On the cyclicity of solar magnetic fields during cycles 21–23

ISSN 0884�5913, Kinematics and Physics of Celestial Bodies, 2012, Vol. 28, No. 3, pp. 142–148. © Allerton Press, Inc., 2012.Original Russian Text © U.M. Leiko, 2012, published in Kinematika i Fizika Nebesnykh Tel, 2012, Vol. 28, No. 3, pp. 62–72.

142

INTRODUCTION

To date, as a result of numerous studies of cyclicity observed in solar activity (SA), the solar cycle isthought to be represented as a complex interaction in the systems of strong and weak local and large�scalemagnetic fields, respectively [11, 16].

In relation with the anomalous 23rd cycle and a decreasing general level of SA, as well as with theexpected long�standing minimum of SA, the features in evolution of the solar magnetic fields attract agrowing interest. Investigations of configuration and total value of magnetic flux in the solar photosphere[2] revealed significant distinctions in behavior of minima before 23rd and 24th SA cycles, supporting thelong�standing tendency in decreasing SA. As was shown in [16], a progressive diminishing in the strengthof the polar magnetic field during the last three cycles is caused by an increase in the value of magneticdipole moment. Since the magnetic fields of the sun govern various phenomena related with SA, investi�gating features in cyclicity of the solar magnetic fields is an actual task. The aim of this work is to performa comparative analysis of this cyclicity for weak and strong components of the solar magnetic field duringthe last three cycles.

For performing the analysis, we have chosen the data which characterize the magnetic flux corre�sponding to the weak large�scale and strong local components of the solar magnetic field. These are thetemporal rows of general magnetic field of the sun as a star (GMF) and the total average monthly area ofsunspots (Sq).

Sunspots are the most visible manifestation of the local magnetic fields. Their total area on the disk isproportional to the total magnetic flux of spots [8]. This allows one to estimate magnetic flux of the stronglocal component of the field using the observations of Sq.

The general magnetic field of the sun is proportional to the difference between the fluxes of the low�latitude magnetic fields in photosphere with the opposite polarity [4, 5, 7, 13, 14]. Consequently, the vari�ations of GMF are caused by the space�time structure of the low�latitude large�scale solar magnetic fields.

In this study, we have analyzed the cyclic variations in the average monthly values of the aforemen�tioned indexes during the last three cycles. The long�standing tendency in decreasing SA is confirmed. Itis shown that both components of the solar magnetic field weaken in the periods of the so�called monop�olarity of the sun.

DATA AND THE METHOD OF THEIR PROCESSING

For the study, we used regular Stanford’s row of the daily measurements of GMF [http://wso.stan�ford.edu/] and Greenwich’s rows of the monthly values for the total area of sunspots and relative numbersof sunspots (Wolf’s numbers) [http://solarscience.msfc.nasa.gov/greenwch/].

Indexes of the average monthly values of the area of suspots and Wolf’s numbers are well known. Anadvantage of the row values for the total area of sunspots is its duration and internal regularity [8, 11, 12].

The general magnetic field of the sun is measured by a magnetograph using an integral beam of lightfrom the visible disk of the sun. It is determined as a convolution between the distribution of the longitu�dinal component of the surface magnetic field and the weight function of the magnetograph.

On the Cyclicity of Solar Magnetic Fields During Cycles 21–23U. M. Leiko

Astronomical Observatory, Shevchenko National University, ul. Observatornaya 3, Kiev, 04053 UkraineReceived April 15, 2011

Abstract—The cyclicity of weak local and strong large�scale components of the low�latitude solarmagnetic field during the last three cycles of solar activity is studied using the average monthly valuesfor the total area of sunspots and general magnetic field of the sun as a star. A local decrease in the valueof magnetic flux is found for both components of the magnetic field in the phase of growing solar activ�ity. This decrease coincides in time with the intervals of monopolarity for the polar magnetic field ofthe sun.

DOI: 10.3103/S0884591312030051

SOLARPHYSICS

KINEMATICS AND PHYSICS OF CELESTIAL BODIES Vol. 28 No. 3 2012

ON THE CYCLICITY OF SOLAR MAGNETIC FIELDS DURING CYCLES 21–23 143

Details of the magnetographic observations of GMF are described in various papers [4, 5, 7, 13, 14].In essence, a signal of the magnetograph is proportional to the difference between the magnetic fields withthe positive and negative polarity (asymmetry) of magnetic fields in photosphere. In addition, the basicrole in formation of the signal of magnetograph is played by the area and topology of magnetic fields in thephotosphere [5]. In observing GMF, the problem is to obtain one average value of B for twenty�four hours.Magnetographic observations of GMF were carried out in four observatories. Starting from 1992, themeasurements were carried out in Sazerland’s station at the South�African observatory (BiSON group)[15]. The data row of GMF obtained there has a good correlation with Stanford’s row, but the former datadiffer by approximately two times from the latter.

Daily variations in the strength of GMF B of the sun obtained in Stanford’s observatory [13] are shownin Fig. 1. The measured values of B are relatively small—from 10 µT in the minimum of SA, to 200 µT inthe maximum. Therefore, the asymmetry in the low�latitude large�scale magnetic fields has also a maxi�mum in the periods of high SA, as well as the asymmetry of strong local fields [17].

The Stanford’s row of measurements of GMF has the length N = 13014, corresponding to the obser�vation interval of May 15, 1975, to December 31, 2010, with the number of missed observations Nmis =2449 (18.8% of the total length). As one can see from Fig. 1 (at the bottom), the number of the missedobservations for several months was approximately 20 in each case, that is generally caused by the meteo�rological conditions. Consequently, we face with the problem of restoring the data. There are severalapproaches for solving this problem: interpolation, the use of the data obtained in other observatories, andassigning the zero values of B in the days of missed observations [4, 6, 7].

In forming the average monthly rows of B and the modulus B of GMF, we have considered two cases:(1) an irregular row without the missed data of observations; (2) a regular row, which is obtained using theobservational data of GMF collected during the preceding solar turn. Correlation coefficients between thevalues of GMF corresponding to the ith turn, and the values for i–27, i–28, i–29, i–2 turn are equal to0.66, 0.63, 0.53, and 0.57, respectively. We have taken into account the known fact that the spectrum ofGMF contains a numerous group of peaks in the range of the periods of revolution, which are caused bythe recurrence and coherence in the large�scale magnetic structures [6, 7].

Using the daily values of GMF, the total monthly and average monthly rows of the values B and |B| ofGMF were formed, the total monthly rows of the positive (+B) and negative (–B) components of GMF,and the numbers of the missed data Nmis. When forming the average monthly rows in the case of irregularrows, the number of observations for the given month was taken into account.

Comparison of the average monthly values of B and |B| of GMF in the case of regular and irregular rowsshows (Fig. 2) that the values of |B| are nearly the same in both of the cases. A somewhat worse agreementis observed in the case of B values. Obviously, the missed observations have no significant impact on theaverage monthly characteristics of GMF. Owing to this, in the following estimations, we will use the aver�age monthly indexes obtained using the regular rows of these data.

The study of various indexes of solar activity in the framework of a unitary method is frequently usedto compare the results of analysis. Such a method was used in [1] when studying the northern�southernasymmetry in the solar activity, where a brightness of the green coronal emission line, Wolf’s numbers, andtotal magnetic flux were taken as the indexes of SA. As was indicated in [1], this method allowed one to

200

0

–200

2010200520001995199019801975 1985T, years

B, µT

01020

Nmis, days

Fig. 1. Daily variations in the value of GMF of the sun, measured in Stanford’s observatory (upper curve), and the numberof the missed monthly observations (lower curve).

144


LEIKO

compare the results of analysis that are relevant to the objects which appear as a result of completely dif�ferent mechanisms of interaction between the magnetic field and the substance.

Just the same method was used in our work. The temporal rows of GMF, Wolf’s numbers, and total areaof sunspots on the disk of the sun were smoothed by 13 points, and comparative analysis of the obtainedcyclic curves was performed.

FEATURES IN THE CYCLIC VARIATIONS OF MAGNETIC FIELDS

Variations of GMF can be studied by two ways when analyzing the changes in the values of B and |B| forGMF of the sun. The corresponding plots of the average monthly values are displayed in Fig. 3, and thedaily values of GMF are displayed in Fig. 1.

40

20

0

–20

200–20–40 B, µT

80

40

8040200 10060

|B|, µT (b)(a)

Fig. 2. Correlation dependence for the average monthly values of |B| and B in the case of (a) regular and (b) irregular rowsof the values of GMF of the sun.

20

0

–20

201020001980 1990T, years

B, µT

100

50

0

|B|, µT

4000

2000

0

Sq, MDP

200

100

0

W (a)

(b)

(c)

(d)

Fig. 3. Variations in the values of the average monthly Wolf numbers W, total area of sunspots Sq, and general magneticfields of the sun |B| and B in the 21st–23rd cycles. Bold lines were obtained as a result of smoothing by 13 points.



Qualitative analysis of the daily and monthly curves of B values which are modulated by an 11�yearcycle of the sun shows that the last (23rd) cycle differs from the preceding two both in power and in dura�tion. The 23rd cycle is weaker and more prolonged than the preceding ones. In addition, the lower valuesof B corresponding to the GMF in 23rd cycle indicate that the asymmetry of the large�scale magneticfields in the photosphere is also lower than in the preceding cycles, since the asymmetry of magnetic fieldsis proportional to the level of SA.

According to the curve in Fig. 3 (smoothed by 13 points), the cyclic variations in GMF of the sun areas follows. One can observe the alternating periods with the positive and negative polarity of GMF duringthe 21st cycle, while the negative and positive polarities generally prevail in the 22nd and 23rd cycles,respectively. Using the cyclicity data, one cannot conclude whether a definite polarity of GMF is domi�nating, since the duration of the observation period of GMF is insufficiently long. The spectra corre�sponding to the periods which characterize the topology of the surface magnetic fields, have also a differ�ent structure of cycles [6].

The modulus |B| of the magnetic field in the photosphere characterizes only the value of its asymmetrybut not the sign. As was already mentioned, the value of the asymmetry depends on the level of SA and,therefore, it follows the 11th�year cyclicity.

The cyclic variations of the modulus |B| of GMF are similar to the cyclic changes in the Wolf numbersW and the total area of sunspots Sq (two upper panels in Fig. 4). These two indexes indirectly characterizethe magnetic flux corresponding to the weak local component of the solar magnetic field. However, as wasshown in [8], the area of sunspots is a more important physical parameter than the Wolf number. Thisallows one to obtain the sufficiently accurate estimates of magnetic flux corresponding to the strong localcomponent of the low�latitude magnetic field of the sun. This conclusion is confirmed by the dataobtained in other studies [12].

Three cyclic curves in Fig. 3 have a large degree of similarity. As follows from the analysis of positionsof minima on the curves, the minima after the 21st and 23rd cycles of |B| occur later than the minima ofthe Wolf numbers W and the total area of sunspots Sq (Table 1). The opposite situation is observed afterthe 22nd cycle. One should underline that the minima are determined using the smoothed cyclic curvesand they can differ from the physical onset of the cycle (appearance of the high�latitude sunspots corre�sponding to a new cycle). Duration of the cycles determined with the help of the corresponding curves isalso different. The 21st and 22nd cycles of SA for strong local magnetic fields are more prolonged than thecycles for the weak large�scale fields. The opposite picture is observed for the 23rd cycle.

1000

02010200019901980

T, years

1000

0

Sq, MDP

S

N

Fig. 4. Variation of the average monthly values of Sq for the northern (N) and southern (S) hemispheres in the 21st–23rdcycles.

Table 1. Epochs of minima and duration of the cycles of SA according to different indexes (in years)

Cycle |B| GMF Sq W

21 1976.8–1986.6 9.8 1976.2–1986.2 10.0 1976.2–1986.2 10

22 1986.6–1995.9 9.3 1986.2–1996.6 10.4 1986.2–1996.6 10.4

23 1995.9–2009.4 13.5 1996.6–2008.8 12.2 1996.6–2009.1 12.5

146


LEIKO

The general property of the three smoothed cyclic curves are the downfalls near the maxima of SA.However, the downfalls on the cyclic curves of GMF |B| and on the curves of Sq are observed in the phaseof growing SA, while that on the curve of W is in the phase of receding SA. The instants of the first maxi�mum, local minimum, and the second maximum are listed in Table 2 for all of the indexes under study.We can see that the instants of the first maximum of Sq coincides with the instants of maxima of W, andthe moments of maxima of Sq coincides with the moments of the second maximum of W, which occur inthe phase of decreasing Wolf’s numbers.

The difference in behavior of the cyclicity for Sq and W indexes is easily explained. It is known thatdifferent indexes of SA have a different physical meaning and correspond to different aspects of SA. Inrecent time, there has been a discussion concerning the reliability of one or other indexes, their physicalsense, and expediency in their use for certain investigations of SA. It was shown, for example, that the Wolfnumber, the number of groups of sunspots and their total area on the disk are not equivalent [8, 11, 12].These indexes represent physically different characteristics of the formation process of sunspots. A rela�tionship between these indexes was studied in [12]. The most physically sound index is, in the opinion ofmany researchers, the total area of sunspots which is proportional to the magnetic flux.

The local minimum near the phase of SA maximum (the so�called Gnevyshev’s downfall) is observedin many other indexes. To date, its origin is unclear. The Gnevyshev’s downfall near a maximum of thecycle was discovered on the cyclic curves of integral indexes of the magnetic field in the photosphere [9].

One can assume that the double�structured maxima on the cyclic dependences of Sq and W can beassociated with the northern�southern asymmetry of SA, since the epochs of SA maxima are different inthe northern and southern hemispheres. However, this is not so. The double�structured maxima are alsoobserved on the smoothed cyclic curves of Sq and W for both northern and southern hemispheres (Fig. 4).

Table 2. Instants of the onset, minimum, and termination of the downfalls on the smoothed curves of the averagemonthly values of the Wolf numbers W, total area of sunspots Sq, modulus |B| of GMF, and intervals of the magneticfield monopolarity of the sun

Cycle W Sq |B| GMF Monopolarity interval of the sun

21 1979.9 1979.9 1979.6 “–”

1981.0 1980.9 1980.3 1979.9–1981.6

1981.2 1982.0 1981.3

22 1989.4 1989.4 1989.6 “+”

1990.8 1990.3 1990.6 1990.05–1991.25

1991.1 1991.1 1991.5

23 2000.3 2000.3 2000.1 “–”

2001.1 2001.1 2001.3 1999.85–2001.9

2000.8 2002.2 2003.3

1000

0

–1000

2010200019901980T, years

1

2

B, µT

Fig. 5. Variations of the average monthly values of the positive and negative components of |B| during the 21st–23rd cycles.



The southern�northern asymmetry has a different character of the double�structured maximum. Thepresence of such double�maximum structure on the cyclic curves for separate hemispheres has beenknown for a long time [2]. However, this phenomenon was not observed in all of the cycles. The double�structured maxima on the cyclic curves of Sq corresponding to the northern and southern hemisphereshave a different character. The downfall in the phase of growing SA is observed only on the cyclic curvesfor the southern hemisphere, while that in the phase of decreasing SA is observed for the northern hemi�sphere.

The double�maximum structure also have smoothed cyclic curves corresponding to the positive andnegative components of |B| for the general magnetic field of the sun (Fig. 5). The downfalls correspondingto these components are observed in the phase of growing SA, while the asymmetry has the largest valuesin the 21st cycle, moderate values in the 22nd cycle, and it is barely absent in the 21st–23rd cycles.

As is known, the activity of the high�latitude and low�latitude magnetic fields is developed in oppositephases. The changes in polarity of the polar magnetic field in the northern and southern hemispheres donot occur simultaneously [10]. Therefore, the high�latitude field in both of the hemispheres has the samepolarity for some time, and the so�called monopolarity of the sun takes place. The intervals of this monop�olarity in the 21st–23rd cycles are listed in the last line of Table 2.

We see that the intervals of smaller activity in all of the three cyclic curves coincide with the intervals ofmonopolarity of the magnetic field of the sun.

Therefore, despite the fact that the activity of the high�latitude and low�latitude magnetic fields occursin the counterphase, there is a period of time where the change in topology of the high�latitude and low�latitude magnetic fields occurs synchronously.

MAIN RESULTS AND CONCLUSIONS

The comparative analysis of cyclicity for SA indexes has been carried out, determining variations inarea of sunspots and magnetic flux of strong and weak components of the low�latitude magnetic field—the total monthly average area of sunspots, Wolf’s numbers and general magnetic field of the sun as a star.We have confirmed the anomalous character of the 23rd cycle: it is longer in time than the two precedingcycles and weaker in power for all of the indexes under study.

Some details in the cyclicity of these indexes have been found. An interesting feature is a downfall onthe smoothed temporal dependences of Sq and |B| for the general magnetic field of the sun in the growingphase of SA and in the receding phase of W.

Different character of the cyclic curves for Sq and W in epochs of high activity confirms the conclu�sions that these indexes represent physically different characteristics relevant to the process of solar spotformation [8, 11, 12].

The downfall on the cyclic curve of |B| for the general magnetic field of the sun indicates a decrease inasymmetry for the large�scale low�latitude magnetic fields, and consequently, the change in their area,topology, and magnetic flux.

In addition, the downfall on the cyclic curve for Sq indicates a decrease in the magnetic flux of stronglocal component of the low�latitude magnetic field.

Such a downfall is found in all other indexes of SA [9], but its nature proves to be still unknown.A synchronous decrease in the magnetic flux of weak and strong components of the low�latitude mag�

netic field in an epoch of monopolarity for the high�latitude magnetic field is an interesting detail of solarmagnetism and its cyclicity.

REFERENCES1. O. G. Badalyan, V. N. Obridko, Ya. Rybak, and Yu. Sikora, “Quasibiennial Oscillations of the North�South

Asymmetry,” Astron. Rep. 49, 659 (2005).2. Yu. I. Vitinskii, M. Kopetskii, and G. V. Kuklin, Statistics of Spot Formation Activity of the Sun (Nauka, Moscow,

1986) [in Russian].3. K. G. Ivanov and A. F. Kharshiladze, “Beginning of the New Solar Cycle (Cycle 24) in the Large Scale Open

Solar Magnetic Field,” Geomagn. Aeron. 48, 279 (2008).4. V. A. Kotov, “Forty Years of Measurements of the Mean Magnetic Field of the Sun: View from Today,” Bull.

Crim. Astrophys. Observ. 105, 45 (2009).5. V. A. Kotov, N. N. Stepanyan, and Z. A. Shcherbakova, “Contribution of the Background Magnetic Field and

Fields of Active Regions and Spots to the General Solar Magnetic Field,” Izv. Krym. Astrofiz. Observ. 56, 75–83 (1977).

148


LEIKO

6. U. M. Leiko, “Analysis of Spectra of General Solar Magnetic Field Power on Different Phases of ActivityCycle,” Visn. Kiev. Univ., Ser. Astron., No. 37, 29–37 (2001).

7. A. V. Mordvinov and L. A. Plyusnina, “Coherent Structures in the Dynamics of the LargeScale Solar MagneticField,” Astron. Rep. 45, 652 (2001).

8. Yu. A. Nagovitsyn, “To the Description of Long Term Variations in the Solar Magnetic Flux: The Sunspot AreaIndex,” Astron. Lett. 31, 557 (2005).

9. V. N. Obridko and B. D. Shelting, “Global Solar Magnetology and Reference Points of the Solar Cycle,”Astron. Rep. 47, 953 (2003).

10. M. I. Pishkalo, V. P. Babii, and V. G. Ivanchuk, “The North�South Asymmetry of Solar Activity and Reversalsof Global Solar Magnetic Field during 21–23 Activity Cycles,” Visn. Kiev. Univ., Ser. Astron., Nos. 41–42, 86–90 (2005).

11. E. M. Roshchina and A. P. Sarychev, “Rhythm of Physical Sunspot Cycles,” Solar Syst. Res. 44, 81 (2010).12. A. P. Sarychev and E. M. Roshchina, “Comparison of Three Solar Activity Indices Based on Sunspot Observa�

tions,” Solar Syst. Res. 43, 151 (2009).13. P. H. Scherrer, J. M. Wilcox, L. Svalgaard, et al., “The Mean Magnetic Field of the Sun: Observations at Stan�

ford,” Solar Phys. 54, 353–361 (1977).14. A. B. Severny, “The Polar Fields and Time Fluctuations of the Genaral Magnetic Field of the Sun,” in Solar

Magnetic Fields, Proceedings of the IAU Symposium No. 43 (Dordrecht, 1971), pp. 675–695.15. W. J. Chaplin, A. M. Dumbill, Y. Elsworth, et al., “Studies of the Solar Mean Magnetic Field with the Birming�

ham Solar�Oscillations Net Work (BiSON),” Mon. Not. R. Astron. Soc. 343, 813–818 (2003).16. V. N. Obridko and B. D. Shelting, “Anomaly in the Evolution of Global and Large�Scale Solar Magnetic Fields

as the Precursor of Several Upcoming Low Solar Cycle,” Astron. Lett. 35, 279–285 (2009).17. M. Temmer, J. Rybak, P. Bendik, et al., “Hemispheric Sunspot Numbers Rn and Rs from 1945–2004: Cataloge

and N�S Asymmetry Analysis for Solar Cycle 18–23,” Astron. Astrophys. 447, 735–743 (2006).

Documents

On the cyclicity of solar magnetic fields during cycles 21–23