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

2. www.***.com 2 Contents 1. Introduction ・ Taylor relaxation ・ Nandy’s results 2. Observation and data analysis ・ Solar Flare Telescope ・ Data selection ・ Analysis of alpha 3. Results ・ Flux, Force-free parameter alpha, scatter of alpha, time scale of relaxation 4. Discussion Helicity think shop @ Beijing, China, Oct-2009

3. www.***.com 3 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) Helicity think shop @ Beijing, China, Oct-2009

4. www.***.com 4 Taylor relaxation (1974 Phys.Rev. Letter, 33, 1139) Helicity think shop @ Beijing, China, Oct-2009 Non-linear Force-free fields 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). → heating? magnetic flux injection, helicity injection, foot-point motion →

5. www.***.com 5 Nandy et al. (2003 ApJL, 597, L73) Vector Magnetograms: 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. Helicity think shop @ Beijing, China, Oct-2009

6. www.***.com 6 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. Helicity think shop @ Beijing, China, Oct-2009

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

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

9. www.***.com 9 Solar Flare Telescope Helicity think shop @ Beijing, China, Oct-2009 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. 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.

10. www.***.com 10 Solar Flare Telescope 1992-2006 Apr (Sakurai et al., PASJ, 47, 81, 1995) Wavelength : 6303-0.08 Å Objective Lens diameter : 20 ｃｍ 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. Helicity think shop @ Beijing, China, Oct-2009 Characteristics of Photospheric Vector Magnetograms

11. www.***.com 11 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. Helicity think shop @ Beijing, China, Oct-2009

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

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

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

15. www.***.com 15 Results (Force-free α) region3region4region1 Negative helicity injected gradually. region2 Positive helicity injected gradually. Helicity think shop @ Beijing, China, Oct-2009

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

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

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

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

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

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

22. www.***.com 22 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? Helicity think shop @ Beijing, China, Oct-2009

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