North-south asymmetry in Rieger-type periodicity during solar cycles 19-23
Eka Gurgenashvili, Teimuraz V. Zaqarashvili, Vasil Kukhianidze, Ramon Oliver, Jose Luis Ballester, Mausumi Dikpati, Scott W. McIntosh
aa r X i v : . [ a s t r o - ph . S R ] J u l North-south asymmetry in Rieger-type periodicity during solarcycles 19-23
Eka Gurgenashvili , Teimuraz V. Zaqarashvili , , , Vasil Kukhianidze , Ramon Oliver , ,Jose Luis Ballester , , Mausumi Dikpati , Scott W. McIntosh ABSTRACT
Rieger-type periodicity has been detected in different activity indices overmany solar cycles. It was recently shown that the periodicity correlates withsolar activity having a shorter period during stronger cycles. Solar activity levelis generally asymmetric between northern and southern hemispheres, which couldsuggest the presence of a similar behavior in the Rieger-type periodicity. Weanalyse the sunspot area/number and the total magnetic flux data for northernand southern hemispheres during solar cycles 19-23 which had remarkable north-south asymmetry. Using wavelet analysis of sunspot area and number duringthe north-dominated cycles (19-20) we obtained the periodicity of 160-165 daysin the stronger northern hemisphere and 180-190 days in the weaker southernhemisphere. On the other hand, south-dominated cycles (21-23) display theperiodicity of 155-160 days in the stronger southern hemisphere and 175-188days in the weaker northern hemisphere. Therefore, the Rieger-type periodicityhas the north-south asymmetry in sunspot area/number data during solar cycleswith strong hemispheric asymmetry. We suggest that the periodicity is causedby magnetic Rossby waves in the internal dynamo layer. Using the dispersionrelation of magnetic Rossby waves and observed Rieger periodicity we estimatedthe magnetic field strength in the layer as 45-49 kG in more active hemispheres(north during the cycles 19-20 and south during the cycles 21-23) and 33-40 kG in Abastumani Astrophysical Observatory at Ilia State University, Tbilisi, Georgia IGAM, Institute of Physics, University of Graz, Universit¨atsplatz 5, 8010 Graz, Austria, Email:[email protected] Departament de F´ısica, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain Institute of Applied Computing & Community Code (
IAC ), UIB, Spain Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, Colorado80307, USA.
1. Introduction
Short-term variation in gamma ray flares with period of 155-160 days was discoveredby Rieger et al. (1984) during solar cycle 21. The periodicity later was detected in al-most all activity indices (Dennis 1985; Bai and Sturrock 1987; Lean and Brueckner 1989;Bai and Cliver 1990; Lean 1990; Kile and Cliver 1991; Oliver et al. 1998; Ballester et al.1999; Krivova and Solanki 2002; Dimitropolou 2008). Carbonell and Ballester (1990) andCarbonell and Ballester (1992) reported the 155-day periodicity in records of the sunspotarea during cycles 14-20 and 12-21, respectively. They found that the periodicity was clearlyseen during cycles 16-21, but was absent during cycles 12-15. Ballester et al. (2002) analyzedthe records of photospheric magnetic flux and found that the periodicity appeared duringcycle 21, but it was absent in cycle 22.The Rieger type periodicity is found also in historical data sets during the earlier cycles.Using two historical aurorae data sets, Vaquero et al. (2010) tried to evaluate presence ofRieger period during the cycles 3-4. They have detected the 150 day period in one auroraldataset during 1777-1781 (cycle 3), but they could not confirm the same periodicity forthe cycle 4. Silverman (1990) investigated the occurrence of auroras during 16th and 18thcenturies and found 158 and 182-185 days period for the years of 1570-72,1736-39 and 1787-90, respectively. Ballester et al. (1999) analysed daily number of sunspot groups between1610 and 1995 and found near 158 day period around the maximum of solar cycle 2. Aftercycle 2, no strong evidence for the periodicity was found until the 20th century.Therefore, the Rieger periodicity of 154 days is not a permanent feature of solar activity,but it varies from cycle to cycle. It was also shown that the periodicity usually appearsduring 1-3 years near the cycle maxima and it may vary from 130 to 185 days (Lean 1990;Oliver et al. 1998; Zaqarashvili et al. 2010a). Recently, Gurgenashvili et al. (2016) analyzedlong-term sunspot data for solar cycles 14-24 and showed that the Rieger periodicity isanti-correlated with solar cycle strength: stronger cycles show shorter periods. Observedcorrelation suggests that the periodicity is related to the dynamo layer in the solar interior.Most promising explanation of the Rieger-type periodicity is connected to magneticRossby waves in the solar tachocline (Zaqarashvili et al. 2010a). The differential rotation 3 –and toroidal magnetic field trigger the instability of spherical harmonics of magnetic Rossbywaves with period of 155-160 days, which leads to the quasi-periodic emergence of mag-netic flux towards the surface. The dispersion relation of magnetic Rossby waves dependson the magnetic field strength (Zaqarashvili et al. 2007, 2009), therefore the observed pe-riodicity should depend on solar activity level, which fairly corresponds to observations(Gurgenashvili et al. 2016). Recent discovery of Rossby waves by STEREO and SDO coro-nal bright point observations (McIntosh et al. 2017) fully confirmed the Rossby wave scenarioas a mechanism for Rieger-type periodicity.Solar activity generally shows north-south asymmetry in many indicators (Sp¨orer 1894;Maunder 1904; Babcock 1959; Waldmeier 1971; Roy 1977; Carbonell et al. 1993; Oliver and Ballester1994; Ballester et al. 2005; Temmer et al. 2002, 2006; Li et al. 2002; Gigolashvili et al.2005; McIntosh et al. 2013, 2014a,b, 2015), which means that the strength of the cycle isdifferent in northern and southern hemispheres. If the Rieger-type periodicity depends onthe activity strength, then it should also display the north-south asymmetry. The differentperiodicity in northern and southern hemispheres then may allow to estimate the differencein magnetic field strength in the dynamo layer over hemispheres, which might be a clue forthe understanding of hemispheric asymmetry.Here we analyze several available hemispheric activity indices in order to find the valuesof the Rieger periodicity in northern and southern hemispheres separately during activitycycles which have remarkable north-south asymmetry.
2. North-south asymmetry in solar activity
We use three different data sets to study the north-south asymmetry in the Rieger-type periodicity: 1) Greenwich Royal Observatory (GRO) daily and monthly sunspot areaUSAF/NOAA for northern and southern hemispheres (http://solarscience.msfc.nasa.gov/greenwch.shtml),which are available during 1874-2016, 2) Kanzelh¨ohe Solar Observatory (KSO) and Skalnat´ePleso Observatory (SPO) hemispheric sunspot number data (http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/447/735), which are available in the interval 1945-2004 (Temmer et al.2006), 3) The Mount Wilson total magnetic flux (MWTF) data which are available between1966-2002.North-South asymmetry was also presented during the Maunder minimum (MM, 1645-1715), when the solar activity was extremely low. Vaquero et al. (2015) and Usoskin et al.(2015) analyzed several data sets including both direct and indirect data catalog publishedby Sp¨orer nearly 130 years ago, sunspot latitudes in the butterfly diagram during MM 4 –published by Ribes and Nesme-Ribes almost 20 years ago, aurorae historical reports duringMM, Cosmogenic radionuclides etc. They have calculated the asymmetry index using thesedata sets and confirmed a strong south-dominated hemispherical asymmetry during MM.The Sp¨orer data are given in the paper of Vaquero et al. (2015) and http://haso.unex.es.We are interested to seek for the Rieger periodicity in the cycles with remarkable north-south asymmetry in order to avoid statistically insignificant correlation between activityand periodicity. Therefore, we first study the long-term north-south asymmetry using GROsunspot data from 1901 to 2016, which correspond to the cycles 14-24, because earlierdata is not fully reliable (Cliver and Ling 2016; Cliver 2017; Erwin et al. 2013; Willis et al.2016a,b). Figure 1 (upper panel) shows monthly averaged sunspot area vs time. Fromcoloured polygons one can see that the north-south asymmetry is remarkable near the cyclemaxima in most cases and different hemisphere dominates at different phase of correspond-ing cycle. For example, the southern hemisphere was more active during the ascending anddescending phases of cycle 14, while the northern hemisphere was dominating near the cy-cle maximum. Similar result was previously noticed by Newton and Milsom (1955), whoshowed that the northern hemisphere was dominant in the early phases of cycles 12 - 15with a switch to south-dominance later in each cycle. The opposite behaviour was foundduring cycles 17 - 18. Therefore, full dominance of one hemisphere is not well established.Cycles 19-23 seem exceptions as the asymmetry in these cycles are very strong and can beconsidered as statistically significant.Due to the small value of north-south asymmetry in most cycles, it is very important tostudy the statistical significance. Carbonell et al. (2007) used several data sets and estimatedthe statistical significance of north-south asymmetry using different statistical analysis, suchas Binomial distribution, Excess, Normal approximation to the Binomial distribution andPearson’s chi-square test. Similar analysis was performed later by Zhang & Feng (2015).In order to find the statistical significance of north-south asymmetry (SSNSA) in thecycles 19-23 we carried out cycle-to-cycle statistical analysis using the Binomial distribution(see the Table 1) P k = n ! k !( n − k )! p k q n − k . (1)where n is the total number of sunspot area, k is the sunspot area for one hemisphere, p is the probability for one hemisphere to be stronger and q is the probability of the anotherhemisphere. In our case p = q = 0 . P < . . < P < < P < P >
P < .
3% 86 % 86 % 85 % 84.5 % 80 %0 . < P <
5% 6 % 6 % 5.7 % 5 % 5.4 %5% < P <
10% 0.6 % 0.6 % 0.4 % 0.2 % 0.2 %
P >
10% 7.4 % 7.5 % 8.7 % 10.5 % 14.6 %Table 1: Estimated statistical significance of north-south asymmetry during cycles 19-23.of asymmetry and its statistical significance are high in the cycles 19-23, therefore we useonly the data of these cycles for further analysis. Figure 1 shows that the cycles 19-20 arenorth dominated and cycles 21-23 are south-dominated.
3. North-south asymmetry in Rieger-type periodicity
As it is noted in the previous section, we have three data sets: Greenwich observatorydaily sunspot area, the joint catalogue of the KSO and SPO, where one can find the daily andmonthly sunspot number, as well as smoothed monthly data for both hemispheres separately(Temmer et al. 2006) and the Mount Wilson total magnetic flux (MWTF) data (for cycles20-23, which starts from January 1965 and runs till May 2002).We used the Morlet wavelet analysis (Torrence and Compo 1998) to find the Rieger-typetimescale in the three data series. Figures 2-3 and 4-5 show the wavelets of north-dominatedand south-dominated cycles, respectively. Figure 2 shows the wavelet analysis performed us-ing GRO data for cycles 19-20. It is clearly seen that the northern hemisphere was dominantin almost whole cycle (panel a). The Rieger-type timescale in cycle 19 was of order of 158-172days in the northern hemisphere and 172-182 days in the southern hemisphere. The cycle 20displays the periodicity of 160-165 days in the northern hemisphere and 182-198 days in thesouthern hemisphere. The cycle-by-cycle global wavelets are computed and plotted alongsideeach wavelet in sunspot data, where blue (red) color denotes the global wavelet for cycle 19(20). The global wavelet analysis gives peaks at 160 (180) days in the northern (southern)hemisphere in the cycle 19 and at 165 (190) days in the northern (southern) hemisphere inthe cycle 20. Wavelet analysis reveals that the period of the Rieger-type duration is shorterin the northern hemisphere (by 20-25 days) than the southern one during both cycles.Figure 3 shows the wavelet analysis of KSO/SPO data during cycles 19-20. The Rieger-type timescale was of order of 158-170 days (with a peak at 165 days) in the northernhemisphere and 174-190 (with a peak at 175 days) days in the southern hemisphere in cycle19. In the cycle 20, the Rieger periodicity was 151-156 days (with a peak at 155 days) in 6 –the northern hemisphere and 185-190 days (with a peak at 188 days) in the southern hemi-sphere. KSO/SPO data also show that the stronger northern hemisphere displays shorterperiodicity than the weaker southern hemisphere. Hence the north-south behavior of theRieger periodicity agree qualitatively in GRO and KSO/SPO in the cycles 19 and 20.The N-S asymmetry in the cycles 21-23 shifted to the southern hemisphere (Verma1992). We performed the wavelet analysis of the south dominated cycles separately forsunspot data. Figure 4 represents the wavelet analysis of GRO data for the south-dominatedcycles 21-23. The global wavelets are plotted on right-hand-side, where blue, black and redcolors correspond to the cycle 21, 22 and 23, respectively. As it is expected, the weakernorthern hemisphere now shows longer periodicity: 160-187 days with peak at 183 days forthe cycle 21, 168-190 days with peak at 180 days for the cycle 22 and 170-185 days (peak at175 days) in the cycle 23. The stronger southern hemisphere displays the shorter periodicityof 155-165 days with peak at 158, 160 and 160 days, for the cycles 21-23, respectively (see thetable 2). The difference between hemispheric periodicity is around 15-23 days very similarto the north-dominated cycles.Figure 5 shows the wavelet analysis of KSO/SPO data for south dominated cycles 21-23.The periodicity in northern hemisphere is of the order of 180-190 days (peak at 188 days)in cycle 21, 175-190 days (peak at 177 days) in cycle 22 and 165-185 days (peak at 174days) during cycle 23. Stronger southern hemisphere shows the period of 150-165 days withpeaks at 155, 158 and 161 days for the cycles 21, 22 and 23, respectively. However, the cycle22 displays another stronger peaks at 190 days in the southern hemisphere in both GROand KSO/SPO data, which is out of general picture in N-S asymmetry. This interestingdisagreement will be discussed later.Figure 6 presents MWTF data during cycles 20-23 with corresponding wavelet analysis.The upper panel shows that only cycle 22 displays remarkable N-S asymmetry with moreactive southern hemisphere. The cycles 20, 21 and 23 have almost no hemispheric asymmetry.Wavelet analysis gives the periodicity of 160-172 days (with a peak at 168 days) in the cycle20, 160-180 days (with peak at 170 days) in the cycle 21, 165-180 day period (peak at 175)in the cycle 22 and 160-175 days (with a peak at 170 days) in cycle 23 in the northernhemisphere. The southern hemisphere shows the periodicity of 158-168 days (with a peakat 165 days) in the cycle 20, 180-190 days (with a peak at 187 days) in the cycle 21, 150-160days (with a peak at 155 days) in the cycle 22 and 160-180 days (with a peak at 170 days)in cycle 23. In contrast with GRO and KSO/SPO data, the total magnetic flux shows noclear north-south asymmetry in the Rieger periodicity during cycles 20 and 23. The cycles21-22 show some N-S asymmetry in magnetic flux but not as significant as in the sunspotdata. 7 –The wavelet analysis of sunspot data (GRO, KSO/SPO) clearly show that the Riegertimescale is characterized by the hemispheric asymmetry: the stronger hemisphere dis-plays shorter periodicity of the order of 160-165 days, while weaker hemisphere displayslonger periodicity of the order of 175-190 days. This result fairly agrees with the finding ofGurgenashvili et al. (2016) that the stronger cycles generally show shorter periodicity. Herethe hemisphere (e.g. northern hemisphere in cycles 19-20 and southern hemisphere in cycles21-23) with higher activity level has shorter periodicity.In addition, activity maxima during cycles 19-20 are shifted with 1-2 years in northernand southern hemispheres (see Figures 2a and 3a). The southern hemisphere reaches itsmaximum before the northern hemisphere during cycle 19, while it is opposite during thecycle 20 where northern hemisphere reaches the maximum first. The north-south phase shiftof solar cycles in sunspot data was studied in details by Dikpati et al. (2007). They showedthat the shift of cycle maxima is more pronounced than the shift of minima (see Figure 5 ofthe paper). Our result fairly agrees with their finding. The Rieger periodicity displays thesimilar phase shift as it is seen on Figures 2 and 3. This is in agreement with the previousresult that the Rieger periodicity in full disc data appears near the cycle maxima.On the other hand, the Rieger periodicity shows different behavior in the total magneticflux. Here no clear north-south asymmetry is seen. Howard (1974) examined magnetic fluxdata from Mount Wilson magnetograph during 1967-1973 and reported that the total fluxin the north was greater than in the south by only a 7%, therefore asymmetry is missing inthe MWTF data. Chumak et al. (2003) studied the behavior of the total sunspot area andmagnetic flux during the year 1989 and showed that there is not always positive correlationbetween active regions and total magnetic flux: sometimes the flux increases or decreases,while the sunspot areas remain the same. The difference between the Rieger periodicity insunspot area/number (GRO, KSO/SPO) and total magnetic flux (MWTF) can be relatedwith the lack of the permanent positive correlation. The lack of correlation might reflect thefact that the total magnetic flux is a sum of strong sunspot and weak plage fluxes which mayhave different behavior. During cycle 21, Rabin et al. (1991) found quasi periodic pulsationsonly in the strong flux, which were uncorrelated between the hemispheres until 1983, thanthey appear to be synchronized. Ballester et al. (2002) studied MWTF data for cycles 20-23and found a correlation between impulses in strong flux and flares, but not with weak flux.On the other hand, Lean and Brueckner (1989) reported that the Rieger periodicity was notsignificant in the plage index. This point surely needs more detailed study. 8 –
4. Discussion
Rieger type periodicity has been detected during last two centuries in different activityindices, which showed that it is not a permanent feature of the solar activity but varies fromcycle to cycle. It was recently shown that the Rieger periodicity correlates with solar cyclestrength being shorter during stronger cycles and therefore it could be related to the internaldynamo layer, where strong toroidal magnetic field is generated (Gurgenashvili et al. 2016).Quasi-periodic variation of the dynamo magnetic field with Rieger-type periodicity triggerscorresponding variations in activity indices owing to the modulation of erupted magnetic flux.If the Rieger periodicity is the feature of the dynamo layer then it may carry informationabout its physical parameters.The mechanism of solar activity still remains as one of the major unsolved problems insolar physics, but the cycles are supposed to be caused by large-scale dynamo action in thesolar interior (Charbonneau 2010). The tachocline, thin layer between radiative and con-vective envelopes, is suggested to be the location of dynamo action. However, there are alsodynamo models without tachocline. The magnetic field strength according to the dynamomodels without tachocline is less than 10 kG, but the models with tachocline predict muchstronger field ( >
10 kG) (Charbonneau 2013). Therefore, the estimation of the magneticfield strength is very important as it may put some limitation on dynamo models in thesolar/stellar interiors.Solar activity displays different levels of activity between northern and southern hemi-spheres. This north-south asymmetry is generally small with weak statistical significance,but it becomes remarkable during some (more stronger) cycles. The asymmetry probablyreflects the difference between dynamo magnetic field strengths in northern and southernhemispheres, but the mechanism of the difference is unknown. Even rough estimation ofthe difference between hemispheric magnetic fields in the dynamo layer may give us a hintto understand the triggering mechanism for the asymmetry. The strength of dynamo mag-netic field in different hemispheres can be estimated from the observed Rieger periodicity inhemispheric data.We used the hemispheric data of GRO daily and monthly sunspot area, joint KSO/SPOdaily and monthly sunspot numbers and the Mount Wilson total magnetic flux to find theRieger periodicity in northern and southern hemispheres during cycles 19-23, when the north-south asymmetry of solar activity was remarkable (see Figure 1, upper panel). Figure 1 showsthat the northern hemisphere was much more active during the cycles 19-20, but the southernhemisphere became stronger during the cycles 21-23. Wavelet analysis of sunspot data(GRO, KSO/SPO) revealed that the Rieger periodicity was significantly different in bothhemispheres being 160-165 days in the northern hemisphere and 175-190 days in the southern 9 –hemisphere during north-dominated cycles, while it became 155-160 days in the northernhemisphere and 175-188 days in the southern hemisphere during the south-dominated cycles(see Table 2 for details). Therefore, the periodicity clearly reflects the north-south asymmetryin solar activity.Cycle Period Period Period Period Period PeriodNumber ( N, GRO) (S, GRO) (N, KSO/SPO) (S,KSO/SPO) (N, MWTF) (S, MWTF)19 158 177 156 176 - -20 165 190 152 188 168 16521 183 158 188 155 170 18722 180 160 177 158 175 15523 175 160 174 161 170 170Table 2: Estimated Rieger Periods (days) for both hemispheres from GRO (column 2 − −
5) and MWTF Data (column 6 − ≈
40 kG during stronger solar cycles (16-23) and ≈
20 kG during weaker cycles (14-15 and24). The dispersion relation of fast magnetic Rossby waves (the slow magnetic Rossby wavesmay lead to the long-term variation of solar cycles as suggested by Zaqarashvili et al. (2015))in the dynamo layer can be written as (Gurgenashvili et al. 2016) ω f = − m Ω s + q (1 + s ) + B max πρ Ω R n ( n + 1) n ( n + 1) , (2)where ω f is the frequency of fast magnetic Rossby waves, Ω is the equatorial angular velocity, s is the parameter of the differential rotation, ρ is the density, R is the distance from thesolar center to the dynamo layer, B max is the dynamo magnetic field strength at 45 degree, m and n are toroidal and poloidal wave numbers, respectively. Only the magnetic field 10 –strength is unknown parameter in the dispersion relation, therefore it can be deduced fromthe observed periodicity. Gurgenashvili et al. (2016) showed that the spherical harmonicwith m = 1 and n = 4 may confidently explain the observed periodicity for 30 −
50 kGmagnetic field.We use the dispersion relation (Eq. 2) for estimation of magnetic field strength in thenorthern and southern hemispheres during cycles 19-23. The differential rotation parameterswere not estimated for the northern and southern hemispheres separately for these cycles,therefore initially we set s = 0 in the equation (2). Based on the GRO data, we calculate themaximum magnetic field strength as 48 kG (38 kG) in the northern (southern) hemisphereduring north-dominated cycle 19, 45 kG (33 kG) in the northern (southern) hemisphereduring north-dominated cycle 20, 49 kG (36 kG) in the southern (northern) hemisphereduring south-dominated cycle 21, 48 kG (38 kG) in the southern (northern) hemisphereduring south-dominated cycle 22 and 48 kG (40 kG) in the southern (northern) hemisphereduring south-dominated cycle 23. These calculations show that the difference between dy-namo magnetic field strengths in northern and southern hemispheres during cycles 19-23 isof the order of 10 kG, which is a quite significant value (see Figure 7). Non-zero differentialrotation parameter s in Eq. (2) changes the estimated value of magnetic field strength (seethe Table 3), however the hemispheric difference still remains of the order of 10 kG. It mustbe mentioned, however, that the estimation of magnetic field strength is rather rough andfuture detailed analysis (including numerical simulations) is needed to increase the accuracy.Figure 7 shows that the estimated magnetic field strength does not significantly vary duringcycles 21-23, while the cycle amplitude has been continuously declining. This may sup-port the evidence that the sunspot cycle is an ”interference” pattern of overlapping 22-yearbands (McIntosh et al. 2014a). Moreover, it is seen from Figure 7 that the difference betweensouthern and northern hemispheric magnetic field strengths is also decreasing, which couldbe a result of interaction of the bands. This point needs detailed study in the future.Cycle number 19 19 20 20 21 21 22 22 23 23Differential rotation, s .
19 0 0 .
16 0 0 .
14 0 0 .
14 0 0 .
17 0 B max (kG), north 40 49 37 45 28 36 30 38 31 40 B max (kG), south 28 39 23 33 43 49 42 48 40 48Table 3: Estimated Magnetic field strength for northern and southern hemispheres dur-ing the cycles 19-23. The meanings of differential rotation parameter s are obtained byJavaraiah et al. (2005).The estimated large difference between dynamo field strengths in the two hemispheresneeds to be explained in the future. It may become as a key point to resolve the problem 11 –of solar dynamo and activity cycles. It is possible that the observed north-south asymmetryis owing to the overlapping of 11-year oscillating dynamo magnetic field with some steadyfield component. In this case, the steady field of 5 kG may cause required 10 kG differencein hemispheric magnetic field. Dikpati et al. (2006) showed that the steady (non-reversing)toroidal field can be generated in the lower tachocline due to a steady dynamo in the caseof low magnetic diffusivity with the strength of > ∼
190 days) in the southern hemisphere, which is somehowout of regularity. This long-period peak may correspond to the higher harmonic of magneticRossby waves. For example, if the shorter period of 158 days is caused by m=1, n=4 har-monic (as it is suggested above) then the harmonic with m=1, n=5 would give the periodof ∼
210 days, which is not far from the observed peak. The long period peaks can be seenalso in other cycles and might correspond to the regular pattern. It requires further detailedstudy.In contrast of sunspot number/area data, total magnetic flux does not show any re-markable north-south asymmetry in the Rieger periodicity. Therefore, it seems that thetotal magnetic flux does not clearly manifest the north-south asymmetry. This is probablycaused by the fact that used MWTF contains both, strong sunspot flux and weak plage flux,from which only the strong flux has N-S asymmetry. This is an interesting question to beanswered in the future.
5. Conclusions
We carried out the wavelet analysis of the hemispheric sunspot area (GRO), sunspotnumber (KSO/SPO) and Mount Wilson Total Magnetic flux data during solar cycles (19-23)with remarkable north-south asymmetry: the northern hemisphere was dominated duringcycles 19-20 and the southern one was dominated during the cycles 21-23. The analysisof sunspot area/number data showed that the Rieger type periodicity is also asymmetric 12 –with hemispheres. We obtained the periods of 160-165 days in the northern hemisphereand 180-190 days in the southern hemisphere during cycles 19-20, while 155-160 days inthe northern hemisphere and 175-188 days in the southern hemisphere during the cycles21-23. Therefore, the Rieger-type periodicity in sunspot area/number data correlates withhemispheric activity levels in the same sense as it correlates with cycle strength based onfull disc data (Gurgenashvili et al. 2016): the hemisphere with stronger activity displays theperiodicity with shorter period. Hence, the Rieger periodicity is connected to the internaldynamo layer, where the magnetic field and the solar cycles are generated. The magneticfield might be modulated by magnetic Rossby waves, which leads to the quasi-periodicemergence of magnetic flux. This scenario is fully supported by recent direct observationsof Rossby waves using STEREO and SDO coronal bright point data (McIntosh et al. 2017).In addition, activity manifests a phase shift of 1-2 years between northern and southernhemispheres, which is clearly seen during the cycles 19-20(see more detailed analysis inDikpati et al. (2007)). The Rieger periodicity also takes place at different times (with similar1-2 year shift) in the two hemispheres which means that the quasi-periodic flux emergencecorrelates to the maximum phase of solar cycles. The obtained periodicity and the dispersionrelation of magnetic Rossby waves were used to estimate the magnetic field strength in thetachocline as 45-48 kG in more active hemisphere (northern hemisphere during the cycles19-20 and the southern one during cycles 21-23) and 32-38 kG in the weaker hemisphere.The north-south difference in the dynamo magnetic field strength is almost 10 kG, whichreaches to almost 25 % of estimated magnetic field. The significant hemispheric differenceof the field strength induces future challenges for dynamo models.
Acknowledgements
We thank J. Boyden who kindly provided us with the MWTFrecords. The Mount Wilson 150 Foot Solar Tower is operated by UCLA, with funding fromNASA, ONR, and NSF, under agreement with the Mount Wilson Institute. This work wassupported by Georgian Shota Rustaveli National Science Foundation (projects PhDF2016-130 and 217146) and by the Austrian “Fonds zur F¨orderung der wissenschaftlichen Forschung”(FWF) project P26181-N27. This paper is resulted from discussions at the workshop of ISSI(International Space Science Institute) team (ID 389) ”Rossby waves in astrophysics” orga-nized in Bern (Switzerland).
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23 24 S un s po t a r ea Fig. 1.— Greenwich Royal Observatory monthly averaged hemispheric sunspot area datafor cycles 14-24. Blue color denotes excess of the northern hemisphere, and yellow shadescorrespond to the excess of the southern hemisphere. 14 –Fig. 2.— Top panel (a) represents GRO monthly averaged hemispheric sunspot area for cy-cles 19-20 with blue (yellow) color in case of excess northern (southern) hemisphere. Middlepanel (b) and bottom panel (c) represent the wavelet of northern and southern hemisphere,respectively. Global wavelet results are plotted to the right, where blue (red) color corre-sponds to cycle 19 (20). 15 –Fig. 3.— Top panel (a) represents KSO/SPO monthly averaged hemispheric sunspot numberfor cycles 19-20 with blue (yellow) color in case of excess northern (southern) hemisphere.Middle panel (b) and bottom panel (c) represent the wavelet of northern and southernhemispheres, respectively. Global wavelet results are plotted to the right, where blue (red)color corresponds to the cycle 19 (20). 16 –Fig. 4.— Top panel (a) represents GRO monthly averaged hemispheric sunspot area forcycles 21-23 with blue (yellow) color in case of excess northern (southern) hemisphere. Middlepanel (b) and bottom panel (c) represent the wavelet of northern and southern hemispheres,respectively. Global wavelet results are plotted to the right, where blue, black and red colorscorrespond to the cycles 21, 22 and 23, respectively. 17 –Fig. 5.— Top panel (a) represents KSO/SPO monthly averaged hemispheric sunspot numberfor cycles 21-23 with blue (yellow) color in case of excess northern (southern) hemisphere.Middle panel (b) and bottom panel (c) represent the wavelet of northern and southernhemispheres, respectively. Global wavelet results are plotted to the right, where blue, blackand red colors correspond to the cycles 21, 22 and 23, respectively. 18 –Fig. 6.— Top panel (a) represents Mount Wilson total magnetic flux daily hemispheric datafor cycles 20-23 with blue (yellow) color in case of excess northern (southern) hemisphere.Bottom (middle) left panel represent the wavelet of northern (southern) hemisphere. Globalwavelet results are plotted to the right, where green, blue, black and red lines correspond tocycle 20-23, respectively. 19 – C yc l e - ava r a g e d S un s po t a r ea
19 20 21 22 23