Comparison of solar activity proxies: eigen vectors versus averaged sunspot numbers

We explore the links between the averaged sunspot numbers (SSN) and a modulus summary curve (MSC) of two largest eigenvectors of the solar background magnetic field (SBMF) derived from principal component analysis. MSC has rather close correspondence with the whole set of SSN revealing close cycle timings, duration, and maxima times for the cycles 12–24, 6, 7, and −4, −3, while for a few cycles in the mid-18th and mid-19th centuries there are discrepancies in the maximum amplitudes, durations, and times of the maxima. Possible reasons of these discrepancies related to uncertainties in the SSN observations in the 18th–19th centuries, in MSC definition and the different solar activity entities they represent: toroidal (SSN) and poloidal (MSC) magnetic fields, are discussed. Wavelet and Fourier spectral analysis of SSN and MSC series reveal within 95 per cent confidence levels the same prominent period of 10.7 yr, whereas SSN series show a period of 101 yr and MSC of 342 yr close to or above 95 per cent red-noise level. The correlation coefficients between SSN and MSC series vary from 0.25 for the whole SSN data set (from 1700), to 0.56 for the data sets from 1860, to 0.67 for the data sets from 1900 when all SSN restorations agree. These SSN and MSC data sets are confirmed to be closely but not identically related representing the solar activity in different entities of solar dynamo. Use of the summary curve and MSC of eigenvectors of SBMF can provide additional information to SSN for better understanding of solar activity.