N-S Asymmetry and Solar Cycle Distribution of Superactive Regions from 1976 to 2017

: There were 51 superactive regions (SARs) during solar cycles (SCs) 21–24. We divided the SARs into SARs 1 , which produced extreme space weather events including ≥ X5.0 ﬂares, ground level events (GLEs), and super geomagnetic storms (SGSs, Dst < − 250 nT), and SARs 2 , which did not produce extreme space weather events. The total number of SARs 1 and SARs 2 are 31 and 20, respectively. The statistical results showed that 35.5%, 64.5%, and 77.4% of the SARs 1 appeared in the ascending phase, descending phase, and in the period from two years before to the three years after the solar maximum, respectively, whereas 50%, 50%, and 100% of the SARs 2 appeared in the ascending phase, descending phase, and in the period from two years before to the three years after the solar maximum, respectively. The total number of SARs during an SC has a good association with the SC amplitude, implying that an SC with a higher amplitude will have more SARs than that with a lower amplitude. However, the largest ﬂare index of a SAR within an SC has a poor association with the SC amplitude, suggesting that a weak cycle may have a SAR that may produce a series of very strong solar ﬂares. The analysis of the north–south asymmetry of the SARs showed that SARs 1 dominated in the southern hemisphere of the sun during SCs 21–24. The SAR 2 dominated in the different hemispheres by turns for different SCs. The solar ﬂare activities caused by the SARs with source locations in the southern hemisphere of the sun were much stronger than those caused by the SARs with source locations in the northern hemisphere of the sun during SCs 21–24.


Introduction
There are generally a large number of active regions (ARs) during a solar cycle. However, only a small number of ARs, which are defined as superactive regions (SARs), can produce very strong solar activities. A SAR is a special AR, which usually produces more and stronger solar flares than those ARs that are not SARs. The soft X-ray flare index of an AR is the sum of the numerical multipliers of M and X class X-ray flares for the disk transit of the AR, e.g., 0.1 for an M1 class flare and 1.0 for an X1 class flare. The criteria of a SAR proposed by different researchers were a little different [1][2][3]. If an AR satisfies the four conditions, including the largest area > 1000 µh, the flare index > 10, the peak flux of 10.7 cm > 1000 s.f.u, and the short-term total solar irradiance decrease < −0.1%, then the AR is defined as a SAR, as proposed by Chen et al. [3]. The comparison among the criteria proposed by different researchers have been made by Chen et al. [3] and by Le et al. [4]. According to the criteria proposed by Chen et al. [3], the SAR 12673 that occurred in September 2017 is also a SAR. The total number of SARs during SCs 21-23, which were listed in the appendix of the article by Chen et al. [3] is 45, and the number of the SARs during SC 24 includes the five SARs listed in the article by Chen and Wang [5] and the SAR 12673 is 6. Thus, the total number of SARs during SCs 21-24 is 51. Solar soft X-ray flares with intensities ≥X5.0, ground-level events (GLEs), and super geomagnetic storms (SGSs, Dst < −250 nT) are defined as extreme space weather events in this study. It was found that some SARs produced extreme space weather events [4,6], whereas other SARs did not produce extreme space weather events. According to whether a SAR produced extreme space weather events, we divided the SARs into two subgroups: SARs 1 , which produced extreme space weather events, and SARs 2 , which did not produce extreme space weather events.
The solar cycle distribution of various solar activities, solar wind, and space weather phenomena has been studied (e.g., [6][7][8][9][10][11]). What is the pattern of the solar cycle distribution of the SARs 1 and SARs 2 from 1976 to 2017? To answer the question, the SC distribution of the two subgroups of the SARs from 1976 to 2017 will be studied. The north-south (N-S) asymmetry of various parameters is an important property of solar activities. Solar activities in the two hemispheres of the sun are controlled by the dynamo actions in the two hemispheres of the sun. The N-S asymmetry can be used to check or verify whether the dynamo action in the two hemispheres is synchronized or whether there exists observational evidence for differences in the dynamo action in the two hemispheres [12], indicating that the study of the N-S asymmetries of solar activities is very important. The N-S asymmetries of the various solar activities such as solar flares, solar flares index, and sunspot activities have been extensively studied (e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein). The N-S asymmetry of the SARs was studied by Chen et al.. However, the N-S asymmetry of SARs 1 and SARs 2 has not been studied. What is the pattern of the N-S asymmetry of the SARs 1 and SARs 2 from 1976 to 2017? To answer the question, the N-S asymmetry of the SARs 1 and SARs 2 from 1976 to 2017 will be studied. Duchlev [31] found a long-term period of about 11 solar cycles in the filament asymmetry variation by using the cumulative index for the filament N-S asymmetry. N-S asymmetry of the cumulative index for many solar activities has been studied (e.g., [20,32,33]). The N-S asymmetry of the cumulative numbers of the SARs in the northern and southern hemispheres of the sun will be investigated in this study. The N-S asymmetry of the solar flare activities caused by the SARs in the northern and southern hemispheres of the sun will also be studied. The relationship between the number of SARs and the SC amplitude will be studied. The relationship between the SC amplitude and the largest flare index caused by a SAR will be studied. The rest part of the article is organized as follows. Section 2 is data analysis. Section 3 is a summary and discussion.

Solar Cycle Distribution of the SARs from 1976 to 2017
SMMSNs are usually used to describe the solar cycle. The period from the first month of a solar cycle to the month when the SMMSNs reach their maximum is defined as the ascending phase of the solar cycle (SC). The period from one month after the maximum of the SMMSNs to the last month of the SC is defined as the descending phase of the SC. The SARs 1 and SARs 2 were selected from the article by Le et al. [4]. According to the article by Le et al. [4], 51 SARs and the extreme space weather caused by the corresponding SARs 1 were compiled and listed in Table A1 of the appendix. According to Table A1 and the new series of SMMSNs launched on 1 July 2015, the SC distribution of the SARs 1 and SARs 2 from 1976 to 2017 is shown in Figure 1. The numbers of SARs 1 and SARs 2 during different periods of an SC, and the statistical results during SCs 21-24 were listed in Table 1. In Table 1, N a , N d and N 23 indicate the numbers of the SARs that occurred during the ascending phase, the descending phase, and the period from two years before to three years after the solar maximum for each SC, respectively. N t indicates the total number of SARs during an SC, i.e. N t = N a + N d . The largest SMMSNs in an SC were defined as the SC amplitude in this study. In Table 1, N sa , N sd , N s23 , and N st indicate the sum of N a , N d and N 23 and N t during SCs 21-24. The derived N sa /N st , N sd /N st and N s23 /N st for SARs 1 are 35.5%, 64.5% and 80.6%, respectively. The derived N sa /N st , N sd /N st and N s23 /N st for SARs 2 are 50%, 50%, and 100%, respectively. The results of the SC distribution showed that most of the SARs appeared around solar maximum.
The flare index (FI) caused by each SAR is directly copied from the article by Chen et al. [3] and the article by Chen and Wang [5]. The FI caused by SAR 12673 is calculated according to the calculation method recommended in the article by Chen et al. [3]. For the convenience of the description, we use SAR max to indicate the SAR that has the largest FI during an SC. As shown in Figure 1, the SAR max of each SC always occurred in the descending phase of the SC. The correlation coefficient (CC) between the total number of SARs within an SC and the SC amplitude is calculated, and the statistical significance (SS) of the CC is also estimated and shown in the right panel of Figure 2. Statistical significance means that it is unlikely to have occurred by chance, and the results are reliable when the percentage of statistical significance is above 95%. As shown in Figure 2, the CC between the total number of SARs within an SC and the SC amplitude is 0.996 and the SS is over 95%, indicating that the total number of SARs within an SC has a good correlation with the SC amplitude. The derived CC between the largest FI caused by a SAR during an SC and the SC amplitude is 0.50 (shown in the left panel of Figure 2). The SS for the derived CC is lower than 95% (shown in the left panel of Figure 2), indicating that the largest FI of a SAR max during an SC has a poor correlation with the SC amplitude.

N-S Asymmetry
To study the N-S asymmetry of SARs 1 and SARs 2 during SCs 21-24, the numbers of SARs 1 and SARs 2 in the two hemispheres of the sun during each SC are listed in Table 2.
In Table 2, we use N and S to indicate the number of SARs in the northern and southern hemispheres of each SC, respectively. We can see from Table 2 that the SARs 1 dominated in the southern hemisphere of the Sun during SCs 21-23, whereas N-S is equal to zero in SC 24. The SARs 1 in the northern and southern hemispheres of the sun were SAR 11429 and SAR 12673, respectively. The FI caused by SAR 12673 was 28.06, whereas the FI caused by SAR 11429 was 11.87. It is evident that the FI caused by AR 12673 was much larger than that caused by SAR 11429. As shown in the appendix, SAR 12673 produced an X9.2 and an X8.3 flare. In addition, SAR 12673 produced a GLE event. The flare stronger than X5 caused by SAR 11429 was an X5. 9. These indicate that the solar activities caused by SAR 12673 were stronger than that caused by SAR 11429. In this context, the SARs 1 mainly appeared in the southern hemisphere of the sun during SCs 21-24, i.e., the extreme space weather events were mainly produced by the SARs from the southern hemisphere of the sun during SCs 21-24. As shown in Table 2, the SARs 2 dominated in the northern hemisphere during SCs 21 and 23, whereas the SARs 2 dominated in the southern hemisphere during SCs 22 and 24.  Table 3. We can see from Table 3 that the sum of the flare indices caused by the SARs with source locations in the northern hemisphere was larger than that caused by the SARs with source locations in the southern hemisphere of the sun during the ascending phases for SCs 21, 23, and 24. The sum of the flare indices caused by the SARs with source locations in the southern hemisphere was larger than that caused by the SARs with source locations in the northern hemisphere of the sun during the ascending phases of SC22. As shown in Table 3, the activities of the solar flares caused by the SARs with source locations in the southern hemisphere were always stronger than those caused by the SARs with source locations in the northern hemisphere during the descending phase for SCs 21-24. We can also see from Table 3 that the total flare indices during a whole SC caused by the SARs with source locations in the southern hemisphere were slightly stronger than those in the northern hemisphere of the sun for SC21, whereas the total flare indices during a whole SC caused by the SARs with source locations in the southern hemisphere were always much stronger than those caused by the SARs with source locations in the northern hemisphere of the sun for SCs 22-24.  According to Table 2, the cumulative numbers of the SARs 1 and SARs 2 during different periods, which include a different number of SCs, are shown in Table 4. A Student's t-test is a statistical test for a noninteger and dimensional time series [17], which is used to test the statistical significance of the N-S asymmetries of the difference for both the number and the cumulative number of the SARs in the northern and southern hemispheres of the sun during the period from SC 21 to SC 24. The Student's t-test is also used to test the statistical significance of the N-S asymmetry of the flare indices caused by the SARs in the northern and southern hemispheres of the sun during the period from SC 21 to SC 24 shown in 3. The Student's t-test values are set at a 95% probability level. We found that the N-S asymmetries of both the number and the cumulative number of the SARs 1 during SCs 21-24 shown in Table 4 are significant, whereas the N-S asymmetry of the cumulative numbers of the SARs 2 during SCs 21-24 shown in Table 4 is not significant. The N-S asymmetry of the flare indices caused by the SARs from the southern and the northern hemispheres of the sun during SCs 21-24 shown in Table 3 is significant.

Summary and Discussion
The main results are summarized as follows: (i) There were 51 SARs during SCs 21-24. Of the 51 SARs, 31 SARs belong to SARs 1 and 20 SARs are SARs 2 . The statistical results show that N sa /N st , N sd /N st and N s23 /N st of SARs 1 are 35.5%, 64.5% and 77.4%, respectively, whereas N sa /N st , N sd /N st and N s23 /N st for SARs 2 are 50%, 50%, and 100%, respectively, indicating that most of the SARs appeared around the solar maximum, which is very similar to those of strong solar proton events [11], major geomagnetic storms [6] and GLEs [10]. It has been found that stronger storms have the tendency to occur around the solar maximum [9,33]. The SAR that produced the largest FI during each SC always occurred in the descending phase of the SC. (ii) The number of the SARs during an SC has a good correlation with the SC amplitude, implying that an SC with higher amplitude will have more SARs than that with lower amplitude. However, the largest FI of a SAR during an SC has a poor correlation with the SC amplitude, indicating that a weak SC will have a small number of SARs. However, a weak SC may have a SAR that can produce very strong solar flares. It has been predicted that SC 25 may be a weak SC [34][35][36], implying that the total number of SARs in SC 25 will be small. However, we cannot rule out the possibility that SC 25 may have a SAR that can produce a series of very strong solar activities, including flares and CMEs, and then cause GLEs and even extreme geomagnetic storms. (iii) N-S asymmetries of both the number and cumulative number of SARs 1 in the two different hemispheres of the sun during the period from SC 21 to SC 24 are significant, i.e., the SARs 1 dominated in the southern hemisphere of the sun during the period from SC 21 to SC 24. This indicated that the extreme solar activities and space weather events during the periods from SC 21 to SC 24 were mainly caused by the SARs 1 in the southern hemisphere of the sun. However, the N-S asymmetry of the SARs 2 during the period from SC 21 to SC 24 is not significant, i.e., the SAR 2 dominated in the different hemispheres by turns for different SCs. N-S asymmetry of the flare indices caused by the SARs from the two different hemispheres of the Sun during the period from SC 21 to SC 24 is inferred to exist. The solar flare activities caused by the SARs with source locations in the southern hemisphere of the sun were much stronger than those caused by the SARs with source locations in the northern hemisphere of the sun during SCs 21-24.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The total number of SARs during solar cycles 21-24 is 51, which are listed in Table A1. In the table, columns 1-9 are sequential number, the SC, the NOAA number of the SAR, ≥X5.0 flares caused by the SAR, latitude of the SAR, CL of the SAR, GLE No., SGS caused by the SAR, respectively. The shorter horizontal line in the table is the dividing line between the ascending and descending phases of the corresponding SC.