The Gleissberg Cycle Of The Sunspot And The Differential Rotation Of The Sun

In this dissertation, two important problems in solar physics have been invested. One is the periodicities of the solar activities, and another is the differential rotation of the Sun. There is a close relationship between the two problems.The periodicity of the Sun has been researched for more than one and half centuries. Sunspots are the most significant symbols on the Sun, and others solar activities have many important relations with them. The periodicity of the solar activities is very complex, nevertheless, the 11 years cycle of the sun is beyond the disputations. With the enrichment of the observational data and improvement of the analysis methods, the Gleissberg cycle has been widely accepted. However, the variation of the length of the Gleissberg cycle and how does it impact on the Schwabe cycle have not been known clearly yet. We have investigated the Gleissberg cycle through yearly sunspot number more than 300 years, by the methods of Fourier transformation and Wavelet analysis. The results not only confirm some previously obtained results, but also give the variation of the length of the Gleissberg cycle during the 300 years. As the Schwabe cycle is modulated by the Gleissberg cycle, the activities of the solar cycles in the valleys of the Gleissberg cycle are relative weaker than those of the other cycles. We select 6 solar cycles which are in the valleys of the Gleissberg cycle, and then we predict that solar cycles 24-25 will be at the valley of the Gleissberg cycle. Based on the similarities of the active levels among the solar cycles which are at the valleys of the Gleissberg cycle, we predict the active levels of the minimum and maximum years of solar cycles 24-25.The Sun is a gas ball which is composed of the plasmas, so the rotation of the Sun is different from the solid Earth. The Sun exhibit a rotation that changes with the latitude and the depth of the Sun, which is called the differential rotation. Base on the synoptic maps of the photosphere magnetic fields, we first built up time-longitude stackplots of the positive, negative and total fields. Through the slopes of the tilted structures on these stackplots, we derived the rotation rates of the different fields. In addition, we also studied the differences of the rotation rates between the positive and negative fields.Solar differential rotation is a fundamental ingredient of solar dynamo theory. The poloidal fields were changed into toroidal fields by the differential rotation in the Sun. The magnetic fields inside the Sun are increased with the distortions, and the magnetic flux including the strong magnetic fields emerged from below the photosphere forms the sunspot. The change of the magnetic fields is the essential reason for cyclical changes of solar activities. The research on the variation of solar rotation rate by the magnetic field will help to reveal the physical nature of the cyclical changes of solar activities.The main results of this dissertation are shown as follows:1. Based on the yearly sunspot numbers from 1700 to 2008, we confirmed the Schwabe cycle and the Gleissberg cycle of solar activities by the methods of Fourier transformation and Wavelet analysis. The Gleissberg cycle of solar activities is also existed in the smoothed values of the maximum, the minimum and the total numbers of each solar cycle. The variation of the length of the Gleissberg cycle is derived through the method of Wavelet analysis. We guess that the variation express a longer scale period in the solar activities.2. Through the variation of the length of the Gleissberg cycle in more than 300 years, we predict that solar cycles 24-25 will be at the valley of the Gleissberg cycle, so the active levels of solar cycles 24-25 will be very low. Based on averaging the active levels of the solar cycles which are at the valleys of the Gleissberg cycle, we predict the sunspot number of the maximum years of solar cycles 24-25 will be 63.6±21.1, and minimum years will be 2.2±2.1. The difference between the prediction result of the minimum year of solar cycle 24 and actual yearly sunspot number in 2008 does not exceed±1.3. Employing the synoptic magnetic maps during solar cycles 21-23, we first build up time-longitude stackplots for different polarities. The rotation rates of the three solar cycles averaged over each cycle are calculated separately for the positive, negative and total fields. The latitude profiles of rotation of the positive and negative fields exhibit equatorial symmetries with each other, and those of the total fields lie between them. In addition, leader polarities always rotate faster than followers. The results obtained here confirm some previously discovered properties of the solar rotation, and also give some new findings. In addition, the rotation differences between two kinds of polarities may present some important constraints on solar dynamo model.4. The differences in rotation rates between leader and follower polarities are obtained. They are very small near the equator, and increase as latitude increases. In the latitude range of 5°-20°, these differences reach 0.05 deg/day, and the mean difference for solar cycle 22 is somewhat smaller than cycles 21 and 23 in these latitude regions. Then, the differences reduce again at latitudes higher than 20°.The recording time of yearly sunspot is only more than 300 years, so it is relatively short to study the Gleissberg cycle using these data. In the statistical work, too little samples will affect the accuracies of the predictions. Based on the stackplots built from the photosphere magnetic fields, we derived more detailed results about the differential rotation rates of the positive, negative and total magnetic fields by cross-correlation technique. This method still needs to be further improved to get better results for higher latitude regions.