The variation of relative magnetic helicity around major flares
Sung-Hong Park, Jeongwoo Lee, Gwang-Son Choe, Jongchul Chae, Hyewon Jeong, Guo Yang, Ju Jing, Haimin Wang
aa r X i v : . [ a s t r o - ph . S R ] A p r THE VARIATION OF RELATIVE MAGNETIC HELICITYAROUND MAJOR FLARES
SUNG-HONG PARK, , JEONGWOO LEE, GWANG-SON CHOE, , JONGCHULCHAE, HYEWON JEONG, GUO YANG, , JU JING, , AND HAIMIN WANG , ABSTRACT
We have investigated the variation of magnetic helicity over a span of severaldays around the times of 11 X-class flares which occurred in seven active regions(NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720) using the mag-netograms taken by the Michelson Doppler Imager (MDI) on board the
Solarand Heliospheric Observatory ( SOHO ). As a major result we found that eachof these major flares was preceded by a significant helicity accumulation, (1.8–16) × Mx over a long period (0.5 to a few days). Another finding is that thehelicity accumulates at a nearly constant rate, (4.5–48) × Mx hr − , and thenbecomes nearly constant before the flares. This led us to distinguish the helicityvariation into two phases: a phase of monotonically increasing helicity and thefollowing phase of relatively constant helicity. As expected, the amount of helic-ity accumulated shows a modest correlation with time-integrated soft X-ray fluxduring flares. However, the average helicity change rate in the first phase showseven stronger correlation with the time-integrated soft X-ray flux. We discussthe physical implications of this result and the possibility that this characteristichelicity variation pattern can be used as an early warning sign for solar eruptions. Subject headings:
Sun: flares – Sun: magnetic fields Center for Solar-Terrestrial Research, New Jersey Institute of Technology, 323 Martin Luther KingBoulevard, 101 Tiernan Hall, Newark, NJ 07102; [email protected]. Big Bear Solar Observatory, 40386 North Shore Lane, Big Bear City, CA 92314. Astronomy Program and FPRD, Department of Physics and Astronomy, Seoul National University,Seoul 151-742, Korea. Department of Astronomy and Space Science, Kyung Hee University, Yongin 449-701, Korea. Princeton Plasma Physics Laboratory, Princeton, NJ 08543-0451.
1. INTRODUCTION
Magnetic helicity is a measure of twists, kinks, and inter-linkages of magnetic field lines(Berger & Field 1984) and has been an important parameter in solar dynamo theories (Parker1955). While the source of the magnetic helicity lies below the surface of the Sun, it wasrecently recognized as a useful parameter in describing solar features observed above surfacesuch as spiral patterns of sunspot fibrils, helical patterns in filaments and coronal massejections (CMEs; for a review, see Brown et al. 1999). Naturally magnetic helicity studieshave been directed to the energy buildup and instability leading to eruptions and CMEs (e.g.,Rust 2001; Kusano et al. 2004; Phillips et al. 2005). More recently, several studies werecarried out to relate the change of magnetic helicity to the problem of impending or triggeringsolar flares. Moon et al. (2002a) studied the magnetic helicity change around major flaresto find its rapid helicity change before flares, and concluded that a sudden helicity injectionmay trigger flares. Moon et al. (2002b) applied the same approach to seven homologousflares in the active region, NOAA 8100, over a period of 6.5 hr to find a good correlationbetween the amount of incremental helicity and the soft X-ray flux during each homologousflare. The results from both studies thus point to the idea that the helicity change occurringover short timescales (around a half hour) can be a significant factor in triggering flares.Kusano et al. (2003) proposed annihilation of magnetic helicity as a triggering mechanismfor solar flares. Numerical simulations were carried, which show that, if the helicity is sharplyreversed within a magnetic arcade, reconnection quickly grows in the helicity inversion layer,driving explosive dynamics. Yokoyama et al. (2003) studied flare activities in active regionNOAA 8100 to find that most of the flare events occurred about half a day after the helicityinjection rate changed its sign, and the positions of H α emission in flares well correspondto the helicity inversion lines in space. Sakurai & Hagino (2003) studied two active regionsappeared in 2001 (NOAA 9415 and 9661), both of which have produced X-class flares. Theirfinding was, on the contrary, that the magnetic helicity integrated over the regions evolvedslowly and did not show abrupt changes at the time of the flares, although the distributionsof magnetic helicity changed significantly over a few days in the regions.In this paper, we study long term (a few days) variations of the magnetic helicity aroundmajor X-class flares. While some of the above studies suggest short-term helicity change asan important topic for flare triggering, Hartkorn & Wang (2004) found that the rapid helicitychange at the time of a flare can occur as an artifact under the influence of flare emissionon the spectral line adopted in MDI measurements. This means that a short term variationduring strong flares can hardly be measured with enough accuracy. However we can study along-term variation of the magnetic helicity with active region magnetograms gathered overmany days excluding the times of flares. Our research is therefore focused on a possiblecharacteristic helicity evolution pattern that is associated with flare impending mechanisms. 3 –
2. CALCULATION OF MAGNETIC HELICITY
By magnetic helicity, we refer to the relative magnetic helicity in the rest of this pa-per, i.e., the helicity relative to that of the potential field state. With the time-dependentmeasurement of longitudinal magnetic fields in the photosphere, we can only approximatelydetermine the change rate of the relative magnetic helicity (Demoulin & Berger 2003). Wefurther use a simplified expression for the helicity change rate (Chae 2001) given by (cid:18) dH r dt (cid:19) LCT = − Z s A p · v LCT ) B n dS (1)where B n is the normal component of the magnetic field; A p is the vector potential ofthe potential field; v LCT represents the apparent horizontal motion of field lines; dS is thesurface integral element and the integration is over the entire area of the target active region.Although this expression does not explicitly include the helicity change by the vertical motionof field lines (see Kusano et al. 2002), D´emoulin & Berger (2003) pointed out that it actuallyaccommodates both the vertical and horizontal motions of flux tubes as far as no flux tubenewly emerges from or totally submerges into the surface. As we will show later in presentingthe result of helicity calculation, this requirement is not always met.We determine the quantities in the above equation using full disk MDI (Scherrer et al.1995) magnetograms following the procedure described in Chae & Jeong (2005). First, we ap-proximately determine B n from the line-of-sight magnetic field B l in the MDI magnetograms,simply considering the projection effect, i.e., B l = B n cos ψ where ψ is the heliocentric angleof the point of interest, assuming that the magnetic field on the solar photosphere is normalto the solar surface. Second, A p is calculated from B n by using the Fast Fourier Trans-form method as usual. The extent of the spatial domain of the Fourier transform is takenabout twice wider than the active region area in order to minimize the artifacts arising fromthe periodic boundary condition in the fast Fourier transform (Alissandrakis 1981). Third, v LCT is calculated using the local correlation tracking (LCT) technique (November & Simon1988). For local correlation tracking, we align all magnetograms in each event to the firstimage of the data set after correcting the differential rotation. We set the FWHM of theapodizing window function to 10 ′′ and the time interval between two frames to 60 minutes,and performed LCT for all pixels with an absolute flux density greater than 5 G. Only thepixels with cross correlation above 0.9 are considered.In selecting data we found that use of 1 minute cadence full-disk MDI (Scherrer etal. 1995) magnetograms is adequate for our purpose of investigating the long-term helicityevolution. However, there are occasionally found data gaps in the 60 minute cadence dataset in which case we supplement the data gaps with 96 minute MDI magnetograms. The 4 –time interval of the supplemented data set is therefore not longer than 96 minute. To reducethe effect of the geometrical projection, we selected the active regions lying within 60%of the solar radius from the apparent disk center. Note that we use only full disk MDImagnetograms that have 2 ′′ × ′′ pixel size. Therefore the LCT velocities calculated here mayhave been systematically underestimated compared with the LCT velocities calculated withthe higher resolution (0.6 ′′ × ′′ ) MDI data (Longcope et al. 2007).After the helicity change rate is determined as a function of time, we integrate it withrespect to time to determine the amount of helicity accumulation:∆ H = Z tt (cid:18) dH r dt (cid:19) dt (2)where t and t are the start and end time of the helicity accumulation, respectively. If t isa time when the magnetic field is in the potential state, ∆ H is simply the helicity, H ( t ), attime t . However, there is no guarantee that we can observe, by chance, an active region inthe potential energy state. We therefore set t as the earliest time without significant helicityaccumulation at which the average value of the helicity change rate over four hours is lessthan our nominal threshold in helicity change rate, 1 × Mx hr − . If that time cannotbe determined, we define t as the time when the data set starts or when the previouslyaccumulated helicity is released by a flare. The exact time of t here is unimportant becauseit is only a trial value. After determining H ( t ), we redefine t as the time when the resultinghelicity starts to increase from a nearly constant value.
3. Magnetic Helicity Variation
We present the helicity variation calculated for seven active regions in Figures 1 and2. In both figures we plot the magnetic helicity accumulation together with the GOES softX-ray light curve and magnetic flux as functions of time. The soft X-ray light curve is shownto indicate the flare times and the magnetic flux is shown to check the above-mentionedrequirement for the approximation made in Equation (1). Note that the fluxes shown in thispaper are total unsigned magnetic flux, i.e., sum of the absolute amounts of positive andnegative fluxes, because net magnetic flux may show little change despite significant fluxchange in each polarity.For the events shown in Figure 1 we can see that the helicity accumulates at a monotonicrate of change about 0.5–2 days before the flare onset, and then becomes almost constantbefore the flares. For convenience, we distinguish the magnetic helicity variation in twostages: a phase of monotonically increasing helicity (phase I) and the following phase of 5 –relatively constant helicity (phase II). This pattern is obvious for the four flares (2001 October25, 2004 November 7, and 2005 January 16 and 17). For the 2005 January 15 event, thehelicity increased up to 22:00 UT on January 14 and then decreased afterward. In this case,we do not consider that the flare occurred in phase II. It is then noted that these flares tookplace after a significant amount, ∼ (1.8–11) × Mx , of helicity accumulation.In Figure 2, we show the result for the other four active regions. Like the events inFigure 1, these flares also occurred after a significant helicity accumulation, ∼ (1.9–16) × Mx . However, they occurred in the middle of the continuous helicity accumulation, unlikethose events shown in Figure 1. In other word, the flares in Figure 2 occurred in phaseI, while those in Figure 1 occurred in phase II. One common trend is, however, that allthe events are apparently associated with a considerable amount of helicity build-up beforethe flares, whether they occurred in phase I or in phase II. In case where flares occur inphase II, it may imply that solar active regions can wait for major flares after the helicityaccumulated to some limiting amount. This is seemingly contrary to the general belief thata flare occurs as soon as the system reaches some threshold. An active region may evolve toa certain stage where the helicity no longer increases, and the system waits until it unleashesthe stored energy by producing flares due to certain mechanism of triggering.Since we claimed that these large flares are always preceded by significant accumulationof helicity, as a reference we check the corresponding helicity variation in non-flaring times.We show such data in Figure 3. For all active regions under investigation, the amount ofhelicity change during nonflaring periods (Fig. 3) is much less than that around the majorflare time. This convinces us that the above monotonically increasing helicity before majorflares is a process associated with the flares and is not occurring in nonflare times. Anotherpoint to note in Figure 3 is that not only the helicity but also the total unsigned magneticflux changes much less during the nonflaring time compared with the period before majorflares. This implies that the increase of the magnetic helicity before major flares is, in part,related to the simultaneous increase of total unsigned magnetic flux.It is also worthwhile to mention how the characteristic pattern of the helicity variationfound here will depend on the sign of helicity. In our result obtained for seven active regions,similar amounts of both of positive and negative helicity were accumulated continuously andsimultaneously during the whole time. It is therefore unlikely that counting the helicity inone and the other polarity separately yields a significantly different conclusion. On the otherhand, some studies suggested that the sign-reversal of the helicity injection rate is importantfor flare activity and we need to compared them with the present result. Kusano et al. (2003)emphasized spatially sharp reversal of helicity sign triggers magnetic reconnection based onmodel simulation. While the model prediction is interesting and compelling, we excluded 6 –from the outset (see §
1) the rapid helicity change during the flare time due to observationallimitation. Our conclusion is valid only for the long term variation of helicity. Yokoyamaet al. (2003) have found that flares tend to occur after reversal of helicity injection ratechanged its sign. Although this is occasionally seen in our samples, (i.e., in the case of AR10030 and AR 10720) as well, it is not always the case and we are unsure whether this is anecessary condition for the flares. More often than not, the helicity either remains constantor increases in one sign when the flare occurs.
4. Correlation with Soft X-ray Flux
We compare the helicity change rate, dH/dt and accumulation amount, ∆ H with thetime integrated soft X-ray flux taken as the proxy for the flare energy release. In addition wecheck the helicity accumulation time, τ , defined as the time interval of helicity accumulationmeasured from t and the first coming flare. Prior to make such a comparison, the range ofuncertainty of each quantity needs to be known. In general it is hard to trace all the possibleuncertainties involved with each quantities in Equation (1). Fortunately, our targeted quan-tity given by Equation (2) involves integration in space and time and the uncertainty in eachmeasured quantity is not propagating, but rather may cancel out in the process of spatialand time integration if it is random in nature. We thus focus the uncertainty estimate onlyon the linear approximation of the helicity variation that we are after. We first find out thebest-fit linear function to the points ∆ H ( t i ) lying in phase I (i.e., t ≤ t i ≤ t + τ ) in the formof F ( t ) = a ( t − t ) + F ( t ). Next we calculate the standard deviation, σ , of the scatter pointswith respect to this linear function, and plot two additional lines corresponding to the ± σ levels of the scatter points. Finally, we read the y -axis offsets of these two lines to determine σ ∆ H and the x-axis offsets to determine σ τ , respectively. In addition, we calculate the uncer-tainty of the slope a itself in the form of (∆ H − σ ∆ H ) / ( τ + σ τ ) ≤ a ≤ (∆ H + σ ∆ H ) / ( τ − σ τ ).The center value of a here is taken as the average helicity change rate in the rest of thispaper. Therefore, by the average helicity change rate, we do not mean the average of thequantities given in Equation (1), but we refer to the best fit slope to the helicity variation(eq. [2]) in phase I. The uncertainties shown in Figure 4 and Table 1 are those associatedwith our linear function fit only.In Figure 4, we plot, as symbols, the helicity parameters against the GOES soft X-ray fluxes integrated over the flaring time ( F X , hereafter). Each symbol is identified withthe event ID number in the figure together with uncertainty range represented by the bar(see also Table I). The solid lines show the least-squares linear fits to the data points. Thecorrelation coefficients (CCs) of the linear fits are also given in each panel. Figure 4 a shows 7 –that there is a fairly good correlation (CC=0.86) between the helicity change rate and F X .The amount of helicity accumulation also shows a modest correlation with F X (CC=0.68)as shown in Figure 4 b , although not as good as for the helicity change rate. On the otherhand, the correlation between helicity accumulation time τ and the soft X-ray flux is verypoor with a weak tendency that the longer accumulation time τ , the weaker soft X-ray flux F X (Fig. 4 c ).We initially expected, on a general basis, that the helicity change ∆ H would stronglycorrelate with F X . It is therefore puzzling why the helicity change rate dH/dt shows evena better correlation with F X in Figure 4. As a possibility, we considered that τ may be afactor in complicating the relationship between ∆ H and F X . A intriguing idea is that themagnetic energy decays much faster than the magnetic helicity in the presence of magneticdiffusion (Berger 1999). We thus compare ∆ H with τ in Figure 4d, which unfortunatelyshows no obvious correlation between them. The small number of events used in this studyis another restriction for finding a trend here. With the present result alone, it is fair topresume that the weaker correlation between F X and ∆ H may arise from our inaccuratedetermination of the helicity accumulation amount due to unknown initial time of helicitybuild-up.
5. SUMMARY
We have investigated the variation of magnetic helicity over a time span of several daysaround the times of 11 X-class flares which occurred in seven active regions using MDImagnetograms to find the following results.First, a substantial amount of helicity accumulation is found before the flare in all theevents. The helicity increases at a nearly constant rate, (4.5–48) × Mx hr − , over aperiod of 0.6 to a few days, resulting in total amount of helicity accumulation in the rangeof (1.8–16) × Mx . Such a wide range of helicity accumulation indicates that each activeregion has its own limit of helicity storage to keep a stable magnetic structure in the corona.The finding of a monotonically increasing phase is similar to the earlier one by Sakurai &Hagino (2003) that the magnetic helicity integrated over the regions evolved slowly and didnot show abrupt changes at the time of the flares. The helicity increase over days beforethe flares reconfirms the conventional idea that helicity accumulation by a certain amountis necessary for a large flare to occur (Kusano et al. 1995; Choe & Lee 1996).Second, there is a strong positive correlation between the average helicity change rateof phase I and the corresponding GOES X-ray flux integrated over the flaring time. The 8 –amount of helicity accumulation during phase I also correlates with the soft X-ray flux, asexpected, but the correlation is stronger with the helicity change rate. This result probablyimplies that the helicity change rate is more accurately determined than the amount ofhelicity change itself as the initial time of helicity build-up is poorly determined.If the above correlations hold for a large number of events, we may predict the flarestrength (the integrated X-ray flux) based on the helicity change rate. Monitoring of helicityvariation in target active regions may also aid the forecasting of flares. A warning sign offlares can be given by the presence of a phase of monotonically increasing helicity, as wefound that all the major flares occur after significant helicity accumulation. As a referencewe have checked helicity variation of the six active regions in non-flaring times to find muchlower helicity change rates compared with those around the major flares. We thus concludethat the relative magnetic helicity can be a powerful tool for predicting major flares.The authors wish to thank the referee for valuable comments on the manuscript. Thework is supported by NSF grant ATM-0548952 and NASA grant NNG0-6GC81G. J.L. wassupported by NSF grant AST 06-07544 and NASA grant NNG0-6GE76G. G.S.C. was sup-ported by DOE contract DE-AC02-76-CH03073 and NASA grant NNH04AA16I. REFERENCES
Alissandrakis, C. E. 1981, A&A, 100, 197Berger, M. A., & Field, G. B. 1984, J. Fluid Mech., 147, 133Berger, M. A. 1999, in M. R. Brown, R. C. Canfield, and A. A. Pevtsov (eds.) MagneticHelicity in Space and Laboratory Plasmas, Geophys. Monogr., 111, 11Brown, M. R., Canfield, R. C., & Pevtsov, A. A. (eds.) 1999, Magnetic Helicity in Space andLaboratory Plasmas, Geophys. Monogr., 111Chae, J. 2001, ApJ, 560, L95Chae, J., & Jeong, H. 2005, J. Korean Astron. Soc., 38, 295Choe, G. S., & Lee, L. C. 1996, ApJ, 472, 372D´emoulin, P., & Berger, M. A. 2003, Sol. Phys., 215, 203Hartkorn, K., & Wang, H. 2004, Sol. Phys., 225, 311 9 –Kusano, K., Suzuki, Y., & Nishikawa, K. 1995, ApJ, 441, 942Kusano, K., Maeshiro, T., Yokoyama, T., & Sakurai, T. 2002, ApJ, 577, 501Kusano, K., Yokoyama, T., Maeshiro, T., & Sakurai, T. 2003, Adv. Space Res., 32, 1931Kusano, K., Maeshiro, T., Yokoyama, T., & Sakurai, T. 2004, ApJ, 610, 537Longcope, D. W., Ravindra, B., & Barnes, G. 2007, ApJ, 668, 571Moon, Y.-J., Chae, J., Wang, H., & Park, Y. D. 2002a, ApJ, 580, 528Moon, Y.-J., Chae, J., Choe, G. S., Wang, H., Park, Y. D., Yun, H. S., Yurchyshyn, V., &Goode, P. R. 2002b, ApJ, 574, 1066November, L. J., & Simon, G. W. 1988, ApJ, 333, 427Parker, E. N. 1955, ApJ, 122, 293Phillips, A. D., MacNeice, P. J., & Antiochos, S. K. 2005, ApJ, 624, L129Rust, D. M. 2001, J. Geophys. Res., 106, 25075Sakurai, T., & Hagino, M. 2003, Adv. Space Res., 32, 1943Scherrer, P. H., et al. 1995, Sol. Phys., 162, 129Yokoyama, T., Kusano, K., Maeshiro, T., & Sakurai, T. 2003, Adv. Space Res., 32, 1949
This preprint was prepared with the AAS L A TEX macros v5.2.
10 –Table 1. List of flares, helicity and accumulation time
ID Flares AR Peak time F X a | dH/dt b | | ∆ H c | τ d number ( UT ) (10 − J/m ) (10 Mx hr − ) (10 Mx ) ( hr )1 X 1.3 on Oct 25, 2001 9672 15:02 2.3 6.2 ± ± ±
22 X 3.0 on Jul 15, 2002 0030 20:08 1.4 13.3 ± ± ±
13 X 1.5 on Mar 17, 2003 0314 19:05 1.3 6.4 ± ± ±
84 X 1.5 on Mar 18, 2003 0314 12:08 1.3 13.3 ± ± ±
15 X 18 on Oct 28, 2003 0486 11:10 20.0 48.4 ± ± ±
26 X 10 on Oct 29, 2003 0486 20:49 9.1 46.8 ± ± ±
17 X 1.2 on Feb 26, 2004 0564 02:03 0.75 4.5 ± ± ±
38 X 2.2 on Nov 07, 2004 0696 16:06 2.1 19.8 ± ± ±
19 X 1.3 on Jan 15, 2005 0720 00:43 1.3 22.2 ± ± ±
210 X 2.8 on Jan 15, 2005 0720 23:00 6.6 22.5 ± ± ±
111 X 4.1 on Jan 17, 2005 0720 09:52 9.1 40.8 ± ± ± a Integrated GOES X-ray flux. b Average helicity change rate of phase I. c The amount of helicity accumulation during phase I. d Helicity accumulation time.
11 – H e li c i t y A cc u m u l a t i o n [ M x ] I II GO E S X - r ay F l u x [ - W a tt s m e t er - ] AR 9672 T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] H e li c i t y A cc u m u l a t i o n [ M x ] I II GO E S X - r ay F l u x [ - W a tt s m e t er - ] AR 10696 T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ]
15 16 17Time [day] Jan 2005-600-400-2000200400600 H e li c i t y A cc u m u l a t i o n [ M x ] I I II I II GO E S X - r ay F l u x [ - W a tt s m e t er - ] AR 10720 T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] Fig. 1.— Time variations of helicity accumulation, magnetic flux, and
GOES
X-ray flux forthree active regions. The helicity is shown as cross symbols and the magnetic flux is shownas diamonds. The
GOES
X-ray flux is shown as the dotted lines. Phase I, the interval overwhich the helicity accumulation is considered, and phase II, the following phase of relativelyconstant helicity, are marked. . . . . . . T i m e [ d ay ] J u l - - - -
50 0 50 100 150
Helicity Accumulation [10 Mx ] I GOES X-ray Flux [10 -4 Watts meter -2 ] AR
300 400 500 600 700 800
Total Unsigned Magnetic Flux [10 Mx] T i m e [ d ay ] M a r -
200 0 200 400 600 800
Helicity Accumulation [10 Mx ] II . . . . . GOES X-ray Flux [10 -4 Watts meter -2 ] AR Total Unsigned Magnetic Flux [10 Mx] T i m e [ d ay ] O c t - - - - Helicity Accumulation [10 Mx ] II GOES X-ray Flux [10 -4 Watts meter -2 ] AR
700 800 900 1000 1100 1200
Total Unsigned Magnetic Flux [10 Mx] T i m e [ d ay ] F e b - - - -
100 0 100
Helicity Accumulation [10 Mx ] I . . . . . . . . GOES X-ray Flux [10 -4 Watts meter -2 ] AR
100 200 300 400 500
Total Unsigned Magnetic Flux [10 Mx] F i g . . — S a m e a s i n F i g . , bu t f o r a dd i t i o n a l e v e n t s .
13 – H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 9673 H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 9675 H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 10031 H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 10033 H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 10491 H e li c i t y A cc u m u l a t i o n [ M x ] T o t a l U n s i g n e d M ag n e t i c F l u x [ M x ] AR 10565
Fig. 3.— Time variations of helicity accumulation, and magnetic flux for six nonflare activeregions. The helicity is shown as crosses, and the magnetic flux is shown as diamonds. 14 –
10 20 30 40 50 60Helicity Change Rate [10 Mx hr -1 ]0.00.51.01.52.0 I n t e g r a t e d X - r ay F l u x [ J m - ] (a) CC = 0.86 Mx ]0.00.51.01.52.0 I n t e g r a t e d X - r ay F l u x [ J m - ]
12 34 5 67 891011 (b)
CC = 0.68
20 40 60Helicity Accumulation Time [hr]0.00.51.01.52.0 I n t e g r a t e d X - r ay F l u x [ J m - ]
12 34 5 6 7891011 (c)
CC = -0.24
20 40 60Helicity Accumulation Time [hr]51015 H e li c i t y A cc u m u l a t i o n [ M x ]
12 34 5 6 7891011 (d)
Fig. 4.— Helicity parameters with
GOES
X-ray flux integrated over the flaring time. Cor-relations of the integrated soft X-ray flux with ( a ) average helicity change rate of phase I,( b ) the amount of helicity accumulation during phase I, and ( c ) helicity accumulation time.Correlation coefficient (CC) is specified in each panel. In ( dd