1. The quantitative analysis of the spiral chirality of penumbral filament 1 Helicity Thinkshop on Solar Physics, Oct. 2013, Beijing Liu J.H., Su J.T. et al. Shijiazhuang University Key Laboratory of Solar Activity, NAOC

2. Outlines 1. Background of penumbral filament(fibrals) and Screw pinch instability 2. Unwinding and twist change in penumbral filaments (Su et al. 2010, ApJ, 710, 170); 3. Screw pinch instability and penumbral filaments charality; 4. Screw pinch instability and a C2.6 flare.

3. 1. Background of penumbral filaments(fibrals) Uncombed model: It takes the penumbra as a collection of horizontal flux tubes in a more vertical background field. (Solanki & Motavon 1993). Gap model: A field-free model which takes the filaments as the non- magnetized convecting hot gas protruding into the background of potential magnetic fields. (Spruit and Scharmer 2006; Scharmer and Spruit 2006). By studying the expasion, unwinding, shrinking, twisting motion of the penumbral filament, Su et al. consider that the penumbral filaments are the twisted magnetic flux tubes in nature. (Su et al. 2010) There are two schematic models are intensely studied regarding the origin of the penumbral filaments.

4. 4 pitch : the distance in which the field line makes one revolution around the flux tube, is R is the radius of the flux tube and L is its length. (Priest 1984, Ryutova et al. 2008) “screw pinch” configuration Long, magnetic cylindrical flux tubes are subject to helical instabilities, and a magnetic flux tube with both azimuthal and axial components twists into a kinked helical shape. Background of Screw pinch instability

5. 5 Safty factor: The screw pinch instability turns on when the safety factor is Screw pinch instability

6. 6 1. (h/R) > 2.62, the magnetic field components preserve their initial direction and chirality. 2. 1.63 < (h/R) < 2.62, the axial magnetic field reverses but the chirality of the filament remains the same. 3. 1.14 < (h/R) 1.63, the axial magnetic field reversal is accompanied by reversed chirality. For the kink mode m=1: Ryutova, Berger & Title 2008 Model:

7. 7 Considering the chirality Only and for the kink mode m=1: (h/R) >1.63, the chirality of the filament remains the same. 1.14<(h/R) <1.63, the chirality of the filament reverse. (h/R) <1.14, very strong twist, will lead to disruption of the filament.

8. 2. Unwinding and twist change in penumbral filaments Twist from right- to left-handedness G-band images of AR NOAA 10930 ， red frame mark the position where the penumbra filament studied, A right-handed filament expanding and unwinding, a left-handed filament come into being, shrinking and twisting. Su et al. 2010, ApJ, 710, 170

9. Using the Space-time image, the screw pitch can be deduced (Su et al. 2010):

10. Considering the penumbral filaments as twisted flux in nature, the charality development and reversal, the unwinding and twisting motion of the penumbral filaments, connecte with the Screw pinch instability. So does the flare. High resolution observing evidences and quantitative analysis are shown as following. Quantitative analysis on the relationship between Screw pinch instability and penumbral filaments charality, and flare

11. 11 Expansion and unwinding stage: right-handed twist Temporal development of the G-band images SOT/Hinode. 3. Screw pinch instability and penumbral filaments charality

12. 12 h/R and h/L: on expansion and unwinding stage TimeT(m)h(Km)R(Km)L_av(Km)h/Rh/L 11:48~12:06 2039634715151.140.26 12:06~12:24 2447539515151.200.31 12:30~13:27 52103064615151.590.68 11:48~13:27 UT Dec 10 1.14<(h/R) <1.63, the filament unwind rapidly, and its chirality reversed about 6 hours later. The increasing trend of h/R reveals the unwinding motion of the punumbra filament. The increasing trend of h/L imply that, accompany with the unwinding motion, the instability decrease. This is consistent with the theory of Ryutova et al. 2008.

13. 13 Shrinking and twist increasing stage: chirality reversed to left-handed

14. 14 Time(UT)T(m)h(Km)R(Km)L_av(Km)h/Rh/L 3:23~4:55 86185852613223.531.41 4:57~5:48 74159847813223.341.21 6:04~6:48 4290735913222.520.69 h/R and h/L: on shrinking and twist increasing stage 3:23~6:48 UT Dec 11 (h/R) >1.63, the chirality of the filament remains the same. This is consistent with the theory of Ryutova et al. 2008. The decreasing trend of h/R reveals the twisting motion of the punumbra filament. The decreasing trend of h/L imply that, along with the twisting motion, the instability increase.

15. 15 4. Screw pinch instability and a C2.6 flare Safety factor: h/L<1 (ratio of pintch to length) instability (Ryutova et al. 2008) Taking the distance between two nearby bright point in the G-band images as the estimated screw pitch: From 04:23UT to 5:07 UT of Dec. 11 h_estimate=1754~1036 Km and L~1322Km, h/L=1.33~0.78, a C2.6 flare occurred at 05:13 UT.

16. At 5:07 UT Dec 11 Safty factor h/L=0.78<1 11-DEC, 05:08- -05:17-- 05:23, C2.6 Probably the flare is triggered by the turning on of the screw pitch instability Initial bright point is located at the PIL region of the penumbral filament

17. Sumarry The temporal development and the changes of punumbral filament chirality can be studied quantitatively through the screw pitch instability, h/R, h/L, which is consistent with the theory of Ryutova et al. 2008. The decreasing/increasing trend of h/R reveals the twisting/unwinding motion of the punumbra filament. The decreasing/increasing trend of h/L imply that, along with the twisting/unwinding motion, the instability increase/decrease. The screw pitch instability may probably responsible for the onset of the C2.6 flare. 17

18. 18 Thanks!