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Evolution of sunspot activity and inversion of the Sun’s polar magnetic field in the current cycle
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ScienceDirect Advances in Space Research 55 (2015) 2739–2743 www.elsevier.com/locate/asr
Evolution of sunspot activity and inversion of the Sun’s polar magnetic field in the current cycle A.V. Mordvinov a,⇑, V.M. Grigoryev a, D.V. Erofeev b a
Institute of Solar-Terrestrial Physics of Siberian Branch of Russian Academy of Sciences, Lermontov st., 126a, Irkutsk 664033, Russia b Ussuriysk Astrophysical Observatory, Russia Received 24 December 2014; received in revised form 7 February 2015; accepted 11 February 2015 Available online 18 February 2015
Abstract A spatiotemporal analysis of the Sun’s magnetic field was carried out to study the polar-field inversion in the current cycle in relation to sunspot activity. The causal relationship between these phenomena was demonstrated in a time-latitude aspect. After decay of long-lived activity complexes their magnetic fields were redistributed into the surrounding photosphere and formed unipolar magnetic regions which were transported to high latitudes. Zones of intense sunspot activity during 2011/2012 produced unipolar magnetic regions of the following polarities, whose poleward drift led to the inversion of the Sun’s polar fields at the North and South Poles. At the North Pole the polar field reversal was completed by May 2013. It was demonstrated that mixed magnetic polarities near the North Pole resulted from violations of Joy’s law at lower latitudes. Later sunspot activity in the southern hemisphere has led to a delay in magnetic polarity reversal at the South Pole. Thus, the north–south asymmetry of sunspot activity resulted in asynchronous polar field reversal in the current cycle. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Solar activity; Sun spots; Solar cycles; Electric and magnetic fields; Solar magnetism
1. Introduction The Sun’s magnetic field exhibits multi-scale and hierarchical behavior. During the 22-year solar cycle the poloidal and toroidal components of the Sun’s magnetic field are transformed into each other and interact with magnetic fields of lesser spatial scales. Emerging segments of the Sun’s toroidal magnetic field appear at the solar surface as active regions (ARs) composed of magnetic bipoles. According to Joy’s law, a typical AR is angled at about 5 degrees, with leading sunspots being closer to the helioequator than following sunspots. Activity complexes (ACs) are composed of interrelated ARs which recur over ⇑ Corresponding author.
E-mail addresses: [email protected] (A.V. Mordvinov), [email protected] (V.M. Grigoryev), [email protected] (D.V. Erofeev). http://dx.doi.org/10.1016/j.asr.2015.02.013 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
several solar rotations. As a rule, long-lived ACs are also characterized by positive tilt angles to the solar equator. After ACs decay, their magnetic fields are redistributed in the surrounding photosphere. According to the empirical concept of Babcock and Leighton, unipolar magnetic regions (UMRs) of following polarities migrate polewards and form the new-cycle polar field while UMRs of leading polarities migrate equatorward (Leighton, 1969). Further development of this concept led to numerical simulations of magnetic flux transport at the Sun’s surface due to differential rotation, meridional flows, and supergranular diffusion (Wang et al., 1989; Wang, 2009). Taking into account the magnetic fluxes of ARs and their tilts as the initial conditions, these models reproduced the build-up and reversals of the Sun’s polar field (Baumann et al., 2004; Dikpati et al., 2004; Schrijver and Liu, 2008; Jiang et al., 2014).
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Based on the Babcock–Leighton mechanism, the flux transport dynamo improved our understanding of longterm changes in sunspot activity and possible causes of the grand minima (Choudhuri et al., 1995; Choudhuri and Karak, 2009; Karak and Choudhuri, 2011; Olemskoy and Kitchatinov, 2013; Karak et al., 2014). According to the flux transport dynamo, positive tilts of magnetic bipoles initiate a latitudinal divergence of opposite magnetic polarities. Further divergence of opposite polarities results in transformation of the toroidal field to the new-cycle poloidal field. The results of numerical modeling describe the main features of cyclic evolution of the Sun’s magnetic fields. Recent analyses of the Sun’s zonal magnetic flux revealed its significant north–south asymmetry that has led to an asynchronous polar-field reversal at the Sun’s poles (Svalgaard and Kamide, 2013; Mordvinov and Yazev, 2014; Kitchatinov and Khlystova, 2014; Sun et al., 2015). Here we investigate the further development of the polar-field inversion in the current cycle in more detail. We examined the solar magnetic fields and changes in their zonal structure in causal relation to sunspot activity. Special attention is paid to UMRs of leading magnetic polarities which sometimes migrate polewards. In particular, whether violations of Joy’s law are responsible for mixed magnetic polarities near the North Pole in the current cycle. 2. Evolution of the Sun’s background magnetic fields in relation to sunspot activity The current cycle 24 started after a deep and prolonged minimum. Due to the long period of spotless days and weak background magnetic fields (Hoeksema, 2010) it became possible to detect the remnant magnetic fields which formed after the decay of the first ACs (Mordvinov and Yazev, 2014). To study the evolution of the Sun’s magnetic fields we analyzed synoptic maps composed of the SOLIS/VSM measurements (Harvey and Worden, 1998). In order to exclude small-scale magnetic fields and measurement errors the original synoptic maps were denoised and smoothed using the walelet decomposition technique. Synoptic maps show the background magnetic fields over the entire solar surface (in the gray-to-white palette). Fig. 1a shows a wavelet denoised synoptic map for Carrington rotation 2079 (January–February 2009) as an example of magnetic field distribution which is characteristic of the beginning of solar cycle 24. In the very beginning of the current cycle there were no sunspots and the background fields were very weak and fragmentary. Negative polarity dominated near the North Pole, while positive polarity dominated at the South Pole. As the cycle progressed, ACs appeared. At the beginning of the current cycle, sunspot activity prevailed in the northern hemisphere. After decay of the first ACs, their magnetic fields dispersed into the surrounding photosphere and formed UMRs of following (positive) polarity. A cau-
Fig. 1. Synoptic maps of solar magnetic fields for CRs 2079 (a), 2102 (b), and 2149 (c) are shown in the gray-to-white palette. Magnetic fields (>200 G in modulus) are shown in black. These are superimposed on given synoptic maps from the nine preceding CRs. The solid/dashed arrows show UMRs of following/leading polarities.
sal relation between ACs, their remnant magnetic fields and high-latitude UMRs is evident at the beginning of the current cycle. The second synoptic map in Fig. 1(b) shows magnetic fields at the phase of activity rise (CR 2102 occurred in October 2010). To study the background magnetic fields in relation to recurrent ACs we superimposed strong preceding magnetic fields on the weak magnetic fields. Strong fields (above 200 G in modulus) are summarized over CRs 2094–2102, thus the black spots in Fig. 1(b) show long-lived ACs which had existed in the course of CR 2102 and during the time interval of nine CRs preceding CR 2102. The black and white arrows indicate UMRs of positive and negative polarities whose evolution is determined by the Sun’s differential rotation and the meridional flows. UMRs of predominantly following polarities are transported polewards. Sometimes UMRs of leading polarities are also transported to higher latitudes. For example, the most extended UMR of positive (leading) polarity in the southern hemisphere stretched over latitudes 10° to 70° within longitudes 225–115°. This UMR is marked by a dashed arrow in Fig. 1(b). The reason for such anomalies will be discussed below. In 2013 zonally averaged magnetic flux demonstrated short-term changes and polarity alternations at the North Pole. These fluctuations resulted from highly mixed magnetic polarities in the northern polar zone. Some ambiguity in the polar flux behavior was also caused by the annual change in the pole seeing conditions due to the Earth’s excursions relative to the helioequator. Taking into account this ambiguity, it was concluded that the zonally averaged magnetic flux at the North Pole reversed its sign by May 2013 (Mordvinov and Yazev, 2014).
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Fig. 1(c) shows a wavelet denoised synoptic map obtained before the inversion of the polar magnetic field at the South Pole (CR 2149, April 2014). Mixed magnetic polarities were observed in April 2014 near the North Pole. In the southern hemisphere, multiple UMRs of negative polarity approached southern polar zone (see Fig. 1(c)). These UMRs were formed after the decay of large ACs that had existed in the southern hemisphere during late2013–early-2014. They in fact predetermined the polar field inversion at the South Pole in the near future. 3. Zonal structure of solar magnetic fields and the polarfields inversion in the current cycle The Sun’s magnetic activity in the current cycle is asynchronous in the northern and southern hemispheres. Sunspot areas (AN ; AS ) quantify the north–south asymmetry of magnetic flux in the current cycle (see Fig. 2(a) and (c)). The north–south asymmetry of the magnetic flux is well defined and both hemispheric fluxes vary in a pulsed regime. To study in detail the inversion of the polar magnetic fields we analysed series of low-resolution synoptic maps composed of SOLIS/VSM measurements during 2009– 2014. Successive synoptic maps of the photospheric magnetic fields were longitudinally averaged for every carrington rotation. Then, a time-latitude diagram was composed of the longitude averages rotation by rotation (CRs 2079– 2152). The magnetic field structure obtained in such a way
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was smoothed using the wavelet decomposition technique. The wavelet-denoised diagram adequately characterizes the distribution of dominant magnetic polarities, although at any given latitude both magnetic polarities are generally mixed. Fig. 2(b) depicts the time-latitude diagram of solar magnetic fields described above. In addition, black spots in Fig. 2(b) localize zones of intense sunspot activity (with spot areas above 70 lsh). The diagram shown in Fig. 2(b) reveals cyclic patterns of opposite magnetic polarities which drift equatorward along with sunspot activity zones. These patterns are the surface manifestations of deep-seated magnetic fields (Choudhuri et al., 1995). In the time-latitude diagram, inclined patterns represent the poleward flux transport due to surface meridional flows. They are mostly related to vast UMRs seen in the synoptic maps (see Fig. 1). Poleward-drifting patterns of following polarities appeared at latitudes about 30°. They were composed of weak, surface magnetic fields that had resulted from the decay of ACs and then transported polewards due to surface meridional flows at about V = 15 m/s velocity (Hathaway, 1996). Thus, zones of intense sunspot activity produced extensive UMRs that reached the Sun’s polar zones. In the northern hemisphere the UMR of positive polarity originated from the sunspot activity impulse that peaked in 2011 (CR 2116). The largest AC observed within this period included active region NOAA 1476. It took about 1.6 years for the remnant field to reach the North
Fig. 2. Changes in sunspot areas in the northern/southern hemisphere (a/c); a time-latitude diagram of the averaged magnetic fields is shown in the grayto-white palette (b). Zones of intense sunspot activity (>70 millionths of the solar hemisphere or lsh) are shown in black. The extended UMRs of negative/positive polarities are marked with white/black arrows. The solid/dashed arrows show the poleward transport of following/leading polarities. Domains of anomalous (negative) tilt are indicated by black contours.
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Pole. We can estimate the meridional transport time by the ratio of the distance between the upper boundary of sunspot belt and the pole to the mean velocity of the meridional flow. The distance corresponds to 60° on the solar surface. The transport time T ¼ ð2pR0 =6Þ=V is estimated to be to 1.55 yr, where R0 is the Sun’s radius. This estimate approximately agrees with the observed transport time. Low sunspot activity at the beginning of the current cycle resulted in a negative polarity UMR in the southern hemisphere. Several large ACs were observed in mid-2012 (e.g., NOAA 1504). After decay of these ACs, multiple UMRs of negative polarity were formed and started to drift southward. These UMRs contributed most of the poleward flux of negative magnetic polarity. It took about two years for those UMRs to approach the South Pole. Throughout the rising phase of solar cycle 24, two UMRs of leading (negative) polarity were observed in the northern hemisphere. These ‘anomalous’ UMRs are marked with white dashed arrows in Fig. 2(b). The UMRs of leading (negative) polarity reached high latitudes and complicated magnetic field structure near the North Pole. At the beginning of the current cycle, the UMR of leading (positive) polarity also appeared in the southern hemisphere. This UMR stretched to the South Pole and strengthened the polar field. Subsequent UMRs resulted in the predominance of negative polarity within a wide latitude range. According to the Babcock–Leighton concept, magnetic fields of decaying ACs are dispersed into the surrounding photosphere. The remnant fields are also characterized by a tilt angle that is intrinsic to the emerging magnetic bipoles. According to Joy’s law the tilts of bipolar ARs are positive on average, so their leading magnetic poles are closer to the solar equator as compared to the following ones. However, Joy’s law is not rigorous — it is only a statistical regularity. Tilt angles in fact reveal large random variations, and a significant number of the ARs demonstrate negative tilts, with leading poles at higher latitudes than their following poles. As a result, a large-scale magnetic field formed by the Babcock–Leighton mechanism should undergo large random fluctuations. Tilt angles of sunspot groups have been measured in Ussuriysk Astrophysical Observatory (Erofeev, 2001). On average, tilt angles are positive, and tilts increase with increasing latitude in agreement with Joy’s law. Significant number (about 28%) of the spot groups, however, demonstrate negative tilts. We estimated averaged tilts of sunspot groups in the current cycle to compare their time-latitude distribution with the time-latitude diagram of solar magnetic fields above. Domains of anomalous (negative) tilt angles were superimposed on Fig. 2(b) and marked by black contours. Within these domains Joy’s law is violated: leading sunspots appear at higher latitudes compared to those of following sunspots. This comparison makes it obvious that UMRs of leading polarities are associated with domains of negative
tilts. So, the two pronounced UMRs of leading (negative) polarity analyzed in the northern hemisphere mentioned above originated from domains of negative tilts at latitudes of 10–15°. Also, the UMR of leading (positive) polarity that appeared in the southern hemisphere in late 2010 was associated with the domains of negative tilts located at a latitude of about 15°. However, domains of negative tilts near the solar equator (such as two domains in 2012–2013) yield no pronounced poleward drifting UMRs. This possibly is explained by the fact that the velocity of meridional flow decreases near the equator. 4. Conclusion The spatiotemporal analysis of the Sun’s magnetic field clearly demonstrated the causal relationship between sunspot activity and polar field inversion. Special features of the polar field inversion in the current cycle are interpreted according to the flux transport dynamo. The north–south asymmetry of sunspot activity on the rising phase of the current cycle led to the asynchrony of the polar field reversal. The UMR of crucial importance that led to the polar field reversal at the North Pole originated from the decay of ACs in 2011. It took about 1.6 years for the UMR to reach the pole and led to the reversal at the North Pole. There was long period of short-term changes in zonally averaged polar magnetic flux, however, the reversal completed by May 2013. In parallel with UMRs of following polarity, two UMRs of leading polarity reached the northern polar zone and led to mixed magnetic polarity there. These UMRs of negative polarity originated from low-latitude magnetic bipoles which are characterized by negative tilt angles contrary to Joy’s law. Thus, the Sun’s polar fields are mainly determined by the properties of low-latitude magnetic fields. A moderate activity rise in mid-2012 resulted in most of the poleward magnetic flux in the southern hemisphere. It took about two years for the UMR of negative polarity to approach the South Pole. This UMR had reached subpolar zone by late-2013 when strong sunspot activity occurred in the southern hemisphere. The later sunspot activity in the southern hemisphere has led to the delay of the polar-field reversal at the South Pole compared to that at the North Pole. Thus, our analysis demonstrates that the Sun’s polar field reversal is approaching its completion. Acknowledgments This work utilizes SOLIS data obtained by the NSO Integrated Synoptic Program (NISP), managed by the National Solar Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation. The authors also employ
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sunspot database of MSFC of NASA. This work was supported by the project II.16.3.1 under the Program of Fundamental Research of SB RAS. References Baumann, I., Schmitt, D., Schu¨ssler, M., Solanki, S.K., 2004. Evolution of the large-scale magnetic field on the solar surface: a parameter study. Astron. Astrophys. 426, 1075–1091. Choudhuri, A.R., Karak, B.B., 2009. A possible explanation of the Maunder minimum from a flux transport dynamo model. Res. Astron. Astrophys. 9, 953–958. Choudhuri, A.R., Schu¨ssler, M., Dikpati, M., 1995. The solar dynamo with meridional circulation. Astron. Astrophys. 303, L29–L32. Dikpati, M., de Toma, G., Gilman, P.A., Arge, C.N., White, O.R., 2004. Diagnostics of polar field reversal in solar cycle 23 using a flux transport dynamo model. Astrophys. J. 601, 1136–1152. Erofeev, D.V., 2001. The relationship between solar activity and the largescale axisymmetric magnetic field. Solar Phys. 198, 31–50. Harvey, J., Worden, J., 1998. In: Balasubramaniam, K.S., Harvey, J., Rabin, D. (Eds.), Synoptic Solar Physics, ASP Conf. Ser., vol. 140. pp. 161–173. Hathaway, D.H., 1996. Doppler measurements of the Sun’s meridional flow. Astrophys. J. 460, 1027–1033. Hoeksema, J.T., 2010. Evolution of the large-scale magnetic field over three solar cycles. In: Kosovichev, A.G., Andrei, A.H., Rozelot, J.-P. (Eds.), Solar and Stellar Variability: Impact on Earth and Planets, Proc. IAU Symp., vol. 264, pp. 222–228.
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Jiang, J., Cameron, R.H., Schu¨ssler, M., 2014. Effects of the scatter in sunspot group tilt angles on the large-scale magnetic field at the solar surface. Astrophys. J. 791, 5. Karak, B.B., Choudhuri, A.R., 2011. The Waldmeier effect and the flux transport solar dynamo. Mon. Not. R. Astron. Soc. 410, 1503–1512. Karak, B.B., Jiang, J., Miesch, M.S., Charbonneau, P., Choudhuri, A.R., 2014. Flux transport dynamos: from kinematics to dynamics. Space Sci. Rev. 186, 561–602. Kitchatinov, L.L., Khlystova, A.I., 2014. North–south asymmetry of solar dynamo in the current activity cycle. Astron. Lett. 40, 663–666. Leighton, R.B., 1969. A magneto-kinematic model of the solar cycle. Astrophys. J. 156, 1–26. Mordvinov, A.V., Yazev, S.A., 2014. Reversals of the Sun’s polar magnetic fields in relation to activity complexes and coronal holes. Solar Phys. 289, 1971–1981. Olemskoy, S.V., Kitchatinov, L.L., 2013. Grand minima and north–south asymmetry of solar activity. Astrophys. J. 777, 71. Schrijver, C.J., Liu, Yang, 2008. The global solar magnetic field through a full sunspot cycle: observations and model results. Solar Phys. 252, 19– 31. Sun, X., Hoeksema, J.T., Liu, Yang, Zhao, Junwei, 2015. On polar magnetic field reversal and surface flux transport during solar cycle 24. Astrophys. J. 798, 114. Svalgaard, L., Kamide, Y., 2013. Asymmetric solar polar field reversals. Astrophys. J. 763, 23. Wang, Y.-M., 2009. Coronal holes and open magnetic flux. Space Sci. Rev. 144, 383–399. Wang, Y.M., Nash, A.G., Sheeley, N.R., 1989. Magnetic flux transport on the sun. Science 245, 712–718.
ScienceDirect Advances in Space Research 55 (2015) 2739–2743 www.elsevier.com/locate/asr
Evolution of sunspot activity and inversion of the Sun’s polar magnetic field in the current cycle A.V. Mordvinov a,⇑, V.M. Grigoryev a, D.V. Erofeev b a
Institute of Solar-Terrestrial Physics of Siberian Branch of Russian Academy of Sciences, Lermontov st., 126a, Irkutsk 664033, Russia b Ussuriysk Astrophysical Observatory, Russia Received 24 December 2014; received in revised form 7 February 2015; accepted 11 February 2015 Available online 18 February 2015
Abstract A spatiotemporal analysis of the Sun’s magnetic field was carried out to study the polar-field inversion in the current cycle in relation to sunspot activity. The causal relationship between these phenomena was demonstrated in a time-latitude aspect. After decay of long-lived activity complexes their magnetic fields were redistributed into the surrounding photosphere and formed unipolar magnetic regions which were transported to high latitudes. Zones of intense sunspot activity during 2011/2012 produced unipolar magnetic regions of the following polarities, whose poleward drift led to the inversion of the Sun’s polar fields at the North and South Poles. At the North Pole the polar field reversal was completed by May 2013. It was demonstrated that mixed magnetic polarities near the North Pole resulted from violations of Joy’s law at lower latitudes. Later sunspot activity in the southern hemisphere has led to a delay in magnetic polarity reversal at the South Pole. Thus, the north–south asymmetry of sunspot activity resulted in asynchronous polar field reversal in the current cycle. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Solar activity; Sun spots; Solar cycles; Electric and magnetic fields; Solar magnetism
1. Introduction The Sun’s magnetic field exhibits multi-scale and hierarchical behavior. During the 22-year solar cycle the poloidal and toroidal components of the Sun’s magnetic field are transformed into each other and interact with magnetic fields of lesser spatial scales. Emerging segments of the Sun’s toroidal magnetic field appear at the solar surface as active regions (ARs) composed of magnetic bipoles. According to Joy’s law, a typical AR is angled at about 5 degrees, with leading sunspots being closer to the helioequator than following sunspots. Activity complexes (ACs) are composed of interrelated ARs which recur over ⇑ Corresponding author.
E-mail addresses: [email protected] (A.V. Mordvinov), [email protected] (V.M. Grigoryev), [email protected] (D.V. Erofeev). http://dx.doi.org/10.1016/j.asr.2015.02.013 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
several solar rotations. As a rule, long-lived ACs are also characterized by positive tilt angles to the solar equator. After ACs decay, their magnetic fields are redistributed in the surrounding photosphere. According to the empirical concept of Babcock and Leighton, unipolar magnetic regions (UMRs) of following polarities migrate polewards and form the new-cycle polar field while UMRs of leading polarities migrate equatorward (Leighton, 1969). Further development of this concept led to numerical simulations of magnetic flux transport at the Sun’s surface due to differential rotation, meridional flows, and supergranular diffusion (Wang et al., 1989; Wang, 2009). Taking into account the magnetic fluxes of ARs and their tilts as the initial conditions, these models reproduced the build-up and reversals of the Sun’s polar field (Baumann et al., 2004; Dikpati et al., 2004; Schrijver and Liu, 2008; Jiang et al., 2014).
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Based on the Babcock–Leighton mechanism, the flux transport dynamo improved our understanding of longterm changes in sunspot activity and possible causes of the grand minima (Choudhuri et al., 1995; Choudhuri and Karak, 2009; Karak and Choudhuri, 2011; Olemskoy and Kitchatinov, 2013; Karak et al., 2014). According to the flux transport dynamo, positive tilts of magnetic bipoles initiate a latitudinal divergence of opposite magnetic polarities. Further divergence of opposite polarities results in transformation of the toroidal field to the new-cycle poloidal field. The results of numerical modeling describe the main features of cyclic evolution of the Sun’s magnetic fields. Recent analyses of the Sun’s zonal magnetic flux revealed its significant north–south asymmetry that has led to an asynchronous polar-field reversal at the Sun’s poles (Svalgaard and Kamide, 2013; Mordvinov and Yazev, 2014; Kitchatinov and Khlystova, 2014; Sun et al., 2015). Here we investigate the further development of the polar-field inversion in the current cycle in more detail. We examined the solar magnetic fields and changes in their zonal structure in causal relation to sunspot activity. Special attention is paid to UMRs of leading magnetic polarities which sometimes migrate polewards. In particular, whether violations of Joy’s law are responsible for mixed magnetic polarities near the North Pole in the current cycle. 2. Evolution of the Sun’s background magnetic fields in relation to sunspot activity The current cycle 24 started after a deep and prolonged minimum. Due to the long period of spotless days and weak background magnetic fields (Hoeksema, 2010) it became possible to detect the remnant magnetic fields which formed after the decay of the first ACs (Mordvinov and Yazev, 2014). To study the evolution of the Sun’s magnetic fields we analyzed synoptic maps composed of the SOLIS/VSM measurements (Harvey and Worden, 1998). In order to exclude small-scale magnetic fields and measurement errors the original synoptic maps were denoised and smoothed using the walelet decomposition technique. Synoptic maps show the background magnetic fields over the entire solar surface (in the gray-to-white palette). Fig. 1a shows a wavelet denoised synoptic map for Carrington rotation 2079 (January–February 2009) as an example of magnetic field distribution which is characteristic of the beginning of solar cycle 24. In the very beginning of the current cycle there were no sunspots and the background fields were very weak and fragmentary. Negative polarity dominated near the North Pole, while positive polarity dominated at the South Pole. As the cycle progressed, ACs appeared. At the beginning of the current cycle, sunspot activity prevailed in the northern hemisphere. After decay of the first ACs, their magnetic fields dispersed into the surrounding photosphere and formed UMRs of following (positive) polarity. A cau-
Fig. 1. Synoptic maps of solar magnetic fields for CRs 2079 (a), 2102 (b), and 2149 (c) are shown in the gray-to-white palette. Magnetic fields (>200 G in modulus) are shown in black. These are superimposed on given synoptic maps from the nine preceding CRs. The solid/dashed arrows show UMRs of following/leading polarities.
sal relation between ACs, their remnant magnetic fields and high-latitude UMRs is evident at the beginning of the current cycle. The second synoptic map in Fig. 1(b) shows magnetic fields at the phase of activity rise (CR 2102 occurred in October 2010). To study the background magnetic fields in relation to recurrent ACs we superimposed strong preceding magnetic fields on the weak magnetic fields. Strong fields (above 200 G in modulus) are summarized over CRs 2094–2102, thus the black spots in Fig. 1(b) show long-lived ACs which had existed in the course of CR 2102 and during the time interval of nine CRs preceding CR 2102. The black and white arrows indicate UMRs of positive and negative polarities whose evolution is determined by the Sun’s differential rotation and the meridional flows. UMRs of predominantly following polarities are transported polewards. Sometimes UMRs of leading polarities are also transported to higher latitudes. For example, the most extended UMR of positive (leading) polarity in the southern hemisphere stretched over latitudes 10° to 70° within longitudes 225–115°. This UMR is marked by a dashed arrow in Fig. 1(b). The reason for such anomalies will be discussed below. In 2013 zonally averaged magnetic flux demonstrated short-term changes and polarity alternations at the North Pole. These fluctuations resulted from highly mixed magnetic polarities in the northern polar zone. Some ambiguity in the polar flux behavior was also caused by the annual change in the pole seeing conditions due to the Earth’s excursions relative to the helioequator. Taking into account this ambiguity, it was concluded that the zonally averaged magnetic flux at the North Pole reversed its sign by May 2013 (Mordvinov and Yazev, 2014).
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Fig. 1(c) shows a wavelet denoised synoptic map obtained before the inversion of the polar magnetic field at the South Pole (CR 2149, April 2014). Mixed magnetic polarities were observed in April 2014 near the North Pole. In the southern hemisphere, multiple UMRs of negative polarity approached southern polar zone (see Fig. 1(c)). These UMRs were formed after the decay of large ACs that had existed in the southern hemisphere during late2013–early-2014. They in fact predetermined the polar field inversion at the South Pole in the near future. 3. Zonal structure of solar magnetic fields and the polarfields inversion in the current cycle The Sun’s magnetic activity in the current cycle is asynchronous in the northern and southern hemispheres. Sunspot areas (AN ; AS ) quantify the north–south asymmetry of magnetic flux in the current cycle (see Fig. 2(a) and (c)). The north–south asymmetry of the magnetic flux is well defined and both hemispheric fluxes vary in a pulsed regime. To study in detail the inversion of the polar magnetic fields we analysed series of low-resolution synoptic maps composed of SOLIS/VSM measurements during 2009– 2014. Successive synoptic maps of the photospheric magnetic fields were longitudinally averaged for every carrington rotation. Then, a time-latitude diagram was composed of the longitude averages rotation by rotation (CRs 2079– 2152). The magnetic field structure obtained in such a way
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was smoothed using the wavelet decomposition technique. The wavelet-denoised diagram adequately characterizes the distribution of dominant magnetic polarities, although at any given latitude both magnetic polarities are generally mixed. Fig. 2(b) depicts the time-latitude diagram of solar magnetic fields described above. In addition, black spots in Fig. 2(b) localize zones of intense sunspot activity (with spot areas above 70 lsh). The diagram shown in Fig. 2(b) reveals cyclic patterns of opposite magnetic polarities which drift equatorward along with sunspot activity zones. These patterns are the surface manifestations of deep-seated magnetic fields (Choudhuri et al., 1995). In the time-latitude diagram, inclined patterns represent the poleward flux transport due to surface meridional flows. They are mostly related to vast UMRs seen in the synoptic maps (see Fig. 1). Poleward-drifting patterns of following polarities appeared at latitudes about 30°. They were composed of weak, surface magnetic fields that had resulted from the decay of ACs and then transported polewards due to surface meridional flows at about V = 15 m/s velocity (Hathaway, 1996). Thus, zones of intense sunspot activity produced extensive UMRs that reached the Sun’s polar zones. In the northern hemisphere the UMR of positive polarity originated from the sunspot activity impulse that peaked in 2011 (CR 2116). The largest AC observed within this period included active region NOAA 1476. It took about 1.6 years for the remnant field to reach the North
Fig. 2. Changes in sunspot areas in the northern/southern hemisphere (a/c); a time-latitude diagram of the averaged magnetic fields is shown in the grayto-white palette (b). Zones of intense sunspot activity (>70 millionths of the solar hemisphere or lsh) are shown in black. The extended UMRs of negative/positive polarities are marked with white/black arrows. The solid/dashed arrows show the poleward transport of following/leading polarities. Domains of anomalous (negative) tilt are indicated by black contours.
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Pole. We can estimate the meridional transport time by the ratio of the distance between the upper boundary of sunspot belt and the pole to the mean velocity of the meridional flow. The distance corresponds to 60° on the solar surface. The transport time T ¼ ð2pR0 =6Þ=V is estimated to be to 1.55 yr, where R0 is the Sun’s radius. This estimate approximately agrees with the observed transport time. Low sunspot activity at the beginning of the current cycle resulted in a negative polarity UMR in the southern hemisphere. Several large ACs were observed in mid-2012 (e.g., NOAA 1504). After decay of these ACs, multiple UMRs of negative polarity were formed and started to drift southward. These UMRs contributed most of the poleward flux of negative magnetic polarity. It took about two years for those UMRs to approach the South Pole. Throughout the rising phase of solar cycle 24, two UMRs of leading (negative) polarity were observed in the northern hemisphere. These ‘anomalous’ UMRs are marked with white dashed arrows in Fig. 2(b). The UMRs of leading (negative) polarity reached high latitudes and complicated magnetic field structure near the North Pole. At the beginning of the current cycle, the UMR of leading (positive) polarity also appeared in the southern hemisphere. This UMR stretched to the South Pole and strengthened the polar field. Subsequent UMRs resulted in the predominance of negative polarity within a wide latitude range. According to the Babcock–Leighton concept, magnetic fields of decaying ACs are dispersed into the surrounding photosphere. The remnant fields are also characterized by a tilt angle that is intrinsic to the emerging magnetic bipoles. According to Joy’s law the tilts of bipolar ARs are positive on average, so their leading magnetic poles are closer to the solar equator as compared to the following ones. However, Joy’s law is not rigorous — it is only a statistical regularity. Tilt angles in fact reveal large random variations, and a significant number of the ARs demonstrate negative tilts, with leading poles at higher latitudes than their following poles. As a result, a large-scale magnetic field formed by the Babcock–Leighton mechanism should undergo large random fluctuations. Tilt angles of sunspot groups have been measured in Ussuriysk Astrophysical Observatory (Erofeev, 2001). On average, tilt angles are positive, and tilts increase with increasing latitude in agreement with Joy’s law. Significant number (about 28%) of the spot groups, however, demonstrate negative tilts. We estimated averaged tilts of sunspot groups in the current cycle to compare their time-latitude distribution with the time-latitude diagram of solar magnetic fields above. Domains of anomalous (negative) tilt angles were superimposed on Fig. 2(b) and marked by black contours. Within these domains Joy’s law is violated: leading sunspots appear at higher latitudes compared to those of following sunspots. This comparison makes it obvious that UMRs of leading polarities are associated with domains of negative
tilts. So, the two pronounced UMRs of leading (negative) polarity analyzed in the northern hemisphere mentioned above originated from domains of negative tilts at latitudes of 10–15°. Also, the UMR of leading (positive) polarity that appeared in the southern hemisphere in late 2010 was associated with the domains of negative tilts located at a latitude of about 15°. However, domains of negative tilts near the solar equator (such as two domains in 2012–2013) yield no pronounced poleward drifting UMRs. This possibly is explained by the fact that the velocity of meridional flow decreases near the equator. 4. Conclusion The spatiotemporal analysis of the Sun’s magnetic field clearly demonstrated the causal relationship between sunspot activity and polar field inversion. Special features of the polar field inversion in the current cycle are interpreted according to the flux transport dynamo. The north–south asymmetry of sunspot activity on the rising phase of the current cycle led to the asynchrony of the polar field reversal. The UMR of crucial importance that led to the polar field reversal at the North Pole originated from the decay of ACs in 2011. It took about 1.6 years for the UMR to reach the pole and led to the reversal at the North Pole. There was long period of short-term changes in zonally averaged polar magnetic flux, however, the reversal completed by May 2013. In parallel with UMRs of following polarity, two UMRs of leading polarity reached the northern polar zone and led to mixed magnetic polarity there. These UMRs of negative polarity originated from low-latitude magnetic bipoles which are characterized by negative tilt angles contrary to Joy’s law. Thus, the Sun’s polar fields are mainly determined by the properties of low-latitude magnetic fields. A moderate activity rise in mid-2012 resulted in most of the poleward magnetic flux in the southern hemisphere. It took about two years for the UMR of negative polarity to approach the South Pole. This UMR had reached subpolar zone by late-2013 when strong sunspot activity occurred in the southern hemisphere. The later sunspot activity in the southern hemisphere has led to the delay of the polar-field reversal at the South Pole compared to that at the North Pole. Thus, our analysis demonstrates that the Sun’s polar field reversal is approaching its completion. Acknowledgments This work utilizes SOLIS data obtained by the NSO Integrated Synoptic Program (NISP), managed by the National Solar Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation. The authors also employ
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