1. Modelling the Global Solar Corona: Filament Chirality Anthony R. Yeates and Duncan H Mackay School of Mathematics and Statistics, University of St. Andrews

2. Two types of chirality : Sinistral and Dextral. Northern Hemisphere - Dextral Southern Hemisphere - Sinistral (Martin et al. 1995, Leroy 1983,1984) Differential rotation produces the opposite results. What other global effects could cause the hemispheric pattern ? As exceptions to hemispheric pattern occur – model must predict them as well. Hemispheric Pattern

3. Previous Simulations. Simulations ran in NH for 54 days – vary initial helicity. Day 0 Day 54 Graph of Fraction of Skew vs Tilt angle (Joys Law). Negative Helicity(-0.2) Positive Helicity (+0.2)

4. Long Term Simulations Previous work (Mackay and van Ballegooijen 2005) indicates that: Dominant Chirality : Dominant Helicity & Tilt Angles. Minority Chirality : Minority Helicity & Large +ve tilt angles. Theory requires testing with actual observations – part of PhD thesis of Mr Anthony Yeates. Aims: - Determine the chirality and location of all filaments (6 month). - Continuous sim. (without resetting the photo/coronal field) to simulate the evolution of the photo/coronal fields (flux emergence). - Test the chirality produced by model with observed chirality at the exact observed location of each filament.

5. Observational Data Filament Chirality Observations: 255 filaments (123 definite chirality) - tested from barbs (7 days, statistical test) Position added to Kitt-Peak magnetograms (CR1949-1954, 1999). N-hemisphere – 88% follow hemispheric pattern. S-hemisphere – 73% follow hemispheric pattern.

6. Observational Data (cont.) Photopsheric flux distribution: 6 KP synoptic maps (CR1949-1954) Used to produce a continuous series of photopsheric boundary conditions. - Start from rotation 1949. - Evolve forward in time using flux transport effects. differential rotation meridional flow Supergranular diffusion flux emergence (119 bipoles)

7. Coupled 3D Model. Evolve, Suns large-scale field, B, through the induction equation. Flux Transport Model : at the photosphere the field is subject to differential rotation, meridonal flows and surface diffusion. Shears the surface fields ~ coronal field diverges from equilibrium. Physical time scale. Magneto-Frictional Relaxation : in the corona use a magneto- frictional method along with a radial outflow velocity at source surface. Coronal field relaxes to a non-linear force-free field, j x B = 0. Relaxation time scale ~ not physical

8. 3D Inserting Bipoles Day 250Day 251 Bipoles are inserted as an isolated field containing either +ve or -ve helicity both in the photosphere and corona.

9. Skew Comparison

10. Results with Hemispheric Distribution of Twist Shapes: observed chirality Colours: correct wrong 109 filaments dextral * sinistral Up to 96.9% correct Results improve the longer the simulation is run.

11. Conclusions Convincing explanation for the hemispheric pattern of filaments through: flux emergence, surface transport and reconnection of large scale active region fields. Transport of helicity from low to high latitudes over many months is a fundamental element of the coronal evolution – agreement gets better the longer the simulations are run (Sun has long term memory). Long term continuous simulation of coronal field (rather a independent extrapolations). Immediate improvements: Better description of flux emergence. Include observed active region twist.

12. Coronal Evolution

13. Observed Chiralities * dextral sinistral undetermined. 123 with definite chirality (255). 88 % follow pattern (N hemi). 73% follow pattern (S Hemi).

14. Emerging flux Use a semi-automated procedure: –compare successive magnetograms; –find “new” bipolar regions; –measure key properties; –insert as ideal bipoles into simulation. CR1948 CR1948 rotated CR1949 Total: 118 bipolar regions

15. Potential Field? Potential FieldForce-Free Field Coronal fields in Simulation are far from potential (low heights).

16. Bipole Twist  = 0  >0 Untwisted Positive Helicity

17. Simulated Hemispheric Pattern * dextral sinistral weak. 207 locations 71 % follow pattern (N hemi) 75 % follow pattern (s hemi)

18. Results with Opposite Twist Shapes: observed chirality 109 filaments Colours: correct wrong Only 61.5% correct dextral * sinistral undetermined.

19. Flux Transport Model(2). Form of Coronal Diffusion. Outflow Velocity. Resolution : nx= 361, ny=293,nz=53 Bipole Description.

20. Statistical Test for Filament Chirality T-test: used to classifify chirality from individual barbs. n : no. of barbs (x1, x2, x3, ….., xn) xi = +1 (dextral) ; -1 (sinistral) The number of dextral barbs is  ns = n – nd Now assume nd following a binomial distribution with parameters (n,p) and assume p = 0.5 is 0 if neither chirality is significant. The classification scheme is then where we choose T = 1.5 (For large n, t should approximate a normal distribution with mean n and variance 1)