Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number,Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, Di, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show （1） for 46 months （94%） of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri - Di plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level a = 5%, and for 36 months （73%） the fitting is even better, for a = 1%; （2） time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; （3） the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log/~ = 0.704 lnDi - 0.291.

Evolution of a Long-lived Sunspot Group and Its Associated Solar-terrestrial Events

A long-lived sunspot group (AR9604) on the south hemisphere that lasted five solar rotations and produced some strong bursts is analyzed. The focus is on its evolving features. Its whole life was successfully maintained by four Emerging Flux Regions (EFRs). Apart from the one that lasted only a short time and did not produce any bursts, the other three EFRs have the following common features: (1) A positive writhe of magnetic flux tubes and a twist of the field lines of the same sign, indicating kink instability. (2) A clockwise rotation and a high tilt because the writhe was right-handed. (3) A compact 'island δ' structure of the sunspot group indicating concentrated kink instability. Since magnetic reconnection easily occurs at the kinked point of a very kink-unstable flux tube, these features should be the inducement of the strong bursts.

Support Vector Machine combined with K-Nearest Neighbors for Solar Flare Forecasting

A method combining the support vector machine （SVM） the K-Nearest Neighbors （KNN）, labelled the SVM-KNN method, is used to construct a solar flare forecasting model. Based on a proven relationship between SVM and KNN, the SVM-KNN method improves the SVM algorithm of classification by taking advantage of the KNN algorithm according to the distribution of test samples in a feature space. In our flare forecast study, sunspots and 10cm radio flux data observed during Solar Cycle 23 are taken as predictors, and whether an M class flare will occur for each active region within two days will be predicted. The SVM- KNN method is compared with the SVM and Neural networks-based method. The test results indicate that the rate of correct predictions from the SVM-KNN method is higher than that from the other two methods. This method shows promise as a practicable future forecasting model.

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.

Low Dimensional Chaos from the Group Sunspot Numbers

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent （MLE） for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 （month^- 1）. Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19 A line over the wavelength interval from 150mA redward of the line center to 150mA blueward, in steps of 10mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.

A quantity characterizing variation of observed magnetic twist in solar active regions

An alternative parameter RJz is introduced as the ratio of one of two kinds of opposite-sign current to the total current and is used to investigate the relationship between this quantity and the hemispheric helicity sign rule（HSR） that has been established by a series of previous statistical studies. The classification of current in each hemisphere obeys the following rule： if the product of the current and the corresponding longitudinal field component contributes a consistent sign with respect to the HSR,it is called ＂HSR-compliant＂ current,otherwise it is called ＂HSR-noncompliant＂ current. Firstly,consistency between the butterfly diagram of RJz and current helicity was obtained in a statistical study.Active regions with RJzsmaller than 0.5 tend to obey the HSR whereas those with RJz greater than 0.5 tend to disobey it. The ＂HSR-compliant＂ current systems have a 60% probability of realization compared to 40% for ＂HSR-noncompliant＂ current systems. Overall,the HSR is violated for active regions in which the ＂HSR-noncompliant＂ current is greater than the ＂HSR-compliant＂ current. Secondly,the parameter RJz was subsequently used to study the evolution of current systems in the case analyses of flare-productive active regions NOAA AR 11158 and AR 11283. It is found that there is a ＂RJz-quasistationary＂ phase that is relatively flare quiescent and ＂RJz-dynamic＂ phase that is characterized by the occurrence of large flares.

An Electron Density Model above the Sunspot from a Mapping of NOAA 7260 at 17 GHz

The brightness temperature distribution of microwave emission in a solar active region generally shows a ring structure, with a dip at the centre. However, no dip was found in the Nobeyama Radioheliograph left handed circular polarization (LCP) image on 1992 August 18; instead, there was a peak. This is a completely LCP source with zero right-handed circular polarization (RCP). We examine this structure in terms of the joint effect of gyroresonance and bremsstrahlung mechanism with a raised electron density above the central part of the sunspot, and the commonly assumed temperature and vertical dipole magnetic field models. The raised electron density is found to be 1.4 × 1011 cm-3 at the chromosphere base.

Can Asymmetry of Solar Activity be Extended into Extended Cycle?

With the use of the Royal Greenwich Observatory data set of sunspot groups, an attempt is made to examine the north-south asymmetry of solar activity in the 'extended' solar cycles. It is inferred that the asymmetry established for individual solar cycles does not extend to the 'extended' cycles.

A Running Average Method for Predicting the Size and Length of a Solar Cycle

The running correlation coefficient between the solar cycle amplitudes and the max-max cycle lengths at a given cycle lag is found to vary roughly in a cyclical wave with the cycle number, based on the smoothed monthly mean Group sunspot numbers available since 1610. A running average method is proposed to predict the size and length of a solar cycle by the use of the varying trend of the coefficients. It is found that, when a condition （that the correlation becomes stronger） is satisfied, the mean prediction error （16.1） is much smaller than when the condition is not satisfied （38.7）. This result can be explained by the fact that the prediction must fall on the regression line and increase the strength of the correlation. The method itself can also indicate whether the prediction is reasonable or not. To obtain a reasonable prediction, it is more important to search for a running correlation coefficient whose varying trend satisfies the proposed condition, and the result does not depend so much on the size of the correlation coefficient. As an application, the peak sunspot number of cycle 24 is estimated as 140.4 ± 15.7, and the peak as May 2012 ±11 months.

Historical Dataset Reconstruction and a Prediction Method of Solar 10.7cm Radio Flux

We reconstruct the developing history of solar 10.7 cm radio flux （F10.7） since 1848, based on the yearly sunspot number and the variations. A relationship between the maximum and the linear regression slope of the first 3 years starting from minimum of the solar cycle is considered. We put forward a method of predicting the maximum of F10.7 by means of the slope-maximum relationship. Running tests for cycles 19 to 23 indicate that the method can properly predict the peak of F10.7.

Estimating the Size and Timing of the Maximum Amplitude of Solar Cycle 24

A simple statistical method is used to estimate the size and timing of maximum amplitude of the next solar cycle （cycle 24）. Presuming cycle 23 to be a short cycle （as is more likely）, the minimum of cycle 24 should occur about December 2006 （±2 months） and the maximum, around March 2011 （±9 months）, and the amplitude is 189.9 ± 15.5, if it is a fast riser, or about 136, if it is a slow riser. If we presume cycle 23 to be a long cycle （as is less likely）, the minimum of cycle 24 should occur about June 2008 （±2 months） and the maximum, about February 2013 （±8 months） and the maximum will be about 137 or 80, according as the cycle is a fast riser or a slow riser.

Temporal variation of hemispheric solar rotation

The daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from 1945 January 1 to 2010 December 31 are used to investi- gate the temporal variation of rotational cycle length through the continuous wavelet transformation analysis method. Auto-correlation function analysis of daily hemi- spheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. The results obtained from the wavelet transformation analysis are that no direct relationship exists between the variation trend of the rotational cy- cle length and the solar activity in the two hemispheres and that the rotational cycle length of both hemispheres has no significant period appearing at 11 yr, but has a sig- nificant period of about 7.6 yr. Analysis concerning the solar cycle dependence of the rotational cycle length shows that acceleration seems to appear before the minimum time of solar activity in the whole disk and the northern hemisphere, respectively. Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and that the rotational cycle length of the whole disk as well as the northern and southern hemispheres, also has phase shifts with corresponding solar activity. In addition, the temporal variation of the north-south （N- S） asymmetry of the rotational cycle length is also studied. This displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle, as well as in the considered time interval, and has two significant periods of 7.7 and 17.5 yr. Moreover, the rotational cycle length and the N-S asymmetry of solar activity are highly corre- lated. It is inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24.

A New Method to Determine Epochs of Solar Cycle Extrema

A weighted average method is proposed to determine the epochs of solar cycle extrema and hence the solar cycle lengths. Comparing to the previous methods, this method has the advantage that the extremum epochs are easily and uniquely determined.

Phase shifts of the paired wings of butterfly diagrams

Sunspot groups observed by the Royal Greenwich Observatory/US Air Force/NOAA from 1874 May to 2008 November and the Carte Synoptique solar filaments from 1919 March to 1989 December are used to investigate the relative phase shift of the paired wings of butterfly diagrams of sunspot and filament activi- ties. Latitudinal migration of sunspot groups （or filaments） does asynchronously occur in the northern and southern hemispheres, and there is a relative phase shift between the paired wings of their butterfly diagrams in a cycle, making the paired wings spa- tially asymmetrical on the solar equator. It is inferred that hemispherical solar activity strength should evolve in a similar way within the paired wings of a butterfly diagram in a cycle, demonstrating the paired wings phenomenon and showing the phase rela- tionship between the northern and southern hemispherical solar activity strengths, as well as a relative phase shift between the paired wings of a butterfly diagram, which should bring about almost the same relative phase shift of hemispheric solar activity strength.