Mei Zhang & Chuanyu Wang (National Astronomical observatories, Chinese Academy of Sciences)

1. Hemispheric Helicity Sign Rule indicated by Large-Scale Photospheric Magnetic Fields Mei Zhang & Chuanyu Wang (National Astronomical observatories, Chinese Academy of Sciences) Canfield-fest, Boulder, CO

2. Plan of the Talk • Motivation • Method • Results • Future works Canfield-fest, Boulder, CO

3. Hemispheric helicity sign rule Magnetic fields are observed to emerge into each hemisphere with a preferred helicity sign: Positive in southern hemisphere; Negative in northern hemisphere. (Pevtsov et al. 1995, Bao & Zhang 1998, Hagino & Sakurai 2005) (Image credit: A. Pevtsov) Canfield-fest, Boulder, CO

4. However, more twists…. 1. Why different parameters give different strength of tendency? For example, Pevtsov et al. (2001): In the first four years of cycle 23 (July 1997-September 2000) Northern: αbest<0 62.9%; Southern: αbest>0 69.9% Northern: hc<0 50%; Southern: hc>0 57.5% Canfield-fest, Boulder, CO

5. However, more twists…. 2. Is this rule preserved for the whole solar cycle? Bao et al. (2000): NO for the ascending phase of cycle 23 (Huairou data) Pevtsov et al. (2001): Yes for the first four years of cycle 23 (Mees data) Hagino & Sakurai (2005): Yes for maximums; NO for minimums (Mitaka data, 1983-2000) Pevtsov et al. (2008): No agreement on the ‘wrong-sign’ years (19 years’ data of different instruments) Canfield-fest, Boulder, CO

6. An observation & explanation Zhang (2006): 17200 magnetograms (January 1997 - August 2004) Weak fields: Following established hemispheric rule Strong fields: Helicity sign opposite to that of weak fields hc = αbest*Bz2 Canfield-fest, Boulder, CO

7. Confirmed by Hinode Su et al. 2009, ApJ 679, L103 Canfield-fest, Boulder, CO

8. Note that most observations are made in active regions. We take an approach by studying the helicity sign rule indicated by large-scale photospheric magnetic fields. • Our Motivation is to address: • Does the same helicity sign rule exist outside active regions? • Does it change over the solar cycle? Canfield-fest, Boulder, CO

9. The Method Pevtsov & Latushko (2000) were the first to study the current helicity of the global Sun outside active regions, by applying a reconstruction technique to MDI full-disk longitudinal magnetograms. Pevtsov & Latushko., 2000, ApJ,528：999-1003 We use the same reconstruction technique, but apply different analysis method which strengthens the results. Canfield-fest, Boulder, CO

10. Reconstruction of vector magnetic field Suppose that large-scale magnetic fields are evolving rather slowly and the variations of longitudinal magnetic fields within certain time duration are caused by the changing positions on the solar disk only, then using MDI magnetograms observed at different days allows us to reconstruct the vector magnetogram of the global photosphere. Canfield-fest, Boulder, CO

11. Parameters used Differential rotation: Spatial resolution: △S=184’’ Time interval: △t=5 days Reference:Pevtsov & Latushko., 2000, ApJ,528：999-1003 Canfield-fest, Boulder, CO

12. Snapshot heliographic maps Roger K. Ulrich & John E. Boyden., 2006, Sol. phys.,235:17-29 We combine observations of the solar magnetic fields made at different times into a representation of the whole solar surface at a particular specified time which referred to as a “snapshot heliographic map’’ (different from tranditional Carrington map). Canfield-fest, Boulder, CO

13. Obtained vector magnetic fields Constructed snapshot heliographic maps of Br, Bθ ,Bφfrom top to bottom panels respectively, of one solar rotation (~ CR1914). White background represents positive values of Br (pointing up), Bθ (pointing to the north) and Bφ(pointing to the left) respectively. Contours correspond to ± 2, 4, 8, 16, 32, 64G for Brand Bθ , and ±0.5, 1, 2G for Bφ . Canfield-fest, Boulder, CO

14. The calculation of current helicity Our method: calculating the hc map and then averaging along longitudinal direction to get hc profile √ Pevtsov & Latushko (2000) method: averaging along longitudinal direction before calculating hc profile √ Canfield-fest, Boulder, CO

15. Current helicity map The current helicity density hc map. White background represents positive values of hc. Contours correspond to hc= ±0.1,0.2, 0.4, 0.8 ×10-5G2m-1. It is interesting to see that the active region in the southern hemisphere shows a bulk area of negative hc values, which are opposite to that of surrounding regions. This seems to be consistent with the result of Zhang (2006) where strong and weak fields are found to have opposite helicity signs. Canfield-fest, Boulder, CO

16. Hemispheric rule The profile of averaged hcwith the latitude, using our method. The profile of hcwith the latitude, using Pevtsov & Latushko’s approach. Our plot shows clearly the hemispheric rule, that is, positive helicity sign in the southern hemisphere and negative helicity sign in the northern hemisphere, for all latitudes. Canfield-fest, Boulder, CO

17. A few notes: • We have used only one MDI magnetogram each day, having done none of smoothing between different magnetograms. The plot (below) in Pevtsov & Latushko (2000) was obtained using a few months’ MDI data. Pevtsov & Latushko.(2000) Canfield-fest, Boulder, CO

18. A few notes: 2. We estimate that our method gives a clearer tendency because: First, there may be some very useful information of hc contained in the Bθ magnetogram that Pevtsov & Latushko (2000) ignored. We noticed that Bθ are usually larger than Bφand have a strong variation in longitudinal direction. This indicates that the second term may be a larger term in the equation. Second, our method gives each point on the synoptic map an equal weight whereas theirs are more heavily influenced by strong fields because they averaged the Br and Bφbefore calculating hc. Particularly, the difference may become more evident if the strong and weak fields show opposite helicity signs as reported in Zhang (2006) and also indicated in our hc figure. Canfield-fest, Boulder, CO

19. Check the dependence of the result on different magnetograms used In the previous figure we have used the first magnetogam of each day (solid line in this figure). Now we have used other magnetograms of each day and constructed other 14 different synoptic maps of vector magnetic field and hence get other 14 hcprofiles (dotted lines). They all clearly show the same hemispheric rule. Canfield-fest, Boulder, CO

20. Check the dependence of the result ondifferent time interval & different sliding square window size The solid line shows the profile using △t=5 days, and the dotted and dashed lines show the profiles using △t=3 and 4 days respectively. The solid line shows the profile using △S=184”, and the dotted and dashed lines show the profiles using △S=90” and 224” respectively. We changed the △t and △S, and get similar profiles. This means that our result is also independent of the parameters we chose. Canfield-fest, Boulder, CO

21. Conclusion 1: We conclude that the large-scale magnetic fields show clear and consistent current helicity pattern that follows the established hemispheric rule, that is, positive helicity sign in the southern hemisphere and negative helicity sign in the northern hemisphere. This hemispheric sign pattern is everywhere in the global magnetic field, including weak fields outside active regions, independent of the longitudinal magnetograms and the parameters we have used. Canfield-fest, Boulder, CO

22. Solar-cycle variation? We check three time periods of cycle 23: • September 1996 – minimum, ascending phase • August 2001 • maximum • June 2007 • minimum, descending phase Canfield-fest, Boulder, CO

23. Solar-cycle variation? We use three different instruments: • September 1996: MDI/SOHO + KPVT/NSO • August 2001: MDI/SOHO + KPVT/NSO • June 2007: MDI/SOHO + SOLIS/NSO Canfield-fest, Boulder, CO

24. Solar-cycle variation? Furthermore, we now calculate: This will remove the influence of the different calibrations between different instruments, as well as the variation of magnetic flux over the solar cycle. Canfield-fest, Boulder, CO

25. September 1996 Left: MDI; Right: KPVT Top: different 15 magnetograms Middle: different △t Bottom: different △S Canfield-fest, Boulder, CO

26. August 2001 Left: MDI; Right: KPVT Top: different 15 magnetograms Middle: different △t Bottom: different △S Canfield-fest, Boulder, CO

27. August 2001 Left: MDI; Right: KPVT Top: different 15 magnetograms Middle: different △t Bottom: different △S Canfield-fest, Boulder, CO

28. June 2007 Left: MDI; Right: SOLIS Top: different 15 magnetograms Middle: different △t Bottom: different △S Canfield-fest, Boulder, CO

29. Conclusion 2: The hemispheric helicity sign rule is evident in the global magnetic field, extending to 60 degrees high in latitudes, in both solar minimum and maximum phases, and independent of the instruments and the parameters that we have used. Canfield-fest, Boulder, CO

30. Reference: • C.Y. Wang, M. Zhang, Current helicity pattern of large-scale magnetic field on the photosphere, 2009, Science in China, Series G, Vol. 52, No.11, 1713. • C.Y. Wang, M. Zhang, Hemispheric helicity sign rule indicated by large-scale photospheric magnetic field at three different phases of solar cycle 23, 2010, ApJ, in press. Canfield-fest, Boulder, CO

31. Further works • Check the full solar cycle, not just three periods • Check the magnitude, not just the signs • Preliminary results: • The sign rule preserves for the whole cycle • There seems existing a weak dependence of the magitudes of hc* --- smaller in magnitude during the maximum Canfield-fest, Boulder, CO

32. A hint? • Berger & Ruzmaikin (2000): calculation of magnetic helicity transported into the southern hemisphere, created by differential rotation in the convection zone. Canfield-fest, Boulder, CO

33. Thank You ! Canfield-fest, Boulder, CO