Steps toward a high precision solar rotation profile: Results from SDO/AIA coronal bright point data

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1 Astronomy & Astrophysics manuscript no. Rotaon c ESO 214 October 1, 214 Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data D. Sudar 1, I. Skokić 2, R. Brajša 1, and S. H. Saar 3 1 Hvar Observatory, Faculty of Geodesy, Kačićeva 26, 1 Zagreb, Croaa 2 Cybrotech Ltd, Bohinjska 11, 1 Zagreb, Croaa 3 Harvard-Smithsonian Center for Astrophysics, 6 Garden Street, Cambridge, MA 2138, USA Release October 1, 214 ABSTRACT Context. Atmospheric Imaging Assembly is an instrument on-board Solar Dynamics Observatory satellite. It is capable of detecng and idenfying coronal bright points in the solar corona. Aims. We present the results of solar differenal rotaon profile by tracing coronal bright points detected by Atmospheric Imaging Assembly. We also invesgated problems related to detecon of coronal bright points resulng from instrument and detecon algorithm limitaons. Methods. To determine the posions and idenficaon of coronal bright points we used the segmentaon algorithm. Linear fit of central meridian distance and latude versus me was ulised to obtain related velocies of the tracer. Results. We obtained 96 velocity measurements in me interval of only 2 days. Differenal rotaon profile can be expressed as ω rot = (14.47±.1+(.6±1.) sin 2 (b)+( 4.7±1.7) sin 4 (b)) day 1. Conclusions. Data and methods presented in this paper show a great potenal to obtain very accurate velocity profiles, both for rotaon and meridional moon and, consequently, Reynolds stresses. The amount of coronal bright point data that could be obtained from this instrument should also provide a great opportunity to study changes of velocity patterns with a temporal resoluon of only a few months. Other possibilies are studies of evoluon of coronal bright points and proper moons of magnec elements on the Sun. Key words. Sun: rotaon - Sun: corona - Sun: acvity 1. Introducon We present the results of solar rotaon profile obtained by tracing coronal bright points (CBs) which were observed by Atmospheric Imaging Assembly (AIA) instrument on board Solar Dynamics Observatory (SDO) satellite (Lemen et al. 212). The most frequently used and oldest tracer of solar differenal profile are sunspots (ewton & unn 1951; Howard et al. 1984; Balthasar et al. 1986; Brajša et al. 22a). One of the advantages of using sunspots is very long me coverage. On the other hand, there are numerous disadvantages: sunspots have complex and evolving structure, their distribuon in latude is highly non-uniform and it does not extend to higher solar latudes. umber of sunspots is also highly variable during the solar cycle which makes measurements of solar differenal rotaon profile almost impossible in the minimum of solar acvity. CBs are more uniformly distributed in latude and are numerous in all phases of the solar cycle. They also extend over all solar latudes. They were used as tracers of solar rotaon since the beginning of the space age (Dupree & Henze 1972). In recent years there are numerous studies invesgang solar differenal rotaon by using CBs as tracers. Kariyappa (28); Hara (29) used Yohkoh/SXT data while Brajša et al. (21, 22b, 24); Vršnak et al. (23); Wöhl et al. (21) used SOHO-EIT observaons. Kariyappa (28) also used Hinode/XRT full-disk images to determine the solar rotaon profile. Send offprint requests to: D. Sudar, :davor.sudar@gmail.com Other tracers are used as well: magnec fields (Wilcox & Howard 197; Snodgrass 1983; Komm et al. 1993) and Hα filaments (Brajša et al. 1991). Apart from tracers, Doppler measurements can also be used (Howard & Harvey 197; Ulrich et al. 1988; Snodgrass & Ulrich 199). Helioseismic measurements also show differenal rotaon below the photosphere all the way down to the bottom of the convecve zone (Kosovichev et al. 1997; Schou et al. 1998). Further below, the rotaon profile becomes uniform for all latudes (cf. eg. Howe 29). For further details about solar rotaon, its importance for solar dynamo models, comparison between different sources see the reviews by Schröter (1985); Howard (1984); Beck (2); Ossendrijver (23); Rüdiger & Hollerbach (24); Sx (24); Howe (29); Rozelot & einer (29). In this work we will use CB data obtained by SDO/AIA in only two days to assess the quality of the data, idenfy sources of errors and calculate solar differenal rotaon profile. We will also invesgate the possibility to use CB data from SDO/AIA for further studies of other related phenomena (meridional flow, rotaon velocity residuals and Reynolds stress). CB data from SDO/AIA were also used in other works. Lorenc et al. (212) discussed rotaon of the solar corona based on 69 structures from 674 images detected in 9.4 nm channel using an interacve method of detecon. Dorotovič et al. (214) presented a hybrid algorithm for detecon and tracking of CBs. McIntosh et al. (214b) used detecon algorithm presented in their previous paper (McIntosh & Gurman 25) to idenfy CBs in SDO/AIA 19.4 nm channel and correlate their proper- 1

2 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data es with those of giant convecve cells. Using more SDO/AIA data and extending analysis back to SOHO era, McIntosh et al. (214a) concluded that CBs almost exclusively form around the verces of giant convecve cells Data and reducon methods We have used preliminary data from Atmospheric Imaging Assembly (AIA) instrument on board Solar Dynamics Observatory (SDO) satellite (Lemen et al. 212). The spaal resoluon of the instrument is.6 /pixel. For comparison, SOHO/EIT resoluon is /pixel while Hinode/XRT has a resoluon of 1.32 /pixel. To obtain posional informaon of coronal bright points (CBs) we used the segmentaon algorithm which uses the 19.3 nm AIA channel to search for localized, small intensity enhancements in the EUV part of the spectrum compared to the smoothed background intensity. More details about the detecon algorithm can be found in Martens et al. (212) which is based on the algorithm by McIntosh & Gurman (25). This resulted in measurements of posions of individual CBs covering two days (1st and 2nd of January 211). Time interval between two successive images was 1 minutes. In top panel of Fig. 1 we show the distribuon of detected CBs and compare it to the full disk image of the Sun in the 19.3 nm channel obtained on 1st of January 211 (bottom panel of the same Figure). In the bottom panel white circles show CBs that were detected on one image by the segmentaon algorithm. We can see that CBs are scarce in acve regions, partly because of difficules in detecng them above such bright areas. The segmentaon algorithm provides coordinates in pixels (centroids of CBs on the image) and we converted them to heliographic coordinates taking into account current distance of the Sun given in FITS files (Ros a et al. 1995, 1998). osions of objects on the limb of the Sun are fairly inaccurate. Liming the data to ±58 from the centre of the Sun or.85r of the projected solar disk removes this problem (cf. Balthasar et al. 1986). As can be seen from Fig. 2, calculated velocies show some scatter because the shifts are fairly small in a very short me (1 min). Significant variaons in brightness and structure of CBs also influence calculaon of the centroid points. However, trends are visible, especially in azimuthal moon which is known to be a significantly larger effect. That is why we have chosen to approximate the moon with a linear fit to calculate the velocies: li ωmer = 2 bi 2!2 bi li ω syn =!2 (1),, (2) where ω syn is a synodic rotaonal velocity, ωmer is a meridional angular velocity, li is central meridian distance (CMD) and bi is latude of each measurement for a single CB. We have also removed all CBs which had less than 1 measurements of posion in order for linear fits to be more robust. This is equivalent to 1 minutes or about 1 at the equator. 2 y [pixels] x [pixels] 1 2 Fig. 1. Distribuon of CBs detected by the segmentaon algorithm (top panel) and image of the Sun in the 19.3 nm channel obtained by SDO/AIA on 1st of January 211. White circles show detected CBs on this image (bottom panel). To obtain a true rotaon of CBs on the Sun we need to convert synodic velocies to sidereal. For the transformaon we have used Eq. 7 from Skokic et al. (214). Trying to idenfy the same object on subsequent images with an automac method is bound to result in some misidenficaon. Resulng velocies are usually very large and can easily be removed by applying a simple filter for velocies Even the human factor can introduce such errors. For example, Sudar et al. (214) analysed solar rotaon residuals and meridional moons of sunspot groups from the Greenwich hotoheliographic Results and found that they have to use a filter 8< ωrot <19 day 1 for rotaonal velocity in order to eliminate these erroneous measurements. The Greenwich hotoheliographic Results catalogue is being invesgated and revised partly in order to remove such problems (Willis et al. 213a,b; Erwin et al. 213). In this work we have also used a 8< ωrot <19 day 1 filter for rotaonal velocies to remove such

3 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data b [deg] σ(ω rot ) [deg/day] CMD [deg] t [days] t [days] Fig. 2. Moon of a single CB. Top panel: latude, b, over me, t; bottom panel: central meridional distance, CMD over me, t. outliers. In addion we applied a filter -4<ω mer <4 day 1 for meridional velocies because it also helps in removing the outliers. Finally, we discarded all the CBs with less than 1 measurements of posion. After compleng all the procedures described above, we had 96 measurements of velocies obtained by tracing CBs in just two days. Olemskoy & Kitchanov (25) pointed out that nonuniform distribuon of tracers can result in false flows. This effect is most notable for meridional moon and rotaon velocity residuals, but can easily be removed by assigning the calculated velocity to the latude of the first measurement of posion (Olemskoy & Kitchanov 25; Sudar et al. 214). Although the effect is negligible for solar rotaon, we want to point out that we applied this correcon even for rotaon velocity profiles in this work. Even when the tracers are uniformly distributed over the solar surface, the distribuon of tracers over latude would be nonuniform. As we move from equator to the pole, area of each latude bin becomes gradually smaller, so we would observe progressively less tracers. 3. Results In this work we present the moon of CBs obtained by SDO/AIA instrument. For better understanding of the results and potenal of future studies, it is very useful to analyse the accuracy and errors of this dataset Coronal bright point no. Fig. 3. Errors of rotaonal velocity,ω rot, for each of the 96 measurements. Heliographic latude [deg] Heliographic longitude [deg] Fig. 4. Distribuon of rotaon velocity (ω rot ) errors in heliographic coordinates. Error scale is in day 1. In Fig. 3 we show errors of the calculated rotaonal velocies,ω rot, for each CB obtained with linear fitng of longitude vs me measurements. Although the errors can go up to 3 day 1, the majority is below 1 day 1. In Fig. 4 we show these errors in heliographic coordinates to check their spaal distribuon on the solar surface. Larger errors are shown with brighter shades and we can see that larger errors roughly correspond to acve regions shown in the bottom panel of Fig. 1. This correlaon with acve region is probably a consequence of detecon algorithm design and difficules involving detecon of CBs over bright background. In Fig. 5 we show the distribuon of CBs in heliographic coordinates with arrows showing the velocity vector. As expected, the dominant direcon is that of solar rotaon. Latudinal dependence of rotaonal velocity is usually expressed as (Howard & Harvey 197; Schröter 1985): ω rot (b)=a+ B sin 2 b+ C sin 4 b, (3) where b is the latude. arameter A represents equatorial velocity, while B and C depict the deviaon from rigid body rotaon. The problem with Eq. 3 is that funcons in this expression

4 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data 6 Table 1. Coefficients of solar rotaon profile. Heliographic latude [deg] Type A [ day 1 ] B [ day 1 ] C [ day 1 ] n A, B, C 14.47±.1 +.6± ± A, B = C 14.59± ± ± A, B, C = 14.62±.8-2.2± orthern hemisphere A, B, C 14.43± ± ± A, B = C 14.55± ± ± A, B, C = 14.57± ± Southern hemisphere A, B, C 14.5± ± ± A, B = C 14.65± ± ± A, B, C = 14.69± ± Heliographic longitude [deg] Fig. 5. Distribuon of CBs in heliographic coordinates with arrows showing the direcon and strength of the velocity vector A, B, C B=C C= ω (deg/day) Fig. 7. Comparison of three different fitng procedures for the solar differenal rotaon profile. Average values ofω rot in 5 bins in latude, b, are also shown with their respecve errors b (degrees) Fig. 6. Solar differenal rotaon profile obtained with data from SDO/AIA. Open circles are individual measurements, while the solid line is the best fit defined by Eq. 3 for the A B C case. are not orthogonal so parameters are not independent of each other (Duvall & Svalgaard 1978; Snodgrass 1984; Snodgrass & Howard 1985; Snodgrass & Ulrich 199). This crosstalk among the coefficients is parcularity bad for B and C. The effect of crosstalk does not affect the actual shape of the fit (ω rot (b)), but it creates confusion when directly comparing coefficients from different authors or obtained by different indicators. To alleviate this problem, frequently the parameter C is set to zero since its effect is noceable only on higher latudes. This is almost a standard pracse when observing rotaon by tracing sunspots or sunspot groups because their posions do not extend to high latudes (Howard et al. 1984; Balthasar et al. 1986; ulkkinen & Tuominen 1998; Brajša et al. 22a; Sudar et al. 214). Another method to reduce the crosstalk problem is to set C/B rao to some fixed value. Scherrer et al. (198) set the rao C/B=1 while Ulrich et al. (1988), after measuring the covariance of B and C, set the rao to C/B= In Fig. 6 we show individual measurements of rotaonal velocies,ω rot, with respect to latude, b, as open circles. With a solid line we show the result of the best fit to the data of a funconal form given in Eq. 3. Coefficients of the fit are given in Table 1. We also fitted the rotaon profile for orthern and Southern solar hemisphere separately because of possible asymmetry (cf.eg. Wöhl et al. 21) and shown the results in the same table. Coefficient A shows a larger value for the Southern hemisphere for all 3 fit funcons. Jurdana-Šepić et al. (211) reported that coefficient A is larger when solar acvity is smaller. According to the SIDC data (SILSO World Data Center 211) we can see that orthern hemisphere is more acve both when looking at the monthly smoothed means and daily sunspot data. This fits the findings by Jurdana-Šepić et al. (211). However, judging by the errors of the coefficients, this difference between South and orth is stascally low and the hypothesis that this is a result of asymmetric solar acvity needs to be verified with a larger data sample. In Fig. 7 we show a comparison between different fitng techniques: A B C(solid line), A B=C(dashed line) and A B, C= (dotted line). In the same figure we also show average values ofω rot in bins 5 wide in latude, b, with their respecve errors. 4. Discussion In Table 2 we show a comparison for solar differenal profile (Eq. 3) from a number of different sources including the results 4

5 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data Table 2. Comparison with some other results. Method/object me period A [ day 1 ] B [ day 1 ] C [ day 1 ] A G [ day 1 ] B G [ day 1 ] C G [ day 1 ] Ref CBs ± (1) CBs ± ± ± (2) CBs ± ± ± (3) CBs ± ± ± (4) CBs 1-2 Jan ±.1 +.6± ± (5) CBs 1-2 Jan ± ± ± (5) CBs 1-2 Jan ±.8-2.2± (5) sunspots ± ± (6) sunspots ± ± (7) sunspot groups ± ± (8) sunspot groups ± ± (9) sunspots ± ± (1) sunspot groups ± ± (1) Hα filaments ± ± ± (11) magnec features ± ± ± (12) magnec features ±.2-2.± ± (13) Doppler (14) Doppler (15) References. (1) Dupree & Henze (1972); (2) Hara (29); (3) Brajša et al. (24); (4) Wöhl et al. (21); (5) this paper; (6) ulkkinen & Tuominen (1998); (7) Balthasar et al. (1986); (8) Sudar et al. (214); (9) Brajša et al. (22a); (1) Howard et al. (1984) (11) Brajša et al. (1991); (12) Snodgrass (1983); (13) Komm et al. (1993); (14) Howard & Harvey (197); (15) Snodgrass (1984); from this paper (Table 1). Since we found no stascally significant difference between orthern and Southern hemisphere we only include the results for both hemispheres combined. Results in Table 2 come from a wide variety of different techniques, tracers and instruments. Snodgrass (1984) suggested that the rotaon profile should be expressed in terms of Gegenbauer polynomials since they are orthogonal on the disk. This eliminates the cross-talk problem between coefficients in Eq. 3. Using the expansion in terms of Gegenbauer polynomials solar rotaon profile becomes: ω rot (b)=a G T 1 (sin b)+ B GT2 1 (sin b)+ C GT4 1 (sin b), (4) where A G, B G and C G are coefficients of expansion and T 1 (sin b), T2 1(sin b) and T 4 1 (sin b) are Gegenbauer polynomials as defined by Snodgrass & Howard (1985) in their equaon (2). As Snodgrass & Howard (1985); Snodgrass & Ulrich (199) pointed out, the relaonship between coefficients A, B and C from standard rotaon profile (Eq. 3) and coefficients A G, B G and C G from Eq. 4 is linear. Therefore, it is not necessary to recalculate the fits with expansion to Gegenbauer polynomials, we can just calculate A G, B G and C G from A, B and C. We used the relaonship given in Snodgrass & Howard (1985) (their equaon (4)) since there seems to be a typo for a similar relaonship for coefficients C and C G in Snodgrass & Ulrich (199). In Table 2 we also show the values of coefficients A G, B G and C G. Results in this paper roughly match all other previously published works. The accuracy of coefficients is lower when compared with other results which is a consequence of fairly small number of data points (n=96). For example Wöhl et al. (21) had more than 5 data points in the me interval of 8 years. However, we used the data spanning only 2 days. It is conceivable that with AIA/SDO CB data we could reach 5 data points in only 4 months and achieve similar accuracy in solar rotaon profile coefficients. This means that with AIA/SDO data it is possible to measure rotaon profile several mes per year and track possible changes in solar surface differenal rotaon directly with a very simple tracer method. This is also true for meridional moon and Reynolds stress, both of which probably vary within the solar cycle (cf. e.g Sudar et al. 214). 5. Summary and Conclusion Using preliminary results from SDO/AIA instrument we idenfied a large number of CBs which resulted in 96 rotaon velocity measurements. We obtained a fairly good differenal solar rotaon profile in spite of the fact that we used data from two days only. CBs are also very good tracers since they extend to much higher latudes than sunspots. They are also quite numerous in all phases of the solar cycle while sunspots are often absent in the minimum of the cycle. We will also invesgate the potenal of preliminary SDO/AIA CB data to determine meridional moons, rotaon velocity residuals, Reynolds stresses and diffusion in subsequent papers. It is quite conceivable that errors of the differenal rotaon profile coefficients would drop significantly when more data is used. From our analysis, we can expect to obtain 4-5 velocity measurements per day. Time interval of 4 months seems adequate to obtain 5 velocity measurements which should be sufficient to match the most accurate results obtained by tracer methods (for example Wöhl et al. (21)). Moreover, the spaal resoluon of SDO/AIA is better than comparable instruments (SOHO/EIT and Hinode/XRT). This opens up an intriguing possibility to measure solar rotaon profile almost from one month to the next. Such studies could provide new insight into mechanisms responsible for solar rotaon. We already know that meridional moon exhibits some changes during the course of the solar cycle and the same is probably true for Reynolds stress. Sudar et al. (214) found by averaging almost 15 years of sunspot data that meridional moon is slightly changing within the solar cycle and hinted that the Reynolds stresses are probably changing too. We have also found a small asymmetry in rotaon profile for two solar hemispheres and suggested that this might be related to different solar acvity on the hemispheres. This needs to be verified with a larger dataset because difference in rotaon profiles are of low stascal significance. Having more detailed temporal resolu- 5

6 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data on and direct results (without the need to average many solar cycles) could prove to be very informave. lanned SDO mission duraon of 5 1 years will cover a large poron of the solar cycle which would result in enormous amount of velocity data and help in understanding the nature of solar rotaon profile. Time interval of 1 minutes between successive images also offers a good opportunity to study the evoluon of CBs and possible effect this might have on detected solar surface velocity fields. For example Vršnak et al. (23) reported that longer lasng CBs show different results than short-lived CBs. Sx, M. 24, The sun : an introducon, 2nd ed., by Michael Sx. Astronomy and astrophysics library, Berlin: Springer, 24. ISB: Sudar, D., Skokić, I., Ruždjak, D., Brajša, R., & Wöhl, H. 214, MRAS, 439, 2377 Ulrich, R. K., Boyden, J. E., Webster, L., adilla, S.., & Snodgrass, H. B. 1988, Sol. hys., 117, 291 Vršnak, B., Brajša, R., Wöhl, H., et al. 23, A&A, 44, 1117 Wilcox, J. M. & Howard, R. 197, Sol. hys., 13, 251 Willis, D. M., Coffey, H. E., Henwood, R., et al. 213a, Sol. hys., 288, 117 Willis, D. M., Henwood, R., Wild, M.., et al. 213b, Sol. hys., 288, 141 Wöhl, H., Brajša, R., Hanslmeier, A., & Gissot, S. F. 21, A&A, 52, A29 Acknowledgements. This work has received funding from the European Commission F7 project eheroes (284461, ) and SOLARET project (312495, ) which is an Integrated Infrastructure Iniave (I3) supported by F7 Capacies rogramme. It was also supported by Croaan Science Foundaon under the project 6212 Solar and Stellar Variability. SS was supported by ASA Grant X9AB3G to the Smithsonian Astrophysical Observatory and contract S2H171R from Lockheed-Marn to SAO. We would like to thank SDO/AIA science teams for providing the observaons. We would also like to thank Veronique Delouille and Alexander Engell for valuable help in preparaon of this work. References Balthasar, H., Vázquez, M., & Wöhl, H. 1986, A&A, 155, 87 Beck, J. G. 2, Sol. hys., 191, 47 Brajša, R., Vršnak, B., Ruždjak, V., Schroll, A., & ohjolainen, S. 1991, Sol. hys., 133, 195 Brajša, R., Wöhl, H., Vršnak, B., et al. 22a, Sol. hys., 26, 229 Brajša, R., Wöhl, H., Vršnak, B., et al. 21, A&A, 374, 39 Brajša, R., Wöhl, H., Vršnak, B., et al. 22b, A&A, 392, 329 Brajša, R., Wöhl, H., Vršnak, B., et al. 24, A&A, 414, 77 Dorotovič, I., Shahamatnia, E., Lorenc, M., et al. 214, Sun and Geosphere, 9, 81 Dupree, A. K. & Henze, Jr., W. 1972, Sol. hys., 27, 271 Duvall, Jr., T. L. & Svalgaard, L. 1978, Sol. hys., 56, 463 Erwin, E. H., Coffey, H. E., Denig, W. F., et al. 213, Sol. hys., 288, 157 Hara, H. 29, ApJ, 697, 98 Howard, R. 1984, ARA&A, 22, 131 Howard, R., Gilman,. I., & Gilman,. A. 1984, ApJ, 283, 373 Howard, R. & Harvey, J. 197, Sol. hys., 12, 23 Howe, R. 29, Living Reviews in Solar hysics, 6, 1 Jurdana-Šepić, R., Brajša, R., Wöhl, H., et al. 211, A&A, 534, A17 Kariyappa, R. 28, A&A, 488, 297 Komm, R. W., Howard, R. F., & Harvey, J. W. 1993, Sol. hys., 145, 1 Kosovichev, A. G., Schou, J., Scherrer,. H., et al. 1997, Sol. hys., 17, 43 Lemen, J. R., Title, A. M., Akin, D. J., et al. 212, Sol. hys., 275, 17 Lorenc, M., Rybanský, M., & Dorotovič, I. 212, Sol. hys., 281, 611 Martens,. C. H., Attrill, G. D. R., Davey, A. R., et al. 212, Sol. hys., 275, 79 McIntosh, S. W. & Gurman, J. B. 25, Sol. hys., 228, 285 McIntosh, S. W., Wang, X., Leamon, R. J., et al. 214a, ApJ, 792, 12 McIntosh, S. W., Wang, X., Leamon, R. J., & Scherrer,. H. 214b, ApJ, 784, L32 ewton, H. W. & unn, M. L. 1951, MRAS, 111, 413 Olemskoy, S. V. & Kitchanov, L. L. 25, Astronomy Letters, 31, 76 Ossendrijver, M. 23, A&A Rev., 11, 287 ulkkinen,. & Tuominen, I. 1998, A&A, 332, 755 Roša, D., Vršnak, B., & Božić, H. 1995, Hvar Observatory Bullen, 19, 23 Roša, D., Vršnak, B., Božić, H., et al. 1998, Sol. hys., 179, 237 Rozelot, J.-. & einer, C., eds. 29, Lecture otes in hysics, Berlin Springer Verlag, Vol. 765, The Rotaon of Sun and Stars Rüdiger, G. & Hollerbach, R. 24, The Magnec Universe, by G. Rüdiger and R. Hollerbach. ISB Wiley Interscience, 24. Scherrer,. H., Wilcox, J. M., & Svalgaard, L. 198, ApJ, 241, 811 Schou, J., Ana, H. M., Basu, S., et al. 1998, ApJ, 55, 39 Schröter, E. H. 1985, Sol. hys., 1, 141 SILSO World Data Center. 211, Internaonal Sunspot umber Monthly Bullen and online catalogue Skokić, I., Brajša, R., Roša, D., Hržina, D., & Wöhl, H. 214, Sol. hys., 289, Snodgrass, H. B. 1983, ApJ, 27, 288 Snodgrass, H. B. 1984, Sol. hys., 94, 13 Snodgrass, H. B. & Howard, R. 1985, Sol. hys., 95, 221 Snodgrass, H. B. & Ulrich, R. K. 199, ApJ, 351, 39 6