1 Introduction

Long-term measurements of solar magnetic fields revealed a significant weakening of the Sun’s polar fields (Hoeksema 2010; Petrie 2015). During recent decades, sunspot activity levels have also decreased systematically. In Cycle 24, magnetic activity was characterized by a significant north–south asymmetry and by an asynchronous reversal of the Sun’s polar fields (Sun et al. 2015; Golubeva and Mordvinov, 2016, 2017). This unusual behavior of solar activity is a challenge to the dynamo theory.

The flux-transport dynamo models initiated by Wang and Sheeley (1991) and first developed by Durney (1995) and Choudhuri, Schüssler, and Dikpati (1995) generally reproduce the main features of polar field buildup and reversals. Incorporating data on the magnetic fluxes of active regions (ARs) and their tilts as initial conditions, the models reproduce time-spatial patterns of large-scale magnetic fields in Cycles 15 – 21 (Baumann et al. 2004; Cameron et al. 2018; Jiang et al., 2013, 2014).

The latitudinal dependence of AR tilts relative to the equator (Joy’s law) is a basic property of emergent magnetic flux (Kosovichev and Stenflo 2008; Pevtsov et al. 2014; McClintock and Norton 2016). The predominance of positive-tilt ARs was the key ingredient in the Babcock–Leighton dynamo (Babcock 1961; Leighton 1969) and remains in its modern extensions (Choudhuri and Karak 2012; Olemskoy and Kitchatinov 2013; Muñoz-Jaramillo et al. 2013). Analysis of sunspot data from the Mount Wilson and Kodaikanal observatories revealed changes in sunspot group tilts from cycle to cycle (Erofeev 2004; Dasi-Espuig et al., 2010, 2013; McClintock and Norton 2013).

The polar field buildup mainly depends on the appearance of emergent flux, AR tilts, and the speed of the meridional flows. Nevertheless, flux transport modeling could not reproduce weak polar field in Cycles 23 and 24 (Jiang et al. 2010; Upton and Hathaway 2014). Remnant flux of following polarities contributed most of the polar flux. However, remnant flux surges of opposite polarities sometimes also occur. In terms of Hale’s law, these surges usually correspond to dominant leading polarities in every hemisphere.

Joy’s law recognizes the latitudinal dependence of the AR tilt as a weak tendency with significant scatter (Pevtsov et al. 2014; McClintock and Norton 2016; Tlatova et al. 2018). In many of the bipolar magnetic groups, leading-polarity spots appear at higher latitudes than the following-polarity spots. The decay of negative-tilt ARs results in leading-polarity unipolar magnetic regions (UMRs) at higher latitudes than the latitudes for following-polarity regions. Starting from higher latitudes, leading-polarity UMRs are usually transported poleward.

The poleward transport of abnormal UMRs causes related leading-polarity surges (Yeates, Baker, and van Driel-Gesztelyi 2015; Mordvinov, Grigoryev, and Erofeev 2015; Mordvinov et al. 2016; Lockwood et al. 2017). Leading-polarity surges are usually associated with large activity complexes nearby or within the domains of the negative-tilt predominance. Leading-polarity surges result in the cancellation of opposite magnetic polarities in the Sun’s polar zones and in the polar field weakening in Cycles 23 – 24 (Kitchatinov, Mordvinov, and Nepomnyashchikh 2018).

Sometimes, peculiar ARs appear whose orientation violates Hale’s polarity law (Li and Ulrich 2012). These ARs play an important role in the Sun’s polar field evolution (Stenflo and Kosovichev 2012). There are empirical and theoretical reasons to expect that ARs of opposite (anti-Hale) orientation also contribute to the polar field weakening (Jiang, Cameron, and Schüssler 2015). The polar effect of anti-Hale ARs could be estimated by taking their exact orientation into account (McClintock and Norton 2016; Li 2018).

We analyzed synoptic magnetograms and essential properties of magnetic bipolar regions to study the Sun’s polar field buildup in Cycles 20 – 24. A time-latitude analysis of large-scale magnetic fields enables us to study individual features of recent cycles. Taking into account the time-latitude distribution of the emergent magnetic flux and its peculiar properties, we interpret multiple polar field reversals in Cycles 20 and 21.

2 Evolution of the Sun’s Magnetic Fields in Cycles 21 – 24

The photospheric synoptic maps from the Wilcox Solar Observatory (WSO) characterize cyclic and long-term changes in the Sun’s magnetic fields on a stable native scale for 1976 – 2018 (Duvall et al. 1977). We studied changes in the radial component magnetic field (\(B\)) derived from the WSO synoptic maps. Magnetic flux values at latitude \(75^{\circ }\) were assembled in chronological order. The magnetic fluxes in the northern/southern hemispheres are shown in blue/red (Figures 1a, c). This approach presents the high-latitude magnetic fields at a cadence of about 9 hours. The time series quantifies the polar field buildup in details. We smoothed the time series using an algorithm that is based on the non-decimated wavelet transform (Starck and Murtagh 2006). The denoised time series of the magnetic flux (\(B_{{\pm}\,75}\)) are shown in black (Figures 1a, c). Figures 1a, c show cyclic patterns in the Sun’s magnetic field and the polar field reversals. Annual variations appear in high-latitude magnetic fields due to the Earth’s excursions relative to the helioequator.

Figure 1
figure 1

Changes in magnetic fluxes at heliographic latitude \({\pm}\,75 ^{\circ }\) in the northern (a) and southern (c) hemispheres derived from the WSO synoptic maps. The original and denoised values of the polar fluxes are shown in blue/red and black, respectively. The solid/dashed vertical arrows depict the effects of remnant flux surges for following/leading polarities. Zonally averaged magnetic fields are shown in red-to-blue shading (b). Zones of intense sunspot activity, domains of negative tilt, and anti-Hale ARs are shown in black, green, and yellow, respectively.

Full size image

We analyzed changes in high-latitude magnetic fields to understand the polar field buildup in relation to the remnant flux transport. Figure 1b is compiled of zonally averaged magnetic fields that are chronologically ordered rotation by rotation. Positive/negative polarities are shown in blue/red. The color bar saturates at 1.0 G. Blue/red contours indicate domains of magnetic fields that exceed 0.5 G in absolute value. The time-latitude diagram demonstrates cyclic variations in the zonal structure of solar magnetic fields and also characterizes their long-term behavior. During epochs of activity maxima, global rearrangements of the magnetic fields occur.

Most of the Sun’s magnetic flux first appears as ARs that tend to concentrate within activity complexes (ACs) (Gaizauskas et al. 1983). Long-lived ACs represent persistent patterns in magnetic flux emergence (Schrijver and Zwaan 2000). The zones of intense sunspot activity are shown as black spots that overlap on the time-latitude distribution of the magnetic fields. They are identified using zonally averaged sunspot areas that exceed the threshold of 80 μhem/deg. As the cycle progresses, zones of sunspot activity migrate toward the equator according to Spoerer’s law. As the ACs evolved and after their decay, the remnant magnetic fields were dissipated and formed UMRs. The diffusion and advection of the remnant flux determine the further evolution of UMRs (DeVore et al. 1985; Wang and Sheeley 1991). The UMRs of predominantly following polarities are transported poleward as a result of meridional flows (Hathaway and Rightmire 2011).

This diagram shows cyclic rearrangements of large-scale magnetic fields and polar field reversals. After the decay of a large AC, its magnetic fields are dispersed into the surrounding photosphere. Long-lived ACs produce the remnant flux that forms an extensive surge approaching the polar zones. The remnant flux surges are seen as inclined features that are stretched from middle to high latitudes (Figure 1b). They are shaped by differential rotation and meridional flows. In each hemisphere, several surges were usually formed during an 11 yr activity cycle. The approach of the most extensive surges to the Sun’s poles reverses the polar-field. These events are marked by solid yellow arrows in Figure 1b. First surges are usually caused by ARs appearing at latitudes of about \(30^{\circ }\). The shape of these arrows typically corresponds to the averaged velocity profile of meridional flows (Hathaway and Rightmire 2011).

Large domains of highly concentrated magnetic flux show long-living ACs in Cycles 21 – 23. Subsequent surges of following polarities strengthened the high-latitude magnetic fields of new polarities and widened their latitudinal extent. These surges are also marked with solid arrows (Figure 1b). The corresponding magnetic flux changes in \(B_{{\pm}\,75}\) are marked with vertical solid arrows in Figures 1a, c.

According to the Babcock–Leighton concept, the leading-polarity UMRs migrate to the equator where the opposite polarities are annihilated through their reconnection. In the time-latitude diagram, however, the leading-polarity surges are sometimes transported poleward in Cycles 21 – 24. They are marked by dashed yellow arrows in Figure 1b. The poleward transport of opposite magnetic fields results in their cancellation and leads to a decrease in total polar flux (Kitchatinov, Mordvinov, and Nepomnyashchikh 2018).

The extensive following-polarity surges seen in (Figure 1b) accelerate changes in the polar fields (solid arrows, Figures 1a, c). The leading-polarity surges result in local maxima or minima in the polar field buildup according to their polarity (dashed arrows, Figures 1a, c). As a rule, the leading-polarity surges originated after the decay of ARs that are characterized by a high magnetic flux density and non-Joy tilts (Yeates, Baker, and van Driel-Gesztelyi 2015; Mordvinov, Grigoryev, and Erofeev 2015). At high latitudes, leading-polarity surges migrate faster than one should expect in accordance with the typical velocity of meridional flows (Hathaway and Rightmire 2011). This fast propagation of open and closed magnetic fields is possible because of their interchange reconnection (Wang and Sheeley 2004).

In this study, we analyzed sunspot group tilts \(\gamma_{i}\), \(i =1, 2, \ldots , 84\,226\) taken from the DPD catalog (Györi et al. 2004; Baranyi 2015) for 1974 – 2017. We considered the sunspot group tilts in a time-latitude aspect. The scattered distribution of the tilt angles was averaged at each point over its vicinity, which covers 0.87 years in time and \(2^{\circ }\) in latitude. We treat ARs as test magnets and average their tilts without any weights. The local means or medians of noisy and scattered data provide robust estimates of the averaged tilt distribution. The domains of negative-tilt predominance are shown in green (Figure 1b).

Anti-Hale ARs are shown by yellow markers. They were identified using the catalog of bipolar magnetic regions for Cycle 21 (Sheeley and Wang 2016). In Cycles 22 and 23, anti-Hale ARs were identified using Mount Wilson Observatory sunspot records (Howard 1991) and daily magnetograms that were derived by Sokoloff, Khlystova, and Abramenko (2015). A similar technique was applied for Helioseismic and Magnetic Imager/Solar Dynamic Observatory data to determine anti-Hale ARs in Cycle 24.

During solar activity maxima, bipolar ARs of different orientation coexist at the same latitudes. However, our approach and the data we used are not able to identify the effects of individual ARs. The time-latitude distributions show zonally averaged magnetic fields and AR tilts. We can identify a combined effect of multiple ARs. Generally, remnant flux surges are formed through dispersal and interaction of mixed magnetic fields and the further poleward transport of dominant magnetic polarities.

The DPD catalog includes about 75500 ARs that obey Joy’s law. After their decay, UMRs of following polarities are usually formed at higher latitudes. The remnant flux of these ARs contributes most of the polar flux buildup. Regardless of their east-west orientation, anti-Hale ARs of appropriate north–south orientation contribute a minor remnant flux of the same polarity. The decay of non-Joy and anti-Hale ARs of the same north–south orientation results in leading-polarity remnant flux. The decay of anti-Hale ARs of opposite north–south orientation weakened the remnant flux because opposite magnetic polarities were canceled.

Taking into account the variety of AR configurations, it is reasonable to describe cyclic patterns in solar activity using universal terms. We studied dominant polarities in large-scale magnetic patterns in terms of Hale’s law. The term “following-polarity” surge indicates a predominance of ARs that obey Hale’s and Joy’s laws, while the term “leading-polarity” surge indicates a predominance of abnormal ARs and possible deviations from the Babcock–Leighton scenario. Surges of following- and leading-polarities correspond to the regular and stochastic components in remnant flux that is transported to the Sun’s polar zones (Kitchatinov, Mordvinov, and Nepomnyashchikh 2018).

In Cycle 21, multiple reversals of the Sun’s polar fields were observed in both hemispheres. At the North Pole, the polar field changed its dominant polarity from positive to negative by early 1980. Then, the leading-polarity surge approached the pole by early 1981 and resulted in a short-term predominance of positive (leading) polarity (Figure 1b). The poleward transport of positive polarity led to the corresponding increase in \(B _{75}\) that is shown with the dashed arrow in Figure 1a. The leading-polarity surge originated in the decay of the long-lived ACs that occurred at latitudes \(10\,\mbox{--}\,15^{\circ }\) throughout 1979 – 1980 (Figure 1b). These ACs were characterized by the well-defined domains of non-Joy tilt.

The main domain was surrounded by anti-Hale ARs (marked yellow). Positive-(following) polarity UMRs originated in the decay of non-Joy ARs. Positive polarity also resulted from the decay of anti-Hale ARs that surround the domain of negative tilt. In this particular case, the decay of anti-Hale ARs and non-Joy ARs results in a positive-polarity surge that reached the North Pole and led to the second reversal (Figures 1b, 2b). This surge is marked with a dashed arrow that takes its starting point into account. The next surge of following (negative) polarity changed the dominant polarity from positive to negative at the North Pole.

Figure 2
figure 2

Changes in sunspot areas in the northern (a) and southern (c) hemispheres for 1976 – 1986. The time-latitude distribution of the averaged magnetic fields is shown in red-to-blue shading (b). Zones of intense sunspot activity, domains of negative tilt, and anti-Hale ARs are shown in black, green, and yellow, respectively.

Full size image

At the South Pole, multiple reversals occurred late in 1980, early in 1982, and late in 1982. The leading-polarity surge originated in the decay of ACs with abnormal tilts that were concentrated at \(5\,\mbox{--}\,30 ^{\circ }\) for 1981 – 1982 (Figure 1b). The poleward transport of negative-polarity flux changed the dominant polarity from positive to negative in 1982. The incoming flux of opposite polarity is also visible in \(B_{ - 75}\) as the local minimum marked with the dashed arrow in Figure 1c.

Surges of opposite magnetic polarities were also observed in both hemispheres throughout Cycle 22 (Figure 1b). Unlike Cycle 21, the domains of negative tilt predominance were less concentrated in the southern hemisphere. Under such conditions, a three-fold reversal of the polar fields was hardly noticeable in the southern hemisphere. The leading polarities led to a disappearance of polar magnetic flux at both poles, but the incoming fluxes were insufficient to change the dominant magnetic polarities.

Leading-polarity surges also occurred in Cycles 23 – 24 (dashed arrows, Figure 1b). Their effects on high-latitude fields are also marked with dashed arrows (Figures 1a, c). Their possible sources were identified using high-resolution synoptic maps (Mordvinov et al. 2016; Lockwood et al. 2017; Kitchatinov, Mordvinov, and Nepomnyashchikh 2018).

Cycle 24 was characterized by a low activity that evolved asynchronously in the northern and southern hemispheres. The emergent magnetic flux peaked late in 2011 in the northern hemisphere. The decaying ARs resulted in dominant flux of following (positive) polarity that led to polar field reversal by early 2013 (Mordvinov and Yazev 2014; Sun et al. 2015; Petrie and Ettinger 2017). The crucial surge is marked with the solid arrow, while two adjacent surges of leading (negative) polarity are marked with dashed arrows. Prolonged surges of positive polarity originated in the decay of small ARs that existed in the northern hemisphere during 2014 – 2015.

Thus, the time-latitude diagram depicts long-living patterns of emergent magnetic flux and its decay that led to the formation of remnant-flux surges. The poleward transport of UMRs of mixed magnetic polarities and their subsequent cancellation and accumulation led to the polar field buildup. Global rearrangements of solar magnetic fields and polar field reversals clearly shows the causal relations between the local and large-scale magnetic fields. The time-latitude distribution of emergent magnetic flux and its further transformations determine the evolution of the Sun’s polar fields and individual properties of Cycles 21 – 24.

3 A Close Look at the Polar Field Reversals in Cycle 21

To study the polar field reversals in Cycle 21, we analyzed synoptic maps from Kitt Peak Observatory (Jones et al. 1992). The synoptic maps of the photospheric magnetic fields are uniformly sampled over the longitude and sine latitude (\(360\times 180\) pixels). These maps present measurements of solar magnetic fields at higher resolution on an independent scale; ftp://vso.nso.edu/kpvt/synoptic/mag . Figures 2a, c show changes in sunspot areas in the northern (a) and southern (c) hemispheres. Figure 2b depicts zonally averaged magnetic fields in red-to-blue shading by analogy with Figure 1b.

The time-latitude diagram shows the evolution of large-scale magnetic fields in more detail. The crucial surges N1/S1 resulted in the polar field reversals at the northern/southern poles. Zones of intense sunspot activity are shown in black; they correspond to a sunspot area density \({>} \,100~\upmu \mbox{hem/deg}\). The leading-polarity surges N2/S2 led to the short-term predominance of positive/negative polarities at the northern/southern poles. Subsequent surges N3 and S3 changed the signs of the polar-fields as these were after the first reversal. The domains of negative-tilt predominance are shown in green. Anti-Hale ARs are marked with yellow markers. The degree of tilt averaging corresponds to a spatiotemporal element of size 0.26 years in time and \(2^{\circ}\) in latitude.

The time-latitude diagram (Figure 2b) depicts the evolution of the large-scale magnetic fields in more detail. The distribution of emergent flux, its further decay, and the formation of the remnant flux surges agree with the spatiotemporal patterns shown in Figure 1b. The crucial surges of following and leading polarities resulted in peculiar features of Cycle 21 and multiple polar field reversals at the northern and southern poles. It of interest that ARs with “incorrect” orientations contribute 37% of the total magnetic flux that erupted during Cycle 21 (Wang and Sheeley 1989).

It should be noted that previous analyses of the poleward migration of chromospheric filaments (Makarov, Fatianov, and Sivaraman 1983) revealed no triple polar field reversals in Cycle 21. Possibly, stable filaments do not have time to form under fast changes in dominant magnetic polarities.

4 A Triple Polar Field Reversal in Cycle 20

The Sun’s magnetic activity varies on a secular timescale. During the first half of the twentieth century, the amplitudes of the 11-year cycles tended to increase. After the highest Cycle 19, a low-amplitude Cycle 20 occurred for 1964 – 1976. Since then, the level of magnetic activity has decreased. This long-term variability comprises a complete secular (Gleissberg) cycle. Taking into account the abrupt change in the long-term tendency, it is of interest to study the evolution of the magnetic activity after Cycle 19.

The effects of magnetic field structure are also observed in the Sun’s chromosphere. Large unipolar magnetic fields are outlined by chromospheric filaments that trace the lines of polarity inversions. Long-term chromospheric observations were compiled in the synoptic maps of large-scale magnetic fields (McIntosh 1979). Makarov, Fatianov, and Sivaraman (1983) analyzed similar synoptic maps for 1945 – 1981. They studied the global evolution of magnetic fields and found triple reversals of the polar field in Cycles 19 and 20 in the northern hemisphere. So far, there is no convincing physical explanation for these phenomena.

In Cycle 20, the sunspot activity developed asynchronously in the northern and southern hemispheres. The sunspot areas peaked in 1967/1969 in the northern/southern hemispheres (Figures 3a, c). We analyzed synoptic maps from the McIntosh (1979) archive to study the time-latitude distribution of the Sun’s large-scale magnetic fields in Cycle 20. The proxy maps satisfactorily agree with synoptic magnetograms (Snodgrass, Kress, and Wilson 2000). The McIntosh archive covers the period 1964 – 2009 (Webb et al. 2017).

Figure 3
figure 3

Changes in sunspot areas in the northern (a) and southern (c) hemispheres for 1966 – 1974. The distribution of zonally averaged values sign (\(B\)) depicts the time-latitude behavior of large-scale magnetic fields in red-to-blue shading (b). Zones of intense sunspot activity, domains of negative tilt, and anti-Hale ARs are superimposed in black, green, and yellow, respectively. The solid/dashed arrows depict the remnant flux surges of following/leading polarities.

Full size image

The \(\mbox{H}\upalpha \) synoptic charts display lines of magnetic polarity inversion that outline polarity boundaries of large-scale magnetic fields. The polarities of magnetic patterns were inferred from magnetograms (McIntosh 1979; Makarov, Fatianov, and Sivaraman 1983; Makarov and Sivaraman 1986). The digitized maps quantify magnetic patterns by \({\pm}\,1\) according to their polarities. These maps show the distribution of polarity signs without regard to magnetic field strength. The time-latitude distribution of the sign (\(B\)) value shows the appearance of dominant magnetic polarities taking their signs into account.

Figure 3b shows a time-latitude diagram that is compiled of zonally averaged proxy maps for 1966 – 1974. The averaged values of sign (\(B\)) are shown in red-to-blue shading. The diagram depicts dominant magnetic polarities and their changes in Cycle 20. Zones of intense sunspot activity are shown in black, by analogy with Figure 1b. For the period 1966 – 1974, we used sunspot group tilt data from the Mount Wilson Observatory (Howard 1991). Domains of negative tilt predominance were identified from the averaged tilt distribution. The degree of tilt averaging corresponds to a spatiotemporal element of size 0.26 years in time and \(2^{\circ }\) in latitude.

Both sunspot activity and emergent flux are characterized by significant north–south asymmetry. At the South Pole, the polar field reversed at about 1970.2 that is due to the remnant flux surge of negative polarity is marked with a solid arrow (Figure 3b). At the North Pole, the polar field first reversed at 1968.8, changing its sign from negative to positive. It was a regular reversal due to the poleward transport the following (positive) polarity.

In the northern hemisphere, multiple long-lived ACs occurred in 1967 – 1970. A huge surge of leading polarity was formed after the decay of the large activity centers in 1969 – 1970. The domains of non-Joy tilt surrounded the activity center in 1969. Anti-Hale ARs also occurred within the low-latitude base of the negative-polarity surge. It is under such conditions that surges of leading polarity are usually formed. The remnant flux of negative polarity was transported poleward and resulted in the second reversal. Negative polarity dominated at the North Pole from 1971.0 – 1971.5.

The decay of subsequent ACs resulted in the next surge of following (positive) polarity that led to the third reversal at the North Pole. In the southern hemisphere, the decay of usual ARs produced an extensive surge of negative polarity that reached the South Pole and led to a regular reversal. These changes in dominant magnetic polarities at the Sun’s poles agree with the results derived from the poleward migration of chromospheric filaments in Cycle 20 (Makarov, Fatianov, and Sivaraman 1983).

5 Conclusions

Synoptic magnetograms and their analogs from the McIntosh archive were analyzed to study the Sun’s polar-field buildup in Cycles 20 – 24. The evolution of the polar magnetic field of the Sun was studied in relation to cyclic changes in its sunspot activity and large-scale magnetic fields. The extended analysis improved our understanding of polar field evolution with new essential detail. Thus, the causal and evolutionary relations between decaying ACs, remnant flux surges, and polar magnetic field buildup are evident in their time-latitude behavior.

The peculiar properties of recent cycles have shown that the polar field buildup depends on emergent magnetic flux, its subsequent dispersal, and its poleward transport. These processes determine inherent time-latitude patterns that vary from cycle to cycle. Following-polarity surges originate after the decay of long-lived activity centers where ARs with positive (Joy) tilts dominate. Crucial surges of following polarity resulted in polar field reversals. Subsequent surges of following polarities led to a strengthening of the polar flux.

Leading-polarity surges originate in the decay of ARs that violate Joy’s and Hale’s laws. In averaged time-latitude distributions of tilt angles, multiple domains of negative tilt predominance were found. Persistent domains of negative tilt predominance might be caused by some anomalies in the sub-photospheric toroidal field; they also appear in recurrent magnetic bipoles in the upper atmosphere. Sometimes, anti-Hale ARs are concentrated near or within domains of negative-tilt predominance. Generally, it is difficult to distinguish the effect of non-Joy and anti-Hale ARs. A combined effect of non-Joy and anti-Hale ARs resulted in remnant flux surges of leading polarities (in terms of Hale’s law). The poleward transport of opposite magnetic polarities led to the multiple reversals in Cycles 20 and 21. The cancellation of opposite magnetic polarities results in a weaker solar polar flux in Cycles 21 – 24.