1. Vu Pham A new dynamo pattern revealed by the tilt angle of bipolar sunspot groups Egor Illarionov Moscow State University Helicity Thinkshop on Solar Physics Beijing, 2013 A. Tlatov, E. Illarionov, D. Sokoloff, and V. Pipin. MNRAS, 2013

2. Vu Pham Solar dynamo 1 - differential rotation - mirror asymmetry (α-effect) Mean-field dynamo equation:

3. Vu Pham Current helicity: Zhang et al., 2010 2 Current helicity Twist

4. Vu Pham Current helicity: Zhang et al., 2010 2 - follow the propagation of dynamo waves - oscillate with 11-year period - are in general anti- symmetric - some domains have the “wrong” sign

5. Vu Pham Joy’s law and Hale polarity law: bipolar regions are tilted with preferred polarity Tilt is a possible link between toroidal and poloidal magnetic field Stenflo and Kosovichev (2012) gave effective method for algorithmic isolation of bipoles Algorithm suggested by Tlatov et al. (2010) provides considerably richer data sample Tilt as a tracer for mirror asymmetry 3

6. Vu Pham Recognizing bipolar groups Smoothing 3×3 pixels 4

7. Vu Pham Recognizing bipolar groups Smoothing 3×3 pixels Selection domains with |B|>B min 4

8. Vu Pham Recognizing bipolar groups R=7 ° +dL Smoothing 3×3 pixels Selection domains with |B|>B min Compute center and flux, define search area 4

9. Vu Pham Recognizing bipolar groups 1 A Smoothing 3×3 pixels Selection domains with |B|>B min Compute center and flux, define search area Find the nearest domain of opposite polarity with similar flux: ||F 1 |-|F 2 ||/(|F 1 |+|F 2 |)<ε 4

10. Vu Pham Smoothing 3×3 pixels Selection domains with |B|>B min Compute center and flux, define search area Find the nearest domain of opposite polarity with similar flux: ||F 1 |-|F 2 ||/(|F 1 |+|F 2 |)<ε Repeat the search Recognizing bipolar groups 1 A 4

11. Vu Pham Recognizing bipolar groups α Smoothing 3×3 pixels Selection domains with |B|>B min Compute center and flux, define search area Find the nearest domain of opposite polarity with similar flux: ||F 1 |-|F 2 ||/(|F 1 |+|F 2 |)<ε Repeat the search Coincide => bipole Compute tilt 4

12. Vu Pham Example: MDI, 11/04/2011 5

13. Vu Pham 1 magnetogram per day KPVT, MDI and HMI data (Cycles 21-24) Tilt corresponds to individual domains Rich data sample: AR + ER (up to 50 MSH 1 ) 15 bipoles per day 1 1 MSH= 3.044×10 6 km 2. The round shaped spot with area S (in MSH) has a diameter d = 1969√S km. Key features 6

14. Vu Pham Flux, MDI data Simple tests Prevalent E-W direction of tilt, KPVT data, B min =10 G — 50-300 MSH — >300 MSH 7

15. Vu Pham 2-year time bins and 5° latitudinal bins Amplitude of Gaussian approximation defines hemicircle (Left-Right) for averaging Mean tilt is a median of sample (robust statistic) Student criteria for conf. int. Averaged tilt RightLeft 8

16. Vu Pham Butterfly diagram: >300 MSH MDI data, B min =10 G 9 - +- +

17. Vu Pham Joy’s law: MDI & HMI, S>300 MSH - MDI data, B min =10 G 10 - HMI data, B min =15 G

18. Vu Pham Joy’s law: KPVT, S>300 MSH - Cycle 21 - Cycle 22 - Cycle 23 11

19. Vu Pham Tilt data, KPVT B min =10 G >300 MSH Positive tilt Negative tilt 1212 Negative PositiveNegative Positive B min =100 G >100 MSH

20. Vu Pham Tilt data, KPVT B min =10 G >300 MSH Positive tilt Negative tilt 1212 Negative PositiveNegative Positive B min =100 G >100 MSH

21. Vu Pham Tilt data, KPVT B min =10 G >300 MSH Positive tilt Negative tilt 1212 Negative PositiveNegative Positive B min =100 G >100 MSH

22. Vu Pham Butterfly diagram: 50-300 MSH MDI data, B min =10 G - +- + 13

23. Vu Pham Joy’s law: MDI & HMI - 50<S<300 MSH, MDI data, B min =10 G - 20<S<100 MSH, HMI data, B min =15 G 14

24. Vu Pham Joy’s law: KPVT, B min =10 G - 50<S<300 MSH - S>300 MSH 15

25. Vu Pham Tilt data, KPVT 50-300 MSH B min =10 G Positive tilt Negative tilt 16 Negative PositiveNegative Positive

26. Vu Pham Tilt data with high time-latitude resolution for wide area range (AR & ER) For large bipoles tilt is positive in the Northern and negative in the Southern hemisphere with latitudinal profile µ=27sinθ No pronounced variations of tilt angle between cycles and inside cycles (as opposed to current helicity) Inverse Joy’s law for small bipoles Main results Thank you for your attention! 17