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A Statistical Study of the Relation between the Amplitude of Solar Cycle and the Area of Active Regions
CHINESE ASTRONOMY AND ASTROPHYSICS Chinese Astronomy and Astrophysics 38 (2014) 448–453
A Statistical Study of the Relation between the Amplitude of Solar Cycle and the Area of Active Regions† LI Peng1,2
LE Gui-ming2,3
CHEN Yu-lin1
LU Yang-ping1,2 1
CHEN Min-hao1,2
YIN Zhi-qiang3
College of Mathematics & Statistics, Nanjing University of Information Science& Technology, Nanjing 210044 2
National Center for Space Weather, China Meteorological Administration, Beijing 100081 3
National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012
Abstract Based on the observational data of sunspots, the relation between the amplitude of solar cycle and the total area of all active regions occurred in a solar cycle has been investigated. The result shows that the amplitude of solar cycle has a good correlation with the total area of all active regions occurred in the solar cycle. The relation between the amplitude of solar cycle and the area of the largest active region during a solar cycle has also been investigated. The result shows that the amplitude of solar cycle has a poor correlation with the area of the largest active region during a solar cycle, and there is no fixed relation between the peak time of a solar cycle and the time when the largest active region occurred in the solar cycle. Key words
sun: activity, sunspots, methods: statistics 1.
INTRODUCTION
It has been several centuries since the observation of sunspot numbers began. That there exists a period of about 11 yr in the solar activity may be apparently found out from the †
Supported by Project of National Major Scientific Research Plan (2012CB957801), National Natural
Science Foundation (41074132, 41274193), and Special Project for Public Welfare Profession of Quality Inspection (200710123) Received 2013–11–29; revised version 2013–12–27
A translation of Acta Astron. Sin. Vol. 55, No. 3, pp. 211–215, 2014 [email protected]; [email protected]
0275-1062/14/$-see front matter © 2014 B.V. AllScience rights reserved. c Elsevier 0275-1062/01/$-see front matter 2014 Elsevier B. V. All rights reserved. doi:10.1016/j.chinastron.2014.10.011 PII:
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
449
observational data. In general, the smoothed monthly mean values of sunspot numbers are adopted to describe the solar activity, and the interval between the two successive minimums of smoothed monthly mean values of sunspot numbers is defined as a solar activity cycle. The time when a minimum occurs is the end of the former solar cycle, and also the beginning of the next cycle. In this paper, the maximum of smoothed monthly mean values of sunspot numbers is known as the amplitude or intensity of the solar cycle. Some studies indicate that as the Schewabe period of solar activity is concerned, it is equivalent to adopt the sunspot number or the sunspot group number [1] . Besides the sunspot number or the sunspot group number, other parameters may be used to describe the solar activity, such as the solar radio flux at the wavelength of 10.7 cm [2] , and the area of active regions [3] , etc.. In a solar cycle a wealth of active regions may occur. What is the relation between the total area of all active regions in a solar cycle and the amplitude of the solar cycle? During each solar cycle, there exists an active region with the largest area. Is the area of the largest active region in an intense solar cycle bigger than that in a weak one? In other words, what correlation does exist between the amplitude of solar cycle and the area of the largest active region occurred in the solar cycle? This is the second subject of this paper. Besides, does there exist a fixed sequential relation between the time when the largest active region occurs in a solar cycle and the peak time of the cycle? This is the third subject to be studied in this paper. 2.
DATA ANALYSIS
From the website http://solarscience.msfc.nasa.gov/greenwch.shtml the data of total modified area of all active regions in each month for some solar cycles are downloaded. Thus, are obtained the total area of all active regions, the area of the largest active region in each solar cycle, and the time difference between the time when the largest active region occurred in a solar cycle and the peak time of the same solar cycle for the 12th ∼ 23rd solar cycles, which are listed in Table 1. In this table, the first column indicates the ordinal number of solar cycle, the second, the amplitude of solar cycle, the third, the total area of all active regions during the solar cycle, in units of one millionth of solar hemisphere (μh), the fourth, the area of the largest active region in the solar cycle, in units of μh, the fifth, the time difference between the time when the largest active region occurred and the peak time of the solar cycle, in units of month, with the sign − showing advance ahead and the sign +, lag behind. According to Table 1, is obtained a correlation between the total area of all active regions in a solar cycle and the solar cycle amplitude, which is shown in Figure 1. From Figure 1, it is evident that the correlation coefficient (CC) between the total area of all active regions in a solar cycle and the solar cycle amplitude is 0.966 with the confidence level higher than 99%. This demonstrates a very good correlation between them, namely, the more intense the solar cycle, the greater the total area of all active regions in the solar cycle. It may be concluded that an equivalence exists for describing the solar cycle amplitude
450
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
by either the maximum of smoothed monthly mean values of sunspot numbers or the total area of all active regions in the solar cycle.
Fig. 1
The relation between the amplitude of solar cycle and the total area of all active regions occurred in the solar cycle
Table 1
The sum of areas of all active regions, the area of the largest active region
in each solar cycle, and the time difference between the time when the largest active region occurred and the time when the solar cycle reached its maximum for the solar cycles from 12 to 23 Cycle No.
Cycle size
Stotal /μh
Smax /μh
ΔT /month
12
74.6
70155
2425
-13
13
87.9
86840
3038
-23
14
64.2
68422
3339
-12
15
105.4
79094
3590
-6
16
78.1
85607
3716
-27
17
119.2
119653
3627
+9
18
151.8
144546
5402
-1
19
201.3
179395
2805
+10
20
110.6
118463
3202
-9
21
164.5
152762
3100
+18
22
158.5
136188
3600
-4
23
120.8
119883
2610
+42
notes: Stotal indicates the total area of all active regions in a solar cycle, and Smax , the area of the largest active region in a solar cycle
According to Table 1, is obtained a relation between the area of the largest active region in a solar cycle and the amplitude of solar cycle, which is shown in Figure 2. From Figure
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
451
2, it is apparent that the correlation between the area of the largest active region in a solar cycle and the solar cycle amplitude is quite poor, namely, the larger active region may occur in a relatively weak solar cycle, rather than a relatively intense one. From Table 1, it is noted that the largest active region for some solar cycles occurred before the peak time of the cycle, while for other cycles, behind. So, it turns out that there is hardly a fixed sequential relation between the time when the active region with the largest area occurs and the peak time of a solar cycle.
Fig. 2
The relation between the amplitude of solar cycle and the area of largest active region occurred in a solar cycle
3.
CONCLUSIONS AND DISCUSSION
It is concluded from above analysis: (1) The correlation between the amplitude of a solar cycle and the total area of all active regions in this solar cycle is quite strong. (2) The correlation between the amplitude of a solar cycle and the area of the largest active region in this solar cycle is rather weak. (3) There is no fixed sequential relation between the time when the largest active region occurs in a solar cycle and the peak time of this solar cycle. A small difference exists between the smoothed monthly mean value of sunspot numbers and that of sunspot areas [4] , and a certain difference appears also between the daily sunspot number and the daily sunspot area [5] . However, the correlation between the maximum of smoothed monthly mean values in a solar cycle and the total area of all active regions in this cycle is quite good, which means that the smoothed monthly mean value of sunspot numbers is a very nice parameter to describe the periodicity characteristics of solar activity. Thus, the mid-and-long term forecast of solar activity is basically that of sunspot numbers.
452
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
The computational formula of sunspot number is k(10g + f ), in which k is a coefficient determined after the observer or observational apparatus, so as to make the sunspot numbers observed by different observatories homogeneous; g, number of active regions or that of sunspot groups; f , sunspot number observed on the solar disk. Thus, even if the area of one of sunspot groups is large enough, the sunspot number is the same on the basis of the calculation with k(10g + f ), it may, therefore, be one of the causes which result in the poor correlation between the maximum of smoothed monthly mean values of sunspot numbers and the largest area of active regions in a solar cycle. Moreover, the solar cycle amplitude is expressed by the smoothed monthly mean value, while the area of active region is the value observed at a moment. This is probably also one of the causes of the poor correlation between the solar cycle amplitude and the area of the largest active region in a solar cycle. According to the results of analysis on super-intense solar proton events given by CHENG Li-bin et al.[6] , all these events during the 21st ∼23rd cycles occurred at the descending phase of a solar cycle without exception, and the five among these nine superintense solar proton events were brought forth in the active regions with the largest area less than 1 000 μh. Nevertheless, a special attention must be paid as well to the largest active region of a solar cycle. For instance, in the 22nd cycle, on 10th March 1989 in the active region No.5395 of the largest area, an eruption gave rise to a very intense magnetic storm, of which the lowest value of Dst index is −589 nT, and it resulted in a collapse of the power transmission network of Quebec Province in Canada. ZHANG Gong-liang et al. investigated this magnetic storm event [7] . The active region No.5395, because of which the most intense magnetic storm ever since the Dst index began to be recorded happened, was a super-active one [8] . The features of this active region and a series of eruptive events were analyzed in detail [9−10] . YE Zong-hai et al. analyzed the Forbush decrease of cosmic rays caused by this magnetic storm event [11] , while HUANG Qing-ming analyzed the ionospheric storm that had followed this magnetic storm event [12] . In the 23rd cycle, on 28th October 2003, the active region with the largest area gave rise to very intense eruptive events, which brought about not only super-intense solar proton events, but also very violent magnetic storm events [6] . In this cycle the active region No.10486 is also a super-active one [8] . All this demonstrates that to active regions with very large areas a special attention must be paid. In February 2012 during the 24th cycle the peak value 66.9 of smoothed monthly mean sunspot numbers appeared, which means that maybe the 24th solar cycle is a very weak one. According to the distribution features of intense and super-intense magnetic storms in different solar cycles [13−14] , and the statistical analysis of the flares superior to X-class, and of the solar relativistic energetic particle events [15−18] , most violent space weather events occur on the descending phase of solar activity. On the basis of the analysis in this paper, perhaps the 24th cycle is a relatively weak one, at present it is, however, impossible at once to obviate the individual occurrence of very large active regions in this cycle, and to exclude the individual occurrence of active regions with their largest area less than 1 000 μh, which
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
453
would probably generate very intense eruptive events during this cycle. Therefore, even though most likely the peak value of sunspot numbers in the 24th cycle has occurred, it is at this moment impossible to exclude that extremely violent space weather events may individually occur. ACKNOWLEDGEMENTS Thanks to NASA (National Aeronautics and Space Administration) for providing the data of solar active regions. Thanks to the Solar Influences Data Analysis Center (http://sidc.oma.be/) for providing the smoothed monthly mean values of sunspot numbers. References 1
Le G. M., ChJAA, 2004, 4, 578
2
Zhang X. F., Le G. M., Zhang Y. X., ChSBu, 2012, 57, 2078
3
Li K. J., Li Q. S., Chen X. K., et al., Progress in Astronomy, 2000, 18, 312
4
Zhan L. S., Zhao H. J., Liang H. F., Journal of Yunnan Astronomical Observatory, 2003, 2, 43
5
Fligge M., Solanki S. K., SoPh, 1997, 173, 427
6
Cheng L. B., Le G. M., Lu Y. P., et al., Acta Astronomica Sinica, 2014, 55, 203
7
ZHANG G. L., GAO Y. F., NIE H. S., et al., Journal of Space Science, 1990, 10, 81
8
Chen A. Q., Wang J. X., Li J. W., et al., A&A, 2011, 534, 47
9 10
Joshi A., SoPh, 1993, 147, 269 Feynman J., Hundhausen A. J., JGR, 1994, 99, 8451
11
Ye Z. H., Xiao S. Y., Xue S. S., Journal of Space Science, 1990, 10, 280
12
Huang Q. M., Journal of Space Science, 1992, 12, 313
13
Le G. M., Cai Z., Wang H. N., et al., RAA, 2013, 13, 739
14
Le G. M., Yang X. X., Liu Y. H., et al., Ap&SS, 2014, 350, 443
15
Yang X. X., Le G. M., Zhang C. Y., et al., Acta Astronomica Sinica, 2013, 54, 327
16
Yang X. X., Le G. M., Zhang C. Y., et al., ChA&A, 2014, 38, 92
17
Le G. M., Li P., Yang H. G., et al., RAA, 2013, 13, 1219
18
Le G. M., Cai Z. Y., Wang H. N., et al., Ap&SS, 2012, 339, 151
A Statistical Study of the Relation between the Amplitude of Solar Cycle and the Area of Active Regions† LI Peng1,2
LE Gui-ming2,3
CHEN Yu-lin1
LU Yang-ping1,2 1
CHEN Min-hao1,2
YIN Zhi-qiang3
College of Mathematics & Statistics, Nanjing University of Information Science& Technology, Nanjing 210044 2
National Center for Space Weather, China Meteorological Administration, Beijing 100081 3
National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012
Abstract Based on the observational data of sunspots, the relation between the amplitude of solar cycle and the total area of all active regions occurred in a solar cycle has been investigated. The result shows that the amplitude of solar cycle has a good correlation with the total area of all active regions occurred in the solar cycle. The relation between the amplitude of solar cycle and the area of the largest active region during a solar cycle has also been investigated. The result shows that the amplitude of solar cycle has a poor correlation with the area of the largest active region during a solar cycle, and there is no fixed relation between the peak time of a solar cycle and the time when the largest active region occurred in the solar cycle. Key words
sun: activity, sunspots, methods: statistics 1.
INTRODUCTION
It has been several centuries since the observation of sunspot numbers began. That there exists a period of about 11 yr in the solar activity may be apparently found out from the †
Supported by Project of National Major Scientific Research Plan (2012CB957801), National Natural
Science Foundation (41074132, 41274193), and Special Project for Public Welfare Profession of Quality Inspection (200710123) Received 2013–11–29; revised version 2013–12–27
A translation of Acta Astron. Sin. Vol. 55, No. 3, pp. 211–215, 2014 [email protected]; [email protected]
0275-1062/14/$-see front matter © 2014 B.V. AllScience rights reserved. c Elsevier 0275-1062/01/$-see front matter 2014 Elsevier B. V. All rights reserved. doi:10.1016/j.chinastron.2014.10.011 PII:
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
449
observational data. In general, the smoothed monthly mean values of sunspot numbers are adopted to describe the solar activity, and the interval between the two successive minimums of smoothed monthly mean values of sunspot numbers is defined as a solar activity cycle. The time when a minimum occurs is the end of the former solar cycle, and also the beginning of the next cycle. In this paper, the maximum of smoothed monthly mean values of sunspot numbers is known as the amplitude or intensity of the solar cycle. Some studies indicate that as the Schewabe period of solar activity is concerned, it is equivalent to adopt the sunspot number or the sunspot group number [1] . Besides the sunspot number or the sunspot group number, other parameters may be used to describe the solar activity, such as the solar radio flux at the wavelength of 10.7 cm [2] , and the area of active regions [3] , etc.. In a solar cycle a wealth of active regions may occur. What is the relation between the total area of all active regions in a solar cycle and the amplitude of the solar cycle? During each solar cycle, there exists an active region with the largest area. Is the area of the largest active region in an intense solar cycle bigger than that in a weak one? In other words, what correlation does exist between the amplitude of solar cycle and the area of the largest active region occurred in the solar cycle? This is the second subject of this paper. Besides, does there exist a fixed sequential relation between the time when the largest active region occurs in a solar cycle and the peak time of the cycle? This is the third subject to be studied in this paper. 2.
DATA ANALYSIS
From the website http://solarscience.msfc.nasa.gov/greenwch.shtml the data of total modified area of all active regions in each month for some solar cycles are downloaded. Thus, are obtained the total area of all active regions, the area of the largest active region in each solar cycle, and the time difference between the time when the largest active region occurred in a solar cycle and the peak time of the same solar cycle for the 12th ∼ 23rd solar cycles, which are listed in Table 1. In this table, the first column indicates the ordinal number of solar cycle, the second, the amplitude of solar cycle, the third, the total area of all active regions during the solar cycle, in units of one millionth of solar hemisphere (μh), the fourth, the area of the largest active region in the solar cycle, in units of μh, the fifth, the time difference between the time when the largest active region occurred and the peak time of the solar cycle, in units of month, with the sign − showing advance ahead and the sign +, lag behind. According to Table 1, is obtained a correlation between the total area of all active regions in a solar cycle and the solar cycle amplitude, which is shown in Figure 1. From Figure 1, it is evident that the correlation coefficient (CC) between the total area of all active regions in a solar cycle and the solar cycle amplitude is 0.966 with the confidence level higher than 99%. This demonstrates a very good correlation between them, namely, the more intense the solar cycle, the greater the total area of all active regions in the solar cycle. It may be concluded that an equivalence exists for describing the solar cycle amplitude
450
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
by either the maximum of smoothed monthly mean values of sunspot numbers or the total area of all active regions in the solar cycle.
Fig. 1
The relation between the amplitude of solar cycle and the total area of all active regions occurred in the solar cycle
Table 1
The sum of areas of all active regions, the area of the largest active region
in each solar cycle, and the time difference between the time when the largest active region occurred and the time when the solar cycle reached its maximum for the solar cycles from 12 to 23 Cycle No.
Cycle size
Stotal /μh
Smax /μh
ΔT /month
12
74.6
70155
2425
-13
13
87.9
86840
3038
-23
14
64.2
68422
3339
-12
15
105.4
79094
3590
-6
16
78.1
85607
3716
-27
17
119.2
119653
3627
+9
18
151.8
144546
5402
-1
19
201.3
179395
2805
+10
20
110.6
118463
3202
-9
21
164.5
152762
3100
+18
22
158.5
136188
3600
-4
23
120.8
119883
2610
+42
notes: Stotal indicates the total area of all active regions in a solar cycle, and Smax , the area of the largest active region in a solar cycle
According to Table 1, is obtained a relation between the area of the largest active region in a solar cycle and the amplitude of solar cycle, which is shown in Figure 2. From Figure
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
451
2, it is apparent that the correlation between the area of the largest active region in a solar cycle and the solar cycle amplitude is quite poor, namely, the larger active region may occur in a relatively weak solar cycle, rather than a relatively intense one. From Table 1, it is noted that the largest active region for some solar cycles occurred before the peak time of the cycle, while for other cycles, behind. So, it turns out that there is hardly a fixed sequential relation between the time when the active region with the largest area occurs and the peak time of a solar cycle.
Fig. 2
The relation between the amplitude of solar cycle and the area of largest active region occurred in a solar cycle
3.
CONCLUSIONS AND DISCUSSION
It is concluded from above analysis: (1) The correlation between the amplitude of a solar cycle and the total area of all active regions in this solar cycle is quite strong. (2) The correlation between the amplitude of a solar cycle and the area of the largest active region in this solar cycle is rather weak. (3) There is no fixed sequential relation between the time when the largest active region occurs in a solar cycle and the peak time of this solar cycle. A small difference exists between the smoothed monthly mean value of sunspot numbers and that of sunspot areas [4] , and a certain difference appears also between the daily sunspot number and the daily sunspot area [5] . However, the correlation between the maximum of smoothed monthly mean values in a solar cycle and the total area of all active regions in this cycle is quite good, which means that the smoothed monthly mean value of sunspot numbers is a very nice parameter to describe the periodicity characteristics of solar activity. Thus, the mid-and-long term forecast of solar activity is basically that of sunspot numbers.
452
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
The computational formula of sunspot number is k(10g + f ), in which k is a coefficient determined after the observer or observational apparatus, so as to make the sunspot numbers observed by different observatories homogeneous; g, number of active regions or that of sunspot groups; f , sunspot number observed on the solar disk. Thus, even if the area of one of sunspot groups is large enough, the sunspot number is the same on the basis of the calculation with k(10g + f ), it may, therefore, be one of the causes which result in the poor correlation between the maximum of smoothed monthly mean values of sunspot numbers and the largest area of active regions in a solar cycle. Moreover, the solar cycle amplitude is expressed by the smoothed monthly mean value, while the area of active region is the value observed at a moment. This is probably also one of the causes of the poor correlation between the solar cycle amplitude and the area of the largest active region in a solar cycle. According to the results of analysis on super-intense solar proton events given by CHENG Li-bin et al.[6] , all these events during the 21st ∼23rd cycles occurred at the descending phase of a solar cycle without exception, and the five among these nine superintense solar proton events were brought forth in the active regions with the largest area less than 1 000 μh. Nevertheless, a special attention must be paid as well to the largest active region of a solar cycle. For instance, in the 22nd cycle, on 10th March 1989 in the active region No.5395 of the largest area, an eruption gave rise to a very intense magnetic storm, of which the lowest value of Dst index is −589 nT, and it resulted in a collapse of the power transmission network of Quebec Province in Canada. ZHANG Gong-liang et al. investigated this magnetic storm event [7] . The active region No.5395, because of which the most intense magnetic storm ever since the Dst index began to be recorded happened, was a super-active one [8] . The features of this active region and a series of eruptive events were analyzed in detail [9−10] . YE Zong-hai et al. analyzed the Forbush decrease of cosmic rays caused by this magnetic storm event [11] , while HUANG Qing-ming analyzed the ionospheric storm that had followed this magnetic storm event [12] . In the 23rd cycle, on 28th October 2003, the active region with the largest area gave rise to very intense eruptive events, which brought about not only super-intense solar proton events, but also very violent magnetic storm events [6] . In this cycle the active region No.10486 is also a super-active one [8] . All this demonstrates that to active regions with very large areas a special attention must be paid. In February 2012 during the 24th cycle the peak value 66.9 of smoothed monthly mean sunspot numbers appeared, which means that maybe the 24th solar cycle is a very weak one. According to the distribution features of intense and super-intense magnetic storms in different solar cycles [13−14] , and the statistical analysis of the flares superior to X-class, and of the solar relativistic energetic particle events [15−18] , most violent space weather events occur on the descending phase of solar activity. On the basis of the analysis in this paper, perhaps the 24th cycle is a relatively weak one, at present it is, however, impossible at once to obviate the individual occurrence of very large active regions in this cycle, and to exclude the individual occurrence of active regions with their largest area less than 1 000 μh, which
LI Peng et al. / Chinese Astronomy and Astrophysics 38 (2014) 448–453
453
would probably generate very intense eruptive events during this cycle. Therefore, even though most likely the peak value of sunspot numbers in the 24th cycle has occurred, it is at this moment impossible to exclude that extremely violent space weather events may individually occur. ACKNOWLEDGEMENTS Thanks to NASA (National Aeronautics and Space Administration) for providing the data of solar active regions. Thanks to the Solar Influences Data Analysis Center (http://sidc.oma.be/) for providing the smoothed monthly mean values of sunspot numbers. References 1
Le G. M., ChJAA, 2004, 4, 578
2
Zhang X. F., Le G. M., Zhang Y. X., ChSBu, 2012, 57, 2078
3
Li K. J., Li Q. S., Chen X. K., et al., Progress in Astronomy, 2000, 18, 312
4
Zhan L. S., Zhao H. J., Liang H. F., Journal of Yunnan Astronomical Observatory, 2003, 2, 43
5
Fligge M., Solanki S. K., SoPh, 1997, 173, 427
6
Cheng L. B., Le G. M., Lu Y. P., et al., Acta Astronomica Sinica, 2014, 55, 203
7
ZHANG G. L., GAO Y. F., NIE H. S., et al., Journal of Space Science, 1990, 10, 81
8
Chen A. Q., Wang J. X., Li J. W., et al., A&A, 2011, 534, 47
9 10
Joshi A., SoPh, 1993, 147, 269 Feynman J., Hundhausen A. J., JGR, 1994, 99, 8451
11
Ye Z. H., Xiao S. Y., Xue S. S., Journal of Space Science, 1990, 10, 280
12
Huang Q. M., Journal of Space Science, 1992, 12, 313
13
Le G. M., Cai Z., Wang H. N., et al., RAA, 2013, 13, 739
14
Le G. M., Yang X. X., Liu Y. H., et al., Ap&SS, 2014, 350, 443
15
Yang X. X., Le G. M., Zhang C. Y., et al., Acta Astronomica Sinica, 2013, 54, 327
16
Yang X. X., Le G. M., Zhang C. Y., et al., ChA&A, 2014, 38, 92
17
Le G. M., Li P., Yang H. G., et al., RAA, 2013, 13, 1219
18
Le G. M., Cai Z. Y., Wang H. N., et al., Ap&SS, 2012, 339, 151