A QUANTITATIVE STUDY ON MAGNETIC CONFIGURATION FOR ACTIVE REGIONS. and

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1 Solar Physics (2006) 237: DOI: /s C Springer 2006 A QUANTITATIVE STUDY ON MAGNETIC CONFIGURATION FOR ACTIVE REGIONS JUAN GUO and HONGQI ZHANG National Astronomical Observatories, Chinese Academy of Science, Beijing , China ( guojuan@bao.ac.cn) OLEG V. CHUMAK Sternberg Astronomical Institute (SAI), Moscow State University, Moscow , Russia and YU LIU Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA (Received 13 May 2005; accepted 30 January 2006; Published online 28 July 2006) Abstract. As compared with the Mount Wilson Magnetic Classification (MWMC), effective distance (d E ) is a useful parameter because it gives a quantitative measure of magnetic configuration in active regions. We have analyzed magnetograms of 24 active regions of different types with MWMC. We have studied the evolution of magnetic fields of five active regions using d E, total flux (F t ) and tilt angle (Tilt) quantitatively. Furthermore, 43 flare-associated and 25 CME-associated active regions have been studied to investigate and quantify the statistical correlation between flares/cmes and the three parameters. The main results are as follows: (1) There is a basic agreement between d E and MWMC. (2) The evolution of magnetic fields can be described in three aspects quantitatively and accurately by the three parameters, in particular by d E on the analysis of δ-type active regions. (3) The high correlation between d E and flares/cmes means that d E could be a promising measure to predict the flare-cme activity of active regions. 1. Introduction The Mount Wilson Magnetic Classification (MWMC) is one of the well-known qualitative schemes for sunspot classification, which was developed according to the magnetic structure of sunspots. Many results have been acquired in the study of solar activities using MWMC. Künzel (1960) pointed out the first clear connection between flare productivity and magnetic structure, and introduced a new magnetic classification, δ, to supplement Hale s α, β and γ classes. Warwick (1966) confirmed that a large proportion of all major flare events started with the δ configuration. The characteristics of flare-productive sunspot groups have been studied widely since then (Zirin and Tanaka, 1973; Tanaka, 1991; Shi and Wang, 1993; Sammis et al., 2000; Liu and Zhang, 2001). On the other hand, the formation and disintegration of δ-configurations is another important issue (Tang, 1983; Zirin and Liggett, 1987; Liu and Zhang, 2002). However, there are still some problems to

2 26 JUAN GUO ET AL. be solved. For example, how to describe the difference between two active regions which are of identical type with the MWMC (e.g. δ type)? How to describe the evolution when an active region passes though solar disk with slightly changing magnetic field? Obviously, qualitative analysis is incomplete in answering such questions. Some quantitative analysis should be put forward to augment the existing magnetic classifications. To satisfy this requirement, we will introduce a structural parameter (Chumak and Chumak, 1987) named effective distance (d E ) in the present paper. d E describes the degree of the isolation or mutual penetration of the two polarities of an active region quantitatively. It will shed light on quantitative study on magnetic configuration of active regions and on correlations between magnetic structure and other solar indices (e.g. flares and CMEs). Unfortunately, little work has been done with this parameter. Kononovich, Krasotkin, and Chumak (1999) introduced the correspondence d E to magnetic configuration of active regions, but the applications of d E to magnetograms active regions were omitted. Chumak and Zhang (2003), Chumak, Zhang, and Guo (2004) applied the concept of d E to magnetograms of active regions, but they calculated d E separately for bins of longitudinal field strengths in steps of 50 Gauss. They then studied the distribution of d E as a function of field strength, using the first four moments of the distribution. In the present paper, we calculate d E over all data points whose magnetic flux density is above a threshold defined by the noise level. We will analyze the evolution of magnetic field in different active regions in terms of d E, total flux (F t ) and tilt angle (Tilt) synthetically. Furthermore, we will carry out statistical analyses of flare-associated and CME-associated active regions with the three parameters. We will arrange the paper as follows. In Section 2 we introduce the data used in the present paper. In Section 3 we recommend the three parameters F t, Tilt and d E. In Section 4 we demonstrate the evolution of magnetic fields in five active regions using these parameters. In Section 5 we present a statistical study on flare-associated active regions. In Section 6 we present a statistical study on CME-associated active regions. The discussion and summary are given in Sections 7 and 8 respectively. 2. Data Full disk magnetograms with 96-minute cadence taken by SOHO/MDI are used. All full-disk data taken at different times are aligned based on the nonlinear mapping, which takes into account solar differential rotation (Chae et al., 2001). For each active region, we calculate parameters over an area that is sufficiently large to cover the whole region. We only take the magnetograms in which active regions under investigation were near the central meridian ( 45 < l < +45 ). In order to exclude the effect of noise and to keep important weak fields (e.g. newly emerging or decaying regions), 100 Gauss is chosen as the threshold for MDI full disk magnetograms in our measurement of the following parameters.

3 QUANTITATIVE STUDY FOR ACTIVE REGIONS 27 Information on solar events is taken from various sources, including the SEC Solar Event weekly Report at weekly/index.html and the SOHO/LASCO CME catalogs at list/index.html. We also make reference to some work (Tian, Liu, and Wang, 2003; Zhou, Wang, and Cao, 2003) to identify the association between active regions and CMEs. 3. Parameters In this section, we introduce three measurable parameters. All of them can be measured from line-of-sight magnetograms TOTAL FLUX Total flux (F t ) is a quantitative measure of the effective size of active regions (Giovanelli, 1939; McIntosh, 1990; Canfield, Hudson, and McKenzie, 1999; Tian, Liu, and Wang, 2002), which provides us a physical clue as to the energy available for solar major events. F t of an active reign is calculated with the following equation: F t = Fs + Fn, (1) where Fs(Fn) is the flux of the negative (positive) polarity TILT ANGLE Tilt angle (Tilt) is one of the measurable parameters of solar active regions that give us information about subsurface physical processes associated with the creation and subsequent evolution of magnetic flux tubes inside the Sun (Holder et al., 2004). The strong toroidal fields that ultimately form active regions are believed to be created in a strong shear-flow layer beneath the base of the convection zone. These toroidal fields are subject to buoyancy instability once they are brought out into the base of the convection zone, collapsing to form flux tubes and subsequently rising as -shaped loops to the surface (Parker, 1955), forming sunspots or active regions. During their buoyant rise to the surface the toroidal flux tubes are acted upon by various forces, notably the Coriolis force and turbulent convective buffeting. Both of the physical processes imprint their signatures, in the form of twist and tilt, on the rising magnetic flux tubes. Many observational and theoretical results on these signatures have been acquired so far (Hale et al., 1919; D Silva and Choudhuri, 1993; Fan, Fisher, and McClymont, 1994; Fisher, Fan, and Howard, 1995; Longcope and Fisher, 1996; Nandy and Choudhuri, 2001; Wang and Sheeley, 2003). Tilt is defined as the angle between the direction of the polarity axis of an active region and the local latitude (Tian, Liu, and Wang, 1999). The position of each

4 28 JUAN GUO ET AL. Figure 1. A sketch showing the coordinate system used for the determination of tilt angles in the 23rd solar cycle. N and S correspond to the positive and negative polarities, respectively. magnetic polarity could be approximately determined by the flux-weighted center of each polarity in longitudinal magnetic fields. Tilt is calculated with the following equation: tan(tilt) = δy/δx, (2) where δx and δy are Cartesian coordinate differences between the leading and following polarities of an active region in the heliographic plane. Figure 1 is a sketch showing the coordinate system used for determination of Tilt in the 23rd solar cycle EFFECTIVE DISTANCE Effective distance (d E ) was proposed by Chumak and Chumak (1987) as a structural parameter. Chumak and Zhang (2003) found that d E could differ heavily for various threshold levels in the magnetic field strengths. Chumak, Zhang, and Guo (2004) found that the field-strength distribution of d E showed a clear distinction between quiet and flare productive active regions. d E is calculated with the following equation: where d E = (R n + R s )/R sn, (3) R s = (N s /π) 1/2, (4) R n = (N n /π) 1/2, (5) where N s (N n ) is total area of the negative (positive) polarity. R s (R n ) is the equivalent radius of negative (positive) polarity. R sn is the distance between the flux-weighted centers of the two polarities. Figure 2 is a sketch explaining the definition of d E. In geometrical meaning, this parameter describes the degree of isolation or mutual penetration of the two

5 QUANTITATIVE STUDY FOR ACTIVE REGIONS 29 TABLE I Correlation between magnetic class and d E of 24 active regions. Mag. NOAA Date Location class d E Oct 1997 N16W14 β Feb 2000 S29W11 β Dec 2000 N14W06 β Mar 2001 N08W07 β Apr 2001 S06W04 β Apr 2001 N08W06 β Jul 2002 N12W13 β Jul 2002 S07W06 β Feb 2004 N14W09 β Nov 1997 S19W12 βγ May 1998 S17W22 βγ Nov 1999 N10W07 βγ Mar 2003 S13W14 βγ Sep 2000 N14E01 βδ Jan 2005 N13W03 βδ Jun 2000 N20E03 βγδ Jul 2000 N18W09 βγδ Mar 2001 N17W18 βγδ Apr 2001 S21E05 βγδ Sep 2001 S19W08 βγδ Jul 2002 N18W00 βγδ Oct 2003 N04W00 βγδ Oct 2003 S17E04 βγδ Oct 2003 N08W04 βγδ Figure 2. A sketch showing the meaning of the effective distance (d E ). White and black patches indicate positive and negative magnetic fields, respectively. (a) A well-separated bipolar active region with d E less than unity. (b) A highly packed bipolar active region with d E more than unity.

6 30 JUAN GUO ET AL. polarities quantitatively. A well separated bipolar active region usually shows d E less than unit (Figure 2a), e.g. β regions. A highly packed bipolar active region usually shows d E more than unit (Figure 2b), e.g. δ regions. These suggest that the relative distribution of the two polarities in an active region can be roughly described by d E. We have analyzed magnetograms of 24 active regions of different types with MWMC and the results are shown in Table 1. We find that all nine β regions show d E less than unit. Both of the two βδ regions show d E more than unit. Eight out of nine βγδ regions show d E more than unit. For the four βγ regions, there are some discrepancies: one region shows d E more than unit, while three regions show d E less than unit. From the above examples, it is confirmed that there is a basic agreement between d E and MWMC. Moreover, the magnetic classification can be quantified with d E. These suggest that the magnetic evolution of active regions and the relationships between magnetic structure and other solar indices (e.g. flares and CMEs) can be investigated quantitatively with d E. 4. Quantitative Analysis on Magnetic Evolution of Active Regions In this section, we present a quantitative analysis on the evolution of magnetic fields of five active regions: a normal β region, a developing βδ region, a newly-emerging βγδ region, a well-developed βγδ region and a decaying βγδ region. Figures 3 7 show the evolution of magnetic fields of five active regions respectively. Figure 8 shows d E F t Tilt tracks corresponding to the evolution of the five regions respectively. Then comparing the track of an active region with its corresponding evolution in the magnetic field, we can study the evolution of magnetic field in this active region quantitatively and qualitatively A NORMAL β REGION: NOAA10549 NOAA was a normal β region and the magnetic field of this region showed insignificant changes in Figure 3. Figure 8 shows that d E of this region was about 0.6. Tilt of this region only changed a few degrees. F t (indicated by the size of the bubbles) showed insignificant changes A DEVELOPING βδ REGION: NOAA10720 NOAA was a developing βδ region. It appeared on the disk as a normal β region. The positive polarity was located at the south-west side of the negative polarity at the beginning. As the emergence of the magnetic flux, the two polarities grew rapidly, approached and compressed each other during the later days. The

7 QUANTITATIVE STUDY FOR ACTIVE REGIONS 31 Figure 3. A time sequence of the longitudinal magnetic field of a normal β region NOAA in Feb 3 8, White (black) patches are positive (negative) longitudinal magnetic fields. The area of the active region is North is at the top and west is to the right. N and S mark the positions of the weighted centers of positive and negative polarities, respectively. polarity axis rotated clockwise. The region developed into a strong βδ region at the end in Figure 4. Figure 8 shows that d E of this region increased abruptly from about 1.1 to 4.0. Tilt increased from 19 to 67. F t (indicated by the size of the bubbles) increased gradually. The region produced three X-class flares: an X1.2 at 00:00 UT, Jan 15, an X2.6 at 22:25 UT, Jan 15 and an X3.8 at 06:59, Jan 16. The magnitude of the flares increased as the increase of d E, F t and Tilt A NEWLY-EMERGING βγδ REGION: NOAA10488 NOAA was a notable newly-emerging βγδregion in the northern hemisphere in the 23rd solar cycle, which appeared and developed very quickly near the disk center on Oct 27 and exhibited rapid growth over the next three days (Zhang et al., 2003). Figure 5 shows that the region was a typical β region and the negative polarity

8 32 JUAN GUO ET AL. Figure 4. A time sequence of the longitudinal magnetic field of a developing βδ region NOAA in Jan 12 17, White (black) patches are positive (negative) longitudinal magnetic fields. The area of the active region is North is at the top and west is to the right. N and S mark the positions of the weighted centers of positive and negative polarities, respectively. was almost at the south of the positive polarity at the beginning. After another pair of bipolar sunspots P2 and F2 emerged at the east side of P1 and F1 on Oct 28, the region was composed of two pairs of bipolar sunspots. As the development of the active region, the main δ structure formed with the collision of the two distant bipolar groups (Zirin and Liggett, 1987). The region developed to a βγδ region at the end. During the six days of evolution, the polarity axis rotated clockwise then anticlockwise slightly. Figure 8 shows that the evolution of d E of this region was composed of two parts. At the earlier half of the evolution d E was nearly stable at the value around

9 QUANTITATIVE STUDY FOR ACTIVE REGIONS 33 Figure 5. A time sequence of the longitudinal magnetic field of a newly-emerging βγδ region NOAA in Oct 26 31, White (black) patches are positive (negative) longitudinal magnetic fields. The area of the active region is North is at the top and west is to the right. P1 and P2 denote the main parts of the preceeding magnetic polarity. F1 and F2 denote the main parts of the following magnetic polarity. N and S mark the positions of the weighted centers of positive and negative polarities, respectively. 0.9 and at the latter part of the evolution d E increased to Tilt of this region changed from 51 to 2 and then turned to 5. F t (as shown by the size of the bubbles) was small initially and increased rapidly later A WELL-DEVELOPED βγδ REGION NOAA NOAA was a well-developed βγδ region when it appeared on the solar disk. Figure 6 shows that the positive polarity was composed of P1 and P2 at the beginning. P1 was to the west and P2 was to the south of the negative polarity. After P3 emerged at the north-east side of the negative polarity, the positive polarity was composed of P1, P2 and P3. At that time, P1, P2 and P3 took the position around the negative polarity, which resulted in the increase of the degree of mutual

10 34 JUAN GUO ET AL. Figure 6. A time sequence of the longitudinal magnetic field of a well-developed βγδ region NOAA in Oct 20 26, White (black) patches are positive (negative) longitudinal magnetic fields. The field of view is North is at the top and west is to the right. P1, P2 and P3 denote the main parts of the preceeding magnetic polarity. N and S mark the positions of the weighted centers of positive and negative polarities, respectively.

11 QUANTITATIVE STUDY FOR ACTIVE REGIONS 35 Figure 7. A time sequence of the longitudinal magnetic field of a decaying βγδ region NOAA 9026 in Jun 4 10, White (black) patches are positive (negative) longitudinal magnetic fields. The field of view is North is at the top and west is to the right. N and S mark the positions of the weighted centers of positive and negative polarities, respectively. The white box shown At 01:36:30 UT, June 6, indicates the main δ structure and P marks an almost stable sunspot. penetration between the two polarities. Another obvious character of this region was the counter-clockwise rotation of the polarity axis: the north-eastern part of the negative polarity was situated at the north-east of the whole active region at the beginning. Then it continued pushing its way in counter-clockwise sense and was situated at the south-east of the whole active region at the end. In addition, the negative polarity grew and the positive polarity decayed by almost equal quantity, while the change of F t is insignificant during 7 days.

12 36 JUAN GUO ET AL. Figure 8. Five active regions in the (d E F t Tilt) bubble diagram. The abscissa shows Tilt and the ordinate shows d E. The size of the bubble is proportional to the total flux F t. The thick black line with an arrow inside the bubbles denotes the time evolution. The thin arrows point out the occurrences of major flares. Figure 8 shows that d E of this region increased from 2 to 2.7. Tilt of this region decreased from 42 to 13. F t increased gradually then decreased a little. An X1.2 flare occurred in this region at 17:21 UT, Oct 26. At that time, the region showed strong magnetic fields, an abnormal Tilt and a maximum d E in the evolution of 7 days A DECAYING βγδ REGION NOAA 9026 NOAA 9026 was a famous βγδ region, which produced a series of powerful flares and corresponding geomagnetic effects (Kurokawa, Wang, and Ishii, 2002; Zhang, 2004; Wang et al., 2004). In Figure 7, the main delta structure changed obviously from the maximum development to the decay, and disappeared at the end. The region decayed from a βγδ region to a β region. As the evolution of the main delta structure, the flux-weighted center of the negative polarity moved eastwards, while that of the positive polarity moved southwards in Figure 7. As a result, the polarity axis of the region rotated clockwise gradually. Figure 8 shows that d E of this region decreased gradually from 1.9 to 1.1. Tilt of this region changed from 5 to +7. F t increased a little then turned to decrease. The region produced three X-class flares: an X1.1 at 13:30 UT, Jun 6, an X2.3 at 14:58 UT, Jun 6 and an X1.2 at 15:34 UT, Jun 7. At those times, the region showed relatively strong magnetic fields, a normal Tilt and d E more than unit.

13 QUANTITATIVE STUDY FOR ACTIVE REGIONS Statistical Study on Flare-Productive Active Regions Sammis et al. (2000) found that almost all substantial flares occur in βγδregions and there is a general trend for large regions to produce large flares, but the latter trend is less significant than the dependence on the magnetic classes. d E is a quantitative measure of the magnetic classes, which makes it convenient to quantify and examine the correlation between flares and magnetic classes. We study 43 flare-associated active regions. The averages of d E, F t and Tilt are calculated in their duration of five days near their central meridian passage. We also calculated the flare-index of each active region, which is the sum of the numerical multipliers of the X-ray flare classes C, M and X over the duration of five days. For example, a C1 flare is counted as 0.01, an M2 flare is counted as 0.2, an X1 flare is counted as 1, and so on. Figure 9 shows the correlations between the flare-index and the three parameters. For each panel in Figure 9, we divide the data points into bins according to the flare-index, with a bin size of 3. We then calculate the mean value of the parameter for all the data points in every bin. The mean value of the parameter is plotted against the central value of the flare-index in the bin as a diamond. The vertical bar indicates the standard deviation of the parameter in the bin. A least-square linear fit is presented by the solid line in each panel. It is found that there is quite a good correlation between mean d E and the flare index: active regions with high d E tend to produce intense flares and vice versa. There is a relatively good correlation between mean F t and the flare index. There is a poor correlation between mean Tilt and the flare index. The estimated correlation coefficients are as follows: Cd E = 0.81, C Ft = 0.50, C Tilt = Statistical Study on CME-Associated Active Regions Solar coronal mass ejections (CMEs) are the most spectacular form of activities on the Sun. It has been found that CMEs have a strong association with solar flares and erupting prominences (Munro et al., 1979; Webb and Hundhausen, 1987; Gilbert et al., 2000). There is a statistical correlation between CMEs and active regions (Zhou, Wang, and Cao, 2003). To examine a quantitative correlation between CMEs and the CME-associated active regions, we studied 49 CMEs which were originated from 25 active regions. The parameters d E, F t and Tilt are measured about 1 hour prior to the flare start time (as defined in GOES catalogs). Figure 10 shows the correlations between CMEs and the three parameters. For each panel in Figure 10, we divide the data points into bins according to the CME speed, with a bin size of 300 km s 1. We then calculate the mean value of the parameter for all the data points in every bin. The mean value of the parameter is plotted against the central value of the CME speed in the bin as a diamond. The

14 38 JUAN GUO ET AL. Figure 9. Flare index vs. mean d E (top panel), flare index vs. mean F t (middle panel) and flare index vs. mean Tilt (bottom panel) for 43 flare-associated active regions. In each panel, the asterisks denote data points and the solid line denotes a least-square linear fit to the data points. Linear C. C. denotes the correlation coefficient. Each diamond denotes the averaged value of a parameter in each bin of the flare-index, with a bin size of 3. The error bars correspond to 1σ.

15 QUANTITATIVE STUDY FOR ACTIVE REGIONS 39 Figure 10. CME speed vs. d E (top panel), CME speed vs. F t (middle panel) and CME speed vs. Tilt (bottom panel) for 49 CMEs. In each panel, the asterisks denote data points and the solid line denotes a least-square quadratic polynomial fit to the data points. Linear C. C. denotes the correlation coefficient. Each diamond denotes the averaged value of a parameter in each bin of the CME speed, with a bin size of 300 km s 1. The error bars correspond to 1σ.

16 40 JUAN GUO ET AL. vertical bar indicates the standard deviation of the parameter in the bin. A leastsquare quadratic polynomial fit is presented by the solid curve in each panel. It is found that there is a good correlation between d E and the CME speed: active regions with high d E tend to produce fast CMEs and vice versa. The correlation between F t and the CME speed is not so good. There is a poor correlation between Tilt and the CME speed. The estimated correlation coefficients are as follows: Cd E = 0.64, C Ft = 0.39, C Tilt = Discussions The choice of the field of view (FOV) for an active region normally affects the determination of d E, especially for complex active regions, such as NOAA By choosing a small FOV, only including the area of the white box on Jun 6 in Figure 7, Falconer, Moore, and Gary (2002, 2003) presented the correlation between the CME productivity and their measure of global nonpotentiality derived from vector and line-of-sight magnetograms. Tian and Liu (2003) analyzed the relationship between the decrease in net magnetic flux and solar major events in the FOV of Figure 7. Zhang (2004) found that the tilt angle of this region is the same as the normal regions in the northern hemisphere and pointed out that the enhanced networks decayed from the active region also need to be included. This means that the region NOAA 9026 was probably composed of two parts: an old stable part and a quickly developing one. The old one should include not only the stable sunspot P, but also the following enhanced network with opposite polarity. The quickly developing part was the delta structure that developed and decayed quickly nearby the old magnetic configuration (Kurokawa, Wang, and Ishii, 2002). The two parts were mixed together due to complicated process in the solar interior, which might be related to the dynamo mechanism. Selection of samples probably brings some different results between different statistical studies. Shi and Wang (1993) found that more than 95% of X-class flares took place in active regions of δ sunspots, while 23% of 282 δ sunspots produced X-class flares. In our 43 samples, there were 27 δ type regions and 19 of them produced X-class flares. Whether an X-class flare occurs preferentially in a δ region was considered by Shi and Wang (1993), while we focus on the flare index and the corresponding magnetic configurational complexity. For example, consider two δ regions, one producing one X-class flare and another region producing more than one X-class flares. The two regions are treated as the same in the study of Shi and Wang (1993), while they are different in the present work. The latter region may usually show a greater flare index and a more complex magnetic configuration than the former one. Our results are consistent with the general tendency for major flares to occur in complex magnetic configurations.

17 QUANTITATIVE STUDY FOR ACTIVE REGIONS 41 Two bipolar spots emerging near to each other may be treated as a single βγ type region by MWMC, even though there are no obvious connections with each other. This may cause some disagreement between d E and MWMC. 8. Summary As compared with Mount Wilson Magnetic Classification (MWMC), the effective distance (d E ) is a useful parameter, which gives a quantity describing the magnetic configuration of active regions. We have analyzed magnetograms of 24 active regions of different types with MWMC. We have studied the evolutions of the magnetic fields of five active regions using d E, total flux (F t ) and tilt angle (Tilt). Furthermore, 43 flare-associated and 25 CME-associated active regions have been studied to investigate and quantify the statistical correlation between flares/cmes and the three parameters. The main results are as follows: (1) There is a basic agreement between d E and MWMC. Moreover, d E provides a quantitative measure of the magnetic classification. Therefore, the magnetic configurational evolution of active regions and the correlations between magnetic structure and other solar indices (e.g. flares and CMEs) can be investigated quantitatively with d E. (2) The magnetic configuration in active regions can be described in three aspects quantitatively and accurately by d E, F t and Tilt, particularly by d E on the analysis of δ active regions. From the analyses of evolutions of five active regions, it has been found that d E increases (decreases) in the developing (decaying) δ structure, and d E changed insignificantly in stable magnetic configurations. (3) A high correlation between d E and flares/cmes was found. Intense flares and fast CMEs tend to occur in active regions of high d E. Therefore, d E could be a promising measure to predict the flare-cme activity of active regions. In the present paper, we present a quantitative analysis of magnetic configuration and statistical study on flare/cme-associated active regions with d E, F t and Tilt. All the three parameters can be easily measured from line-of-sight magnetograms. There are still other quantities that can be derived from vector magnetograms, such as twist, current helicity and so on. Analyses on magnetic evolution and solar activities by d E together with them will be carried out in a future paper. Acknowledgements We would like to thank the SOHO team for providing the data used in this study. We are grateful to the editor and the unknown referee for valuable comments and suggestions that helped in improving the manuscript. One of the authors (Juan

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