Nonlinearity of the force-free parameter over active regions.

1. Helicity think shop @ Beijing, China, Oct-2009 Nonlinearity of the force-free parameter over active regions. M.Hagino and T.Sakurai National Astronomical Observatory of Japan, Solar Observatory

2. Helicity think shop @ Beijing, China, Oct-2009 Contents • Introduction・Taylor relaxation・Nandy’s results • Observation and data analysis・Solar Flare Telescope・Data selection・Analysis of alpha • Results・Flux, Force-free parameter alpha, scatter of alpha, time scale of relaxation • Discussion

3. Helicity think shop @ Beijing, China, Oct-2009 Taylor relaxation(1974 Phys.Rev. Letter, 33, 1139) A plasma with a high (but finite) electrical conductivity in which the internal energy is negligible compare to the magnetic energy relaxes from an arbitrary turbulent initial state to a force-free state with a spatially constant α which follows from the assumption that the total magnetic helicity is conserved during relaxation to a state of minimum magnetic energy. In solar active regions, there will be a competition between the injection of magnetic helicity through the photosphere and the Taylor relaxation towards constant α state.(See Seehafer et al. 2007 Astron Nachr 328, 10,1166)

4. Helicity think shop @ Beijing, China, Oct-2009 magnetic flux injection, helicityinjection, foot-point motion → Taylor relaxation(1974 Phys.Rev. Letter, 33, 1139) Non-linear Force-free fields 　→　heating? Linear (constant) Force-free fields Potential fields Energy level diagram which describes the Taylor relaxation as a transition from an exited state (non-linear force-free field) to the ground state (constant force-free field).

5. Helicity think shop @ Beijing, China, Oct-2009 Nandy et al. (2003 ApJL, 597, L73) • VectorMagnetograms: 82 ARs（In this paper, they showed a sample region of Taylor relaxation. ）HSP @ Mees Solar Observatory, Maui, Hawaii. • They compared integrated GOES X-ray flux and variance of α.

6. Helicity think shop @ Beijing, China, Oct-2009 Nandy et al. (2003 ApJL, 597, L73) (Left) Change in variance α vs. x-ray energy flux. They found that variance α decreases with increasing flaring activity. (Right) Evolution of variance α as a function of time.They estimate the time scale of the relaxation toward the constant α state. The characteristic time scale τ=8.1 days.

7. Helicity think shop @ Beijing, China, Oct-2009 Nandy et al. (2003 ApJL, 597, L73)

8. Helicity think shop @ Beijing, China, Oct-2009 Solar Flare Telescope

9. Helicity think shop @ Beijing, China, Oct-2009 Solar Flare Telescope T2 & T3 telescopes Now we’re improving the spectro-polarimeter for measuring the full disk vector magnetic fields with the near-infrared (10830, 15650 Å) lines. T1 telescope Ferroelectric liquid crystal polarimeter and Lyot filter are installed. It observes the flares and the vector magnetic fields on the chromosphere with Hα6563 Å. T4 telescope Ferroelectric liquid crystal polarimeter and Lyot filter are installed. It measures the vector magnetic fields on the photosphere with Fe I 6303 Å line.

10. Helicity think shop @ Beijing, China, Oct-2009 Solar Flare Telescope Characteristics of Photospheric Vector Magnetograms 1992-2006 Apr(Sakurai et al., PASJ, 47, 81, 1995)Wavelength : 6303-0.08Å • Objective Lens diameter : 20ｃｍ • CCD camera size : 512×480pix • Time cadence: 3min • 1pixel = 0.66arcsec • The KD*P modulator was used. • To reduce the seeing noise, 128 images were integrated. 2006 Apr- (Hanaoka, Solar Phys, 222,265,2004) • The high speed CCD camera (128×128pixels) • Each data are made by integrated frames (400frames/sec×2 minuets). • Two liquid crystal modulators.

11. Helicity think shop @ Beijing, China, Oct-2009 Data Selection • The primary criterion for data selection of active regions was availability of both vector magnetograms observed from the Solar Flare Telescope and detection of X-ray flux bigger then M5-class from GOES. • The first flare in the region should have occurred in the eastern of the solar central meridian. • To avoid the analysis difficulty from the projection effect, we selected the target regions closer to the central meridian than E40. • A list containing 30 active regions from 1992 to 2006 was generated. For four active regions the decaying time scale was determined by fitting.

12. Helicity think shop @ Beijing, China, Oct-2009 Analysis of Force-free α We measure the force-free parameter (current helicity) from vector magnetograms obtained with the Solar Flare Telescope. To avoid the Faraday rotation and noise effect, we used pixels within the following range. The variance of helicity is fitted by an exponential decay The decay time scale τ can be estimated.

13. Helicity think shop @ Beijing, China, Oct-2009 Results (magnetograms) region2 region1 region4 region3

14. Helicity think shop @ Beijing, China, Oct-2009 region2 region4 region1 region3 Results (Flux)

15. Helicity think shop @ Beijing, China, Oct-2009 region3 region4 region1 region2 Positive helicity injected gradually. Negative helicity injected gradually. Results (Force-free α)

16. Helicity think shop @ Beijing, China, Oct-2009 Results (variance of α)Region 1

17. Helicity think shop @ Beijing, China, Oct-2009 Results (variance of α)Region 2

18. Helicity think shop @ Beijing, China, Oct-2009 Results (variance of α)Region 3

19. Helicity think shop @ Beijing, China, Oct-2009 Because of these data,we cannot decide the time scale. Results (variance of α)Region 4

20. Helicity think shop @ Beijing, China, Oct-2009 Results (variance of α)Region 4 Flare occurred!!

21. Helicity think shop @ Beijing, China, Oct-2009 Results (variance of α)Region 4

22. Helicity think shop @ Beijing, China, Oct-2009 Discussion • The mean value of α showed only gradual changes after the flare. • We estimate the time scale of the decay process (Taylor relaxation) of the variance in α, for four flaring active regions. • The time scales we found are shorter than the time scale reported by Nandy (8 days). However, our time scales are longer than the ideal time scale (1 day). • In an active region which produced several flares during the observation, the variance of α increased once. The variance decreased after the flare again. Can we use this as a flare forecast?

23. Helicity think shop @ Beijing, China, Oct-2009 Thank you!! This is Hagino’s Relaxation!