These results suggest a variation of the fractional radii over an eight-month period. Dynamical effects are ruled out and the result is seen to be the outcome of some photoelectric effect. A phenomenological discussion of the nature of these photoelectric effects is presented, showing that their origin may be in gas streams rather than spot effects.     

Automatic Sunspots Detection on Full-Disk Solar Images using Mathematical Morphology

Sunspots are solar features located in active regions of the Sun, whose number is an indicator of the Sun’s magnetic activity. Therefore accurate detection and classification of sunspots are fundamental for the elaboration of solar activity indices such as the Wolf number. However, irregularities in the shape of the sunspots and their variable intensity and contrast with the surroundings, make their automated detection from digital images difficult. Here, we present a morphological tool that has allowed us to construct a simple and automatic procedure to treat digital photographs obtained from a solar telescope, and to extract the main features of sunspots. Comparing the solar indices computed with our algorithm against those obtained with the previous method exhibit an obvious improvement. A favorable comparison of the Wolf sunspot number time series obtained with our methodology and from other reference observatories is also presented. Finally, we compare our sunspot and group detection to that of other observatories.     

Early latitude observations at the Pulkovo observatory

Pulkovo astrometric observations began in the 1840s using the Repsold transit instrument in the prime vertical and Ertel vertical circle. The first observers on these instruments were W.I. Struve, 1840–1856, and Kh.I. Peters, 1842–1849. In the present work, we collected and analyzed different series of latitude variations from observations made by M.O. Nuren, B. Wanach, A.A. Ivanov, I.N. Bonsdorf, and A.Ya. Orlov. In addition, results are given of investigations of a specific behavior of the Chandler polar motion in this interval, obtained by C. Chandler, Ivanov, Kh. Kimura, Orlov, and N. Sekiguchi. The aim of this paper is to search for and analyze the earliest series of Pulkovo latitudes, in order to evaluate the possibility of their use to study the motion of the pole at the maximum available range of observations. Different methods were used to isolate and analyze the sum of Chandler and annual latitude variations. The annex provides a series of Pulkovo latitude variations for 1840–1848, which may be used to extend latitude variation back to 1840.     

Evolution of the Green Corona in 1996–2002

We analysed the green-line coronal intensities (530.3 nm, Fexiv), both their time- latitudinal distribution as well as the coronal index of solar activity (CI) over the period 1996–2002. Maximum values of the CI (smoothed) were observed in mid-August 2001, even though the `first' peak was observed in the period January–April 2000. The maximum of the Wolf number occurred in 2000, April – July, and the `second peak' occurred in December 2001–March 2002. Both indices have a similar course in the cycle, but their maxima are shifted by 1.5 year. There was high correlation between CI and Wolf number, the 2800 MHz radio flux, the X-ray 0.1–0.8 nm flux and cosmic-ray flux. The CI values in present cycle 23 are lower than those of the two former solar cycles 21 and 22 by about 1/3. Polar branches, which separated from the principal equatorward branch at mid-latitudes in the cycle minimum, 1996, reached the poles around 2000. The new principal branch for cycle 24 split in 2001, turned over around ±60° in 2002.5 and moves to the equator, where it will end in 2019. Minimum between cycles 23 and 24 will occur around 2007.5, cycle maximum 24 around 2012.5. Poleward branches in cycle 24 will reach the solar poles in 2011.     

A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.     

Amplitude and period of the dynamo wave and prediction of the solar cycle

The relation of the solar cycle period and its amplitude is a complex problem as there is no direct correlation between these two quantities. Nevertheless, the period of the cycle is of important influence to the Earth's climate, which has been noted by many authors. The present authors make an attempt to analyse the solar indices data taking into account recent developments of the asymptotic theory of the solar dynamo. The use of the WKB method enables us to estimate the amplitude and the period of the cycle versus dynamo wave parameters in the framework of the nonlinear development of the one-dimensional Parker migratory dynamo. These estimates link the period T and the amplitude a with dynamo number D and thickness of the generation layer of the solar convective zone h. As previous authors, we have not revealed any considerable correlation between the above quantities calculated in the usual way. However, we have found some similar dependences with good confidence using running cycle periods. We have noticed statistically significant dependences between the Wolf numbers and the running period of the magnetic cycle, as well as between maximum sunspot number and duration of the phase of growth of each sunspot cycle. The latter one supports asymptotic estimates of the nonlinear dynamo wave suggested earlier. These dependences may be useful for understanding the mechanism of the solar dynamo wave and prediction of the average maximum amplitude of solar cycles. Besides that, we have noted that the maximum amplitude of the cycle and the temporal derivative of the monthly Wolf numbers at the very beginning of the phase of growth of the cycle have high correlation coefficient of order 0.95. The link between Wolf number data and their derivative taken with a time shift enabled us to predict the dynamics of the sunspot activity. For the current cycle 23 this yields Wolf numbers of order 107±7.     

The Intermediate-Term Quasi-Cycles of Wolf Number and Group Sunspot Number Fluctuations

I apply spectral and auto-correlation analyses to the monthly Wolf number fluctuations for 22 solar cycles and to the group sunspot number fluctuations for 18 solar cycles and find the existence of an 11-month quasi-periodicity in these data. Its strength correlates very well (ρ ⑈ 0.8) with the variance of fluctuations. Moreover, for both Wolf and group sunspot indexes I divide a stationary version of fluctuation time series into two parts: those from periods of low and high solar activity. I find statistically significant quasi-periodicity (9 months) in both high- and low-activity data sets. I also find the quasi-period of about 15 months in the time series of high-activity periods.