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Advances in Space Research 40 (2007) 1917–1920

Monopolar structure of the Sun in between polar reversalsand in Maunder Minimum

D.K. Callebaut a,*, V.I. Makarov b, A.G. Tlatov c

a Physics Department, Campus Groenenborger, University of Antwerp, B-2020 Antwerp, Belgiumb Pulkovo Astronomical Observatory, 196140 St. Petersburg, Russia

c Kislovodsk Solar Station, 357700 Kislovodsk, Russia

Received 1 November 2006; received in revised form 31 January 2007; accepted 16 April 2007

Abstract

After a polar reversal in one hemisphere the Sun has two polar caps of the same sign, leaving it in a kind of monopolar state. It maytake months before a polar reversal occurs in the other hemisphere. The situation may have been extreme in the Maunder Minimumwhere the northern hemisphere most probably did not have polar reversals during several cycles, while the southern hemisphere mayhave had some. This may affect the interplanetary field and thus the cosmic rays reaching the Earth. Using the relation between the Wolfnumber and the speed of the global magnetic field regions the yearly mean Wolf number has to exceed 40 in order to have polar reversals,hence per hemisphere we expect that it must exceed 20. This may be used to give a definition of a deep minimum.� 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Maunder Minimum; Global magnetic regions; Polar reversals; Sunspots; Cosmic rays; Asymmetry

1. Introduction

Early solar cycles and solar activity can be reconstructedusing proxies like tree rings ðC14Þ, polar ice ðBe10Þ, auroras,etc. (Beer et al., 1998; Lee and Lee, 2006; Usoskin et al.,2006). This allows to go much further back in the past(10,000 years and even more) than using direct observa-tions of sunspots which go back to the beginning of1600. Moreover, fairly systematic observations of sunspotsdate from about 1660 (Ribes and Besme-Ribes, 1993). Thehistoric and scientific interests are obvious as those archae-ological investigations allow to understand better the solarmagnetism and the solar variability and thus the space cli-mate. This may be very relevant in making predictions.

The present contribution deals with the Maunder Mini-mum. This period turns out to be more and more interest-ing because of its low sunspot numbers. The Maunder

0273-1177/$30 � 2007 COSPAR. Published by Elsevier Ltd. All rights reserv

doi:10.1016/j.asr.2007.04.107

* Corresponding author.E-mail addresses: Dirk.Callebaut@ua.ac.be (D.K. Callebaut), Solar@

narzan.com (A.G. Tlatov).

Minimum (1645–1715) was a deep minimum, characterizedby very few sunspots (1–2 orders of magnitude less thanduring normal cycles; a more quantitative definition willbe given below). The question arises whether there weresolar cycles at all during the Maunder Minimum althoughthe observations of C14 and Be10 still indicate a more or lesscyclic behavior. However, the period was not always thesame: sometimes it looked rather 22 years (see, e.g. Usoskinet al., 2000; Mursula et al., 2001). Here it will be madeplausible that during the Maunder Minimum polar rever-sals did happen seldom or not at all in the northern hemi-sphere of the Sun and that they may not always havehappened in the southern hemisphere (Callebaut et al.,2005). Without polar reversal the cycle does not reallyend and it is suggested to take as a definition of a cycle thatit contains a polar reversal. In view of the strong asymme-try between both hemispheres during the Maunder Mini-mum, this means that a cycle may have ended in onehemisphere, while it goes on for years (‘‘cycles’’) in theother hemisphere. This implies that the Sun may havehad a ‘‘monopolar’’ structure which may have had an effect

ed.

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on the cosmic rays (and thus on the nuclear deposits on theEarth) as it is expected to have a shorter range in the inter-planetary space. Moreover, it may have an effect on theheliospheric current sheet, cf. the bashful ballerina (Mursu-la and Hiltula, 2003).

The plan of the paper is as follows. The evolution of theglobal unipolar magnetic field regions and polar reversalsduring normal cycles is considered in Section 2. The possi-bility or absence of polar reversals during the MaunderMinimum is considered in Section 3. The relevance of the‘‘monopolar’’ situation for the cosmic ray observationsand geological archives is suggested in Section 4 and theinfluence on the magnetic field far away from the Sun isestimated. The conclusions are given in Section 4.

2. Polar reversals in normal cycles

H a synoptic charts of the Sun allow to study the globalactivity and its temporal variations since cycle 12 whilemagnetic observations are much more recent. The structureand evolution of the global solar magnetic field can bededuced from the emergence and distribution of large scaleunipolar magnetic field regions, also called global magneticregions (GMRs). The latter can be obtained from H a charts(Makarov and Sivaraman, 1989; Callebaut and Makarov,1992; Makarov and Makarova, 1996; Makarov et al.,2002b; Makarov et al., in press). Their field strength is esti-mated to be a few gauss only. The boundaries of thoseGMRs correspond to filament bands, consisting of fila-ments and filament channels. The boundaries are neutralin the line of sight although they can carry huge currents(up to 1011 A) and have a magnetic field aligned alongthem. The boundaries are very irregular at their creationaround the equator but they become more circular whencloser to the poles. The GMRs move steadily to the polesand when such a GMR disappears at the pole and isreplaced by the subsequent GMR (of the opposite polarity)a polar reversal is the result. After a polar reversal the nextboundary exhibits a small equator-ward jump (i.e. it movesto a somewhat lower latitude) and then the polewardmigration of the GMRs and their boundaries ceases andthey stay at around ±40�, ±20� and 0� until the next cyclestarts. Then they start to move again toward the poles.While at rest, after polar reversal and during solar mini-mum, the latitude of the boundaries (which are calledrest-latitudes) oscillate with a period of about 1.3 years(Makarov et al., 2002a).

As stated above, a new GMR reaching and covering apole causes a polar reversal in that hemisphere. However,the polar reversal in the other hemisphere does not happensimultaneously and may be delayed by several months, upto a year. The Sun has then, during the period between thetwo polar reversals, the same magnetic polarity at bothpoles, somewhat looking like a monopole, although regionsnearer to the equator have opposite polarity. Neverthelessit is a particular situation and even if it occurs only duringsome months the question arises to what extent this may

influence the solar magnetic field in the interplanetaryspace and cosmic rays, and how does this affect spaceweather? As one expects the field far away from the Sunto be much weaker in the ‘monopolar’ case than in the nor-mal one (see Section 3.3) it is suggested that observersshould pay extra attention to this, although it is a fairlyshort transition phase with a rather special structure witha vanishing polar cap.

3. Polar reversals during Maunder Minimum

3.1. Deep minimum and limiting Wolf number

Makarov et al. (2001) have shown that the more sun-spots appear, the faster the boundaries of GMRs moveto the poles, hence the faster the polar reversal occurs.From those relations they concluded that the yearly meanWolf number had to be larger than 40 in order to havepolar reversals: Wlim @ 40. For this they were using theentire visible hemisphere. If one extends this relation tothe northern and southern part of the visible hemisphereseparately, one should have instead Wlimh @ 20. Normallythis division does not matter, except that a delay may occurbetween the polar reversals of the two hemispheres (seeSection 2).

If a polar reversal does not happen, it is as if the cycledoes not end, at least not in the corresponding hemisphere.It seems plausible to take the absence of at least one polarreversal as the definition of a deep minimum or, alterna-tively, W < W limh ffi 20 (in one hemisphere).

3.2. Concerning the asymmetry of the Maunder Minimum

According to Ribes and Besme-Ribes (1993), the north-ern hemisphere of the Sun had nearly no sunspots at allduring the Maunder Minimum, while the southern hemi-sphere had few, but still much more than the northernone. According to the considerations above it follows thatthe northern hemisphere had probably no polar reversals atall, while the southern hemisphere may have reached thelimiting Wolf number and thus polar reversals. For the per-iod of 1670–1715 for which frequent and regular observa-tions are available (Ribes and Besme-Ribes, 1993) onehas W > W limh ffi 20 in the southern hemisphere. Thus apolar magnetic field reversal was quite probable in thesouthern hemisphere in this period. Thus the Sun had dur-ing the Maunder Minimum several decades with a ‘‘mono-polar’’ structure.

3.3. Consequences for the cosmic rays

With a ‘‘monopolar’’ structure the solar field in theinterplanetary space looks different from the normal one.The assumption is made, to have a fair comparison, thatthe outgoing flux is the same in Fig. 1a as in Fig. 1b. Theinward fluxes, being equal but opposite to the outgoingones, must be equal too. In Fig. 1b one expects that most

Fig. 1. Far away the field is bipolar in (a), while in (b) it is strongly reduced in comparison. In fact, as the major dipoles in (b) are equal and opposite thefield far away will be even much more reduced.

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field lines close at short distances from the Sun. In fact thelargest distance, from north to south pole, will not be con-nected as both poles have the same polarity. In Fig. 1a, onthe contrary, the north and south poles are connected byfield lines going far into interplanetary space. Hence, inthe ‘monopolar’ situation one does not expect the field tostretch as far as in the ordinary situation. (In fact the fieldstretches to infinity, but we mean that the field strengthdecays faster in the ‘monopolar’ case.) The question ariseswhether this has a noticeable effect in deviating cosmic raysand hence affect the radionuclei reaching the Earth. In factthe reconstruction of the magnetic flux from the deposit ofsuch nuclei shows an irregular period, often longer than 11years (indicating a delay or absence of polar reversals).Moreover, although the amount of nuclei is somewhat lessthan compared to regular cycles, one would have expectedmuch less in view of the reduced solar activity duringMaunder Minimum. This may indicate that the cosmicrays contribute more during the Maunder Minimumbecause the solar field was much weaker, which may beattributed at least partially to the ‘monopolar’ structure.

An estimate of the change may be obtained as follows.Compare the situation of the Sun having had its polarreversals (thus having e.g. 4 GMRs; Fig. 1a, however, cor-responds to the situation before the reversals, still having 6GMRs) with the similar case when one polar reversal islacking (thus the Sun has then 5 GMRs, Fig. 1b). In thecase with 4 GMRs the axis of the magnetic dipole corre-sponding to the two polar caps is roughly the solar diame-ter. In the case with 5 GMRs it is shorter, roughly in the

ratio 4/5. A bipolar field (and that is the relevant one at dis-tances of several solar radii) varies like r�3. Thus, consider-ing in both cases the same (large) distance from the Sun,the magnetic field in the monopolar case would be roughly64/125 times, say a factor 2, smaller than the field in thenormal case, supposing that the fields at the solar surfaceare equal (which is quite reasonable). However, as can beseen on Fig. 1b. there is another dipole with about equalaxis and opposite orientation. Thus the field far away willbe still much smaller than what is expected on the basis ofthe previous calculation: it rather looks like an octupolewhich drops off with distance much faster than a dipole.Of course the configuration in Fig. 1a is multipolar too,but at great distances the dipolar component correspond-ing to the dipole constituted by the polar caps dominates.Hence far away from the Sun one may expect the solar fieldto be much weaker than the one of the non-monopolarSun, even if the fields are not the same at the solar surface.

4. Conclusion

Normal cycles have a ‘monopolar’ structure during afew months only during the lapse of time between thereversals of the two poles. However, the Sun may havehad a ‘monopolar’ structure during several decennia(cycles) of the Maunder Minimum. It is expected that thesolar magnetic field will have a shorter range in the inter-planetary space when the Sun has this ‘monopolar’ struc-ture and it is suggested that this may have an effect (indensity and in orientation) on the cosmic rays: this should

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leave traces with obvious archaeological interest. One mayestimate that the magnetic field far away from the monopo-lar-like Sun will be rather octupolar and thus much, muchweaker than in the normal situation, other parameters keptequal. Moreover, this monopolar character represents, by

its symmetry, an anomaly of the normal north–south polemagnet and may have an effect, e.g., on the southward shiftof the heliospheric current sheet, the ‘‘bashful ballerina’’(Mursula and Hiltula, 2003).

It is suggested to take the following definition for a greatminimum: it occurs when, during a solar cycle, the Sundoes not complete its polarity reversal in one pole or bothpoles. In view of the work of Makarov et al. (2001), thisdefinition may be translated by saying that the yearly aver-age Wolf number may not exceed the critical value of 20 ina hemisphere in order to have a deep minimum.

Acknowledgements

It is a pleasure to thank Prof. C. de Jager (University ofUtrecht, Utrecht and NIOZ, Texel, the Netherlands), Prof.K. McCracken (University of Maryland, USA) and Prof.W. Schmutz (Davos, Switserland) for discussions. Theauthors acknowledge the Grant RFBR 05-02-16229.

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