Indices for the epochs of the solar activity minima

3. Power of the Sector Structure of the Large-Scale Magnetic Field SSPD(t)

[14] In studies of the rotation of the sector structure of the solar magnetic field, the rotation index SSPD(t) was introduced by Vasil'eva et al. [2002]. It is determined by the sum of the spectral density of the power of the magnetic field sector structure. To find the spectral density of the power, we used the Fourier transformation. The Fourier coefficients for each realization can be presented in the form

Figure 4

where the function y(t) is given in N discrete points of the segment [0, T] with the step of realization Dt=T/N. The spectral density is found as

where

and

Let us introduce the index of the sum of the spectral density of the power SSPD. To obtain this index, we sum over the spectral density S for the periods of oscillations T sim

6-15 days

This range corresponds to the periods of oscillations for the 4- and the 6-sector structures of the large-scale magnetic field. Evidently, it is an indication of the presence or absence of different types of the magnetic field sector structure. Comparison of the SSPD(t) index with the index of Wolf numbers W(t) for the period from 1904 to 2005 has revealed that the 11-year activity cycles of the magnetic field sector structure SSPD(t) are shifted by 5-6 years and precede in amplitude and phase the 11-year cycles of the Wolf numbers (Figure 4). This implies that the sector structure of the solar magnetic field actively participates in the magnetic field generation, and therefore it is one of the basic types of motion. The correlation coefficient between the maximums of parameters W_max and SSPD_max is equal to R=0.96. The regression formula can be presented in the form W_max = 195 L_max - 143. The mean square error comprised s=

11 W. Unfortunately, the peak of this function is not achieved yet. Therefore the forecast for cycle 24 is not possible.