Investigation of global solar magnetic field by computational topology methods

This paper analyzes the dynamics of large scale or background solar magnetic field by the methods of computational topology. First of all, we investigate global reversal of the field. A reversal refers to a change in the sign of the field dipole component on the solar poles. The synoptic chart is a synthetic representation of solar structures visible during one rotation of the Sun. A time sequence of synoptic charts, representing the distribution of a sign of background magnetic field averaged over one 27-days-long Carrington rotation, is used here. The rate of change of a number of disconnected components on the charts, formed by unipolar magnetic structures, versus resolution is characterized by the disconnectedness index. The value of this index may coincide with the box dimension of simple fractals. We have established a different behavior of disconnected components for magnetic structures with and without reversals. Reversals are characterized by the disappearance of distinguishing scales of magnetic structures (fractality) and, as a result, by larger scaling interval for estimation of the disconnectedness index. The obtained results may be interpreted as demonstrating a self-organizing criticality in large scale magnetic field dynamics. Moreover, we apply homology theory to estimate ‘spottiness’ of synoptic charts by means of the Betti number β1. It characterizes number of ‘holes’ formed as inclusions into unipolar regions of the magnetic field of opposite sign. It appears that time series of the Betti number as well as index of disconnectedness have two modes, particularly, quasi-biennial oscillation and 11-year oscillations.