Non-axisymmetric Features in Solar Sunspots & Magnetic Fields Distribution

1. NON-AXISIMMETRIC FEATURES IN THE DISTRIBUTIONS OF SUNSPOTS AND PHOTOSPHERIC MAGNETIC FIELDS E.S. VERNOVA, M.I. TYASTO,O.A. DANILOVA IZMIRAN, SPb. Branch, St. Petersburg, Russia; helena@ev13934.spb.edu D. G. BARANOV Ioffe Physical-Technical Institute, St. Petersburg, Russia; d.baranov@bk.ru

2. AimsTo study the non-axisymmetric component of the solar activity, its changes with the 11-year cycle of the Sun, its connection with the active longitudes. MethodAs a measure of the non-axisymmetric component of the solar activity the notion of the longitudinal asymmetry vector is introduced. Modulus of the vector represents the magnitude of the longitudinal asymmetry, while the phase of the vector points to the dominating longitude. Data1. Sunspot data, 1976-2016 (Greenwich- USAF/NOAA ).2. Synoptic maps of the photospheric magnetic field, 1976-2016 (NSO Kitt Peak, KPVT and SOLIS instruments). Each map is represented by a set of 180x360 pixels containing magnetic field strength in gauss 1

3. a Sunspot group Latitude = -11°,longitude =248°, area S=592 Fig.1Vector of the longitudinal asymmetrydefined fora sunspot group as a function of its area S and heliolongitude б Vector: module=S; phase= 2

4. Each daily observation of a sunspot group was associated with a polar vector whose modulus is set equal to the sunspot group area S and whose phase is defined as the longitude of the sunspot group . Next, for a given day (with number k) we introduce the vector sum of all polar vectors corresponding to all N sunspots observed during the day (i=1…N). Finally, for each solar rotation we define the resulting vector as the vector sum for all days of the rotation (k=1…27): Method of the data treatment 3

5. Vector of the longitudinal asymmetry • Sunspot groups living several days or longer make corresponding number of contributions into the vectorof the longitudinal asymmetry . Therefore large long-living sunspot groups play the main role in the magnitude of the longitudinal asymmetry vector. • The method of vector summing of the solar activity reduces the influence of the stochastic component of the solar activity uniformly distributed over longitude. • By means of the vector summing the stable non-axisymmetric component of the solar activity distribution wassingled out. 4

6. Fig. 2Sunspot area (a) and longitudinal asymmetryof the sunspot distribution(b): Gnevyshev-Ohl rule Common features:Longitudinal asymmetry changes in phase with the sunspot area following the 11-year solar cycle. Differences:Module of the longitudi-nal asymmetryvector is 3-4 times smaller than the sunspot area due to reduced contribution of the stochastic compo- nent into the vector sum of the solar activity 5

7. Gnevyshev-Ohl (G-O) rule:the amplitude of an even solar cycle is lower than the amplitude of the following odd cycle. Fig. 2. Relation between maxima of the two successive cycles is shown by the line segments. a. Sunspot area:Gnevyshev-Ohl rule holds true in Solar Cycles 12 - 21. b.Longitudinal asymmetry of the sunspot distribution: only the first pair of each four cycles followed the Gnevyshev-Ohl rule; the next pair followed the “anti-Gnevyshev-Ohlrule”, i.e. the even cycle exceeded the following odd cycle. This is true for Solar Cycles 12 - 23 . Possibly this effect is a manifestation of the 44-year periodicity of the solar activity. 6

8. Fig. 3Sunspot longitudinal distribution for 1874 – 2016 The longitudinal distribution of the large sunspots (Area >100 m.s.h.) is presented in Fig. 3. Sunspots display nearly uniform distribution over the longitude for 1874 – 2016. Preferred longitudes appear when two parts of the solar cycle are considered separately: ascent-maximum phase (АМ) and descent-minimum phase (DМ). The change of the polar field sign and the change of the leading sunspot sign in a hemisphere are the boundaries of the two characteristic periods (AM and DM). The non-axisymmetric component of the solar activity is represented by the phase of the longitudinal asymmetry vector. Distribution of the phase over the longitude was studied for two periods - AM and DM separately. 7

9. Fig. 4.Longitudinal asymmetry of the sunspot distribution for two periods of the solar cycle: (a) ascent-maximum (AM) and (b) descent-minimum (DM) Two phases – AM and DM show opposite patterns of the longitudinal distribution (convex or concave envelope). Corresponding maxima of distribution are located at longitudes ~180° for ascent-maximum and ~0°/360° for descent-minimum. Shifting the DM histogram by 180° and combining it with the AM histogram we obtain total distribution of sunspots in 1874 – 2016 (Fig. 7c). The clearly seen maximum at 180° confirms the stability of the active longitudes. This argues in favour of the rigid rotations of the active longitudes. 8

10. Synoptic maps of the photospheric magnetic field:Resolution of maps:1° in longitude (360steps);180equal steps in sine of the latitude from - 1(South pole)to +1(North pole).Each map contains360x180pixels with the magnetic field strength in gauss (data of theNSO Kitt Peak).Longitudinal distribution of the magnetic field (method):Averaging of the magnetic field over latitudeVector summing ofBi 360 values ofBi for each solar rotation Asymmetry magnitude and dominating longitude for each Carrington rotation(rotations 1646 - 2190) 9

11. Fig. 5 Vector summing of magnetic fields: resulting vector shows the magnitude of the longitudinal asymmetry (vector modulus) and dominating longitude (vector phase) As earlier for the sunspot data, the vector of longitudinal asymmetry is defined by the formula: where Bi - the magnetic field strength in the longitude interval i(i=1:360) CR1689 10

12. Fig. 6Magnetic flux(a) and asymmetry of the flux distribution(b) Latitudes 0°-180° (B >50 GandB<5 G) Comparing the strong and weak magnetic fields:a. Fluxes of the strong and weak magnetic fields are in antiphase. b. Longitudinal asymmetries of the strong and weak fields change in phase. Magnetic flux of the strong fields as well as the asymmetry of both field groups follow the 11-year solar cycle. 11

13. Fig. 7Longitudinal distribution of the strongmagnetic fields(B>50G) Two characteristic periods can be seen in longitudinal distribution of the strong magnetic fields: (a) the ascent-maximum phase (AM) and (b) the descent-minimum phase (DM). For periods AM and DM maxima of the distribution are located around two opposite Carrington longitudes: 180° (AM) и 0°/360° (DM). Shifting the DM histogram by 180°and combining it with the AM histogram gives total distribution of magnetic fields in 1976 - 2016 (c). The maximum clearly seen in Fig. (c). supports the shift of the preferred longitude by 180°during periods of polar reversals and solar activity minima. 12

14. Magnetic fields and active longitudes: From the solar activity minimum to the reversal of the polar field (the AM period, active longitude180°) the sign of the polar magnetic field and the sign of leading sunspots in a hemisphere coincide, while for the period from the reversal to the solar minimum (theDMperiod,active longitude0°/360° ) these polarities are opposite. Connection of the active longitude with the solar cycle phase Longitudinal asymmetry displays maximum at the longitude ~180°for theascent-maximumphase of the solar cycleand at the longitude~0°/360°for the descent-minimum phase. We denote by kthe phase of the 11-year solar cycle such that:k = 1– corresponds to the interval from the minimum to the polar field reversal; k = 2- corresponds to the intervalfrom the reversalto the minimum. Then the location of the distribution maximum (active longitude) is represented by the formula: Active Longitude =  k 13

15. Fig. 8Longitudinal distribution of the weakmagnetic fields(B<5 G) For the weak fields maxima of the longitudinal distribution are located at the longitudes opposite to the longitudes of the strong field concentration: (a) at 0°/360°for the ascent-maximum phase (AM) and (b) at180°for the descent-minimum phase (DM). Combining the AM histogram of distribution with the shifted by 180° DM histogram gives total distribution (c) for 1976 - 2016 with clear minimum at the longitude ~180°(for the strong fields this is the distribution maximum). 14

16. Conclusions 1 Applying the vector summing technique we separated the non-axisymmetriccomponent of the longitudinal distribution of sunspots and magnetic fields (vector of the longitudinal asymmetry). Modulus of the vector represents the magnitude of the longitudinal asymmetry, while the vectorphase points to the dominating longitude. Magnitude of the longitudinal asymmetry Sunspots: The longitudinal asymmetry of sunspots follows the Gnevyshev-Ohl rule only for the first pair out of the four successive solar cycles, while the next pair follows the “anti-rule”, i.e. the even cycle exceeds the odd one. This pattern is repeated during Solar Cycles 12 – 23. Possibly this effect is a manifestation of the 44-year periodicity of the solar activity. Magnetic field: Longitudinal asymmetries of the strong and weak fields change in phase with the magnetic flux of the strong fields following the 11-year solar cycle. The longitudinal asymmetry of the weak fields changes in antiphase with the magnetic flux of these fields. 15

17. Conclusions 2 Phase of the longitudinal asymmetry Phase of the longitudinal asymmetry vector points to the dominating (active) longitude. Distribution of the phase over the longitude was studied for two periods - ascent-maximum and descent-minimum separately. Both for the sunspots and strong magnetic fields the longitudinal distribution displays maximum at the longitude ~180°during ascent-maximum of the solar cycle and at ~0°/360°during descent-minimum. The active longitude changes with the reversals of polarity of the local and global magnetic fields. The maxima of the longitudinal distribution are located at opposite longitudes for the weak and strong magnetic fields. 16

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