PCI analysis of Sunspot and Background Magnetic Field

variations in the cycles 21-23

V.V. Zharkova1, S.I. Zharkov2 , Shepherd S.J.3 and Popova4

Zharkov et al., 2008, Solar Phys., 248Zharkova and Zharkov, 2008, JASR, 45

Zharkova et al., MNRAS, 2012Popova et al, AnnGeo, 2013

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

Automated sunspot detection on SOHO/MDI WL images the original the original imageimage

Detected edges Detected edges

c)c)The found regions (dilated)The found regions (dilated) d) The final detection results d) The final detection results superimposed superimposed e) The extract from d) e) The extract from d)

Zharkov et al, 2005,

Solar Phys., 228

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

North South Asymmetry(averaged by 170 days)

(N-S)/(N+S) (ss –top, ar –bottom) – Zharkov and Zharkova ‘06

Sunspot MF

AR MF

Tilts MT, GT and MT-signaveraged per year

Zharkova and Zharkov, JASR 08

Year MT/sign MT GT

1997 -5.34 4.56 2.831998 +1.91 7.69 5.851999 -1.08 6.54 5.112004/ +0.86 3.16 2.172005 -0.49 2.96 1.87

-6

-4

-2

0

2

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6

8

10

1997 1998 1999 2004 2005

MT

GT

MT/sign

-6

-4

-2

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2

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8

1997 1998 1999 2004 2005

MT

GT

MT/sign

1. SBMF (top) and sunspot MF (bottom)– phase between them is π~11 (Zharkov et al, 2008)

Cycle 23 -Solar Background MF

Sunspot MF

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

PC Analysis of the solar datato find eigenvalues and eigenvectors

Reduces dimensionality of the data array X to Y Searches for eigenvalues of a given array

XT(n,m) obtain matrix

Singular value decomposition of X is X = WΣVT

W(m,m) – matrix of eigenvectors of covariance matrix XXT.

Σ – matrix (m,n) with diagonal eigenvalues V – matrix (m,m) of eigenvectors of XTX

Principal Component Analysis – reduces dimension

Looking for a transformation of the data matrix X (nxp) such that

Y= T X=1 X1+ 2 X2+..+ p Xp

Where =(1 , 2 ,.., p)T is a column vector of weights with

1²+ 2²+..+ p² =1

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

Two main PCs (top) and their residuals (bottom)(lines – minimums of SA)

(Zharkova et al., 2012, MNRAS)

ST22, AOGS12, 13-17 Aug 12, Singapore

~ Sine and cosine waves

Latitudinal ICs in cycles 21-23 (Zharkova et al., 2012, MNRAS)

100 80 60 40 20 0 20 40 60 80

100

Magnitude

Solar latitude (degrees)

0

Main components

All 3 cycles

Cycle 21

Cycle 22

Cycle 23

ICs for 4 largest pairs of eigenvalues

ST22, AOGS12, 13-17 Aug 12, Singapore

21-23 22

21 23

Derivatives of 2 main EOFs

From top left figure above

component 1

component 2

resultant

Cross-correlation of 8 IPs Zharkova et al, MNRAS, 2012

ST22, AOGS12, 13-17 Aug 12,

21-23 22

21 23

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

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

ST22, AOGS12, 13-17 Aug 12, Singapore

Sunspot magnetic flux vs latitudes and CRsin the cycle 23 - 3D-butterfly diagram

(Zharkov et al., 2008, Sol Phys., 258 )

Magnetic field of sunspots (SMF) vs latitude averaged over 1 year – 4 years

shows fine periodical patterns with Δt ~2.5-3 yearsZharkov et al, 2008

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

Halloween events

Cycle 23Magnetic Tilt (left) and EOF

(bottom right)

10

0

80

60

40

20 0 20

40

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0

Mag

nitu

de

Solar latitude (degrees)

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ConclusionsICs 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

BP BT

Ω

BT BP

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.

Popova et al, 2013, AnGeo, 31. 2023

10

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nitu

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21-23

21 –D=700, N=3

22

23- D=104, N=9 Popova et al, 2013, AnGeo, 31. 2023

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