1. PCI analysis of Sunspot and Background Magnetic Field variations in the cycles 21-23 V.V. Zharkova 1, S.I. Zharkov 2, Shepherd S.J. 3 and Popova 4 Zharkov et al., 2008, Solar Phys., 248 Zharkova and Zharkov, 2008, JASR, 45 Zharkova et al., MNRAS, 2012 Popova et al, AnnGeo, 2013

2. Automated data analysis High resolution MF (MDI) – sunspot magnetic field – SMF Automated detection - Solar Feature Catalogues Low resolution MF (WSO) – synoptic maps of BMF Solar Geophysical Data

3. Automated sunspot detection on SOHO/MDI WL images  the original image Detected edges   the original image Detected edges  c) The found regions (dilated) d) The final detection results superimposed e) The extract from d) Zharkov et al, 2005, Solar Phys., 228

4. Sunspot Catalogue (from 1996-05-19 19:08:35 to 2010-05-31 19:51:32) Automated feature detection and data extraction About 40000 observation processed ~370,000 sunspots and 120 000 ARs stored and processed Sunspot Catalogue ( SOHO MDI) ( Zharkov et al., 2005) Space Observations, Accuracy & Image Quality Synoptic Continuum images every 6 hour LOS Magnetogram Data AR Catalogue (Meudon+MDI) ( Benkhalil et al., 2006) Meudon Ca II K3 images Meudon H-alpha images MDI LOS Magnetograms Filaments and prominences (Meudon) ( Fuller et al., 2005) Meudon H-alpha images http://solar.inf.brad.ac.uk Solar Feature Catalogues Zharkova et al., 2005, Sol Phys, 228, 365

5. North South Asymmetry (averaged by 170 days) (N-S)/(N+S) (ss –top, ar –bottom) – Zharkov and Zharkova ‘06 Sunspot MF AR MF

6. Tilts MT, GT and MT-sign averaged per year Zharkova and Zharkov, JASR 08 Year MT/signMTGT 1997 -5.344.562.83 1998 +1.917.695.85 1999 -1.086.545.11 2004/ +0.86 3.16 2.17 2005 -0.492.96 1.87

7. 1. SBMF (top) and sunspot MF (bottom)– phase between them is π~11 (Zharkov et al, 2008) Cycle 23 -Solar Background MF Sunspot MF

8. 2. 1y-4y residuals for BMF (top) and excess SMF (bottom) reveal additional phase of π/4 ~ 2.5 years – Zharkov et al, 2008 Cycle 23 - Solar Background MF Sunspot MF

9. PC Analysis of the solar data to find eigenvalues and eigenvectors Reduces dimensionality of the data array X to Y Searches for eigenvalues of a given array X T (n,m)  obtain matrix Singular value decomposition of X is X = WΣV T W(m,m) – matrix of eigenvectors of covariance matrix XX T. Σ – matrix (m,n) with diagonal eigenvalues V – matrix (m,m) of eigenvectors of X T X

10. Principal Component Analysis – reduces dimension Looking for a transformation of the data matrix X ( n x p ) such that Y=  T X =  1 X 1 +  2 X 2 +..+  p X p Where  =(  1,  2,..,  p ) T is a column vector of weights with  1 ²+  2 ²+..+  p ² =1

11. Eigenvalues vs variances – - revealed 2 main eigenvalues covering 40% of variance –dipole source - another 6 eigenvalues to cover the other 40%

12. Two main PCs (top) and their residuals (bottom)(lines – minimums of SA) (Zharkova et al., 2012, MNRAS) ST22, AOGS12, 13-17 Aug 12, Singapore PCA ~ Sine and cosine waves

13. Latitudinal ICs in cycles 21-23 (Zharkova et al., 2012, MNRAS) Main components All 3 cycles Cycle 21 Cycle 22 Cycle 23

14. ICs for 4 largest pairs of eigenvalues ST22, AOGS12, 13-17 Aug 12, Singapore 21-23 22 2123

15. Derivatives of 2 main EOFs From top left figure above component 1 component 2 resultant

16. Cross-correlation of 8 IPs Zharkova et al, MNRAS, 2012 ST22, AOGS12, 13-17 Aug 12, 21-2322 2123

17. Conclusions: IC components of SBMF: cycles 21-23 There is a pair of largest eigenvalues defining the temporal evolution of SBMF with the opposite polarities in the last 3 cycles  reflects 2 dynamo waves coming from the opposite hemispheres and interacting at the solar maximum. The waves start in the opposite hemispheres but move to the same hemisphere which becomes the active one The maximum amplitudes of both waves decrease nearly by 50% from cycle 21 to 22 and from 22 to 23 The waves intercept at the cycle maximum with the increased turbulence one year prior and after it Latitude of these interception decreases from 21 to 23

18. Conclusions: EOFs components: cycles 21- 23 There is a pair of largest eigenvalues defining the temporal evolution of ICs in latitude, which are the same for all 3 cycles  can reflect 2 dynamo waves coming from the poles – classic dynamo There are other 3 pairs of ICs – each unique for a cycle 21, 22 and 23. The maximum amplitude of ICs decrease nearly twice from cycle 21 to 22 and then from 22 to 23 The waves intercept with the increased turbulence one year prior and after the cycle maximum Latitude of these interception decreases from 21 to 23 (and so the solar activity in these cycles) Cross-correlation show a presence of quadruple sources in all the cycles and possible sextuple in 23

19. ST22, AOGS12, 13-17 Aug 12, Singapore Sunspot magnetic flux vs latitudes and CRs in the cycle 23 - 3D-butterfly diagram (Zharkov et al., 2008, Sol Phys., 258 )

20. Magnetic field of sunspots (SMF) vs latitude averaged over 1 year – 4 years shows fine periodical patterns with Δt ~2.5-3 years Zharkov et al, 2008

21. EOFs and ICs of s/s magnetic field (Zharkova et al. 2012, MNRAS) Halloween events

22. Cycle 23 Magnetic Tilt (left) and EOF (bottom right)

23. Conclusions ICs for sunspots - cycle 23 The variations of the EOFs for the SMF in latitude are also shown to be linked to those of the SBMF. The positions of the maxima and minima of the positive polarity in the EOFs of sunspots follow the patterns of the one of the EOFs (sine), while the sunspot EOFs of negative polarity follow the patterns of the other EOF from the SBMF (cosine). This indicates that the latitudinal variations of the SBMF modulate the latitudinal variations of the SMF. In other words, the SBMF regulates the appearance of magnetic flux tubes on the solar surface, allowing them to have minima at latitudes of ∼ 32◦, 23◦,13◦ and 3◦, where the SBMF (and the sunspot group tilts) has intermediate maxima. The absolute maximum in the tilt magnitudes is approached at the top of the latitudinal zone ±45◦, where SMF EOFs approach zero. Hence, the solar activity of sunspots is modulated by the variations of SBMF

24. BPBP BTBT Ω BTBT BPBP α PARKER DYNAMO Differential rotation Helicity Parker presented a functional scheme for such dynamo as follows. A toroidal magnetic fields is produced from the poloidal field by the action of differential rotation. The inverse process of transforming toroidal magnetic field into poloidal field is realized by the action of alpha-effect.

25. Popova et al, 2013, AnGeo, 31. 2023

26. 21-23 21 –D=700, N=3 22 23- D=10 4, N=9 Popova et al, 2013, AnGeo, 31. 2023

27.  A latitudinal distribution is derived for two primary waves of the background magnetic field (BMF) and two periods:11 and 2.5 years  Observations show that maximums in sunspot components (SMF) correspond to minimums in the BMF components  According to the dynamo theory such waves are result of a composition of two dipoles or one dipole and one quadrupole modes of the poloidal magnetic field  Simulations illustrated that the toroidal and the poloidal magnetic fields have a small phase shift if the intensity of the dynamo waves is equal for both magnetic components  If the dynamo number is a threshold in the upper layers of the convective zone (where observations data for BMF are available), but this number is big in the inner layers (where is generation of the toroidal magnetic field according Parker two-layers model), then maximums in SMF correspond to the BMF minimums Conclusions