Solar Phys (2012) 279:411–418DOI 10.1007/s11207-012-0032-7

Short-Term Periodicity in Solar Mean Magnetic Fieldduring Activity Maximum and Minimum Periods

N. Ye · F.R. Zhu · X.M. Zhou · H.Y. Jia

Received: 6 December 2011 / Accepted: 9 May 2012 / Published online: 8 June 2012© Springer Science+Business Media B.V. 2012

Abstract The short-term periodicity in the solar mean magnetic field (SMMF) observed atthe Wilcox Solar Observatory during the last four activity cycles is investigated by usingLomb–Scargle periodograms. Our results show that the SMMF has main periods of about27, 13.5, and 9 days in both the maximum and minimum years of each activity cycle. TheSMMF has the most dominant period of about 27 days during the activity maxima. However,during the activity minimum years the 13.5-day periodicity is the most significant, exceptfor the minimum of 1984 – 1986. These results indicate that the distribution of active regionsin the activity maximum years is quite different from that in the minimum years.

Keywords Magnetic fields · Periodicity · Solar active region

1. Introduction

The Sun has a strong and complex magnetic field, and solar activity appears to be directlyconnected with the properties of this field. The periodicity in the solar magnetic field hasbeen one of the most active research topics in solar physics. There are a number of stud-ies on the periodicity in solar observational data which are related to the solar magneticfield and its modulation due to solar rotation. In addition to the basic 11-year cycle insunspot numbers and the 22-year cycle in solar magnetic fields, there are shorter period-icities, like the 8 – 11-month periodicity in the solar total UV irradiance, 10.7 cm radio flux,and Ca-K plage index (Pap, Tobiska, and Bouwer, 1990; Oliver, Carbonell, and Ballester,1992), the 150 – 158-day periodicity in strong magnetic fields, solar nuclear gamma rayflares, and sunspot areas (Verma, Joshi, and Paliwal, 1992), periods of 74 days in pro-ton fluence (Das, Nag, and Chatterjee, 1996) and 66 days in polar coronal holes (Daset al., 1994), and the 51-day periodicity in daily sunspot group numbers (Pap, Tobiska,and Bouwer, 1990) and solar flares (Bai, 2003). Of particular importance are the short-term

N. Ye · F.R. Zhu (�) · X.M. Zhou · H.Y. JiaThe Institute of Modern Physics, South-West Jiaotong University, Chengdu, Chinae-mail: zhufr@home.swjtu.edu.cn

412 N. Ye et al.

periods, like 27, 13.5, and 9 days, because they may play an important role in forecast-ing space weather and investigating climate change. The period of about 27 days (Sval-gaard and Wilcox, 1975; Henney and Harvey, 2002; Haneychuk, Kotov, and Tsap, 2003;Neugebauer et al., 2000) in solar magnetic fields and sunspots is the most significantone due to the modulation by solar rotation. The periodicity of 13.5 days in total UV ir-radiance and projected areas of developing complex groups may originate from two ac-tive regions located 180◦ apart in longitude from each other (Donnelly and Puga, 1990;Pap, Tobiska, and Bouwer, 1990; Bobova and Stepanian, 1994). There is also evidence for a13.5-day periodicity in solar magnetic fields observed at the Wilcox Solar Observatory (Dasand Nag, 1999) and by the Solar and Heliosperic Observatory (SOHO) (Boberg et al., 2002).The nine-day periodicity in solar activity can be attributed to triangular distribution of coro-nal holes ≈120◦ apart in longitude (Nayar et al., 2001; Temmer, Vrs̆nak, and Veronig, 2007;Lei et al., 2008). However, so far only a few attempts have been made to investigate the nine-day periodicity in the solar mean magnetic field (SMMF), and to compare the behavior ofthis periodicity in the maximum and minimum years of solar activity separately. Such astudy will provide an excellent chance to investigate the large-scale structure and evolutionof solar magnetic fields. In this paper, the short-term periodicity in the SMMF since 1975will be investigated in detail, by treating activity maximum and minimum years separately,in an attempt to find any difference in the behavior of the short-term periodicity in the ex-treme epochs of solar cycles.

2. Data and Method of Analysis

The solar magnetic field has been measured using a Babcock-type magnetograph attachedto a 23 m vertical Littrow spectrograph at the Wilcox Solar Observatory (Scherrer et al.,1977). Several observations are made daily, centered around local noon. The average stan-dard deviation of all the observations in one day is 0.05 gauss. Each integer value reportedfor the SMMF in µT is a weighted average of all magnetic field measurements for that day.The weighting arises from the effects of solar rotation, limb darkening, and weakening ofthe Zeeman-sensitive absorption line within active regions. Figure 1(a) shows temporal vari-ations in the SMMF represented by more than 10 000 daily records. Similar to sunspots, theSMMF also shows the 11-year solar cycle whose maximum strength occurs at the maximaof solar cycles 21, 22, and 23 and whose minimum strength occurs at the minima of solar

Figure 1 (a) SMMF (µT) vs date in Modified Julian Day (MJD). (b) Power spectrum of SMMF in the periodrange of 2 to 50 days for all the data since 1975. The red dots represent the average values of SMMF foldedby the period and are connected with a continuous curve in panel (b).

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cycles 20/21, 21/22, 22/23, and 23/24. The dominant periods in the SMMF are about 27,13.5, and 9 days, as displayed in Figure 1(b). In order to investigate the difference in theperiodicity between activity minimum and maximum years, the data are classified into twogroups: One group includes three activity maximum years, 1980 – 1982, 1989 – 1991, and2000 – 2002, and the other includes four activity minimum years, 1975 – 1977, 1984 – 1986,1995 – 1997, and 2007 – 2009.

If one uses the conventional Fourier transform in processing the data, which are unevenlyspaced in time and contain large amounts of random noise, a false periodic signal will beproduced. The Lomb–Scargle periodogram, developed by Lomb (1976) and Scargle (1982)and implemented by Horne and Baliunas (1986), is a powerful tool to search periodic pat-terns in a time series. Using the method by Horne and Baliunas (1986), we could detect truemultiple periodic signals in the data, as discussed later in this paper.

The uncertainty in the frequency of the signal can be computed using the formula byKovacs (1981):

�ω = 3πσn

2√

NLtA(1)

where A is the amplitude of the signal, σ 2n is the variance of the noise after the signal has

been subtracted, Lt is the time span of the data set, and N is the number of data points. Thisformula can be applied to unevenly spaced data, although it was derived for evenly spaceddata (Horne and Baliunas, 1986).

3. Results

3.1. Periodicity in Activity Maximum

The normalized power spectra given by the Lomb–Scargle analysis in three activity maxima(cycles 21, 22, and 23) are displayed in Figure 2. We can see the peaks at around 27, 13.5,and 9 days. The most prominent peak is at 27 days; and the peaks at 13.5 and 9 days areweaker. The peak periods and their uncertainties are summarized in Table 1. For all theperiods listed, the false alarm probabilities (also given in Table 1) are very small.

The temporal variation of the detected periodic components in the SMMF can be ob-tained by folding and averaging the data over one period. These results are shown in Fig-ure 3, where the dots are the mean values of the SMMF, and the solid curves are the fittingresults using the harmonic function of the form P0 sin(2πφ + P1) + P2. The values of P0

are also listed in Table 1. The variation amplitudes of the near 27-day period are the largestones among these short periods.

3.2. Periodicity in Activity Minimum

The normalized power spectra given by the Lomb–Scargle analysis in four activity minimaare presented in Figure 4. The SMMF in activity minima also shows periods of about 9,13.5, and 27 days, but the peak at 13.5 days is the highest in the minimum years of 1975 –1977, 1995 – 1997, and 2007 – 2009, the exception being 1984 – 1986. The peak periods andtheir uncertainties are summarized in Table 2. For all the periods listed, the false alarmprobabilities (also given in Table 2) are very small.

Figure 5 is the same as Figure 3, but for the activity minimum years. The values of thecomponent amplitudes are also listed in Table 2. The strongest periodic signals are near the13.5-day period during the activity minimum years, except for 1984 – 1986.

414 N. Ye et al.

Figure 2 Power spectra of SMMF in the period range of 2 to 50 days for activity maximum years of(a) 1980 – 1982, (b) 1989 – 1991, and (c) 2000 – 2002. The red dots represent the average values of SMMFfolded by the period and are connected with a continuous curve in each panel.

Table 1 Peak periods, amplitudes, and false alarm probabilities in the activity maximum years shown inFigure 2.

Cycles 21 22 23

Years 1980 – 1982 1990 – 1991 2000 – 2002

Peak period (days)

9 d 9.24 ± 0.01 9.15 ± 0.01 8.96 ± 0.01

13.5 d 14.13 ± 0.01 13.69 ± 0.01 14.02 ± 0.01

27 d 26.77 ± 0.02 27.02 ± 0.01 26.40 ± 0.01

Amplitude (µT)

9 d 10.3 17.3 15.4

13.5 d 24.6 25.3 13.5

27 d 40.8 57.9 36.8

False alarm probability

9 d 2 × 10−4 4 × 10−12 4 × 10−12

13.5 d < 10−13 < 10−13 5 × 10−10

27 d < 10−13 < 10−13 < 10−13

4. Summary and Discussion

The periodicity in the solar mean magnetic field (SMMF), measured at the Wilcox SolarObservatory from 1975 through 2010, has been examined by dividing the data into activity

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Figure 3 The temporal variationof SMMF folded into one period,in activity maximum years of(a) 1980 – 1982, (b) 1989 – 1991,and (c) 2000 – 2002. In eachpanel, the top, middle, andbottom graphs represent the 9,13.5, and 27-day periodicities.

maximum and minimum years. We found that in both the activity maximum and minimumyears the SMMF shows a 27-day period due to the modulation by solar rotation, a 13.5-dayperiod associated with two active regions located 180◦ apart in longitude, and a nine-dayperiod due to three coronal holes distributed 120◦ apart in longitude from each other. Theamplitudes of all the periodic components in the activity maxima are larger than those in

416 N. Ye et al.

Figure 4 Power spectra of SMMF in the period range of 2 to 50 days for activity minimum years of(a) 1975 – 1977, (b) 1984 – 1986, (c) 1995 – 1997, and (d) 2007 – 2009. The red dots represent the averagevalues of SMMF folded by the period and are connected with a continuous curve in each panel.

Table 2 Peak frequencies, amplitudes, and false alarm probabilities in the activity minimum years shown inFigure 4.

Cycles 20/21 21/22 22/23 23/24

Years 1975 – 1977 1984 – 1986 1995 – 1997 2007 – 2009

Peak period (days)

9 d 9.32 ± 0.01 8.95 ± 0.01 8.93 ± 0.01 8.96 ± 0.01

13.5 d 13.51 ± 0.01 13.72 ± 0.01 13.51 ± 0.01 13.43 ± 0.01

27 d 27.55 ± 0.02 27.19 ± 0.02 27.38 ± 0.04 27.08 ± 0.01

Amplitude (µT)

9 d 2.5 7.1 2.9 2.8

13.5 d 11.0 8.1 7.9 8.2

27 d 9.6 19.5 4.8 2.7

False alarm probability

9 d 3 × 10−3 < 10−13 2 × 10−4 6 × 10−13

13.5 d < 10−13 < 10−13 < 10−13 < 10−13

27 d < 10−13 < 10−13 2 × 10−8 < 10−13

the activity minima, which may be caused by the changes in the intensity of the magneticfield during the solar cycle. The 27-day periodicity is the most significant one among theactivity maximum years, while the 13.5-day periodicity is the most significant one amongthe activity minimum years (except for 1984 – 1986), which shows that the configuration

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Figure 5 The temporal variationof SMMF folded into one period,in activity minimum years of(a) 1975 – 1977, (b) 1984 – 1986,(c) 1995 – 1997, and(d) 2007 – 2009. In each panel,the top, middle, and bottomgraphs represent the 9, 13.5, and27-day periodicities.

of two active regions located 180◦ apart in longitude is more pronounced in the activityminima than in the activity maxima. It reveals differences in the distribution of the solarmagnetic field and the sector structures of the interplanetary magnetic field between theactivity maximum and minimum periods.

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Figure 5 (Continued)

The short-term periodicity of the SMMF in the activity minimum years of 1984 – 1986is different from the other three activity minima studied here, in that the amplitude of the27-day period is larger than the other two periods. It is also peculiar that the amplitudes inthe 9-day and 27-day periods are bigger than those in the other three activity minima. Thereason for this peculiarity requires detailed study.

Acknowledgements This work was supported in part by NSFC (No. 11175147) and by the FundamentalResearch Funds for the Central Universities (No. SWJTU11CX076 and No. SWJTU11BR086).

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