Study Of The Temporal Variation Of Solar Rotation

Differential rotation plays a key role in providing toroidal magnetic field from the poloidal one for solar activity.It is generally accepted that solar differential rotation drives the solar dynamo for generating all solar activity.However,the role of the differential rotation as a participant in the cycle of magnetic activity variation is not yet clear.Hence,study of the variation of differential rotation during the solar cycle and its north-south asymmetry is essential for understanding the variation of the solar magnetic activity,the mechanism of the solar cycle,and the solar internal dynamics,as well as for providing important information on the physical processes responsible for the cause of solar differential rotation.The thesis,which is presented in five chapters,makes a study of the temporal variation of the rotation of solar mean magnetic field,the temporal variation of coronal rotation and the north-south asymmetry of the rotation of the photospheric magnetic field.In chapter one,a brief introduction about solar rotation is presented.The history of the study of solar rotation,two basic methods(trace and spectroscopic)used in investigating the solar surface rotation rate,some theory studies for what cause the differential rotation and what maintains it as well as the meaning of the study of the temporal variation of solar rotation are introduced first.Then the research progress of the photosphere magnetic rotation and coronal rotation are introduced.Some main results of temporal variation of solar rotation are chiefly introduced,including the long-term variation,the solar-cycle phase dependence,the periodicity and the relationship with solar activity.Finally,the previous studies of north-south asymmetry of solar rotation are reviewed,including the north-south difference in solar rotation,the temporal variation and periodicity of north-south asymmetry,and the relationship between the north-south asymmetry of solar rotation with the north-south asymmetry of solar activity.In chapter two,based on continuous wavelet transformation analysis,the daily solar mean magnetic field(SMMF)from 1975 May 16 to 2014 July 31 isanalyzed to reveal its rotational behavior.Both the recurrent plot in Bartels form and the continuous wavelet transformation analysis show the existence of rotational modulation in the variation of the daily SMMF.The dependence of the rotational cycle lengths on solar cycle phase is also studied,which indicates that the yearly mean rotational cycle lengths generally seem to be longer during the rising phase of solar cycles and shorter during the declining phase.The periodicity analysis,through the use of an auto-correlation function,indicates that the rotational cycle lengths have a significant period of about 10.1 years.Furthermore,the cross-correlation analysis indicates that there exists a phase difference of about 2.5 yr between the rotational cycle lengths and solar activity.Based on an auto-correlation analysis of daily solar mean magnetic field of each year during 1975 May 16 to 2015 December 31,the rotation periods of solar mean magnetic field for each year during the considered time are obtained,and then the solar-cycle variation in the rotation of solar mean magnetic field is revisited.It can be found that the yearly rotation periods show an obvious variation with the solar cycle phase,that is the rotation periods are relative longer during rising phase of a solar cycle,and shorter during the declining phase.The wavelet analysis of the yearly rotation period time series indicates the existence of about10.5 yr period in the variation of yearly rotation periods of solar mean magnetic field.The relationship between the yearly rotation periods of solar mean magnetic field and yearly sunspot numbers is also restudied by performing cross-correlation analysis and cross-wavelet analysis,and the results show that there exists a phase difference of about 2.3 yr between the rotation of solar mean magnetic field and solar activity.In chapter three,the solar coronal rotation periods are obtained by applying the wavelet transformation analysis on the data of daily 10.7 cm radio flux covering the period from 1947 February 14 to 2014 August 31,and further the temporal variation of the coronal rotation is revisited.The rotation periods seem to show a weak decreasing trend during the considered time.It is found that there exist significant periods of about 2.1 yr,3.0 yr,4.5 yr,6.6 yr,8.6 yr,and10.3 yr in the temporal variation of the coronal rotation.The dependence of the coronal rotation on solar cycle phase is analyzed.The rotation periods are foundto be varying with the solar cycle phase,and they are relatively longer around the minimum year of the solar cycle.The result based on the cross-correlation analysis between the temporal variation of the rotation periods and the daily10.7 cm radio flux indicates that there exists a phase difference of about 5.5 yr between them.In chapter four,based on the rotation rates of the solar magnetic field during solar cycles 21 to 23,the temporal variation of the differential rotation coefficients A and B in the northern and southern hemispheres are studied,separately.The results show that the equatorial rotation rates of the northern hemisphere are larger than the southern hemisphere in most considered time,and the rotation seems to be more differential in the southern hemisphere than in the northern hemisphere in most considered time.It is found that the north-south asymmetries of rotation coefficients A and B show increasing trends in the considered time,while the north-south asymmetry of solar activity shows a decreasing trend.The relationship between the asymmetry of rotation coefficients and the asymmetry of solar activity is further investigated,and it is found that there exists a negative correlation between the asymmetry of rotation coefficient B and the asymmetry of solar activity.The periodicities in the variation of the rotation coefficients A and B in the northern and southern hemispheres are also studied,and a slightly difference can be found between the northern and southern ones.Moreover,the north-south asymmetries of rotation coefficients A and B have similar periods of 60 months(5.0 yr).Besides,the cross-correlation analysis indicates that there exists an obvious phase difference between the rotation coefficient A of the northern and southern hemispheres,as well as between the rotation coefficient B of northern and southern hemispheres.The differential rotation of the solar magnetic field in the northern hemisphere leads the differential rotation in the southern hemisphere in general.In the last chapter,a brief summary of this thesis is provided and a forecast for the future related research is put forward.