Sung-Hong Park

Space Weather Research LaboratoryNew Jersey Institute of Technology

Study of Magnetic Helicity and Its Relationship with Solar Activities: Flares, CMEs, and Solar Cycle 23

1.1. Correlation Study between Helicity and Flare Index

- Simple Motivation:

1. Helicity ↑ => Non-potentiality ↑ (True) 2. Non-potentiality ↑ => Flare Productivity ↑ (??) (Magnitude & Occurrence Probability)

- Data Analysis

• 378 Active Regions

• Full-disk 96 minute SOHO/MDI magnetograms

• 24-hour profiles of helicity injection rate, dH/dtdH/dt, and unsigned magnetic flux, ΦΦ, right after an active region appears or rotates to a position within 0.6 RSun from the disk center.

• Two parameters, |<dH/dt>| |<dH/dt>| and < <ΦΦ>>, averaged during the entire 24-hour period.

• We compare these two parameters with the flare index derived from GOES soft X-ray observation and calculate flare-productive probability for the next 24-hour time window after the measurement of the parameters.

< Flare Index > < Flare-Productive Probability >

i = GOES class

1.2. Time Profile of dH/dt and Φ

TimeTime [ hours ][ hours ]

dH

/dt

dH

/dt

[10

[10 4040

Mx

Mx 22

hr

hr -1-1

]]ΦΦ

[10

[10 2020

Mx]

Mx]

~46~46

~540~540

~25~25

~470~470

~10~10

~250~250

FFidx idx < 1< 11 < F1 < Fidx idx < 10< 10FFidx idx > 10> 10

1.3. Correlation between Two Parameters and Flare Index

Twice !!

Flaring # 153Non-flaring # 225

| < dH/dt > || < dH/dt > | [10[104040 MxMx22 hr hr-1-1 ]]

1.4. |< dH/dt >| vs. < Φ >

<<ΦΦ

>>

[10

[10 2020

Mx]

Mx]

1.5. Two Parameters vs. Solar Flare Productivity

1.6. Time Profile of ΔH, Φ, and GOES soft X-ray

Fast Increasing Phase

Slow Increasing or Constant Phase

Inverse Sing Helicity Injection Phase

1.7. Daily Flare Index Forecast in NJIT/SWRL website

• Helicity physically considers both structure and evolution of magnetic fields while other previous forecasting studies are based on snap-shot morphology only.

• For 91 AR samples having similarly large magnetic flux, the flaring AR group has the average helicity injection rate about twice greater than that of the non-flaring AR group.

• The flare-productive probability of the helicity parameter for C-class flares shows a well defined cut-off between flare-productive and flare- quiet ARs.

• Helicity accumulates significantly and consistently over 1-1.5 days in major flare producing ARs so that a warning sign of flares can be given by the presence of a phase of monotonically increasing helicity. Some of major flares occurred when the helicity injection became slow (sometimes almost zero) or the opposite sign of helicity started to be injected after the significant helicity accumulation phase.

1.8. Summary

2.1. Relative Magnetic Helicity in an Open Volume (Berger & Field 1984)

where PP is the potential field having the same normal flux distribution as BB on the z = 0 boundary, and AApp is the vector potential for PP. The expression of Equation (2) reduced to that of Equation (1) with the specific AA** and AApp

* * derived by DeVore (2000):

( 2 )( 2 )

( 3 )( 3 )

( 4 )( 4 )

( 5 )( 5 )

( 1 )( 1 )

2.2. 3D NLFF magnetic field data( produced by Jing Ju )

• December 8, 21:20 UT ~ December 14, 5:00 UT

• It is computed with the optimization method (Wheatland et al. 2000) as implemented by Wiegelmann (2004).

• As the boundary conditions for the extrapolation, we use the preprocessed Hinode/SP vector magnetograms in which the net Lorentz force and toque in the photosphere are minimized (Wiegelmann et al. 2006).

• The dimensions of the 3D NLFF field data are 240×132×180 pixel3, which correspond to 288×158×216 Mm3.

2.3. Overview of NOAA AR 10930

Figures from Min & Chae (2009)

G-band ImagesG-band Images

Hinode/FG/Ca II H

Hinode/FG/G-bandHinode/FG/Stokes-V

Hinode/XRT

2.4. Time Profile of Magnetic Helicity, Flux, and GOES X-ray

(1) A negative (left-handed) helicity of -5×1043 Mx2 in the AR corona right before the X3.4 flare.

(2) The major flare is preceded by a significantly and consistently large amount of negative helicity injection (-2×1043 Mx2) into the corona over ~2 days.

(3) The temporal variation of helicity is comparable to that of the rotational speed in the southern sunspot with positive polarity.

(4) In general, the time profile of the coronal helicity is well-matched with that of the helicity accumulation by the time integration of the simplified helicity injection rate (Chae 2001) determined by using SOHO MDI magnetograms

(5) At the time period of the channel structure development (December 11, 4:00-8:00 UT) with newly emerging flux and just right before the C5.7 class flare, the time variation of the coronal helicity shows a rapid and huge increase of negative helicity, but that of the helicity accumulation by MDI magnetograms indicates a monotonous increase of negative helicity.

NLFFMDI

3. AR Helicity Survey during Solar Cycle 23

Cycle 23 Hemispheric Helicity Distribution1999-2002

1998, 2003-2006

4. Long-Term Evolution of Helicity and Flux in ARs

Producing Halo CMEs

- Fan & Gibson (2004)

-Motivation:

Hood & Priest (1981) studied the stability of line line-tied, uniformly twisted, force-free cylindrical flux tubes and found that the tubes become kink-unstable when the number of rotations that each field line winds about the axis between the line-tied ends exceeds 1.25.

Fan & Gibson (2004) performed isothermal MHD simulations of the three-dimensional evolution of the coronal magnetic field as an arched, twisted magnetic flux tube emerges gradually into a pre-existing coronal arcade, under the condition of low β-plasma and high electric conductivity.

1. Φ is almost constant.2. ΔH ~ 8×1043 Mx2

3. ΔH/ Φ2 ~ 0.0074. Δt ~ 4.5 days5. CME linear speed ~ 1333km/s6. CME accel. ~ 7m/s2 : positive accel.

1. Φ is increasing2. ΔH ~ 2×1043 Mx2

3. ΔH/ Φ2 = 0.0094. Δ t ~ 1 day5. 1st & 2nd CME speeds ~ 818 km/s & 1759km/s6. 1st & 2nd CME accel. ~ -81.5 m/s2 & -19.7m/s

negative accel.

4. Long-Term Evolution of Helicity and Flux in ARs

Producing Halo CMEs