Study of magnetic helicity in solar active regions: Study of magnetic helicity in solar active regions: For a better understanding of solar flaresFor a better understanding of solar flares

Sung-Hong ParkSung-Hong Park

Center for Solar-Terrestrial ResearchCenter for Solar-Terrestrial Research

New Jersey Institute of TechnologyNew Jersey Institute of Technology

Magnetic helicity can be transported across the boundary by two kinds of flows as follows:

Berger & Field (1984)

dSBdSvdt

dHnptnpt )(2)(2 AvAB

Vertical flow transport of helical fluxes

Horizontal flow shearing of field lines

A practical approach (Chae et al. 2004) based on the analysis of MDI/SOHO magnetograms was employed to determine the rateof magnetic helicity injection in the solar corona.

Chae’s Method (2001)

S : Photospheric surface of the active regionBn : From MDI/SOHO magnetogramsAp : From Bn (FFT method)VLCT : From temporal variation of Bn ( LCT method )

Helicity Change RateHelicity Change Rate

(a) Horizontal flux rope emergence (b) Vertical flux

rope emergence

Calculation of Magnetic Helicity

Data sets : MDI magnetograms (Example: AR 10696)

- Full-disk field of view

- 1 & 96-min cadence

- Over 12 years (Dec,1995~) of operation with few gaps

- 2 ˝ spatial resolution

- In the filament server, we already have the corrected 96-min full disk MDI magnetograms (1996-2006).

AR 10696 : Normal Component of Magnetic Field, Bn

• Bl=Bn cosφ φ: heliocentric angle

We assume that the magnetic

field on the solar photosphere

is normal to the solar surface.

• Projection effect : Near the disk center (within 60% of the

solar radius from the apparent disk center)

AR 10696 : Calculation of Vector Potential, Ap

• From the FFT method

)(FF

)(FF

221-

py

221-

px

zyx

x

zyx

y

Bkk

jkA

Bkk

jkA

The magnitude of vector potential is the biggest near the polarity inversion line.

AR 10696 : Calculation of LCT velocity field, vLCT

• From the LCT method with two parameters :

w = 10 arcsec

Δ t = 60 or 96 min

Shearing flow near the polarity inversion line

AR 10696 : Helicity Change Rate

Shearing flow near the polarity inversion line injects negative helicity to the corona during first 3000 minutes after the starting time of measurement.

Two kinds of Helicity Study

Our GoalOur Goal : To find a possible characteristic helicity evolution pattern that is associated with a flare impending mechanism.

Approach Approach : We have investigated long term (a few days) variations of the magnetic helicity around eleven X-class flares which occurred in seven active regions (NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720), and compared the results with GOES soft X-ray light curves.

1. Case Study1. Case Study

AR 9672 : LCT Velocity Field and Helicity

Time variations of helicity accumulation, magnetic flux and GOES X-ray flux for 3 active regions

The helicity is shown as cross symbols and the magnetic flux is shown as diamonds. The GOES X-ray flux is shown as the dotted lines. Phase I, the interval over which the helicity accumulation is considered, and phase II, the following phase of relatively constant helicity, are marked.

Time variations of helicity accumulation, magnetic flux and GOES X-ray flux for 4 active regions

Time variations of helicity accumulation, and magnetic flux for 6 non-flare active regions

Our analysis reveals that there were two distinct phases of helicity variation around some major flares (4 among 11 X-class flares).

Phase 1Phase 2

In case where flares occur in phase II, it may imply that solar active regions can wait for major flares after the helicity accumulated to some limiting amount. An active region may evolve to a certain stage where the helicity no longer increases, and the system waits until it unleashes the stored energy by producing flares due to certain mechanism of triggering.

flare

A phase of linearly increasing helicity A phase of relatively constant helicity

Helicity parameters with GOES X-ray flux integrated over the flaring time

Correlation coefficient (CC) is specified in each panel. The uncertainties of the average helicity change rate, the amount of helicity accumulation, and the helicity accumulation time are shown as error bars in each panel.

Our GoalOur Goal : To examine if magnetic helicity injection will carry extra weight in predicting flares

Approach Approach : We have investigated three magnetic parameters (unsigned magnetic flux, magnetic helicity change rate, and magnetic helicity accumulation) of 117 solar active regions and compared them with the soft X-ray flare index for the three time windows of 0-12 hours, 12-24 hours, and 24-48 hours after the quantities are calculated.

2. Statistical Study2. Statistical Study

Definition of magnetic parametersDefinition of magnetic parameters

final initial finalH H H H

dH

dt

HdHdt

: Average Helicity Change Rate

: Helicity Accumulation Change

: Average Unsigned Magnetic Flux

: Helicity Accumulation Time

We calculate these quantities during a period of 24 hours after an active region appears or rotates to a position within 0.6 of the solar radius from the apparent disk center. We then compare these parameters with the flare index derived from GOES X-ray observation for the three time windows after the magnetic helicity measurement:0-12 hours, 12-24 hours, and 24-48 hours.

MethodMethod

(100 10 1 0.1 ) /idx X M C BF I I I I

0

50

100

150

200

250

300

350

400

10 100 1000

Average Unsigned Magnetic Flux [1020 Mx]

Fla

re In

dex

[10

-6 W

m-2

]

0-12hrs

12-24hrs

24-48hrs

Critical Value:Critical Value: 310x10310x1020 20 MxMx

0

50

100

150

200

250

300

350

400

0.01 0.1 1 10 100

Average Helicity Change Rate [1040 Mx2 hr-1]

Fla

re In

dex

[10

-6 W

m-2

]

0-12hrs

12-24hrs

24-48hrs

Critical Value: Critical Value: 5x105x1040 40 MxMx22hrhr-1-1

0

50

100

150

200

250

300

350

400

0.1 1 10 100 1000 10000

Helicity Accumulation Change [1040 Mx2]

Fla

re In

dex

[10

-6 W

m-2

]

0-12hrs

12-24hrs

24-48hrs

Critical Value:Critical Value: 100x10100x1040 40 MxMx22

18 82

71 29

19 81

69 31

18 82

61 39

19 81

90 10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Helicity Change Rate

Helicity Accumulation

Magnetic Flux

(Rate+Flux)

Combination

Flaring

Flare-quiet

0 - 12 hours0 - 12 hours

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

16 84

64 36

17 83

62 38

15 85

56 44

17 83

70 30

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Helicity Change Rate

Helicity Accumulation

Magnetic Flux

(Rate+Flux)

Combination

Flaring

Flare-quiet

12 - 24 hours12 - 24 hours

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

30 70

79 21

31 69

77 23

29 71

72 28

33 67

70 30

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Helicity Change Rate

Helicity Accumulation

Magnetic Flux

(Rate+Flux)

Combination

Flaring

Flare-quiet

24 - 48 hours24 - 48 hours

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

Critical Critical valuevalue

Magnetic parameters with soft X-ray flare index (0-24 hours)

1. Case Study

a. A substantial amount of helicity accumulation is found before the flare in all the events. The helicity increases at a nearly constant rate, (4.5-48)x1040 Mx2hr-1, over a period of 0.6 to a few days, resulting in total amount of helicity accumulation in the range of (1.8-16)x1042 Mx2. b. There is a strong positive correlation between the average helicity change rate of phase I and the corresponding GOES X-ray flux integrated over the flaring time. c. Monitoring of helicity variation in target active regions may also aid the forecasting of flares. A warning sign of flares can be given by the presence of a phase of linearly increasing helicity, as we found

that all the major flares occur after significant helicity accumulation.

Summary & Further works Summary & Further works

2. Statistical Study

a. There seems to be a critical value of magnetic parameters (average helicity change rate, average unsigned magnetic flux, and helicity accumulation change) for a solar active region to produce a flare. b. We could find that the consideration of both critical values of average helicity change rate and average unsigned magnetic flux makes the higher prediction for the probability of occurrence and nonoccurrence of a flare on the active region within 24 hours. It means magnetic helicity injection will carry extra weight in predicting flares.

c. The correlation between magnetic parameters and flare index is weak, but we need to investigate more active regions.

Summary & Further works Summary & Further works

1. More Active Regions a. Case study : To check up whether there is also the characteristic helicity evolution pattern for the more active regions which produced X-class flares

b. Statistical study : To investigate the probability for flare occurrence and nonoccurrence with a critical value of the magnetic parameters, and correlation between flare index and magnetic parameters.

2. Different Data a. Hinode filtergram (FG) data: - better spatial resolution (0.08″) - 2 minute cadence b. IRIM : deeper photosphere, weaker magnetic field

Summary & Further works Summary & Further works