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The statistical properties of strong sunspot area fluctuations
Advances in Space Research 40 (2007) 981–985 www.elsevier.com/locate/asr
The statistical properties of strong sunspot area fluctuations R. Getko Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622 Wrocław, Poland Received 9 October 2006; received in revised form 24 January 2007; accepted 2 February 2007
Abstract For each solar hemisphere and for three solar cycles (No. 16, 17, 18) I select the positive fluctuations as sets of successive deviations, of the same sign, of the sunspot areas (per one solar rotation) from their smoothed values. I evaluate all larger sunspot groups (their areas create about 80% of the sunspot areas during one solar rotation) and then I use them to find activity complexes. I also analyse the number and the longitude distributions of activity complexes which create each fluctuation. Finally, I calculate the longitude distribution of activity complexes which create all positive fluctuations and strong positive fluctuations for each of three solar cycles and each solar hemisphere in the Carrington rotation system. 2007 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Sunspot activity fluctuations; Activity complex; Active longitudes
1. Introduction Vitinskij (1960), when analysing sunspot activity, defined a fluctuation as a set of successive deviations, of the same sign, of the monthly sunspot number from the smoothed curve and the strong fluctuation as a set of deviations from the smoothed values greater than one standard deviation. On the basis of data observed between 1755 and 1982 Vitinskij et al. (1986) demonstrated evolutionary stages of typical strong fluctuations. Firstly, a few large and long-lived sunspot groups appeared in various longitudes at the same time and often far from the equator. Then, during a few rotations larger number of smaller sunspot groups with more uniform longitude distribution appeared closer to the equator. At the last stage, many weak short-lived and uncorrelated sunspot groups remained. This result was obtained on the basis of general statistical properties of strong fluctuations. However, a detailed analysis of individual fluctuations is still missing. Recently, I showed (Getko, 2004) that large activity complexes create strong positive sunspot activity fluctuations, and their lifetime (between 2 and 20 months) depends on
E-mail address: [email protected] 0273-1177/$30 2007 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2007.02.094
the activity level. For longer time scales solar activity could be stronger in some preferred longitudes, and such longitude bands were called ‘active longitudes’ (Dodson and Hedeman, 1972, 1975). Many researches (Wilcox and Schatten, 1967; S˘vestka, 1968; Dodson and Hedeman, 1968) analysed solar flares distributions in Carrington longitude. Bai (1988, 2003), taking the rotation period as a free parameter, studied longitude distribution properties of solar flares and ‘superactive regions’ which produce the majority of major flares. He showed that the number of active longitudes (1–3) and rotation periods in each solar hemisphere were different, and active longitudes persisted in the same locations longer than one 11-year cycle. Because the longitude distribution of solar activity is poorly known and the obtained results are inconsistent I try to find active longitudes which contain activity complexes creating strong fluctuations. I use a term of ‘sunspot area fluctuation’ similar to Vitinskij and select the individual positive and strong positive fluctuations. Then, I analyse the numbers and the positions of all activity complexes which create each fluctuation. On the basis of these data I evaluate the longitude distribution of activity complexes which create all positive fluctuations and strong positive fluctuations for three solar cycles in each solar hemisphere separately in the Carrington rotation system.
R. Getko / Advances in Space Research 40 (2007) 981–985
2. Methods of data analysis
3. Strong fluctuations in the northern hemisphere for cycle 18 I consider six sets of fluctuations, but for detailed analyses I choose only one case of the cycle 18 in the northern hemisphere. In the upper part of Fig. 1 I present curves for Carrington rotation mean sunspot areas (Sk) and smoothed sunspot areas ðS k Þ. In the lower part of Fig. 1 I show the curve for deviations Fk. According to the earlier presented criteria the value of the parameter p for strong fluctuations is p = 250 m.v.h. (0.6r). The dotted horizontal line shows this level. Each strong fluctuation Fi has the number i written above the strongest peak of the sequence of Fk that creates the ith fluctuation. A detailed analysis of individual fluctuations shows that the weak positive fluctuations from low-activity periods are created by small sunspot groups. The stronger fluctuations (from the interval of [200, 250] m.v.h.) are formed by one or two complexes.
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As a database for this study I use the daily sunspot areas for the years 1923–1954 available at the Greenwich Photoheliographic Results (GPHR) and consider their daily areas of each group summed up over a Carrington rotation and the rotational mean of sunspot areas for each solar hemisphere separately. To introduce a term of ‘positive fluctuation’ I define for the kth rotation the deviation (Fk) of the rotational mean sunspot area (Sk) from the smoothed sunspot Pkþ6 area: F k ¼ S k S k for k = 1, . . ., N, where S k ¼ 131 j¼k6 S j is the running mean. This deviation relates to the mean magnetic flux during one rotation. To investigate the strong magnetic flux emergence during a longer time interval, I introduce a sequence of deviations Ki = {Fk:Fk > 0, k = ji + 1, . . ., ji + li} such that maxF k 2K i F k ¼ F i and I call the ith positive fluctuation. Thus, the ith fluctuation is a sequence of positive deviations such that the greatest deviation from this sequence has the index of i. The indices ji + 1 and ji + li describe the first and the last term of this sequence in which li is the number of deviations Fk creating this sequence. Next, I determine the mean longitude, the mean latitude and the rotational sum of each large sunspot group areas for k = ji + 1, . . ., ji + li. I also take into consideration smaller sunspot groups which appear close to the large sunspot groups. Thus, I consider all sunspot groups for which the sum of their areas during the kth rotation is at least 70– 80% of the value of 27Sk. Almost all these groups or sets of groups which are close to one another have a longitudinal extent up to 30. A sunspot group or a set of sunspot groups for which the rotational sum of their areas (r.s.a.) is greater than 5000 millionths of visible hemisphere (m.v.h.) is named as an activity complex, and I determine the number of all activity complexes which create the positive fluctuation, the rotational sum and the mean position of each individual complex and the sum of their areas. To obtain the longitude distribution of such activity complexes during the whole solar cycle I divide the solar disk into 30 wide longitude bins and determine the number of complexes in each of them for all rotations such that Fk > 0. When the complex exists in two or more 30 wide bins I divide its longitudinal range into appropriate parts and assign to each part the value from the interval of (0, 1) which is a ratio of this longitudinal part of the 30 bin occupied by the complex to the width of the bin, i.e. 30. Because the empirical distributions of this time series fF k gNk¼1 for cycles 16–18 and for each hemisphere separately are not normal (the p-values for the Kolmogorov– Liliefors and the Shapiro–Wilk tests are less than 0.01) the three sigma rule should not be used. In such cases I introduced (Getko, 2004) a method that supplies the best value of the parameter p such that the sequence of deviations Fk > p could be treated as a strong fluctuation. Usually such strong fluctuations are created by a few complexes in each hemisphere, sometimes this feature exists also for
weaker positive fluctuations. Therefore, a possibility to decrease the value of the parameter p is to reject, from the set of all weaker positive fluctuations, the fluctuations created by weak sunspot groups which do not create complexes. The set of complexes that create the strong fluctuations enables one to obtain the longitude distribution of these complexes for each of six cases (for each of cycles 16–18 and for each hemisphere separately). Moreover, a similar analysis can be also applied to strong ‘single’ fluctuations which have only one strong maximum and strong ‘deckled’ fluctuations which contain a few local maxima.
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Fig. 1. Two upper curves show mean sunspot areas for each synodic rotation Sk (solid line) and smoothed sunspot areas S k (dotted line) in the northern hemisphere for cycle 18. Both indexes are presented on the left axis. The lower part illustrates fluctuations of the sunspot areas Fk in units of m.v.h. The dashed line shows the zero level, and the dotted horizontal line represents the parameter p, which evaluate positive and strong positive fluctuations. The deviations Fi are shown on the right axis.
R. Getko / Advances in Space Research 40 (2007) 981–985
The weak positive fluctuations from higher activity period are created by 1–3 complexes (r.s.a. in this case is about 5– 6 · 103 m.v.h.). There are also 11 strong fluctuations: 8 very strong (greater than 450 m.v.h. – 1.1r) and 3 weaker (about 300 m.v.h. – 0.7r). This set contains three ‘single’ fluctuations (No. 1236, 1242, 1306), each of them is created by one very strong complex (r.s.a. is about 50 · 103 m.v.h.) and one ‘single’ fluctuation (No. 1283) created by two complexes (r.s.a. is about 30 · 103 m.v.h.). Among four ‘deckled’ fluctuations three fluctuations (No. 1253, 1265, 1277) are created by 2–4 complexes (r.s.a. is about 30 · 103 m.v.h.) and one (No. 1290) is formed by one complex (r.s.a. is about 30 · 103 m.v.h.) which exists during three rotations. The time between five strong fluctuations from the high-activity period is 12–13 rotations. I also find three weaker fluctuations: one ‘single’ from the high-activity period (No. 1285) which is created by two complexes (r.s.a. is about 25 · 103 m.v.h.) and two fluctuations from the low-activity period (No. 1315 – ‘single’ and No. 1327 – ‘deckled’) which are created by one complex (r.s.a. is about 104 m.v.h.). Fig. 2 presents the longitude distribution of complexes creating all positive fluctuations (columns 1 and 3) and strong fluctuations (columns 2 and 4) for each solar hemisphere separately. For the cycle 18 in the northern hemisphere the positive fluctuations shows three active zones:
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the dominant zone 180–210 and two weaker ones 60–90 and 270–300. There is a good correlation between the histograms of all positive fluctuations and of strong fluctuations. However, the probability that a complex creating a strong fluctuation belongs to the interval of 270–300 is smaller than for a complex creating a positive fluctuation. For other cases the correlation is not so good. For example, for the cycle 16 in the northern hemisphere there are four active zones for all positive fluctuations, but there are two dominant active zones and one weaker zone for strong fluctuations. Bai (1988) analysed major solar flares for the years 1955–1985. He investigated the longitude distributions of ‘superactive regions’ (SARs) which produced five and more important flares. They created two active zones in the northern hemisphere during cycles 20 and 21 and three ones during cycle 19. He also found one active zone in the southern hemisphere persisted through three solar cycles and the other which was active during two solar cycles and was dormant during cycle 20. These long-persistent active zones differ from those presented in this paper. Although the SARs produce many flares they do not often create strong fluctuations. Moreover, each of them was also considered during one rotation only, but it was often living during a few solar rotations and was changing its area and position. Thus, its mean position during each rotation, when the strong fluctuation exists,
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Fig. 2. Two left columns show the longitude distribution of complexes creating positive fluctuations and strong fluctuations in the northern hemisphere. Two right columns present the same for the southern hemisphere.
R. Getko / Advances in Space Research 40 (2007) 981–985
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can significantly differ from the position determined by Bai (1988). Moreover, the contribution of such a region to the longitude distribution depends on the strong fluctuation lifetime, but not on the flare activity during one rotation. A different observational analysis of sunspot data was presented by Usoskin et al. (2005). They found that the distribution of sunspots is non-axisymmetric and spot group formation implies the existence of two active longitudes separated by 180. Their results were obtained for all sunspot on the day of their births or when they appeared at the East limb. However, I showed (Getko, 2004) that for strong fluctuations 40–60% of the monthly Wolf number is produced by large complexes which probably create active longitudes, but the remaining part of the Wolf number is produced by smaller structures scattered throughout the whole disk. For negative and weaker positive fluctuations a percentage contribution of such sunspot groups to the Wolf number increases. Thus, these data may influence the results. Ivanov (2003) also identified active zones for the sunspot groups with the rotation-summed areas more than 2000 m.v.h. for cycles 12–23. He obtained four active zones which were spaced by 180 within a pair. However, the complexes creating weak positive fluctuations (containing strong sunspot groups selected by Ivanov) give different longitude distribution than the complexes creating strong fluctuations (see Fig. 2). Moreover, there are also large sunspot groups during the negative fluctuations which are scattered throughout the whole disk and do not create activity complexes. In addition, an activity complex usually contains large recurrent sunspot groups and smaller and short-lived sunspot groups which are not considered by Ivanov. In Fig. 3 I show the longitude distributions for complexes creating strong ‘single’ and ‘deckled’ fluctuations in the northern hemisphere for the cycle 18. It is easy to notice that each of three dominant active longitudes (see Fig. 2) has a different origin. The most significant active longitude (150–210) is created by both types of fluctuations. Two other longitudes are dominated by ‘deckled’ fluctuations, but each of them with different probability. Bai (1988) concluded that the SARs rotate faster than other sunspot regions. However, Gaizauskas et al. (1983) showed that the rotation rate depends on the evolutionary stages of complexes. Sometimes their branches are the most rapidly rotating feature (for the new magnetic flux T = 26.5 days), while different branches move at a slower rate (for the remnant magnetic flux T = 27.9 days). Thus, the Bai’s empirical rotation rate has the significant standard deviation. To verify the rotation rate of complexes I examine a location of strong recurrent groups which form complexes in the northern hemisphere during the whole cycle 18. Only two of them significantly change their position outside the 30 longitude bins. Namely, the group No. 15542 creates the strong ‘deckled’ fluctuation (No. 1267) and moves by about 20 both eastwards and westwards during its lifetime (7 rotations) and the group No. 14417 creates a very strong ‘single’ fluctuation (No. 1236) with very large area (about
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Fig. 3. The upper part of this figure shows the longitude distribution of complexes creating strong ‘single’ fluctuations of the northern hemisphere for cycle 18. The lower part presents the same, but for strong ‘deckled’ fluctuations.
55 · 103 m.v.h.). All the other groups are inside the 30th bins during their lifetimes and change their locations by not more than 10. Thus, movements of strong sunspot groups forming complexes do not change significantly shapes of earlier evaluated histograms. Note that, Ivanov (2003) also showed that the intensive sunspot formation zones stayed at the same Carrington longitude over all their lifetime (from 1.5–2 to 6 years). 4. Conclusions
1. Two kinds of positive fluctuations can be selected: weak and strong ones. The weak fluctuations from low-activity periods of the solar cycle are created by a few sunspot groups that are scattered in the whole hemisphere. Sometimes (usually during high-activity periods) they create one or two weak complexes. The strong fluctuations are created by 1–4 complexes that occur simultaneously. 2. Because of different shapes the strong fluctuations can be divided in two groups: the ‘deckled’ and the ‘single’ ones. The ‘deckled’ fluctuations are characterized by several local maxima living for a few rotations and are created by a few complexes that occur simultaneously. These structures diminish after one or two rotations and are replaced by new complexes which have similar properties. The ‘single’ fluctuations have one maximum and their lifetimes are 1–4 rotations. Such fluctuations usually exist during more intense cycles (for example
R. Getko / Advances in Space Research 40 (2007) 981–985
in cycle 18). They are created by one strong complex that diminishes after one or two rotations. There are also strong ‘single’ fluctuations which are created by a few weaker complexes. 3. A comparison of distributions of complexes indicates that histograms related to strong and all positive fluctuations are different. Complexes creating weak fluctuations are often scattered over the whole hemisphere or exist in different ‘active longitudes’ for both strong and all positive fluctuations (for example the fluctuations from the northern hemisphere in cycle 17). 4. There is only one ‘active longitude’ (180–210 in the northern hemisphere) which exists during three considered solar cycles. The remaining ‘active longitudes’ exist during one solar cycle only. Moreover, distributions of complexes related to ‘single’ and ‘deckled’ fluctuations show different dominant zones.
References Bai, T. Distribution of flares on the Sun during 1955–1985 – ‘hot spots’ (active zones) lasting for 30 years. Astrophys. J. 328, 860–878, 1988. Bai, T. Hot spots for solar flares persisting for decades: longitude distributions of flares of cycles 19–23. Astrophys. J. 585, 1114–1123, 2003. Dodson, H.W., Hedeman, E.R. Some patterns in the development of centers of solar activity, 1962–66, structure and development of solar
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active region, in: Kiepenheuer, K.O. (Ed.), IAU Symposium 35. D. Reidel, Dordrecht, pp. 56–63, 1968. Dodson, H.W., Hedeman, E.R. Large-scale organization of solar activity in time and space, in: McIntosh, P.S., Dryer, M. (Eds.), Solar activity observations and predictions, Progress in Astronautics and Aeronautics, vol. 30. MIT Press, Cambridge, pp. 19–22, 1972. Dodson, H.W., Hedeman, E.R. Comments on the course of solar activity during the declining phase of solar cycle 20 /1970–74/. Sol. Phys. 42, 121–130, 1975. Gaizauskas, V., Harvey, K.L., Harvey, J.W., Zwaan, C.T. Large-scale patterns formed by solar active regions during the ascending phase of cycle 21. Astrophys. J. 265, 1056–1065, 1983. Getko, R. Activity complexes as a cause of strong positive Wolf number fluctuations. Sol. Phys. 224, 291–301, 2004. Ivanov, E.V. Dynamics of active longitudes as inferred from sunspot observations, 1962–66, solar variability as an input to the earth’s environment, in: Proceedings of ISCS 2003 Symposium, Tatranska Lomnica, pp. 105–108, 2003. Royal Observatory, Greenwich Photoheliographic Results. Available from:, 1923–1954. S˘vestka, Z. On long-term forecasts of proton flares. Sol. Phys. 4, 18–29, 1968. Usoskin, I.G., Berdyugina, S.V., Poutanen, J. Preferred sunspot longitudes: non-axisymmetry and differential rotation. A&A. 441, 347–352, 2005. Vitinskij, Ju.I. Fluctuation index of Wolf numbers (in Russian). Solnechnie Dannie 8, 70–75, 1960. Vitinskij, Ju.I., Kopecky, M., Kuklin G.B. Statistics of Sunspot Activity (in Russian). Nauka, Moscow, pp. 236–243, 1986. Wilcox, J.M., Schatten, K.H. Longitude distribution of proton flares as a function of recurrence period. Astrophys. J. 147, 364–367, 1967.
The statistical properties of strong sunspot area fluctuations R. Getko Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622 Wrocław, Poland Received 9 October 2006; received in revised form 24 January 2007; accepted 2 February 2007
Abstract For each solar hemisphere and for three solar cycles (No. 16, 17, 18) I select the positive fluctuations as sets of successive deviations, of the same sign, of the sunspot areas (per one solar rotation) from their smoothed values. I evaluate all larger sunspot groups (their areas create about 80% of the sunspot areas during one solar rotation) and then I use them to find activity complexes. I also analyse the number and the longitude distributions of activity complexes which create each fluctuation. Finally, I calculate the longitude distribution of activity complexes which create all positive fluctuations and strong positive fluctuations for each of three solar cycles and each solar hemisphere in the Carrington rotation system. 2007 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Sunspot activity fluctuations; Activity complex; Active longitudes
1. Introduction Vitinskij (1960), when analysing sunspot activity, defined a fluctuation as a set of successive deviations, of the same sign, of the monthly sunspot number from the smoothed curve and the strong fluctuation as a set of deviations from the smoothed values greater than one standard deviation. On the basis of data observed between 1755 and 1982 Vitinskij et al. (1986) demonstrated evolutionary stages of typical strong fluctuations. Firstly, a few large and long-lived sunspot groups appeared in various longitudes at the same time and often far from the equator. Then, during a few rotations larger number of smaller sunspot groups with more uniform longitude distribution appeared closer to the equator. At the last stage, many weak short-lived and uncorrelated sunspot groups remained. This result was obtained on the basis of general statistical properties of strong fluctuations. However, a detailed analysis of individual fluctuations is still missing. Recently, I showed (Getko, 2004) that large activity complexes create strong positive sunspot activity fluctuations, and their lifetime (between 2 and 20 months) depends on
E-mail address: [email protected] 0273-1177/$30 2007 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2007.02.094
the activity level. For longer time scales solar activity could be stronger in some preferred longitudes, and such longitude bands were called ‘active longitudes’ (Dodson and Hedeman, 1972, 1975). Many researches (Wilcox and Schatten, 1967; S˘vestka, 1968; Dodson and Hedeman, 1968) analysed solar flares distributions in Carrington longitude. Bai (1988, 2003), taking the rotation period as a free parameter, studied longitude distribution properties of solar flares and ‘superactive regions’ which produce the majority of major flares. He showed that the number of active longitudes (1–3) and rotation periods in each solar hemisphere were different, and active longitudes persisted in the same locations longer than one 11-year cycle. Because the longitude distribution of solar activity is poorly known and the obtained results are inconsistent I try to find active longitudes which contain activity complexes creating strong fluctuations. I use a term of ‘sunspot area fluctuation’ similar to Vitinskij and select the individual positive and strong positive fluctuations. Then, I analyse the numbers and the positions of all activity complexes which create each fluctuation. On the basis of these data I evaluate the longitude distribution of activity complexes which create all positive fluctuations and strong positive fluctuations for three solar cycles in each solar hemisphere separately in the Carrington rotation system.
R. Getko / Advances in Space Research 40 (2007) 981–985
2. Methods of data analysis
3. Strong fluctuations in the northern hemisphere for cycle 18 I consider six sets of fluctuations, but for detailed analyses I choose only one case of the cycle 18 in the northern hemisphere. In the upper part of Fig. 1 I present curves for Carrington rotation mean sunspot areas (Sk) and smoothed sunspot areas ðS k Þ. In the lower part of Fig. 1 I show the curve for deviations Fk. According to the earlier presented criteria the value of the parameter p for strong fluctuations is p = 250 m.v.h. (0.6r). The dotted horizontal line shows this level. Each strong fluctuation Fi has the number i written above the strongest peak of the sequence of Fk that creates the ith fluctuation. A detailed analysis of individual fluctuations shows that the weak positive fluctuations from low-activity periods are created by small sunspot groups. The stronger fluctuations (from the interval of [200, 250] m.v.h.) are formed by one or two complexes.
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As a database for this study I use the daily sunspot areas for the years 1923–1954 available at the Greenwich Photoheliographic Results (GPHR) and consider their daily areas of each group summed up over a Carrington rotation and the rotational mean of sunspot areas for each solar hemisphere separately. To introduce a term of ‘positive fluctuation’ I define for the kth rotation the deviation (Fk) of the rotational mean sunspot area (Sk) from the smoothed sunspot Pkþ6 area: F k ¼ S k S k for k = 1, . . ., N, where S k ¼ 131 j¼k6 S j is the running mean. This deviation relates to the mean magnetic flux during one rotation. To investigate the strong magnetic flux emergence during a longer time interval, I introduce a sequence of deviations Ki = {Fk:Fk > 0, k = ji + 1, . . ., ji + li} such that maxF k 2K i F k ¼ F i and I call the ith positive fluctuation. Thus, the ith fluctuation is a sequence of positive deviations such that the greatest deviation from this sequence has the index of i. The indices ji + 1 and ji + li describe the first and the last term of this sequence in which li is the number of deviations Fk creating this sequence. Next, I determine the mean longitude, the mean latitude and the rotational sum of each large sunspot group areas for k = ji + 1, . . ., ji + li. I also take into consideration smaller sunspot groups which appear close to the large sunspot groups. Thus, I consider all sunspot groups for which the sum of their areas during the kth rotation is at least 70– 80% of the value of 27Sk. Almost all these groups or sets of groups which are close to one another have a longitudinal extent up to 30. A sunspot group or a set of sunspot groups for which the rotational sum of their areas (r.s.a.) is greater than 5000 millionths of visible hemisphere (m.v.h.) is named as an activity complex, and I determine the number of all activity complexes which create the positive fluctuation, the rotational sum and the mean position of each individual complex and the sum of their areas. To obtain the longitude distribution of such activity complexes during the whole solar cycle I divide the solar disk into 30 wide longitude bins and determine the number of complexes in each of them for all rotations such that Fk > 0. When the complex exists in two or more 30 wide bins I divide its longitudinal range into appropriate parts and assign to each part the value from the interval of (0, 1) which is a ratio of this longitudinal part of the 30 bin occupied by the complex to the width of the bin, i.e. 30. Because the empirical distributions of this time series fF k gNk¼1 for cycles 16–18 and for each hemisphere separately are not normal (the p-values for the Kolmogorov– Liliefors and the Shapiro–Wilk tests are less than 0.01) the three sigma rule should not be used. In such cases I introduced (Getko, 2004) a method that supplies the best value of the parameter p such that the sequence of deviations Fk > p could be treated as a strong fluctuation. Usually such strong fluctuations are created by a few complexes in each hemisphere, sometimes this feature exists also for
weaker positive fluctuations. Therefore, a possibility to decrease the value of the parameter p is to reject, from the set of all weaker positive fluctuations, the fluctuations created by weak sunspot groups which do not create complexes. The set of complexes that create the strong fluctuations enables one to obtain the longitude distribution of these complexes for each of six cases (for each of cycles 16–18 and for each hemisphere separately). Moreover, a similar analysis can be also applied to strong ‘single’ fluctuations which have only one strong maximum and strong ‘deckled’ fluctuations which contain a few local maxima.
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Fig. 1. Two upper curves show mean sunspot areas for each synodic rotation Sk (solid line) and smoothed sunspot areas S k (dotted line) in the northern hemisphere for cycle 18. Both indexes are presented on the left axis. The lower part illustrates fluctuations of the sunspot areas Fk in units of m.v.h. The dashed line shows the zero level, and the dotted horizontal line represents the parameter p, which evaluate positive and strong positive fluctuations. The deviations Fi are shown on the right axis.
R. Getko / Advances in Space Research 40 (2007) 981–985
The weak positive fluctuations from higher activity period are created by 1–3 complexes (r.s.a. in this case is about 5– 6 · 103 m.v.h.). There are also 11 strong fluctuations: 8 very strong (greater than 450 m.v.h. – 1.1r) and 3 weaker (about 300 m.v.h. – 0.7r). This set contains three ‘single’ fluctuations (No. 1236, 1242, 1306), each of them is created by one very strong complex (r.s.a. is about 50 · 103 m.v.h.) and one ‘single’ fluctuation (No. 1283) created by two complexes (r.s.a. is about 30 · 103 m.v.h.). Among four ‘deckled’ fluctuations three fluctuations (No. 1253, 1265, 1277) are created by 2–4 complexes (r.s.a. is about 30 · 103 m.v.h.) and one (No. 1290) is formed by one complex (r.s.a. is about 30 · 103 m.v.h.) which exists during three rotations. The time between five strong fluctuations from the high-activity period is 12–13 rotations. I also find three weaker fluctuations: one ‘single’ from the high-activity period (No. 1285) which is created by two complexes (r.s.a. is about 25 · 103 m.v.h.) and two fluctuations from the low-activity period (No. 1315 – ‘single’ and No. 1327 – ‘deckled’) which are created by one complex (r.s.a. is about 104 m.v.h.). Fig. 2 presents the longitude distribution of complexes creating all positive fluctuations (columns 1 and 3) and strong fluctuations (columns 2 and 4) for each solar hemisphere separately. For the cycle 18 in the northern hemisphere the positive fluctuations shows three active zones:
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the dominant zone 180–210 and two weaker ones 60–90 and 270–300. There is a good correlation between the histograms of all positive fluctuations and of strong fluctuations. However, the probability that a complex creating a strong fluctuation belongs to the interval of 270–300 is smaller than for a complex creating a positive fluctuation. For other cases the correlation is not so good. For example, for the cycle 16 in the northern hemisphere there are four active zones for all positive fluctuations, but there are two dominant active zones and one weaker zone for strong fluctuations. Bai (1988) analysed major solar flares for the years 1955–1985. He investigated the longitude distributions of ‘superactive regions’ (SARs) which produced five and more important flares. They created two active zones in the northern hemisphere during cycles 20 and 21 and three ones during cycle 19. He also found one active zone in the southern hemisphere persisted through three solar cycles and the other which was active during two solar cycles and was dormant during cycle 20. These long-persistent active zones differ from those presented in this paper. Although the SARs produce many flares they do not often create strong fluctuations. Moreover, each of them was also considered during one rotation only, but it was often living during a few solar rotations and was changing its area and position. Thus, its mean position during each rotation, when the strong fluctuation exists,
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Fig. 2. Two left columns show the longitude distribution of complexes creating positive fluctuations and strong fluctuations in the northern hemisphere. Two right columns present the same for the southern hemisphere.
R. Getko / Advances in Space Research 40 (2007) 981–985
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can significantly differ from the position determined by Bai (1988). Moreover, the contribution of such a region to the longitude distribution depends on the strong fluctuation lifetime, but not on the flare activity during one rotation. A different observational analysis of sunspot data was presented by Usoskin et al. (2005). They found that the distribution of sunspots is non-axisymmetric and spot group formation implies the existence of two active longitudes separated by 180. Their results were obtained for all sunspot on the day of their births or when they appeared at the East limb. However, I showed (Getko, 2004) that for strong fluctuations 40–60% of the monthly Wolf number is produced by large complexes which probably create active longitudes, but the remaining part of the Wolf number is produced by smaller structures scattered throughout the whole disk. For negative and weaker positive fluctuations a percentage contribution of such sunspot groups to the Wolf number increases. Thus, these data may influence the results. Ivanov (2003) also identified active zones for the sunspot groups with the rotation-summed areas more than 2000 m.v.h. for cycles 12–23. He obtained four active zones which were spaced by 180 within a pair. However, the complexes creating weak positive fluctuations (containing strong sunspot groups selected by Ivanov) give different longitude distribution than the complexes creating strong fluctuations (see Fig. 2). Moreover, there are also large sunspot groups during the negative fluctuations which are scattered throughout the whole disk and do not create activity complexes. In addition, an activity complex usually contains large recurrent sunspot groups and smaller and short-lived sunspot groups which are not considered by Ivanov. In Fig. 3 I show the longitude distributions for complexes creating strong ‘single’ and ‘deckled’ fluctuations in the northern hemisphere for the cycle 18. It is easy to notice that each of three dominant active longitudes (see Fig. 2) has a different origin. The most significant active longitude (150–210) is created by both types of fluctuations. Two other longitudes are dominated by ‘deckled’ fluctuations, but each of them with different probability. Bai (1988) concluded that the SARs rotate faster than other sunspot regions. However, Gaizauskas et al. (1983) showed that the rotation rate depends on the evolutionary stages of complexes. Sometimes their branches are the most rapidly rotating feature (for the new magnetic flux T = 26.5 days), while different branches move at a slower rate (for the remnant magnetic flux T = 27.9 days). Thus, the Bai’s empirical rotation rate has the significant standard deviation. To verify the rotation rate of complexes I examine a location of strong recurrent groups which form complexes in the northern hemisphere during the whole cycle 18. Only two of them significantly change their position outside the 30 longitude bins. Namely, the group No. 15542 creates the strong ‘deckled’ fluctuation (No. 1267) and moves by about 20 both eastwards and westwards during its lifetime (7 rotations) and the group No. 14417 creates a very strong ‘single’ fluctuation (No. 1236) with very large area (about
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Fig. 3. The upper part of this figure shows the longitude distribution of complexes creating strong ‘single’ fluctuations of the northern hemisphere for cycle 18. The lower part presents the same, but for strong ‘deckled’ fluctuations.
55 · 103 m.v.h.). All the other groups are inside the 30th bins during their lifetimes and change their locations by not more than 10. Thus, movements of strong sunspot groups forming complexes do not change significantly shapes of earlier evaluated histograms. Note that, Ivanov (2003) also showed that the intensive sunspot formation zones stayed at the same Carrington longitude over all their lifetime (from 1.5–2 to 6 years). 4. Conclusions
1. Two kinds of positive fluctuations can be selected: weak and strong ones. The weak fluctuations from low-activity periods of the solar cycle are created by a few sunspot groups that are scattered in the whole hemisphere. Sometimes (usually during high-activity periods) they create one or two weak complexes. The strong fluctuations are created by 1–4 complexes that occur simultaneously. 2. Because of different shapes the strong fluctuations can be divided in two groups: the ‘deckled’ and the ‘single’ ones. The ‘deckled’ fluctuations are characterized by several local maxima living for a few rotations and are created by a few complexes that occur simultaneously. These structures diminish after one or two rotations and are replaced by new complexes which have similar properties. The ‘single’ fluctuations have one maximum and their lifetimes are 1–4 rotations. Such fluctuations usually exist during more intense cycles (for example
R. Getko / Advances in Space Research 40 (2007) 981–985
in cycle 18). They are created by one strong complex that diminishes after one or two rotations. There are also strong ‘single’ fluctuations which are created by a few weaker complexes. 3. A comparison of distributions of complexes indicates that histograms related to strong and all positive fluctuations are different. Complexes creating weak fluctuations are often scattered over the whole hemisphere or exist in different ‘active longitudes’ for both strong and all positive fluctuations (for example the fluctuations from the northern hemisphere in cycle 17). 4. There is only one ‘active longitude’ (180–210 in the northern hemisphere) which exists during three considered solar cycles. The remaining ‘active longitudes’ exist during one solar cycle only. Moreover, distributions of complexes related to ‘single’ and ‘deckled’ fluctuations show different dominant zones.
References Bai, T. Distribution of flares on the Sun during 1955–1985 – ‘hot spots’ (active zones) lasting for 30 years. Astrophys. J. 328, 860–878, 1988. Bai, T. Hot spots for solar flares persisting for decades: longitude distributions of flares of cycles 19–23. Astrophys. J. 585, 1114–1123, 2003. Dodson, H.W., Hedeman, E.R. Some patterns in the development of centers of solar activity, 1962–66, structure and development of solar
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active region, in: Kiepenheuer, K.O. (Ed.), IAU Symposium 35. D. Reidel, Dordrecht, pp. 56–63, 1968. Dodson, H.W., Hedeman, E.R. Large-scale organization of solar activity in time and space, in: McIntosh, P.S., Dryer, M. (Eds.), Solar activity observations and predictions, Progress in Astronautics and Aeronautics, vol. 30. MIT Press, Cambridge, pp. 19–22, 1972. Dodson, H.W., Hedeman, E.R. Comments on the course of solar activity during the declining phase of solar cycle 20 /1970–74/. Sol. Phys. 42, 121–130, 1975. Gaizauskas, V., Harvey, K.L., Harvey, J.W., Zwaan, C.T. Large-scale patterns formed by solar active regions during the ascending phase of cycle 21. Astrophys. J. 265, 1056–1065, 1983. Getko, R. Activity complexes as a cause of strong positive Wolf number fluctuations. Sol. Phys. 224, 291–301, 2004. Ivanov, E.V. Dynamics of active longitudes as inferred from sunspot observations, 1962–66, solar variability as an input to the earth’s environment, in: Proceedings of ISCS 2003 Symposium, Tatranska Lomnica, pp. 105–108, 2003. Royal Observatory, Greenwich Photoheliographic Results. Available from: