1. Kinetic and Magnetic Helicities of Solar Active Regions Ram Ajor Maurya, Ashok Ambastha And Vema Reddy Udaipur Solar Observatory Physical Research Laboratory, India

2. Outline  Objectives  Introduction and background  The Data and Sample of Active Regions  Measurement of Helicities – Kinetic and Magnetic  Results Evolution of Helicity in NOAA 10930 : 8-15 Dec 2006 Hemispheric Distribution Association of Kinetic and Magnetic Helicities Variations in Helicities and transient activities  Summary and Conclusions

3. Objective  Evolution of Kinetic and Magnetic Helicities in ARs  Variation in Helicities During Energetic Transients  Latitudinal distribution of Kinetic and Magnetic Helicities  Association of Kinetic and Magnetic Helicities?

4.  Active regions: 3D magnetic structure extending from sub-photosphere to coronal heights  magnetic helicity observed at the photosphere is due to shear at larger depths and strong turbulence in the convection zone (Pevtsov, et al. 1994).  The kinetic helicity of turbulent flows twists the rising flux tube (Longcope et al. 1998).  The other possibility of twist in the rising tube is dynamo action (Choudhuri 2003).  flux tube created at the base of the convection zone, rises toward the photosphere where turbulent flows braid and intertwine (Priest and Forbes 2002). Kinetic helicity of sub-photospheric flow Magnetic helicity of photospheric magnetic fields Introduction

5.  What is Helicity ? Helicity of a vector field is a measure of linkage and twistedness of the field lines. Kinetic Helicity ? Magnetic Helicity ?

6. Hemispheric Trend of Helicity Parameters: ReferenceHelicity Parameter North (-ve) %(no.) South (+ve) %(no.) TotalDate Hale (1926)HV64(16)50(13)511901-1944 Richardson (1941)HV71661411901-1944 Seehafer (1990)hchc 91(11)75(3)16SC21-22 Martin, et al. (1994)FC100(26)72(34)47SC22 Pevtsov, et al. (1995) α best 76(25)69(25)691991-1995 Abramenko, et al. (1996)hchc 79(15)86(18)401988-1994 Bao and Zhang (1998)hchc 84(169)79(177)4221988-1997 Longocope, et al. (1998) α best 62(58)66(73)2031991-1995 Bao, et al. (2000) α av 59(152)65(26)87SC23 Pevtsov, et al. (2003)FC80(558)86(633)23102000-2001 Lim and Chae (2009)FC95(19)100(18)451996-2001 Hk ?Hk ? Some background HV - Hα sunspot vorticity, h c – current helicity, FC - Hα filament chirality, α av, α best force free parameter

7. Kinetic Helicity.. Some background  Komm et. al. 2007: Kinetic helicity on average is negative (positive) in northern (southern) hemisphere  Zhao and Kosovichev (2004): sub-surface kinetic helicity have a prepondence opposite to the current helicity.  Komm et al. (2004): strong signal in kinetic helicity at the location of the active region during the epoch when flares occur. Kinetic helicity and Flares

8. (Maurya, Ambastha and Tripathy, 2009, Astrophys. J., 706, L235) GOES-12 flux for 1.0 - 0.8Å (solid line) and 0.5 - 0.4Å (dotted line). The horizontal lines with labels R i, i = 1,... 5, represent time span taken for the five data sets. Solar oscillations could be excited by the mechanical impulse of large flare (Wolf 1972).  Flare related effects on p-modes: Chaplin et al. (2000), Ambastha et al.(2003), Howe et al. (2004).

9.  presence of three sheared layers in the depth range 0 to 10 Mm of 44 ARs  two extrema in meridional velocity profiles of these ARs were found to be located at the depths of 1.92±0.15 and 4.69±0.30 Mm.  ARs having two extrema possessed as large as twice the mean magnetic field (MI) and mean GOES X-ray flux.  presence of steep gradients in meridional velocity at depths ranging from 1.5 to 5 Mm  hemispheric trend of gradient: negative (positive) signs in the northern (southern) hemisphere.  ARs of larger MI possessed steeper gradient in meridional velocity profiles.  flaring activity of ARs are associated with depth of the first extremum of vertical vorticity. (Maurya and Ambastha, 2010, Astrophys. J., 714, L196)

10. Observational Data and Active Regions Total : 91 North: 32 South: 59  GONG: Jul 2001- Aug 2007  MSFC: Jul 2001- Oct 2004  Hinode: Nov 2006 – Aug 2007

11. Local Helioseismology: Ring Diagram Analysis Full disc time series y x Tracked and filtered time series Data Cube3DFFTRing-Fitting Inversion Horizontal: u x, u y Vertical: u z (cont. eqn., Komm, et al. 2004) ∆ω = k x U x + k y U y (Hill, 1988)

12. Measurement of Helicity  Vertical and helical fluctuations are an integral part of any turbulent fluid

13. Average flow in the Active Region NOAA 10486

14. 3D Flow Structure Beneath the NOAA 10486

15. Kinetic Helicity in the Active Region NOAA 10486

16. Velocity and Magnetic Fields in NOAA 10486

17. Evolution of Kinetic and Magnetic Helicities in NOAA 10930

18. Latitudinal Distribution of Magnetic Helicity Hemispheric Trend: North: < 0 (66%) North: α z av < 0 (66%) South > 0 (63%) South : α z av > 0 (63%) Max. PDF: -9.37×10 -9 (+1.72×10 -9 ) m -1 Average α z av : -1.39×10 -9 (+3.05×10 -9 ) m -1

19. Latitudinal Distribution of Vertical Kinetic Helicity Hemispheric Trend: North: ()< 0 (47%) North: (h k1 z ) av < 0 (47%) South()> 0 (53%) South: (h k1 z ) av > 0 (53%) Max. PDF: +2.50×10 -8 (-4.48×10 -9 ) ms -2 () Average (h k1 z ) av : 1.88×10 -9 (-7.62×10 -9 ) ms -2 North: ()< 0 (69%) North: (h k2 z ) av < 0 (69%) South()> 0 (56%) South: (h k2 z ) av > 0 (56%) () Max. PDF: -4.37×10 -8 (3.44×10 -9 ) ms -2 Average (ω 2 z ) av : -6.99×10 -8 (1.69×10 -8 ) ms -2

20. Relation Between Kinetic and Magnetic Helicities Par.Corr. Coeff. (h k1 z ) av -0.07 (h k2 z ) av +0.23

21. Summary and Conclusions  Magnetic helicity parameter α z av shows significant hemispheric trend - in agreement with earlier reports.  The average vertical vorticity for the depth range 2.5-12 Mm shows an opposite hemispheric trend while there is no hemispheric trend for the depth range 0.0-2.5 Mm.  There is no clear hemispheric preponderance for the average vertical kinetic helicity for the depth range 0.0-2.5 Mm while strong hemispheric trend is discernible for the depth range 2.5-12 Mm.  We do not find any clear association between the twists of surface magnetic fields and sub- surface flows.  Absolute mean magnetic field of ARs shows a mild correlation with the twist of magnetic fields while no association with the twist of sub-surface flows.  The GOES XHR flux also shows a mild correlation with vertical vorticity averaged over depths 2.5-12 Mm.  photospheric magnetic helicity has not a cause and effect relation with the sub-photospheric kinetic helicity in the depth range 0-12 Mm.

26. Latitudinal Distribution of Current Helicity Hemispheric Trend: North: () < 0 (56%) North: ( h c z ) av < 0 (56%) South() > 0 (47%) South : ( h c z ) av > 0 (47%) Max. PDF: 0.00×10 -9 ( 0.00×10 -9 ) m -1 () Average ( h c z ) av : -1.93×10 -9 (+0.00×10 -9 ) m -1

27. Latitudinal Distribution of Vertical Vorticity Hemispheric Trend: North: ()< 0 (56%) North: (ω 1 z ) av < 0 (56%) South()> 0 (51%) South: (ω 1 z ) av > 0 (51%) Max. PDF: -1.12×10 -7 (+8.62×10 -9 ) s -1 () Average (ω 1 z ) av : -2.56×10 -9 (+3.83×10 -8 ) s -1 North: ()< 0 (41%) North: (ω 2 z ) av < 0 (41%) South()> 0 (39%) South: (ω 2 z ) av > 0 (39%) Max. PDF: +3.50×10 -7 (-1.17×10 -7 ) s -1 () Average (ω 2 z ) av : +9.89×10 -9 (-9.99×10 -8 ) s -1

28. Relation Between Kinetic and Current Helicities Par.Corr. Coeff. (ω z 1 ) av -0.10 (ω z 1 ) av +0.04 (h k1 z ) av -0.05 (h k2 z ) av +0.26

29. Current Helicity ?