Short-Term Period Variation of Relative Sunspot Numbers

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10-23. The characteristics of some of the periods shorter than - 600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cycles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ～27, ～ 150 and ～360-day are obvious in some solar cycles, all of them are time-variable, also their lengths and amplitudes are variable and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.     

Short-Term Period Variation of Relative Sunspot Numbers

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10-23. The characteristics of some of the periods shorter than ～ 600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cy-cles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ～27,～150 and ～360-day are obvious in some solar cycles,all of them are time-variable,also their lengths and amplitudes are vari-able and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.     

The Hemispheric Asymmetry of Polar Faculae

In this paper, the north?Csouth (N?CS) asymmetry of the polar faculae at relatively low (RLLs), relatively high (RHLs) as well as total latitudes (TLs) respectively, are investigated. It is found that (1) the polar faculae behave in a different asymmetrical way at different latitudinal bands; (2) the asymmetry of solar activity may be a function of latitudes, which is present not only in the low-latitude solar activity but also in the high-latitude solar activity; (3) the N?CS asymmetry of the polar faculae at TLs depends on that at RHLs, and the asymmetry of the polar faculae at RLLs only plays a modulatory role.     

Synchronization of Sunspot Numbers and Sunspot Areas

Sunspot activity is usually described by either sunspot numbers or sunspot areas. The smoothed monthly mean sunspot numbers (SNs) and the smoothed monthly mean areas (SAs) in the time interval from November 1874 to September 2007 are used to analyze their phase synchronization. Both the linear method (fast Fourier transform) and some nonlinear approaches (continuous wavelet transform, cross-wavelet transform, wavelet coherence, cross-recurrence plot, and line of synchronization) are utilized to show the phase relation between the two series. There is a high level of phase synchronization between SNs and SAs, but the phase synchronization is detected only in their low-frequency components, corresponding to time scales of about 7 to 12 years. Their high-frequency components show a noisy behavior with strong phase mixing. Coherent phase variables should exist only for a frequency band with periodicities around the dominating 11-year cycle for SNs and SAs. There are some small phase differences between them. SNs lag SAs during most of the considered time interval, and they are in general more asynchronous around the minimum and maximum times of a cycle than at the ascending and descending phases.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.     

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.     

Wavelet Analysis of Several Important Periodic Properties in the Relative Sunspot Numbers

We investigate the wavelet transform of yearly mean relative sunspot number series from 1700 to 2002. The curve of the global wavelet power spectrum peaks at 11-yr, 53-yr and 101-yr periods. The evolution of the amplitudes of the three periods is studied. The results show that around 1750 and 1800, the amplitude of the 53-yr period was much higher than that of the the 11-yr period, that the ca. 53-yr period was apparent only for the interval from 1725 to 1850, and was very low after 1850, that around 1750, 1800 and 1900, the amplitude of the 101-yr period was higher than that of the 11-yr period and that, from 1940 to 2000, the 11-yr period greatly dominates over the other two periods.     

大行星轨道运动与太阳黑子数的中长周期变化

本文对不同序列的太阳黑子数资料作了分析研究,计算得到了可能的太阳黑子活动的中长周期变化,并分别与由大行星轨道运动引起的日心轨道角动量变化的周期进行比较,发现二者具有比较一致的谱结构。基于本文的讨论和文[17]的结论,我们进一步认为大行星轨道运动是太阳黑子数周期性变化的可能的外部因素。     

太阳黑子数R_Y和R_L的稳定性分析

黑子数用国际系统ＲＩ作标准，与云南天文台ＲＹ、国内联合ＲＬ比较，分别求出总平均值：ｑ（Ｙ）＝０．９３００４±０．００４７２，ｑ（Ｌ）＝０．９１４０９±０．００４４４。这是后者删除“偶然误差”次数多于前者的结果。对国内联合数据的处理，应以一个观测点为准，以此归算作补充的部分数据，才有可能使数据系列保持相对的稳定     

The Effect of Relative Sunspot Numbers,Solar Flare Numbers and Variable Component of 10.7 cm Solar Flux on The Seasonal Variation of 6300 Å Line Intensity at Calcutta

The paper presents the seasonal variation of 6300 Å line intensity at Calcutta with relative sunspot number, solar flare number and variable component of 10.7 cm solar flux. A study has been made and important results have been obtained which are as follows. (i) Intensity of 6300 Å line shows periodic variation with relative sunspot number, solar flare number and variable component of 10.7 cm solar flux during the period 1984–1986 which is the secondary peak of the descending phase of 21st solar cycle. (ii) 6300 Å line intensity at Cachoeira Paulista station, taken by Sahai et al. (1988), also shows periodic variation with solar parameters during the period 1978–1980 which is the peak phase of the solar cycle. (iii) A possible explanation of such a type of variation is also presented.     

Comparison of Polar and Equatorial Magnetic Fields Near Sunspot Minimum

We investigate the polar magnetic fields near sunspot minimum using high-resolution videomagnetograph data from Big Bear Solar Observatory. To avoid the problem of center-to-limb variation of the projected longitudinal field, we compare polar with equatorial field strengths for the same limb distance. Polar fields are stronger than the quiet equatorial field, but no greater than equatorial limb data containing unipolar regions. The difference is entirely in the stronger field elements. The polar background fields are of mixed polarity but show a net weak field opposite in sign to that of the stronger polar elements. We believe this to be the first evidence of widespread background field. No dependence of the measured signal on the B-angle was found, so the high-latitude fields do not change strength near the pole. Further, there was no significant change in the polar fields in the 15-month period studied. We tried to derive a high-latitude rotation rate; our data show motion of high-latitude magnetic elements, but the diurnal trajectory is not much bigger than random motions and field changes, so the result is inconclusive. We suggest that the polar fields represent the accumulation of sunspot remnants, the elements of which last for years in the absence of other fields.     

Duration of Polar Activity Cycles and Their Relation to Sunspot Activity

We have defined the duration of polar magnetic activity as the time interval between two successive polar reversals. The epochs of the polarity reversals of the magnetic field at the poles of the Sun have been determined (1) by the time of the final disappearance of the polar crown filaments and (2) by the time between the two neighbouring reversals of the magnetic dipole configuration (l=1) from the H synoptic charts covering the period 1870–2001. It is shown that the reversals for the magnetic dipole configuration (l=1) occur on an average 3.3±0.5 years after the sunspot minimum according to the H synoptic charts (Table I) and the Stanford magnetograms (Table III). If we set the time of the final disappearance of the polar crown filaments (determined from the latitude migration of filaments) as the criterion for deciding the epoch of the polarity reversal of the polar fields, then the reversal occurs on an average 5.8±0.6 years from sunspot minimum (last column of Table I). We consider this as the most reliable diagnostic for fixing the epoch of reversals, as the final disappearance of the polar crown filaments can be observed without ambiguity. We show that shorter the duration of the polar activity cycle (i.e., the shorter the duration between two neighbouring reversals), the more intense is the next sunspot cycle. We also notice that the duration of polar activity is always more in even solar cycles than in odd cycles whereas the maximum Wolf numbers W _\max is always higher for odd solar cycles than for even cycles. Furthermore, we assume there is a secular change in the duration of the polar cycle. It has decreased by 1.2 times during the last 120 years.     

Oscillations in Solar Faculae. III. The Phase Relations Between Chromospheric and Photospheric Line-of-Sight Velocities

An analysis of line-of-sight velocity oscillation in nine solar faculae was undertaken with the aim of studying phase relations between chromospheric (He?i 10830?Å line) and photospheric (Si?i 10827 Å line) five-minute oscillations. We found that the time lag of the chromospheric signal relative to photospheric one varies from ?12 to 100 seconds and is about 50 seconds on average. We assume that the small observed lag can have three possible explanations: i) convergence of formation levels of He?i 10830?Å and Si?i 10827?Å in faculae; ii) significant increase of five-minute oscillation propagation velocity above faculae; iii) simultaneous presence of standing and travelling waves.     

Reconstruction of Monthly and Yearly Group Sunspot Numbers From Sparse Daily Observations

Some periods before 1820 are poorly covered by sunspot observations. In addition to apparent, long observational gaps, there are also periods when there are only few sparse daily sunspot observations during a long time. It is important to estimate the reliability of the monthly and yearly mean sunspot values obtained from such sparse daily data. Here we suggest a new method to estimate the reliability of individual monthly means. The method is based on comparing the actual sparse data (sample population) to the well-measured sunspot data in 1850–1996 (reference population), and assumes that the statistical properties of sunspot activity remain similar throughout the entire period. For each sample population we first found those months in the reference population that contain the same data set, and constructed the statistical distribution of the corresponding monthly means. The mean and standard error of this distribution represent the mean and uncertainty of a monthly mean sunspot number reconstructed from sparse daily observations. The simple arithmetic mean of daily values can be adequately applied for months which contain more than 4–5 evenly distributed daily observations. However, the reliability of monthly means for less covered months has to be estimated more carefully. Using the estimated, new monthly values, we have also calculated the weighted annual sunspot numbers.     

Bayesian Methods for Reconstructing Sunspot Numbers Before and During the Maunder Minimum

The Maunder Minimum (MM) was an extended period of reduced solar activity in terms of yearly sunspot numbers (SSN) during 1610?–?1715. The reality of this “grand minimum” is generally accepted in the scientific community, but the statistics of the SSN record suggest a need for data reconstruction. The MM data show a nonstandard distribution compared with the entire SSN signal (1610?–?2014). The pattern does not satisfy the weakly stationary solar dynamo approximation, which characterizes many natural events spanning centuries or even millennia, including the Sun and the stars. Over the entire observation period (1610?–?2014), the reported SSN exhibits statistically significant regime switches, departures from autoregressive stationarity, and growing trends. Reconstruction of the SSN during the pre-MM and MM periods is performed using five novel statistical procedures in support of signal analysis. A Bayesian–Monte Carlo backcast technique is found to be most reliable and produces an SSN signal that meets the weak-stationarity requirement. The computed MM signal for this reconstruction does not show a “grand” minimum or even a “semi-grand” minimum.     

用自激励门限自回归分析方法模拟和预报太阳黑子数的长期变化

本文用一种新方法——自激励门限自回归分析方法对太阳黑子相对数年平均值进行拟合和预报检验,并对未来第22周逐年年均值作出预报。 目激励门限自回归分析模型的形式如下: 在对1956至1985年逐年太阳黑子相对数年均值的预报检验中,最大拟会误差为40.6,最小拟合误差为0.3,平均拟合误差为±12.5。 对1986至1997年逐年太阳黑子相对数年均值的预报见表(4)。定出第21周极小在1986年或1987年,极大在1990或1991年,极大值R_M=81.2±16.2。     

太阳黑子面积数与黑子数指标在大气预报中的应用对比分析

分别应用太阳黑子视面积数和太阳黑子相对数代表太阳活动水平与天津夏季降水总量进行相关分析,结果表明黑子面积指标明显优于黑子数.     

Cosmic Ray Intensity Variations in Relation with Solar Flare Index and Sunspot Numbers

From the monthly data of cosmic ray intensity (CRI), sunspot numbers (SSN) and solar flare index (SFI), an attempt has been made to study the relationship between CRI and solar activity (SA) parameters SSN and SFI. The correlation between SA parameters and CRI for different neutron monitoring stations having low, middle and high cut-off rigidity has been investigated. The anti-correlation between SA and CRI is found to exist with some time lag. Based on the method of minimizing correlation coefficient and time-delayed component method, the observed time-lag between SA parameters (SSN and SFI) and CRI has been found to be large for odd solar cycles in comparison to even solar cycles. The results of time-lag analysis between CRI and SSN and between CRI-SFI have also been compared. The findings of correlative study between CRI and SSN are in agreement with earlier results, while the CRI-SFI relationship provides new insights to understand the solar modulation of cosmic rays.     

Modeling the Relationship Between Neutron Counting Rates and Sunspot Numbers Using the Hysteresis Effect

Several studies show that temporal variations in the Galactic cosmic ray (GCR) intensity display a distinct 11-year periodicity due to solar modulation of the galactic cosmic rays in the heliosphere. The 11-year periodicity of GCRs is inversely proportional to, but out of phase with, the 11-year solar cycle, implying that there is a time lag between actual solar cycle and the GCR intensity, which is known as the hysteresis effect. In this study, we use the hysteresis effect to model the relationship between neutron counting rates (NCRs), an indicator of the GCR intensity, and sunspot numbers (SSNs) over the period that covers the last four solar cycles (20, 21, 22, and 23). Both linear and ellipse models were applied to SSNs during odd and even cycles in order to calculate temporal variations of NCRs. We find that ellipse modeling provides higher correlation coefficients for odd cycles compared to linear models, e.g. 0.97, 0.97, 0.92, and 0.97 compared to 0.69, 0.72, 0.53, and 0.68 for data from McMurdo, Swarthmore, South Pole, and Thule neutron monitors, respectively, during solar cycle 21 with overall improvement of 31 % for odd cycles. When combined to a continuous model, the better correlation observed for the odd cycles increases the overall correlation between observed and modeled NCRs. The new empirical model therefore provides a better representation of the relationship between NCRs and SSNs. A major goal of the ongoing research is to use the new non-linear empirical model to reconstruct SSNs on annual time scales prior to 1610, where we do not have observational records of SSNs, based on changes in NCRs reconstructed from ¹⁰Be in ice cores.